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## **Meet the editors**

Dr. Paolo Ferro is an Associate Professor of Metallurgy and Materials Selection at the University of Padua (Italy). He was a scientific director of the research program 'Numerical and Experimental Determination of Residual Stresses in Welded Joints and their Influence on Fatigue Strength'. He won the prize for young researchers 'Aldo Daccò' in 2002. He is a member of the Centre for Mechan-

ics of Biological Materials and the coordinator of the European project on Critical Raw Materials named DERMAP. His research is mainly focused on the analytical and numerical modelling of metallurgical processes. He is the author of more than 130 papers. In addition to his editorial role in different journals, he frequently serves as a reviewer to many other international journals and national as well as international funding agencies.

Dr. Filippo Berto is the Chair of Mechanics and Materials at the Norwegian University of Science and Technology, Trondheim. He is the author of more than 500 technical papers, mainly oriented to materials science engineering, the brittle failure of different materials, the notch effect, the application of the finite element method to the structural analysis, the mechanical behaviour of metallic mate-

rials, the fatigue performance of notched components as well as the reliability of welded, bolted and bonded joints. Since 2003, he has been working on different aspects of the structural integrity discipline, by mainly focusing his attention on problems related to the static and fatigue assessment of engineering materials and components. In particular, he has attempted to devise engineering methods suitable for designing components (experiencing different kinds of stress concentration phenomena) against fatigue as well as against static failures.

Contents

**Preface VII**

**in Joints 1**

xing Yan

Ugarte

**Experiments 71**

**Residual Stresses 29**

Chapter 1 **Experimental Techniques to Investigate Residual Stress**

Chapter 2 **Numerical Welding Simulation as a Basis for Structural**

Chapter 3 **Residual Stress Analysis of Laser Remanufacturing 49**

Chapter 4 **Residual Stress in Friction Stir Welding and Laser-Assisted Friction Stir Welding by Numerical Simulation and**

Chapter 5 **Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical Simulation 91**

Chapter 6 **Numerical Simulation of Residual Stresses in Welding and Ultrasonic Impact Treatment Process 121** Lanqing Tang, Ayhan Ince and Jing Zheng

Chapter 7 **Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method 137**

Kimiya Hemmesi and Majid Farajian

Roberto Montanari, Alessandra Fava and Giuseppe Barbieri

**Integrity Assessment of Structures: Microstructure and**

Shi-yun Dong, Chao-qun Song, Xiang-yi Feng, Yong-jian Li and Shi-

Caterina Casavola, Alberto Cazzato and Vincenzo Moramarco

Jon Ander Esnaola, Ibai Ulacia, Arkaitz Lopez-Jauregi and Done

Marco Colussi, Paolo Ferro, Filippo Berto and Giovanni Meneghetti

## Contents

#### **Preface XI**


Chapter 2 **Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures: Microstructure and Residual Stresses 29**

Kimiya Hemmesi and Majid Farajian


Preface

real structures and components.

There is a need for designers and engineers to quantify the residual stresses induced by welding processes as it is the primary joining technique used in the fabrication of civil struc‐ tures and mechanical engineering assemblies. Information on residual stresses is important because of the complexity of predicting distortions of welded structures during assembly, and in the context of a necessity to improve the efficiency and reliability of fatigue life as‐ sessment of structures and structural components. The ability to quantify residual stresses induced by welding processes through experimentation or numerical simulation has today become, more than ever, of strategic importance in the context of improved efficiency and more accurate design. This is an ongoing challenge that started many years ago and has benefited greatly in recent years from the development of high speed computing and ad‐ vanced experimental techniques. Modern design criteria do, in fact, include the effect of re‐ sidual stresses on the fatigue strength of welded joints, thus allowing a more efficient use of materials and a greater reliability of welded structures. The key issue, however, is accurate assessment of the residual stress field. This is the reason why extensive effort has been dedi‐ cated to improving experimental and numerical strategies used to assess residual stresses in structural components. Experimental techniques are highly valuable because they allow val‐ idation of numerical models. However, from the perspective of structural design, experi‐ mental techniques are of less relevance than numerical methods, because they are usually employed once a structure is welded, are expensive and provide limited information related to a discrete number of points in the joint. On the other hand, numerical models allow the complete residual stress field to be modelled and hot spot stresses to be assessed The draw‐ back in using numerical analysis is the complexity and time required because of the implicit transient and non-linear nature of welding processes. For this reason, their use is still scarce in industrial applications in which the design time is a strong limitation. The main challenge is then to develop new, reliable and less time-consuming numerical methods aimed at im‐ proving the quality and the efficiency in determining accurately the residual stress field in

In the light of this challenging and complex scenario, the present book aims to discuss, in the form of a collection of case-studies, recent developments and trends in standard and ad‐ vanced experimental and numerical techniques that can be employed to capture the residual stress field in welded connections. After a comprehensive overview of the main experimen‐ tal techniques that are usually employed nowadays, numerical methods are then considered in detail. In particular, methods for simulating welding processes with particular attention to the modelling of heat sources and reliable stress-strain constitutive laws in the weld zone are discussed and addressed. The case studies presented deal with different welding techni‐ ques including friction stir welding, laser assisted friction stir welding, laser remanufactur‐

## Preface

There is a need for designers and engineers to quantify the residual stresses induced by welding processes as it is the primary joining technique used in the fabrication of civil struc‐ tures and mechanical engineering assemblies. Information on residual stresses is important because of the complexity of predicting distortions of welded structures during assembly, and in the context of a necessity to improve the efficiency and reliability of fatigue life as‐ sessment of structures and structural components. The ability to quantify residual stresses induced by welding processes through experimentation or numerical simulation has today become, more than ever, of strategic importance in the context of improved efficiency and more accurate design. This is an ongoing challenge that started many years ago and has benefited greatly in recent years from the development of high speed computing and ad‐ vanced experimental techniques. Modern design criteria do, in fact, include the effect of re‐ sidual stresses on the fatigue strength of welded joints, thus allowing a more efficient use of materials and a greater reliability of welded structures. The key issue, however, is accurate assessment of the residual stress field. This is the reason why extensive effort has been dedi‐ cated to improving experimental and numerical strategies used to assess residual stresses in structural components. Experimental techniques are highly valuable because they allow val‐ idation of numerical models. However, from the perspective of structural design, experi‐ mental techniques are of less relevance than numerical methods, because they are usually employed once a structure is welded, are expensive and provide limited information related to a discrete number of points in the joint. On the other hand, numerical models allow the complete residual stress field to be modelled and hot spot stresses to be assessed The draw‐ back in using numerical analysis is the complexity and time required because of the implicit transient and non-linear nature of welding processes. For this reason, their use is still scarce in industrial applications in which the design time is a strong limitation. The main challenge is then to develop new, reliable and less time-consuming numerical methods aimed at im‐ proving the quality and the efficiency in determining accurately the residual stress field in real structures and components.

In the light of this challenging and complex scenario, the present book aims to discuss, in the form of a collection of case-studies, recent developments and trends in standard and ad‐ vanced experimental and numerical techniques that can be employed to capture the residual stress field in welded connections. After a comprehensive overview of the main experimen‐ tal techniques that are usually employed nowadays, numerical methods are then considered in detail. In particular, methods for simulating welding processes with particular attention to the modelling of heat sources and reliable stress-strain constitutive laws in the weld zone are discussed and addressed. The case studies presented deal with different welding techni‐ ques including friction stir welding, laser assisted friction stir welding, laser remanufactur‐

ing and multi-pass welding. Finally, numerical strategies to identify and quantify residual stress fields are presented and discussed. The overall aim of the book is to assist in provid‐ ing the background and tools to an efficient and effective advanced design of welded joints.

As Guest Editors of this volume, we believe that the present book fulfils this role and hope that it will be useful to researchers, designers and colleagues who are involved in different aspects of design and investigation of weldments. We would like to thank all the authors for their valuable contributions to this special issue. In addition, we would like to thank the re‐ viewers for their efforts for ensuring the high quality standards for each contribution.

> **Prof. Paolo Ferro** University of Padova Vicenza, Italy

**Chapter 1**

Provisional chapter

**Experimental Techniques to Investigate Residual Stress**

DOI: 10.5772/intechopen.71564

Residual stress arising from welding processes is matter of great concern in industrial practice since it can affect geometry, mechanical behavior and corrosion resistance of components. In order to evaluate residual stress in welded joints and optimize postwelding heat treatments, a lot of work has been devoted to the improvement of measurement methods with increasing sensitivity and accuracy. The chapter presents and discusses some of the experimental techniques commonly used today to determine residual stress in welds and describes recent results and advancements. Destructive (sectioning, contour, hole-drilling, instrumented indentation) and nondestructive (Barkhausen noise, ultrasonic, X-ray and neutron diffraction) methods are illustrated to highlight the

In order to satisfy scientific and industrial needs, a lot of work has been devoted to investigate the state of residual stress in metallic materials and its effects on mechanical properties. A number of comprehensive reviews on the topic can be found in the literature (e.g. see [1–8]). It is well known that residual stress superimposes to external applied stress and plays a crucial role in the failure of components and structures; therefore, it is taken into account in advanced design in the aerospace, automotive and nuclear fields. All manufacturing processes modify the state of stress with either positive or negative consequences; for instance, compressive surface stress increases the fatigue limit, whereas tensile residual stress may decrease the corrosion resistance.

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

Experimental Techniques to Investigate Residual

**in Joints**

Giuseppe Barbieri

Giuseppe Barbieri

Abstract

1. Introduction

Stress in Joints

Roberto Montanari, Alessandra Fava and

Roberto Montanari, Alessandra Fava and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

specific characteristics, advantages and drawbacks.

method, ultrasonic method, X-ray and neutron diffraction

Keywords: residual stress, welding, sectioning method, contour method hole-drilling method, instrumented indentation method, Barkhausen noise

http://dx.doi.org/10.5772/intechopen.71564

**Prof. Filippo Berto** Norwegian University of Science and Technology Trondheim, Norway

#### **Experimental Techniques to Investigate Residual Stress in Joints** Experimental Techniques to Investigate Residual Stress in Joints

DOI: 10.5772/intechopen.71564

Roberto Montanari, Alessandra Fava and Giuseppe Barbieri Roberto Montanari, Alessandra Fava and

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71564 Additional information is available at the end of the chapter

#### Abstract

Giuseppe Barbieri

ing and multi-pass welding. Finally, numerical strategies to identify and quantify residual stress fields are presented and discussed. The overall aim of the book is to assist in provid‐ ing the background and tools to an efficient and effective advanced design of welded joints. As Guest Editors of this volume, we believe that the present book fulfils this role and hope that it will be useful to researchers, designers and colleagues who are involved in different aspects of design and investigation of weldments. We would like to thank all the authors for their valuable contributions to this special issue. In addition, we would like to thank the re‐ viewers for their efforts for ensuring the high quality standards for each contribution.

VIII Preface

**Prof. Paolo Ferro** University of Padova

**Prof. Filippo Berto**

Trondheim, Norway

Norwegian University of Science and Technology

Vicenza, Italy

Residual stress arising from welding processes is matter of great concern in industrial practice since it can affect geometry, mechanical behavior and corrosion resistance of components. In order to evaluate residual stress in welded joints and optimize postwelding heat treatments, a lot of work has been devoted to the improvement of measurement methods with increasing sensitivity and accuracy. The chapter presents and discusses some of the experimental techniques commonly used today to determine residual stress in welds and describes recent results and advancements. Destructive (sectioning, contour, hole-drilling, instrumented indentation) and nondestructive (Barkhausen noise, ultrasonic, X-ray and neutron diffraction) methods are illustrated to highlight the specific characteristics, advantages and drawbacks.

Keywords: residual stress, welding, sectioning method, contour method hole-drilling method, instrumented indentation method, Barkhausen noise method, ultrasonic method, X-ray and neutron diffraction

### 1. Introduction

In order to satisfy scientific and industrial needs, a lot of work has been devoted to investigate the state of residual stress in metallic materials and its effects on mechanical properties. A number of comprehensive reviews on the topic can be found in the literature (e.g. see [1–8]).

It is well known that residual stress superimposes to external applied stress and plays a crucial role in the failure of components and structures; therefore, it is taken into account in advanced design in the aerospace, automotive and nuclear fields. All manufacturing processes modify the state of stress with either positive or negative consequences; for instance, compressive surface stress increases the fatigue limit, whereas tensile residual stress may decrease the corrosion resistance.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

Welding may produce huge effects on the metals: when two pieces of plates or pipes are joined together, temperature ranges from the melting point of the material to room temperature and localized high residual stress coupled with shrinkage is generated near the weld seam. After cooling to room temperature, the locked-in stress is retained leading to distortion and/or buckling. The quantitative measurement of residual stress in welded joints is of the utmost importance for the safe operation of power plants, petrochemical plants, storage tanks and transmission pipelines.

layer removal; (ii) detection of the local change in stress by measuring the strain and (iii) calculation of the residual stress as a function of the measured strain through either an analytical approach or finite element (FE) calculations. The methods described here are: (i)

Experimental Techniques to Investigate Residual Stress in Joints

http://dx.doi.org/10.5772/intechopen.71564

3

The second group of techniques consists of nondestructive methods based on the relationship between residual stress and physical or crystallographic parameters of the material. Here, the attention has been focused on: (i) Barkhausen noise; (ii) ultrasonic; (iii) X-ray and neutron

The sectioning method is a destructive technique used for decades from lots of researchers to measure residual stress in structural parts and welded components. The method was developed for the first time in 1888 by Kalakoutsky to determine longitudinal stresses in a bar by slitting longitudinal strips from the bar and measuring their change in length [9, 10]. The stress analysis is simplified by assuming that transverse stress is negligible and the cutting process

The slitting process is delicate since it should not introduce plasticity or heat in the cut samples maintaining the original residual stress without the influence of external factors [6]. The strains released during the cutting process are generally measured using electrical or mechanical strain gauges [6]. To determine residual stress in a plate, some attentions about sample preparation have to be done; in particular, the number of the longitudinal strips to be cut depends

The use of mechanical strain gauges have been found to be particularly suitable for the sectioning method since the device is not attached to the specimen, is not damaged during the sectioning and can be used in repeated measurements. The stress distribution over a cross section can be determined by measuring the change in length of each strip and by applying the

The main sources of error result from temperature changes and may be practically eliminated

Sectioning method has been extensively used to analyze residual stresses in welded joints, for instance, in A36 steel with fillet welds [11], high strength steel Q460 box sections [12] and thin Al-5456 panels [13]. Strips sliced at regions of high stress gradients can be considerably curved; thus, the change in length measured by the strain gauge is the change in the chord length

In conclusion, the sectioning method is an adequate, accurate and economical technique for residual stress measurement in structural members thanks to its versatility and reliability [8, 10].

rather than the change in arc length, which represents the actual strain [10].

sectioning; (ii) contour; (iii) hole-drilling and (iv) instrumented indentation.

diffraction.

2. Destructive techniques

alone does not produce appreciable strains [8].

on the residual stress gradient [10].

using a reference bar of the same material.

Hooke's law [10].

2.1. Sectioning method

To control such effects, it is necessary to predict the macroscopic transient fields of temperature, strain and stress. In principle, this can be done by solving the equations of continuum mechanics; however, a rigorous analysis of welds is a challenging task. At the macroscopic level, a weld represents a thermo-mechanical problem of computing transient temperature, stress and strain, whereas at the microscopic level, it is a problem of physical metallurgy involving phase transformations, defect recovery, recrystallization and grain growth. Welds may consist of tens of passes, each of which contributes to the mechanical and metallurgical effects. Interactions between thermal, mechanical, metallurgical and, in the molten pool, chemical and fluid processes are quite complex, and experimental measurements are required to validate theoretical and modeling predictions.

Generally, three types of residual stress can be identified on the basis of the range over, which they are observed: the first type (σ<sup>I</sup> ) is termed macro-stress and influences thousands of crystalline grains; the second one (σII), the micro-stress, occurs between different phases or grains and covers a distance of about one grain; the third one (σIII) ranges over few atomic distances. To study the microstructural behavior of the material, σII and σIII are very important because allow for a better understanding the way in which lattice defects, in particular, dislocation arrangements, evolve. The σ<sup>I</sup> stress is taken into consideration in designing engineering structures.

In many cases, the stress near the molten zone reaches the yield stress of the alloy and causes plastic deformation with microstructural changes, namely increase of point defect and dislocation density and decrease of grain size. The stresses σII and σIII are strictly correlated to these microstructural features and are studied by X-ray and neutron diffraction. The techniques for analyzing σII and σIII stresses involve the study of diffraction peak profiles and are not treated here because the topic goes beyond the scope of the chapter.

Several qualitative and quantitative techniques have been developed to measure residual stress. In fact, they measure strain rather than stress, and residual stress is then determined using the specific elastic constants of the material such as Young's modulus and Poisson's ratio. The wide range of available methods makes it impossible to include all of them in this chapter. In the following, some techniques, divided into two groups, namely destructive and nondestructive, will be reviewed.

The techniques of the first group are based on the destruction of the state of equilibrium of the residual stress in a mechanical component so residual stress is measured by its relaxing. The procedure used can be described as follows: (i) creation of a new stress state by machining or layer removal; (ii) detection of the local change in stress by measuring the strain and (iii) calculation of the residual stress as a function of the measured strain through either an analytical approach or finite element (FE) calculations. The methods described here are: (i) sectioning; (ii) contour; (iii) hole-drilling and (iv) instrumented indentation.

The second group of techniques consists of nondestructive methods based on the relationship between residual stress and physical or crystallographic parameters of the material. Here, the attention has been focused on: (i) Barkhausen noise; (ii) ultrasonic; (iii) X-ray and neutron diffraction.

## 2. Destructive techniques

#### 2.1. Sectioning method

Welding may produce huge effects on the metals: when two pieces of plates or pipes are joined together, temperature ranges from the melting point of the material to room temperature and localized high residual stress coupled with shrinkage is generated near the weld seam. After cooling to room temperature, the locked-in stress is retained leading to distortion and/or buckling. The quantitative measurement of residual stress in welded joints is of the utmost importance for the safe operation of power plants, petrochemical plants, storage tanks and

2 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

To control such effects, it is necessary to predict the macroscopic transient fields of temperature, strain and stress. In principle, this can be done by solving the equations of continuum mechanics; however, a rigorous analysis of welds is a challenging task. At the macroscopic level, a weld represents a thermo-mechanical problem of computing transient temperature, stress and strain, whereas at the microscopic level, it is a problem of physical metallurgy involving phase transformations, defect recovery, recrystallization and grain growth. Welds may consist of tens of passes, each of which contributes to the mechanical and metallurgical effects. Interactions between thermal, mechanical, metallurgical and, in the molten pool, chemical and fluid processes are quite complex, and experimental measurements are required to

Generally, three types of residual stress can be identified on the basis of the range over, which

crystalline grains; the second one (σII), the micro-stress, occurs between different phases or grains and covers a distance of about one grain; the third one (σIII) ranges over few atomic distances. To study the microstructural behavior of the material, σII and σIII are very important because allow for a better understanding the way in which lattice defects, in particular, dislocation arrangements, evolve. The σ<sup>I</sup> stress is taken into consideration in designing engineering

In many cases, the stress near the molten zone reaches the yield stress of the alloy and causes plastic deformation with microstructural changes, namely increase of point defect and dislocation density and decrease of grain size. The stresses σII and σIII are strictly correlated to these microstructural features and are studied by X-ray and neutron diffraction. The techniques for analyzing σII and σIII stresses involve the study of diffraction peak profiles and are not treated

Several qualitative and quantitative techniques have been developed to measure residual stress. In fact, they measure strain rather than stress, and residual stress is then determined using the specific elastic constants of the material such as Young's modulus and Poisson's ratio. The wide range of available methods makes it impossible to include all of them in this chapter. In the following, some techniques, divided into two groups, namely destructive and

The techniques of the first group are based on the destruction of the state of equilibrium of the residual stress in a mechanical component so residual stress is measured by its relaxing. The procedure used can be described as follows: (i) creation of a new stress state by machining or

) is termed macro-stress and influences thousands of

transmission pipelines.

validate theoretical and modeling predictions.

here because the topic goes beyond the scope of the chapter.

they are observed: the first type (σ<sup>I</sup>

nondestructive, will be reviewed.

structures.

The sectioning method is a destructive technique used for decades from lots of researchers to measure residual stress in structural parts and welded components. The method was developed for the first time in 1888 by Kalakoutsky to determine longitudinal stresses in a bar by slitting longitudinal strips from the bar and measuring their change in length [9, 10]. The stress analysis is simplified by assuming that transverse stress is negligible and the cutting process alone does not produce appreciable strains [8].

The slitting process is delicate since it should not introduce plasticity or heat in the cut samples maintaining the original residual stress without the influence of external factors [6]. The strains released during the cutting process are generally measured using electrical or mechanical strain gauges [6]. To determine residual stress in a plate, some attentions about sample preparation have to be done; in particular, the number of the longitudinal strips to be cut depends on the residual stress gradient [10].

The use of mechanical strain gauges have been found to be particularly suitable for the sectioning method since the device is not attached to the specimen, is not damaged during the sectioning and can be used in repeated measurements. The stress distribution over a cross section can be determined by measuring the change in length of each strip and by applying the Hooke's law [10].

The main sources of error result from temperature changes and may be practically eliminated using a reference bar of the same material.

Sectioning method has been extensively used to analyze residual stresses in welded joints, for instance, in A36 steel with fillet welds [11], high strength steel Q460 box sections [12] and thin Al-5456 panels [13]. Strips sliced at regions of high stress gradients can be considerably curved; thus, the change in length measured by the strain gauge is the change in the chord length rather than the change in arc length, which represents the actual strain [10].

In conclusion, the sectioning method is an adequate, accurate and economical technique for residual stress measurement in structural members thanks to its versatility and reliability [8, 10].

#### 2.2. Contour method

The contour method (CM) was first proposed by Prime in 2000 [14]. CM is based on the superposition principle assuming that the material behaves elastically during the relaxation of residual stress and that the material removal introduces negligible stress [7, 14].

In 2003, Prime et al. [21] developed a laser measuring system that works by moving one or more precision laser ranging probes over the entire surface with two orthogonal axes of motion, acquiring precision x, y and z spatial coordinates to submicron precision and resolution. A typical scan may take 30 min to an hour to complete with a resolution of 10 microns along the probe direction and 100 microns between scan lines. Noncontact laser surface contouring improves the capability of CM by allowing higher resolution mea-

Experimental Techniques to Investigate Residual Stress in Joints

http://dx.doi.org/10.5772/intechopen.71564

5

iii. Data handling. Data from the two measured surfaces are aligned. Such procedure generally requires flipping, translation and rotation of one data set to match the other. To smooth out noise in the measured surface data and to enable evaluation at arbitrary locations, the data are fitted to bivariate Fourier series. Finally, since the contour must be defined everywhere for calculating the stress, any missing area of the surface is filled

iv. Stress calculation. The residual stress is calculated from the measured surface contours

The multiaxial CM is a variation of the standard CM and its principles have been discussed by DeWald et al. [23]. This method uses displacements to calculate the eigenstrain distribution within the body; then from eigenstrain, the residual stress is determined by means of FE. The motivation for using eigenstrain to determine residual stress in CM is that eigenstrain remains constant upon residual stress redistribution. Hence, multiple cuts can be made without changing the eigenstrain distribution [20, 23]. Implementation of the multi-axial CM involves making multiple cuts along different orientations of a continuously processed prismatic specimen. Initially, the specimen is cut into two halves as in the conventional CM. The new cut surfaces are measured, and the results are averaged. Then, the two halves are cut along their diagonal. The displacements normal to the cut surfaces are contoured and averaged. After all the measurements are completed, the eigenstrain components are obtained from these three different measured and averaged surfaces [20]. The multi-axial CM technique was successfully applied to measure residual stress in variable polarity plasma arc (VPPA)-welded plates of 2024-T35 aluminum alloy [20], thin sheets of Ti-6Al-4 V and thick laser peened plates of 316 L

The validity of CM measurements has been assessed by comparing its results with those from neutron diffraction, X-ray (lab and synchrotron) diffraction and hole drilling [15, 18, 24–26].

Recently, Pagliaro et al. [27] suggested to use superposition to determine internal residual stresses by sectioning with CM and then measuring remaining stress with other methods. This approach allows measurements in parts where the internal stress were previously difficult to access and opens up possibilities to combine the advantages of different techniques [27].

CM has found a number of applications; some of them are of particular relevance such as butt joints of S355 structural steel [28], 80-mm thick ferritic steel welds [24], 70-mm thick dissimilar metal (ferritic to austenitic) welds [15] and ferritic steel plates welded using low and very high heat input processes [25], friction stir welds between 25.4-mm thick plates of

in by extrapolating constant values from the defined region [16].

surement of a surface contour [21].

using a FE model [22].

stainless steel [23].

As shown in Figure 1, the displacements due to the relaxation of the internal stress are compared to an assumed flat surface contour, and the longitudinal residual stress is recreated using a FE model. The forces required to ensure that the measured deformed surface is returned to its original position are directly correlated to the residual stress. The method provides a 2D map having a regular resolution of the residual stress normal to the cut surface [14, 15].

The application of CM involves four steps: (i) cutting, (ii) measurement of surface contour, (iii) data handling and (iv) stress calculation [16].


Figure 1. Schematic principles of the contour method [14].

In 2003, Prime et al. [21] developed a laser measuring system that works by moving one or more precision laser ranging probes over the entire surface with two orthogonal axes of motion, acquiring precision x, y and z spatial coordinates to submicron precision and resolution. A typical scan may take 30 min to an hour to complete with a resolution of 10 microns along the probe direction and 100 microns between scan lines. Noncontact laser surface contouring improves the capability of CM by allowing higher resolution measurement of a surface contour [21].

2.2. Contour method

data handling and (iv) stress calculation [16].

Figure 1. Schematic principles of the contour method [14].

in the cases where there is a high stress gradient [19].

about 10,000 points and the operation takes several hours.

The contour method (CM) was first proposed by Prime in 2000 [14]. CM is based on the superposition principle assuming that the material behaves elastically during the relaxation

As shown in Figure 1, the displacements due to the relaxation of the internal stress are compared to an assumed flat surface contour, and the longitudinal residual stress is recreated using a FE model. The forces required to ensure that the measured deformed surface is returned to its original position are directly correlated to the residual stress. The method provides a 2D map

The application of CM involves four steps: (i) cutting, (ii) measurement of surface contour, (iii)

i. Cutting. The cut of the sample is a crucial step since it must be precise and straight without causing plastic deformation [16, 17]; owing to its suitable characteristics, wire electric discharge machining (wire EDM) is commonly used for the purpose [18]. Special attention is required for an adequate cutting process (single flat cut, proper constraint of the specimen to avoid its movement during cutting, a constant width of cut). Moreover, the type of cutting wire, the material, the geometry of the specimen and the EDM operating parameters are extremely important to realize an optimal cut. Finally, the cutting wire should be as thin as possible to remove the minimum material, particularly

ii. Measuring the surface contour. The contours of the cut surfaces can be measured using a coordinate measuring machine (CMM) [20]; typically, each surface contour is defined by

of residual stress and that the material removal introduces negligible stress [7, 14].

4 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

having a regular resolution of the residual stress normal to the cut surface [14, 15].


The multiaxial CM is a variation of the standard CM and its principles have been discussed by DeWald et al. [23]. This method uses displacements to calculate the eigenstrain distribution within the body; then from eigenstrain, the residual stress is determined by means of FE. The motivation for using eigenstrain to determine residual stress in CM is that eigenstrain remains constant upon residual stress redistribution. Hence, multiple cuts can be made without changing the eigenstrain distribution [20, 23]. Implementation of the multi-axial CM involves making multiple cuts along different orientations of a continuously processed prismatic specimen. Initially, the specimen is cut into two halves as in the conventional CM. The new cut surfaces are measured, and the results are averaged. Then, the two halves are cut along their diagonal. The displacements normal to the cut surfaces are contoured and averaged. After all the measurements are completed, the eigenstrain components are obtained from these three different measured and averaged surfaces [20]. The multi-axial CM technique was successfully applied to measure residual stress in variable polarity plasma arc (VPPA)-welded plates of 2024-T35 aluminum alloy [20], thin sheets of Ti-6Al-4 V and thick laser peened plates of 316 L stainless steel [23].

The validity of CM measurements has been assessed by comparing its results with those from neutron diffraction, X-ray (lab and synchrotron) diffraction and hole drilling [15, 18, 24–26].

Recently, Pagliaro et al. [27] suggested to use superposition to determine internal residual stresses by sectioning with CM and then measuring remaining stress with other methods. This approach allows measurements in parts where the internal stress were previously difficult to access and opens up possibilities to combine the advantages of different techniques [27].

CM has found a number of applications; some of them are of particular relevance such as butt joints of S355 structural steel [28], 80-mm thick ferritic steel welds [24], 70-mm thick dissimilar metal (ferritic to austenitic) welds [15] and ferritic steel plates welded using low and very high heat input processes [25], friction stir welds between 25.4-mm thick plates of aluminum alloys 7050-T7451 and 2024-T351 [29], 2024-T351 aluminum alloy VPPA welds [19], welded Tee-joints [22], welds of 13% Cr–4% Ni steel [30, 31], 316L stainless steel bead-on-plate specimens [32] and AA6061-T6 aluminum alloy friction stir butt welds [33].

While the sectioning technique is easier to determine residual stress over weld cross sections since almost no calculations are needed, CM provides a higher spatial resolution (1 mm spacing) [15].

CM can only be used to obtain high-resolution maps of the stress normal to the cut surface [6], but it is quite insensitive to inhomogeneities in the specimen as long as they do not significantly affect the elastic constants [29]. CM is cheap and powerful and can be used to choose appropriate measurement lines in welded structures for more detailed study, for example using neutron diffraction [7]. A further advantage of CM, compared to the few other methods that can measure a comparable stress map, is that it is relatively simple and inexpensive to perform and the equipment required is widely available [21].

treatment processes, for example shot peening, where more interesting is the evaluation of the residual stress in the first layer of the surface, the method permits to increase the resolution by

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7

The incremental deformation method, proposed by Schwarz and Kockelmann [38], is based on the measure of the incremental deformation during drilling. In addition to the standard hole obtained by high speed milling, Kockelmann proposed also a new hole shape to be obtained by electrochemical erosion. Improvements of the mentioned methods are available in literature in terms of evaluation of relaxation strain and models. One of them, proposed by Beghini et al. [39], takes in consideration the compensation of the principal parameters affecting the accu-

Rosette strain gauge installation: The installation needs to be performed by qualified person in compliance with the instructions of rosette and glue producer. Moreover, special attention should be paid to the cleaning of the surface where the strain gauge is bonded to avoid an

Centering: The eccentricity between the center of the hole and the center of the rosette could

Orthogonality and zeroing: A not accurate orthogonality between hole axis and surface could induce difference in the right measure of the depth of the hole and difficulty in zeroing.

Hole bottom fillet radius: The error in evaluating residual stress increases with the fillet radius

One of the most common fields of HDM application is the evaluation of residual stress induced by welding processes. In fact, residual stress could affect the operative strength of the part, fatigue life and stress corrosion strength. In as-welded conditions, often residual stress is close to yield stress and thermal or mechanical treatments are necessary to reduce it. So, a lot of research work was done for the evaluation of residual stress in different kinds of welding processes and materials [30, 31, 40–45] with the final target to find the correct welding parameters and post processing conditions to minimize the residual stress. Some of these works use HDM as validation of nondestructive techniques such as ultrasonic [41–46], XRD [30] and

In general, for the HDM, the following experimental factors play a crucial role:

reducing the step depth near the surface.

Figure 2. ASTM E837-08 standard: rosette types A, B and C.

racy in the evaluation of residual stress.

alteration of the original state of residual stress.

and decreases with the depth of the hole [40].

neutron diffraction [31].

introduce large error in the evaluation of residual stress.

#### 2.3. Hole-drilling method

The hole-drilling method (HDM) is versatile, easy, cheap, quick and standardized [4–6, 34] and is one of the techniques most used today for measuring residual stress. The principle, proposed more than 80 years ago [35], is based on the fact that relaxation occurs if some material is removed from a part with internal residual stress and it can be evaluated through the induced local deformation. In practical terms, an hole is drilled in the component at the center of a rosette strain gauge and a suitable model is used to determine the internal stress from strain data.

HDM equipment can be laboratory-based or portable, and the technique is applicable to a wide range of materials and components.

Drill speed and feed, centering of rosette and perpendicularity to the analysis surface are the main parameters affecting the measures of internal stress; operator skill and drilling equipment also play a significant role. Today, a modern integrate measure device consists of an automatic system including an high speed turbine (up to 400,000 rpm) with tungsten carbide tools and an electric stepping motor for the vertical cutter advancement with controlled drilling speed (0.1 mm/min); a microscope endowed of two orthogonal centesimal movements for drilling the hole at the center of rosette.

The other crucial aspect is the measure of the strain through rosette strain gauges. The ASTM E837-08 standard of reference for HDM residual stress evaluation [36] prescribes three kinds of rosette (Type A, B and C) as shown in Figure 2.

The ASTM E837-08 standard considers both uniform and nonuniform residual stress.

The evaluation of residual stress by HDM can be done in alternative ways. Since 1988, Schajer [37] introduced the incremental method for evaluating the nonuniform residual stress that allows to decide the number of step and the step depth. In the cases of coating or surface

Figure 2. ASTM E837-08 standard: rosette types A, B and C.

aluminum alloys 7050-T7451 and 2024-T351 [29], 2024-T351 aluminum alloy VPPA welds [19], welded Tee-joints [22], welds of 13% Cr–4% Ni steel [30, 31], 316L stainless steel bead-on-plate

While the sectioning technique is easier to determine residual stress over weld cross sections since almost no calculations are needed, CM provides a higher spatial resolution (1 mm spac-

CM can only be used to obtain high-resolution maps of the stress normal to the cut surface [6], but it is quite insensitive to inhomogeneities in the specimen as long as they do not significantly affect the elastic constants [29]. CM is cheap and powerful and can be used to choose appropriate measurement lines in welded structures for more detailed study, for example using neutron diffraction [7]. A further advantage of CM, compared to the few other methods that can measure a comparable stress map, is that it is relatively simple and inexpensive to

The hole-drilling method (HDM) is versatile, easy, cheap, quick and standardized [4–6, 34] and is one of the techniques most used today for measuring residual stress. The principle, proposed more than 80 years ago [35], is based on the fact that relaxation occurs if some material is removed from a part with internal residual stress and it can be evaluated through the induced local deformation. In practical terms, an hole is drilled in the component at the center of a rosette strain gauge and a suitable model is used to determine the internal stress from

HDM equipment can be laboratory-based or portable, and the technique is applicable to a

Drill speed and feed, centering of rosette and perpendicularity to the analysis surface are the main parameters affecting the measures of internal stress; operator skill and drilling equipment also play a significant role. Today, a modern integrate measure device consists of an automatic system including an high speed turbine (up to 400,000 rpm) with tungsten carbide tools and an electric stepping motor for the vertical cutter advancement with controlled drilling speed (0.1 mm/min); a microscope endowed of two orthogonal centesimal movements

The other crucial aspect is the measure of the strain through rosette strain gauges. The ASTM E837-08 standard of reference for HDM residual stress evaluation [36] prescribes three kinds of

The evaluation of residual stress by HDM can be done in alternative ways. Since 1988, Schajer [37] introduced the incremental method for evaluating the nonuniform residual stress that allows to decide the number of step and the step depth. In the cases of coating or surface

The ASTM E837-08 standard considers both uniform and nonuniform residual stress.

specimens [32] and AA6061-T6 aluminum alloy friction stir butt welds [33].

6 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

perform and the equipment required is widely available [21].

ing) [15].

strain data.

2.3. Hole-drilling method

wide range of materials and components.

for drilling the hole at the center of rosette.

rosette (Type A, B and C) as shown in Figure 2.

treatment processes, for example shot peening, where more interesting is the evaluation of the residual stress in the first layer of the surface, the method permits to increase the resolution by reducing the step depth near the surface.

The incremental deformation method, proposed by Schwarz and Kockelmann [38], is based on the measure of the incremental deformation during drilling. In addition to the standard hole obtained by high speed milling, Kockelmann proposed also a new hole shape to be obtained by electrochemical erosion. Improvements of the mentioned methods are available in literature in terms of evaluation of relaxation strain and models. One of them, proposed by Beghini et al. [39], takes in consideration the compensation of the principal parameters affecting the accuracy in the evaluation of residual stress.

In general, for the HDM, the following experimental factors play a crucial role:

Rosette strain gauge installation: The installation needs to be performed by qualified person in compliance with the instructions of rosette and glue producer. Moreover, special attention should be paid to the cleaning of the surface where the strain gauge is bonded to avoid an alteration of the original state of residual stress.

Centering: The eccentricity between the center of the hole and the center of the rosette could introduce large error in the evaluation of residual stress.

Orthogonality and zeroing: A not accurate orthogonality between hole axis and surface could induce difference in the right measure of the depth of the hole and difficulty in zeroing.

Hole bottom fillet radius: The error in evaluating residual stress increases with the fillet radius and decreases with the depth of the hole [40].

One of the most common fields of HDM application is the evaluation of residual stress induced by welding processes. In fact, residual stress could affect the operative strength of the part, fatigue life and stress corrosion strength. In as-welded conditions, often residual stress is close to yield stress and thermal or mechanical treatments are necessary to reduce it. So, a lot of research work was done for the evaluation of residual stress in different kinds of welding processes and materials [30, 31, 40–45] with the final target to find the correct welding parameters and post processing conditions to minimize the residual stress. Some of these works use HDM as validation of nondestructive techniques such as ultrasonic [41–46], XRD [30] and neutron diffraction [31].

Pappalettere et al. [47–52] applied an electronic speckle pattern interferometry (ESPI) method to avoid the use of conventional rosette strain gauges. The ESPI is based on the correlation between two speckle patterns, each one created by the interference between a reference beam and the image of an object illuminated by a laser. Typically, the two images are of an object before and after some deformation and the technique measures the 3D displacement by evaluating the phase difference of two recorded speckle interferograms. The apparatus consists of a diode-pumped solid state laser source that generates a radiation split into two beams and focused into two monomode optical fibers. One beam is collimated through a biconvex lens and illuminates the sample, whereas the second one passes through a phase shifting piezoelectric system and then it goes to the CCD camera where interferes with the light diffused by the optically rough surface of the specimen. The camera is equipped with an optical imaging system allowing fine focusing of the image. Initial phase and final phase are evaluated by the four-step phase shifting technique. Once the initial and the final phases are determined, it is possible to calculate the amount of displacement of each point into the analysis area. Figure 3 shows the experimental ESPI set-up [47]. In fact, rosette strain gauges introduce a not negligible cost particularly in the case where a relevant number of measurements are required. Moreover, some sources of experimental errors, such as surface preparation, bonding and positioning, are irrelevant using the not contact ESPI.

These investigators were also able to evaluate how drilling speed affects error in HDM and HDM/ESPI and concluded that higher speed helps to increase accuracy and reduce data scattering. For instance, standard deviation in residual stress evaluation in titanium samples changes from less than 3% to about 19% if drilling speed is reduced from 50,000 to 5000 rpm.

2.4. Instrumented indentation method

depth curve obtained from an indentation experiment.

In the last decade, the instrumented indentation has received increasing attention for characterizing the mechanical properties of materials on a local scale. Indenters with different geometry (tetragonal Vickers pyramid, trigonal Berkovich pyramid, sphere, cone and cylinder) have been used; the following considerations refer to a sharp conical indenter (with a half apex angle α). It penetrates normally into a solid where the applied load P and penetration depth h are continuously recorded during one complete cycle of loading and unloading (Figure 5a and b).

Figure 5. (a) Sketch of a sharp indentation on a homogeneous and isotropic material and (b) typical force-penetration

Figure 4. HDM validation of residual stress measurements performed through ultrasonic method. Redrawn from Ref. [42].

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HDM was used to validate the results of the ultrasonic technique in investigations on FSW joints of 5086 plates [42], AISI 304 pipes [43] and plates [44]. The example in Figure 4 shows the good correspondence between ultrasonic and HDM residual stress evaluation.

Figure 3. ESPI strain measurement set-up [47].

Figure 4. HDM validation of residual stress measurements performed through ultrasonic method. Redrawn from Ref. [42].

#### 2.4. Instrumented indentation method

Pappalettere et al. [47–52] applied an electronic speckle pattern interferometry (ESPI) method to avoid the use of conventional rosette strain gauges. The ESPI is based on the correlation between two speckle patterns, each one created by the interference between a reference beam and the image of an object illuminated by a laser. Typically, the two images are of an object before and after some deformation and the technique measures the 3D displacement by evaluating the phase difference of two recorded speckle interferograms. The apparatus consists of a diode-pumped solid state laser source that generates a radiation split into two beams and focused into two monomode optical fibers. One beam is collimated through a biconvex lens and illuminates the sample, whereas the second one passes through a phase shifting piezoelectric system and then it goes to the CCD camera where interferes with the light diffused by the optically rough surface of the specimen. The camera is equipped with an optical imaging system allowing fine focusing of the image. Initial phase and final phase are evaluated by the four-step phase shifting technique. Once the initial and the final phases are determined, it is possible to calculate the amount of displacement of each point into the analysis area. Figure 3 shows the experimental ESPI set-up [47]. In fact, rosette strain gauges introduce a not negligible cost particularly in the case where a relevant number of measurements are required. Moreover, some sources of experimental errors, such as surface prepara-

These investigators were also able to evaluate how drilling speed affects error in HDM and HDM/ESPI and concluded that higher speed helps to increase accuracy and reduce data scattering. For instance, standard deviation in residual stress evaluation in titanium samples changes from less than 3% to about 19% if drilling speed is reduced from 50,000 to 5000 rpm. HDM was used to validate the results of the ultrasonic technique in investigations on FSW joints of 5086 plates [42], AISI 304 pipes [43] and plates [44]. The example in Figure 4 shows the

tion, bonding and positioning, are irrelevant using the not contact ESPI.

8 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

good correspondence between ultrasonic and HDM residual stress evaluation.

Figure 3. ESPI strain measurement set-up [47].

In the last decade, the instrumented indentation has received increasing attention for characterizing the mechanical properties of materials on a local scale. Indenters with different geometry (tetragonal Vickers pyramid, trigonal Berkovich pyramid, sphere, cone and cylinder) have been used; the following considerations refer to a sharp conical indenter (with a half apex angle α). It penetrates normally into a solid where the applied load P and penetration depth h are continuously recorded during one complete cycle of loading and unloading (Figure 5a and b).

Figure 5. (a) Sketch of a sharp indentation on a homogeneous and isotropic material and (b) typical force-penetration depth curve obtained from an indentation experiment.

The contact stiffness S = dP/dh is obtained from the slope of initial part of the unloading curve (Figure 5b).

As the indenter, a rigid cone with α = 70.3�, penetrates the materials, either plastic pile-up at the crater rim (when the ratio between yield stress σy and Young's modulus E, σy/E, is small) or elastic sink-in (when σy/E is large) is observed. The amount of pile-up/sink-in is denoted as hp (Figure 5a). For conical indenters, the projected contact area A is given by:

$$A = \pi a^2 = \pi (\tan^{-1} \alpha)^2 h\_c^2 = 24.5 h\_c^2 \tag{1}$$

The presence of residual stresses modify the indentation curve: with respect the stress-free state the same penetration depth ht is reached at smaller load P in the case of tensile stress while compressive stress induces the opposite effect [53–55]. As shown in Figure 6, at the common penetration depth ht, it is observed that PA (with tensile stress) < PB (stress free) < PC (with compressive stress). The direct comparison of the indentation curve recorded in the investigated zone with that obtained in a zone of the same material without any residual stress allows to understand the

Experimental Techniques to Investigate Residual Stress in Joints

http://dx.doi.org/10.5772/intechopen.71564

To determine the value of residual stress, we will examine in the following the case of a material

Since the average contact pressure due to indentation, Pave (equivalently, the hardness), is unaffected by any pre-existing tensile or compressive elastic stress [53], the relationship

relates the indentation loads P and P0 directly to the real contact areas A and A0 of the material with and without residual stress, respectively. An equibiaxial tensile residual stress at the material surface can be considered equivalent to a tensile hydrostatic stress plus a uniaxial compressive stress component, �σ<sup>H</sup> (see Figure 6). This compressive stress component induces a differential indentation force σHA acting in the same direction as the indentation load P. On these grounds, a tensile residual stress aids indentation by lowering the indentation load

From the initial part of the unloading curve, the real contact area A at maximum load Pmax for

<sup>A</sup> <sup>¼</sup> <sup>P</sup><sup>0</sup> A0

(5)

11

(6)

Pave <sup>¼</sup> <sup>P</sup>

needed to penetrate the material to a given depth, as compared to the virgin material.

<sup>A</sup> <sup>¼</sup> dP dh 1 cE<sup>∗</sup> <sup>2</sup>

with residual tensile stress; a similar analysis can be made for compressive stress.

nature of the stress (tensile or compressive).

the material with the residual stress is

Figure 6. Effect of stress states on the indentation loading curve.

where the contact depth, h<sup>c</sup> = h + hp, contains the contributions of both plastic pile-up around the indenter and elastic sink-in, which is counted negative. The pile-up and contact area can be measured experimentally or determined from numerical analysis (e.g. FE method). Once the contact area A is known, hardness H and Young's modulus E are usually obtained from the indentation curve.

Hardness H is the ratio between applied load P and contact area A (H = P/A).

The indentation modulus M is determined from indentation curve through the equation:

$$M = \frac{S}{2\gamma\beta\sqrt{A}}\sqrt{\pi} \tag{2}$$

where β is a shape factor (β = 1 for axisymmetric indenters and β = 1.03–1.05 for indenters with square or rectangular cross-sections) and γ is a correction factor depending on indenter geometry. In the case of the conical indenter, γ can be written as:

$$\gamma = \pi \frac{\pi/4 + 0.155 \cot \alpha \left[\frac{1 - 2\nu}{4(1 - \nu)}\right]}{\left[\pi/2 - 0.831 \cot \alpha \left[\frac{1 - 2\nu}{4(1 - \nu)}\right]\right]^2} \tag{3}$$

where ν is the Poisson's ratio.

For isotropic materials, the indentation modulus M corresponds to the plane-strain modulus E\*

$$M = E^\* = \left(\frac{1 - \nu^2}{E} + \frac{1 - \nu^2\_{I}}{E\_I}\right) \tag{4}$$

where EI and ν<sup>I</sup> are the Young's modulus and Poisson's ratio of the indenter, respectively. Therefore, E can be easily calculated from M through Eq. (4).

How to correctly determine residual stresses from instrumented indentation test has been debated for some years. Initially, indentation hardness was used as a parameter of the residual stress; however, successive studies [53, 54] reported that the intrinsic hardness is invariant, regardless of the residual stress. Therefore, the change in contact morphologies with residual stress was modeled for constant maximum indentation depth assuming the independence of intrinsic hardness and residual stress [54].

The presence of residual stresses modify the indentation curve: with respect the stress-free state the same penetration depth ht is reached at smaller load P in the case of tensile stress while compressive stress induces the opposite effect [53–55]. As shown in Figure 6, at the common penetration depth ht, it is observed that PA (with tensile stress) < PB (stress free) < PC (with compressive stress).

The contact stiffness S = dP/dh is obtained from the slope of initial part of the unloading curve

As the indenter, a rigid cone with α = 70.3�, penetrates the materials, either plastic pile-up at the crater rim (when the ratio between yield stress σy and Young's modulus E, σy/E, is small) or elastic sink-in (when σy/E is large) is observed. The amount of pile-up/sink-in is denoted as

where the contact depth, h<sup>c</sup> = h + hp, contains the contributions of both plastic pile-up around the indenter and elastic sink-in, which is counted negative. The pile-up and contact area can be measured experimentally or determined from numerical analysis (e.g. FE method). Once the contact area A is known, hardness H and Young's modulus E are usually obtained from the

2 h2

<sup>c</sup> <sup>¼</sup> <sup>24</sup>:5h<sup>2</sup>

<sup>c</sup> (1)

<sup>π</sup> <sup>p</sup> (2)

(4)

hp (Figure 5a). For conical indenters, the projected contact area A is given by:

10 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Hardness H is the ratio between applied load P and contact area A (H = P/A).

etry. In the case of the conical indenter, γ can be written as:

Therefore, E can be easily calculated from M through Eq. (4).

intrinsic hardness and residual stress [54].

γ ¼ π

The indentation modulus M is determined from indentation curve through the equation:

<sup>M</sup> <sup>¼</sup> <sup>S</sup> 2γβ ffiffiffiffi A <sup>p</sup> ffiffiffi

where β is a shape factor (β = 1 for axisymmetric indenters and β = 1.03–1.05 for indenters with square or rectangular cross-sections) and γ is a correction factor depending on indenter geom-

<sup>π</sup>=<sup>4</sup> <sup>þ</sup> <sup>0</sup>:155 cot <sup>α</sup> <sup>1</sup>�2<sup>ν</sup>

<sup>π</sup>=<sup>2</sup> � <sup>0</sup>:831 cot <sup>α</sup> <sup>1</sup>�2<sup>ν</sup>

For isotropic materials, the indentation modulus M corresponds to the plane-strain modulus E\*

where EI and ν<sup>I</sup> are the Young's modulus and Poisson's ratio of the indenter, respectively.

How to correctly determine residual stresses from instrumented indentation test has been debated for some years. Initially, indentation hardness was used as a parameter of the residual stress; however, successive studies [53, 54] reported that the intrinsic hardness is invariant, regardless of the residual stress. Therefore, the change in contact morphologies with residual stress was modeled for constant maximum indentation depth assuming the independence of

E þ

� �

<sup>M</sup> <sup>¼</sup> <sup>E</sup><sup>∗</sup> <sup>¼</sup> <sup>1</sup> � <sup>ν</sup><sup>2</sup>

4 1ð Þ �ν h i

h i h i <sup>2</sup> (3)

4 1ð Þ �ν

<sup>1</sup> � <sup>ν</sup><sup>2</sup> I EI

<sup>A</sup> <sup>¼</sup> <sup>π</sup>a<sup>2</sup> <sup>¼</sup> <sup>π</sup>ð Þ tan <sup>α</sup>

(Figure 5b).

indentation curve.

where ν is the Poisson's ratio.

The direct comparison of the indentation curve recorded in the investigated zone with that obtained in a zone of the same material without any residual stress allows to understand the nature of the stress (tensile or compressive).

To determine the value of residual stress, we will examine in the following the case of a material with residual tensile stress; a similar analysis can be made for compressive stress.

Since the average contact pressure due to indentation, Pave (equivalently, the hardness), is unaffected by any pre-existing tensile or compressive elastic stress [53], the relationship

$$P\_{\text{ave}} = \frac{P}{A} = \frac{P\_0}{A\_0} \tag{5}$$

relates the indentation loads P and P0 directly to the real contact areas A and A0 of the material with and without residual stress, respectively. An equibiaxial tensile residual stress at the material surface can be considered equivalent to a tensile hydrostatic stress plus a uniaxial compressive stress component, �σ<sup>H</sup> (see Figure 6). This compressive stress component induces a differential indentation force σHA acting in the same direction as the indentation load P. On these grounds, a tensile residual stress aids indentation by lowering the indentation load needed to penetrate the material to a given depth, as compared to the virgin material.

From the initial part of the unloading curve, the real contact area A at maximum load Pmax for the material with the residual stress is

$$A = \left(\frac{dP}{dh}\frac{1}{cE^\*}\right)^2\tag{6}$$

Figure 6. Effect of stress states on the indentation loading curve.

where c is a constant depending on the indenter geometry (c = 1.167 for Berkovich indenter, c = 1.142 for the Vickers indenter). An analogous relationship is found for the unstressed material; thus, it can be easily demonstrated that

$$\frac{A}{A\_0} = \left(\frac{dP}{dh}\right)^2 \left(\frac{dP\_0}{dh\_0}\right)^{-2} = \left(1 + \frac{\sigma\_H}{P\_{\text{ave}}}\right)^{-1} \tag{7}$$

surface. The process is not continuous but consists of small steps generated by domains jumping from one position to another. Pulses are random in amplitude, duration and temporal

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BN is exponentially damped as a function of the traveled distance inside the material and the extent of damping determines the depth from which information can be obtained. Such depth mainly depends on the signal frequency together with conductivity and magnetic permeability of the tested material. Measurement depths in steels range from 0.01 to 3.0 mm; since this value is much higher than that of X-ray diffraction (some tens of microns), the BN method allows to

The intensity of BN depends on both stress and microstructure of the material; thus, a suitable calibration is of the utmost importance to properly determine uniaxial and biaxial surface stresses. Grain size, texture and dislocation structures play an important role in BN response; therefore, it is necessary to separate the contribution of stress from that of microstructure through a suitable calibration procedure. Calibration involves measurement of the BN signal on a representative section of the sample material using a known applied stress. A typical uniaxial calibration curve, taken from Kesavan et al. [9], is shown in Figure 7. The handbook [3] reports more details of uniaxial and biaxial stress calibration procedures and related results

As a result of magnetoelastic interaction, in materials with positive magnetic anisotropy (most steels and cobalt alloys), compressive stresses decrease the BN intensity, whereas tensile stresses increase it. Therefore, the measurement of BN intensity allows to determine the

amount of residual stress and also defines the direction of principal stresses.

separation and give rise to a noise-like signal called Barkhausen noise.

quantify subsurface stress without need of removing the surface layer.

for isotropic and anisotropic materials.

Figure 7. Typical uniaxial calibration curve taken from Ref. [9].

where Pave is the average pressure.

The ratio A/A0 is determined from the initial slopes of the unloading parts of the P-h curves. The value of A is calculated through Eq. (6), and at P = Pmax, the average pressure Pave = Pmax/A. The residual stress magnitude σ<sup>H</sup> is found by introducing the calculated values of A/A0 and Pave into Eq. (7).

The stress determined in this way is that of a layer of depth hmax corresponding to Pmax and represents an average value over the layer. With the availability of macro-, micro- and nanoindenters, instrumented indentation can be used to probe local properties at different size scales.

The technique has been successfully used for determining residual stresses in different metallic alloys and recently also in tissues and other soft biological materials (e.g. see [56]).

Owing to its specific characteristics, indentation is quite useful for investigating welded mechanical parts because it allows to determine the residual stress on local scale, namely in the melted and heat affected zones of the joints. Instrumented indentation was applied by Jang et al. [57] for evaluating residual stress in A335 P12 steel welds in electric power plant facilities before and after stress-relaxation annealing. Comparison with the results of conventional saw-cutting tests showed the efficiency of indentation tests. The method was employed by Ullner et al. [58] to determine the local stresses in resistance-spot welded joints of advanced high strength steels.

### 3. Nondestructive techniques

#### 3.1. Barkhausen noise method

Magnetic methods rely on the interaction between magnetization and elastic strain in ferromagnetic materials; they are sensitive to all three types of residual stress, but cannot distinguish between them. Here, only the Barkhausen noise (BN) method, based on the analysis of magnetic domain wall motion, will be presented and discussed.

Ferromagnetic materials consist of magnetically ordered regions called domains; each domain is magnetized along a certain direction and is separated from the others by walls where the direction of magnetization abruptly turns. The net magnetization of a material is the average of the magnetizations within all domains.

Under the action of an external magnetic field, the domain walls move and the resulting change in magnetization is detected as electrical pulses in a coil placed near the material surface. The process is not continuous but consists of small steps generated by domains jumping from one position to another. Pulses are random in amplitude, duration and temporal separation and give rise to a noise-like signal called Barkhausen noise.

where c is a constant depending on the indenter geometry (c = 1.167 for Berkovich indenter, c = 1.142 for the Vickers indenter). An analogous relationship is found for the unstressed

¼ 1 þ

σ<sup>H</sup> Pave �<sup>1</sup>

(7)

dh<sup>0</sup> �<sup>2</sup>

The ratio A/A0 is determined from the initial slopes of the unloading parts of the P-h curves. The value of A is calculated through Eq. (6), and at P = Pmax, the average pressure Pave = Pmax/A. The residual stress magnitude σ<sup>H</sup> is found by introducing the calculated values of A/A0 and

The stress determined in this way is that of a layer of depth hmax corresponding to Pmax and represents an average value over the layer. With the availability of macro-, micro- and nanoindenters, instrumented indentation can be used to probe local properties at different size

The technique has been successfully used for determining residual stresses in different metallic

Owing to its specific characteristics, indentation is quite useful for investigating welded mechanical parts because it allows to determine the residual stress on local scale, namely in the melted and heat affected zones of the joints. Instrumented indentation was applied by Jang et al. [57] for evaluating residual stress in A335 P12 steel welds in electric power plant facilities before and after stress-relaxation annealing. Comparison with the results of conventional saw-cutting tests showed the efficiency of indentation tests. The method was employed by Ullner et al. [58] to determine the local stresses in resistance-spot welded joints of advanced high strength steels.

Magnetic methods rely on the interaction between magnetization and elastic strain in ferromagnetic materials; they are sensitive to all three types of residual stress, but cannot distinguish between them. Here, only the Barkhausen noise (BN) method, based on the analysis of

Ferromagnetic materials consist of magnetically ordered regions called domains; each domain is magnetized along a certain direction and is separated from the others by walls where the direction of magnetization abruptly turns. The net magnetization of a material is the average of

Under the action of an external magnetic field, the domain walls move and the resulting change in magnetization is detected as electrical pulses in a coil placed near the material

magnetic domain wall motion, will be presented and discussed.

alloys and recently also in tissues and other soft biological materials (e.g. see [56]).

material; thus, it can be easily demonstrated that

where Pave is the average pressure.

3. Nondestructive techniques

the magnetizations within all domains.

3.1. Barkhausen noise method

Pave into Eq. (7).

scales.

A A0 <sup>¼</sup> dP dh <sup>2</sup> dP<sup>0</sup>

12 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

BN is exponentially damped as a function of the traveled distance inside the material and the extent of damping determines the depth from which information can be obtained. Such depth mainly depends on the signal frequency together with conductivity and magnetic permeability of the tested material. Measurement depths in steels range from 0.01 to 3.0 mm; since this value is much higher than that of X-ray diffraction (some tens of microns), the BN method allows to quantify subsurface stress without need of removing the surface layer.

The intensity of BN depends on both stress and microstructure of the material; thus, a suitable calibration is of the utmost importance to properly determine uniaxial and biaxial surface stresses. Grain size, texture and dislocation structures play an important role in BN response; therefore, it is necessary to separate the contribution of stress from that of microstructure through a suitable calibration procedure. Calibration involves measurement of the BN signal on a representative section of the sample material using a known applied stress. A typical uniaxial calibration curve, taken from Kesavan et al. [9], is shown in Figure 7. The handbook [3] reports more details of uniaxial and biaxial stress calibration procedures and related results for isotropic and anisotropic materials.

As a result of magnetoelastic interaction, in materials with positive magnetic anisotropy (most steels and cobalt alloys), compressive stresses decrease the BN intensity, whereas tensile stresses increase it. Therefore, the measurement of BN intensity allows to determine the amount of residual stress and also defines the direction of principal stresses.

Figure 7. Typical uniaxial calibration curve taken from Ref. [9].

The advantages of the BN method for stress measurements in welds are that it is fast, reliable and requires no specific surface preparation. Moreover, it can be used for continuous monitoring of stress in industrial processes. A significant example is reported in Figure 8 showing the effect of furnace stress relieving on a welded "T" section [3]; it is noteworthy that the stress profiles of the two seams before stress relieving are asymmetric because the left seam was welded first, being then subjected to a strong heating during the realization of the right seam.

The potential of BN technique for directly assessing fatigue processes and progressive residual

Beside the aforesaid advantages of the BN technique, some drawbacks place a severe restriction on its general applicability: (i) the material must be ferromagnetic; (ii) the total range of stress sensitivity (~ 6 MPa) is low; (iii) the measurement depth is limited to the surface layers and (iv) BN signal saturation may occur when tests are carried out on martensitic steels with

The ultrasonic techniques are based on variations in the velocity of ultrasonic waves, which can be related to the residual stress state through the elastic constants of the material [34, 44]. Like the magnetic methods, the ultrasonic techniques are sensitive to all three kinds of residual

Ultrasonic stress measurement is founded on the linear relation between velocity of the ultrasonic wave and the material stress. This correlation, known as the acoustoelastic effect, estab-

where K is the acoustoelastic constant (AEC) depending on the material and V0 and V are the

In 1967, Crecraft showed that the acoustoelastic law can be employed for stress measurement of engineering materials [35, 42, 45]. Changes in ultrasonic speed can be observed when a material is subjected to a stress, the changes providing a measure of the stress averaged along the wave path. The acoustoelastic coefficients necessary for the analysis are usually calculated using calibration tests. Different types of wave can be employed but the commonly used technique is the longitudinal critically refracted (Lcr) wave method [4]. The Lcr wave is an acoustical wave that is excited when the angle of incidence is slightly smaller than the first critical angle, which is calculated from the Snell's law [44, 68, 69]. It is a bulk longitudinal wave, traveling just below the surface of the specimen. This wave is more sensitive to stress and less sensitive to localized material texture changes [69]. Different ultrasonic configurations can be employed for residual stresses measurements by Lcr technique. As a common experimental setup, longitudinal waves are propagated at the first critical angle by a transmitter transducer and then travel parallel the tested material surface and finally are detected by a receiver transducer. The residual stress in a subsurface layer is measurable while the depth of layer is related to the ultrasonic wavelength, often exceeding a few millimeters [43]. The relation between measured travel-time change of Lcr wave and the corresponding uniaxial stress was derived by Egle and Bray [70]; with knowledge of the weld induced change in travel time and the measured acoustoelastic constant, the stress produced by the weld may be calculated [43]. The principal steps to be followed in the measurement of residual stress by ultrasonic methods are: (i) selection of weld joint or component; (ii) determination of the acoustoelastic constant (AEC) of the material using standard tensile specimen by applying

V ¼ V<sup>0</sup> þ Kσ (8)

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stress relaxation in cyclically loaded welds has been shown by Lachmann et al. [67].

very fine and complex microstructural features.

stress, but are not able to distinguish between them.

lishes the following relationship between the velocity V and the stress σ:

velocities in stress-free and stressed material, respectively [3].

3.2. Ultrasonic method

Vourna et al. [59–61] examined through the BN method joints of an electrical steel (Si 2.18 wt%) welded by means of three different techniques, namely Tungsten Inert Gas (TIG), Plasma and Electron Beam, determining maps of residual stress across melted zone, heat affected zone and base material. The comparison of results with those from X-ray diffraction showed a good agreement. Similar good results were achieved by measurements performed on other types of steels such as API X65 [62], API 5 L X70 [63], AS1548–7-460R [64], structural steel [65] and Cr-Mo steel [66]. As pointed out by many investigators who examined welds of different steels, BN technique requires a precise calibration procedure in all zones, which have a noticeably different microstructure, namely each zone should be separately considered for calibration [59, 60, 61, 63].

Figure 8. Stress relieving on a welded "T" section measured through BN; redrawn from Ref. [3].

The potential of BN technique for directly assessing fatigue processes and progressive residual stress relaxation in cyclically loaded welds has been shown by Lachmann et al. [67].

Beside the aforesaid advantages of the BN technique, some drawbacks place a severe restriction on its general applicability: (i) the material must be ferromagnetic; (ii) the total range of stress sensitivity (~ 6 MPa) is low; (iii) the measurement depth is limited to the surface layers and (iv) BN signal saturation may occur when tests are carried out on martensitic steels with very fine and complex microstructural features.

#### 3.2. Ultrasonic method

The advantages of the BN method for stress measurements in welds are that it is fast, reliable and requires no specific surface preparation. Moreover, it can be used for continuous monitoring of stress in industrial processes. A significant example is reported in Figure 8 showing the effect of furnace stress relieving on a welded "T" section [3]; it is noteworthy that the stress profiles of the two seams before stress relieving are asymmetric because the left seam was welded first, being then subjected to a strong heating during the realization of the right seam. Vourna et al. [59–61] examined through the BN method joints of an electrical steel (Si 2.18 wt%) welded by means of three different techniques, namely Tungsten Inert Gas (TIG), Plasma and Electron Beam, determining maps of residual stress across melted zone, heat affected zone and base material. The comparison of results with those from X-ray diffraction showed a good agreement. Similar good results were achieved by measurements performed on other types of steels such as API X65 [62], API 5 L X70 [63], AS1548–7-460R [64], structural steel [65] and Cr-Mo steel [66]. As pointed out by many investigators who examined welds of different steels, BN technique requires a precise calibration procedure in all zones, which have a noticeably different microstructure, namely each zone should be separately considered for calibration

14 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Figure 8. Stress relieving on a welded "T" section measured through BN; redrawn from Ref. [3].

[59, 60, 61, 63].

The ultrasonic techniques are based on variations in the velocity of ultrasonic waves, which can be related to the residual stress state through the elastic constants of the material [34, 44]. Like the magnetic methods, the ultrasonic techniques are sensitive to all three kinds of residual stress, but are not able to distinguish between them.

Ultrasonic stress measurement is founded on the linear relation between velocity of the ultrasonic wave and the material stress. This correlation, known as the acoustoelastic effect, establishes the following relationship between the velocity V and the stress σ:

$$V = V\_0 + \mathcal{K}\sigma \tag{8}$$

where K is the acoustoelastic constant (AEC) depending on the material and V0 and V are the velocities in stress-free and stressed material, respectively [3].

In 1967, Crecraft showed that the acoustoelastic law can be employed for stress measurement of engineering materials [35, 42, 45]. Changes in ultrasonic speed can be observed when a material is subjected to a stress, the changes providing a measure of the stress averaged along the wave path. The acoustoelastic coefficients necessary for the analysis are usually calculated using calibration tests. Different types of wave can be employed but the commonly used technique is the longitudinal critically refracted (Lcr) wave method [4]. The Lcr wave is an acoustical wave that is excited when the angle of incidence is slightly smaller than the first critical angle, which is calculated from the Snell's law [44, 68, 69]. It is a bulk longitudinal wave, traveling just below the surface of the specimen. This wave is more sensitive to stress and less sensitive to localized material texture changes [69]. Different ultrasonic configurations can be employed for residual stresses measurements by Lcr technique. As a common experimental setup, longitudinal waves are propagated at the first critical angle by a transmitter transducer and then travel parallel the tested material surface and finally are detected by a receiver transducer. The residual stress in a subsurface layer is measurable while the depth of layer is related to the ultrasonic wavelength, often exceeding a few millimeters [43]. The relation between measured travel-time change of Lcr wave and the corresponding uniaxial stress was derived by Egle and Bray [70]; with knowledge of the weld induced change in travel time and the measured acoustoelastic constant, the stress produced by the weld may be calculated [43]. The principal steps to be followed in the measurement of residual stress by ultrasonic methods are: (i) selection of weld joint or component; (ii) determination of the acoustoelastic constant (AEC) of the material using standard tensile specimen by applying varying loads; (iii) ultrasonic velocity measurements in the weld joint or component of interest and (iv) determination of residual stress using AEC [68].

1. The penetration depth in a material of a neutron beam is of the order of some centimeters and that of X-rays is of tens of microns. Therefore, X-ray diffraction measures the residual strain on the surface of the material, whereas neutron diffraction measures the residual strain within a volume of the sample. Owing to its unique deep penetration, neutron diffraction has been used to measure stresses in welds of 50-mm thick steel plates [73]. High energy X-rays from synchrotron sources have the penetration depth in between and

2. The intensities of X-ray diffraction lines depend on the atomic scattering factor f, which is directly proportional to the atomic number Z; thus, in a polyphasic material, the phases rich of light elements will exhibit diffraction patterns of lower intensity with respect to those rich of heavy elements. For instance, in a steel with perlitic structure (ferrite plus cementite), only the diffraction lines of ferrite are revealed, whereas those of cementite

In the case of neutrons, scattering intensity varies quite irregularly with the atomic number Z; therefore, elements with quite different values of Z may scatter neutrons equally well. Furthermore, some light elements, such as carbon, scatter neutrons more intensely than some heavy elements. It follows that structure analyses can be carried out with neutron diffraction that are

Both neutron and X-ray diffraction techniques can be used to study all three kinds of stresses.

Residual stresses in polycrystalline materials change the lattice spacings, which vary according to the orientation of planes relatively to the stress direction. In fact, the crystal lattice is used as a strain gauge. The elastic strain can be calculated from the variation of lattice spacing d: d0, determined by the position of the Bragg peak of stressed (θ) and stress-free (θ0) material:

The strain measured from shift of peak position is the elastic strain along the normal direction

The direction Φ is the projection on the plane XY of the direction OO' forming an angle ψ with

and is determined by measuring d<sup>ψ</sup> and dz, known E and ν. Through X-ray and neutron diffraction, it is possible to measure uniaxial, biaxial and triaxial stress states, an exhaustive

ψ method allows to determine the stress along any direction Φ in the plane XY

� <sup>E</sup>

<sup>ε</sup> <sup>¼</sup> <sup>d</sup> � <sup>d</sup><sup>0</sup> d0

to diffracting planes, i.e. those parallel to the surface of the examined sample.

σφ <sup>¼</sup> <sup>d</sup><sup>ψ</sup> � dz dz

, whereas line broadening is sensitive to σII and σIII.

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¼ �Δθ cot θ (9)

ð Þ <sup>1</sup> <sup>þ</sup> <sup>ν</sup> sin2<sup>ψ</sup> (10)

are used to investigate subsurface stresses.

have a negligible intensity, comparable with background.

impossible, or possible only with great difficulty, with X-ray.

The peak shift method is sensitive to σ<sup>I</sup>

the axis Z. The stress σΦ is given by:

treatment of the topic can be found in Ref. [3].

The sin<sup>2</sup>

(Figure 9).

Javadi et al. [41–43] carried out a series of interesting studies on the ultrasonic method. They compared contact and immersion ultrasonic measurements of welding residual stress in dissimilar joints. A combination of FE welding simulation and Lcr ultrasonic waves was employed to reach the goal, and on the basis of experimental results, they concluded that both of the methods can measure the residual stress with an acceptable accuracy and the selection between them depends on geometry and dimensions of tested structure and also on the available experimental devices [41].

The same investigators developed a method (TLcr) that is the combination of Taguchi method (a technique to optimize welding parameters) and the Lcr ultrasonic method in order to study which process parameter has the highest effect on the longitudinal residual stresses in aluminum plates joined by the FSW process [42]. Finally, Javadi et al. [43] studied the combination of FE and Lcr method (known as FELCR) confirming its ability to evaluate the pipe residual stresses through the thickness.

The ultrasonic technique was also successfully used in the study of residual stress in dissimilar joints [41]; residual stress through the thickness of stainless steel plates with 10 mm thickness [44]; longitudinal residual stress through the thickness of aluminum plates with 8 mm thickness [45]; for assessment of surface/subsurface longitudinal residual stresses in AISI type 316LN stainless steel weld joints made by ATIG and TIG welding processes [68]; welding residual stress through the thickness of stainless steel pipe [43] and prediction of total residual stress and fusion boundary in three pass welded stainless steel plates [71].

In conclusion, the ultrasonic technique is nondestructive, sensitive to microstructures and defects, has sufficiently good spatial resolution (5 mm) for longitudinal residual stresses across welded joints and is easy and simple to use and cost effective [8, 69, 72]. Additionally, the instrumentation is portable and quick to implement [34] and it is well suited for routine inspection procedures and industrial studies of large components, such as steam turbine discs [4]. On the other hand, this method has some difficulties in separating the effects of multiaxial stresses and in measuring the stress in an exact depth; since the penetration depths of the ultrasonic transducers are limited to a few millimeters, measurement of thick materials on both sides is recommended.

#### 3.3. X-ray and neutron diffraction method

X-ray and neutron diffraction methods are based on the measurement of lattice strains by studying the variations of lattice spacings of the polycrystalline material. In other words, these techniques allow to determine the variations of lattice spacings induced by compressive or tensile stresses and to calculate the stresses from the strains, known the elastic constants of the material under investigation. Neutron and X-ray wavelengths used in diffraction experiments are about of the same magnitude; however, neutron diffraction differs from X-ray diffraction in several ways. Two aspects are of particular relevance to the present discussion:

1. The penetration depth in a material of a neutron beam is of the order of some centimeters and that of X-rays is of tens of microns. Therefore, X-ray diffraction measures the residual strain on the surface of the material, whereas neutron diffraction measures the residual strain within a volume of the sample. Owing to its unique deep penetration, neutron diffraction has been used to measure stresses in welds of 50-mm thick steel plates [73]. High energy X-rays from synchrotron sources have the penetration depth in between and are used to investigate subsurface stresses.

varying loads; (iii) ultrasonic velocity measurements in the weld joint or component of interest

Javadi et al. [41–43] carried out a series of interesting studies on the ultrasonic method. They compared contact and immersion ultrasonic measurements of welding residual stress in dissimilar joints. A combination of FE welding simulation and Lcr ultrasonic waves was employed to reach the goal, and on the basis of experimental results, they concluded that both of the methods can measure the residual stress with an acceptable accuracy and the selection between them depends on geometry and dimensions of tested structure and also on the

The same investigators developed a method (TLcr) that is the combination of Taguchi method (a technique to optimize welding parameters) and the Lcr ultrasonic method in order to study which process parameter has the highest effect on the longitudinal residual stresses in aluminum plates joined by the FSW process [42]. Finally, Javadi et al. [43] studied the combination of FE and Lcr method (known as FELCR) confirming its ability to evaluate the pipe residual

The ultrasonic technique was also successfully used in the study of residual stress in dissimilar joints [41]; residual stress through the thickness of stainless steel plates with 10 mm thickness [44]; longitudinal residual stress through the thickness of aluminum plates with 8 mm thickness [45]; for assessment of surface/subsurface longitudinal residual stresses in AISI type 316LN stainless steel weld joints made by ATIG and TIG welding processes [68]; welding residual stress through the thickness of stainless steel pipe [43] and prediction of total residual

In conclusion, the ultrasonic technique is nondestructive, sensitive to microstructures and defects, has sufficiently good spatial resolution (5 mm) for longitudinal residual stresses across welded joints and is easy and simple to use and cost effective [8, 69, 72]. Additionally, the instrumentation is portable and quick to implement [34] and it is well suited for routine inspection procedures and industrial studies of large components, such as steam turbine discs [4]. On the other hand, this method has some difficulties in separating the effects of multiaxial stresses and in measuring the stress in an exact depth; since the penetration depths of the ultrasonic transducers are limited to a few millimeters, measurement of thick materials on both

X-ray and neutron diffraction methods are based on the measurement of lattice strains by studying the variations of lattice spacings of the polycrystalline material. In other words, these techniques allow to determine the variations of lattice spacings induced by compressive or tensile stresses and to calculate the stresses from the strains, known the elastic constants of the material under investigation. Neutron and X-ray wavelengths used in diffraction experiments are about of the same magnitude; however, neutron diffraction differs from X-ray diffraction in

several ways. Two aspects are of particular relevance to the present discussion:

stress and fusion boundary in three pass welded stainless steel plates [71].

and (iv) determination of residual stress using AEC [68].

16 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

available experimental devices [41].

stresses through the thickness.

sides is recommended.

3.3. X-ray and neutron diffraction method

2. The intensities of X-ray diffraction lines depend on the atomic scattering factor f, which is directly proportional to the atomic number Z; thus, in a polyphasic material, the phases rich of light elements will exhibit diffraction patterns of lower intensity with respect to those rich of heavy elements. For instance, in a steel with perlitic structure (ferrite plus cementite), only the diffraction lines of ferrite are revealed, whereas those of cementite have a negligible intensity, comparable with background.

In the case of neutrons, scattering intensity varies quite irregularly with the atomic number Z; therefore, elements with quite different values of Z may scatter neutrons equally well. Furthermore, some light elements, such as carbon, scatter neutrons more intensely than some heavy elements. It follows that structure analyses can be carried out with neutron diffraction that are impossible, or possible only with great difficulty, with X-ray.

Both neutron and X-ray diffraction techniques can be used to study all three kinds of stresses. The peak shift method is sensitive to σ<sup>I</sup> , whereas line broadening is sensitive to σII and σIII.

Residual stresses in polycrystalline materials change the lattice spacings, which vary according to the orientation of planes relatively to the stress direction. In fact, the crystal lattice is used as a strain gauge. The elastic strain can be calculated from the variation of lattice spacing d: d0, determined by the position of the Bragg peak of stressed (θ) and stress-free (θ0) material:

$$
\varepsilon = \frac{d - d\_0}{d\_0} = -\Delta\theta\cot\theta\tag{9}
$$

The strain measured from shift of peak position is the elastic strain along the normal direction to diffracting planes, i.e. those parallel to the surface of the examined sample.

The sin<sup>2</sup> ψ method allows to determine the stress along any direction Φ in the plane XY (Figure 9).

The direction Φ is the projection on the plane XY of the direction OO' forming an angle ψ with the axis Z. The stress σΦ is given by:

$$
\sigma\_{\psi} = \frac{d\_{\psi} - d\_{z}}{d\_{z}} \cdot \frac{E}{(1+\nu)\sin^{2}\psi} \tag{10}
$$

and is determined by measuring d<sup>ψ</sup> and dz, known E and ν. Through X-ray and neutron diffraction, it is possible to measure uniaxial, biaxial and triaxial stress states, an exhaustive treatment of the topic can be found in Ref. [3].

Figure 9. The direction Φ is the projection on the plane XY of the direction forming an angle ψ with the axis Z.

Since the Warren Averbach method [74] appeared in the 1950s, diffraction line broadening analysis is used to study the microstructural evolution of crystalline materials. Two factors contribute to line broadening: (i) the size of coherently diffracting domains (grains, sub-grains or cells) and (ii) micro-strains related to the density of dislocations, stacking faults and twins. Of course, line broadening is related to σII and σIII and a lot of specific literature does exist on the matter; thus, we will not treat here the details of analysis.

X-ray and neutron diffraction has been extensively used to investigate stress state in welds realized with different techniques and materials (steels [73, 75–81], aluminum alloys [82–87], titanium alloys [88, 89] and other alloys). Remarkable results have been achieved; for instance, neutron and synchrotron X-ray diffraction has been successfully used for mapping residual stresses in welded parts (e.g. see [90]).

indicating the presence of tensile stresses. On the basis of these results, the pre-heating of the plates at 300C was identified as the optimal condition to realize EB joints of IN792 DS

Figure 10. {220} peak profiles collected from melted zone of samples welded at the same pass speed of 1.5 m/min with PHT of 200 and 300C. The vertical line indicates the peak position of base material free from the stresses arising from

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Case study 2 presents a study on a joint with a very complex structure. Because of its high melting point and good thermal conductivity, W is a promising armor material for protecting the components of International Thermonuclear Experimental Reactor (ITER) from plasma damage. However, the joining of W to other metals is challenging for the lower thermal expansion of W, its high elastic modulus and brittleness. An experimental campaign has been carried out by authors for realizing thick W-coatings on different metals, and Plasma Spraying was used as deposition technique for its simplicity, the possibility to cover complex and extended surfaces and the relatively low cost. The reported example regards 5-mm thick W coatings deposited on CuCrZr alloy. An appropriate interlayer was optimized to increase the adhesion of W on the metallic substrate and to provide a soft interface with intermediate thermal expansion coefficient for better thermo-mechanical compatibility. The bonding interface with thickness of ~800 μm was realized through successive deposition steps. It consists of a layer of pure Ni (thickness ~200 μm) directly on the CuCrZr substrate followed by a stratification of thinner layers (thickness ~30 μm) obtained by spraying grading mixtures of Al–12% Si, Ni–20% Al, Ni–20% Al and W powders. A detailed description is given in [94, 95]. To verify the quality of joints, high temperature X-ray diffraction (HT-XRD) has been employed at increasing temperatures up to 425C and XRD spectra are shown in Figure 11. The vertical lines indicate the peak positions of the strain-free metals at room temperature.

The positions of Cu and W peaks at 25C correspond to those of the stress-free condition, whereas Al and Ni peaks exhibit significant shifts. This means that residual strains are present in the interlayer but not in coating and substrate. At 425C, all the peaks move towards lower

superalloy.

welding [93].

3.3.2. Case study 2

Woo et al. [86] were able to determine the evolution of temperature and thermal stresses during friction stir welding of Al6061-T6 through in situ, time-resolved neutron diffraction technique. The method allows to deconvolute the temperature and stress from the lattice spacing changes measured by neutron diffraction.

Two case studies taken from the research activity of the authors are now presented to illustrate the application of the technique.

#### 3.3.1. Case study 1

Electron beam (EB) welding has been used to realize seams on 2-mm thick plates of directionally solidified IN792 superalloy [91–93]. The experiments evidenced the importance of preheating the workpieces to avoid the formation of long cracks in the seam and X-ray diffraction (XRD) was used to identify the better pre-heating temperature (PHT). The samples were mounted on a micrometric translating table that allowed to move the samples and irradiate the desired zone.

XRD spectra were collected by focusing the beam on melted zone and Figure 10 compares the {220} peak profiles of samples welded with PHT of 200 and 300C at the same pass speed (1.5 m/min).

The vertical line indicates the peak position of stress-free base material. The peak position of the sample welded with PHT = 300C almost corresponds to that of stress-free material (vertical line), whereas the peak position of sample welded with PHT = 200C is shifted to lower angles

Figure 10. {220} peak profiles collected from melted zone of samples welded at the same pass speed of 1.5 m/min with PHT of 200 and 300C. The vertical line indicates the peak position of base material free from the stresses arising from welding [93].

indicating the presence of tensile stresses. On the basis of these results, the pre-heating of the plates at 300C was identified as the optimal condition to realize EB joints of IN792 DS superalloy.

#### 3.3.2. Case study 2

Since the Warren Averbach method [74] appeared in the 1950s, diffraction line broadening analysis is used to study the microstructural evolution of crystalline materials. Two factors contribute to line broadening: (i) the size of coherently diffracting domains (grains, sub-grains or cells) and (ii) micro-strains related to the density of dislocations, stacking faults and twins. Of course, line broadening is related to σII and σIII and a lot of specific literature does exist on

Figure 9. The direction Φ is the projection on the plane XY of the direction forming an angle ψ with the axis Z.

18 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

X-ray and neutron diffraction has been extensively used to investigate stress state in welds realized with different techniques and materials (steels [73, 75–81], aluminum alloys [82–87], titanium alloys [88, 89] and other alloys). Remarkable results have been achieved; for instance, neutron and synchrotron X-ray diffraction has been successfully used for mapping residual

Woo et al. [86] were able to determine the evolution of temperature and thermal stresses during friction stir welding of Al6061-T6 through in situ, time-resolved neutron diffraction technique. The method allows to deconvolute the temperature and stress from the lattice

Two case studies taken from the research activity of the authors are now presented to illustrate

Electron beam (EB) welding has been used to realize seams on 2-mm thick plates of directionally solidified IN792 superalloy [91–93]. The experiments evidenced the importance of preheating the workpieces to avoid the formation of long cracks in the seam and X-ray diffraction (XRD) was used to identify the better pre-heating temperature (PHT). The samples were mounted on a micrometric translating table that allowed to move the samples and irradiate

XRD spectra were collected by focusing the beam on melted zone and Figure 10 compares the {220} peak profiles of samples welded with PHT of 200 and 300C at the same pass speed

The vertical line indicates the peak position of stress-free base material. The peak position of the sample welded with PHT = 300C almost corresponds to that of stress-free material (vertical line), whereas the peak position of sample welded with PHT = 200C is shifted to lower angles

the matter; thus, we will not treat here the details of analysis.

stresses in welded parts (e.g. see [90]).

the application of the technique.

3.3.1. Case study 1

the desired zone.

(1.5 m/min).

spacing changes measured by neutron diffraction.

Case study 2 presents a study on a joint with a very complex structure. Because of its high melting point and good thermal conductivity, W is a promising armor material for protecting the components of International Thermonuclear Experimental Reactor (ITER) from plasma damage. However, the joining of W to other metals is challenging for the lower thermal expansion of W, its high elastic modulus and brittleness. An experimental campaign has been carried out by authors for realizing thick W-coatings on different metals, and Plasma Spraying was used as deposition technique for its simplicity, the possibility to cover complex and extended surfaces and the relatively low cost. The reported example regards 5-mm thick W coatings deposited on CuCrZr alloy. An appropriate interlayer was optimized to increase the adhesion of W on the metallic substrate and to provide a soft interface with intermediate thermal expansion coefficient for better thermo-mechanical compatibility. The bonding interface with thickness of ~800 μm was realized through successive deposition steps. It consists of a layer of pure Ni (thickness ~200 μm) directly on the CuCrZr substrate followed by a stratification of thinner layers (thickness ~30 μm) obtained by spraying grading mixtures of Al–12% Si, Ni–20% Al, Ni–20% Al and W powders. A detailed description is given in [94, 95].

To verify the quality of joints, high temperature X-ray diffraction (HT-XRD) has been employed at increasing temperatures up to 425C and XRD spectra are shown in Figure 11. The vertical lines indicate the peak positions of the strain-free metals at room temperature.

The positions of Cu and W peaks at 25C correspond to those of the stress-free condition, whereas Al and Ni peaks exhibit significant shifts. This means that residual strains are present in the interlayer but not in coating and substrate. At 425C, all the peaks move towards lower

Author details

Roberto Montanari<sup>1</sup>

References

\*, Alessandra Fava1 and Giuseppe Barbieri2

1 Department of Industrial Engineering, University of Rome Tor Vergata, Rome, Italy

2 Department of Sustainability, ENEA Centro Ricerche Casaccia, Santa Maria di Galeria, Italy

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[2] Finch DN. A Review of Non-destructive Residual Stress Measurement Techniques.

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\*Address all correspondence to: roberto.montanari@uniroma2.it

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Figure 11. XRD spectra collected from W-CuCrZr system. The markers indicate the peak positions of stress-free metals (JCPDS-ICDD database).

angles, in part due to thermal expansion. Table 1 shows the strains, corrected from the effect of thermal expansion, which are quite different in the metals of the system W-CuCrZr. Among them, W exhibits the lowest strain level (~ 5 <sup>10</sup><sup>4</sup> ) both at 25 and 425C; thus, strain substantially does not change as temperature increases. At room temperature, also the strain of Cu is low (~ 1 <sup>10</sup><sup>3</sup> ) but it increases at 425C. In the interlayer, a different behavior between Ni and Al is observed: the strain level in Al is about one order of magnitude higher than that of Ni.

Such results are very interesting if one considers that cracks form in W near the interlayer and then propagate by a brittle and transgranular fracture mechanism towards the substrate. In fact, they demonstrate that interlayer properly works by accumulating stress and protecting the coating. On this basis, HT-XRD permits to evaluate the quality of the deposition and can be used to orientate the work for optimizing structure and composition of the interlayer and to find the right parameters of deposition process.


Table 1. Strains at 25 and 425C.

## Author details

Roberto Montanari<sup>1</sup> \*, Alessandra Fava1 and Giuseppe Barbieri2


### References

angles, in part due to thermal expansion. Table 1 shows the strains, corrected from the effect of thermal expansion, which are quite different in the metals of the system W-CuCrZr. Among

Figure 11. XRD spectra collected from W-CuCrZr system. The markers indicate the peak positions of stress-free metals

substantially does not change as temperature increases. At room temperature, also the strain

between Ni and Al is observed: the strain level in Al is about one order of magnitude higher

Such results are very interesting if one considers that cracks form in W near the interlayer and then propagate by a brittle and transgranular fracture mechanism towards the substrate. In fact, they demonstrate that interlayer properly works by accumulating stress and protecting the coating. On this basis, HT-XRD permits to evaluate the quality of the deposition and can be used to orientate the work for optimizing structure and composition of the interlayer and to

T (C) 25C 425C Al 13.30 10.20 W 0.51 0.54 Cu 0.94 4.42 Ni 1.25 1.92

) but it increases at 425C. In the interlayer, a different behavior

) both at 25 and 425C; thus, strain

them, W exhibits the lowest strain level (~ 5 <sup>10</sup><sup>4</sup>

20 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

find the right parameters of deposition process.

Metal. <sup>ε</sup> <sup>10</sup><sup>3</sup>

of Cu is low (~ 1 <sup>10</sup><sup>3</sup>

Table 1. Strains at 25 and 425C.

than that of Ni.

(JCPDS-ICDD database).


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**Chapter 2**

**Provisional chapter**

**Numerical Welding Simulation as a Basis for Structural**

**Numerical Welding Simulation as a Basis for Structural** 

DOI: 10.5772/intechopen.74466

**Integrity Assessment of Structures: Microstructure and**

**Integrity Assessment of Structures: Microstructure and** 

The importance of welding process modeling is specifically related to the role of the induced welding residual stresses and distortions on the structural behavior of the components under service load. In the absence of reliable information on the magnitude and distribution of residual stresses, it is generally assumed that residual stresses are as high as the yield strength of the material that could lead to overconservatism in design and consequently economic challenges. The more exact the microstructure and residual stress or strain fields is predicted, the better one can judge the risk of structural damage, for example, the formation of fatigue cracks or initiation of failure. In this chapter, the application of finite element approach to the calculation of welding residual stresses is described through three different case studies. SYSWELD has been used for welding simulation. Residual stress measurements are carried out to determine the distribution of residual stresses in three orthogonal directions, on the surface and in the bulk of the material. The numerical results are compared directly with the measured data. The overall aim is to evaluate the use of finite element approach in the accurate calculation of

residual stress states for use in the structural integrity assessments.

**Keywords:** welding simulation, residual stresses, finite element method (FEM), X-ray

In fusion welding, concentrated heat is injected into the joint locally and is dissipated into the weldments, leading to an inhomogeneous temperature field in the welded material.

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Residual Stresses**

**Abstract**

**Residual Stresses**

Kimiya Hemmesi and Majid Farajian

Kimiya Hemmesi and Majid Farajian

http://dx.doi.org/10.5772/intechopen.74466

diffraction, neutron diffraction

**1. Introduction**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter


#### **Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures: Microstructure and Residual Stresses Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures: Microstructure and Residual Stresses**

DOI: 10.5772/intechopen.74466

Kimiya Hemmesi and Majid Farajian Kimiya Hemmesi and Majid Farajian

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74466

#### **Abstract**

[85] Owen RA, Preston RV, Withers PJ, Shercliff HR, Webster PJ. Neutron and synchrotron measurements of residual strain in TIG welded aluminium alloy 2024. Materials Science

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28 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

12:298-303. DOI: 10.1179/174329307X197548

4526(02)01514-4

1002/sia.5946

The importance of welding process modeling is specifically related to the role of the induced welding residual stresses and distortions on the structural behavior of the components under service load. In the absence of reliable information on the magnitude and distribution of residual stresses, it is generally assumed that residual stresses are as high as the yield strength of the material that could lead to overconservatism in design and consequently economic challenges. The more exact the microstructure and residual stress or strain fields is predicted, the better one can judge the risk of structural damage, for example, the formation of fatigue cracks or initiation of failure. In this chapter, the application of finite element approach to the calculation of welding residual stresses is described through three different case studies. SYSWELD has been used for welding simulation. Residual stress measurements are carried out to determine the distribution of residual stresses in three orthogonal directions, on the surface and in the bulk of the material. The numerical results are compared directly with the measured data. The overall aim is to evaluate the use of finite element approach in the accurate calculation of residual stress states for use in the structural integrity assessments.

**Keywords:** welding simulation, residual stresses, finite element method (FEM), X-ray diffraction, neutron diffraction

## **1. Introduction**

In fusion welding, concentrated heat is injected into the joint locally and is dissipated into the weldments, leading to an inhomogeneous temperature field in the welded material.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The maximum temperature in this time-dependent field reaches beyond the melting point in the weld pool, and the minimum value is the ambient temperature being reached after cooling down. Within this temperature field and due to the temperature-dependent physical and mechanical properties, an inhomogeneous thermal stress field is generated. The thermal stresses can either be accommodated elastically or lead to a stress state in which plastic deformations would be inevitable. There is another source of plastic deformation, which is induced during solid-state phase transformations if phase transformation occurs. As a result of the inhomogeneous plastic deformation during welding, some regions do not fit into the space available, and due to geometrical compatibility, a residual stress field arises.

Residual stress and distortion are strongly influenced by the temperature-dependent plasticity. In **Figure 1**, the thermomechanical processes for the development of welding stresses are schematically illustrated. Here in this model from Radaj [6], the plastic zones in front and a linear heat source in a quasi-stationary temperature field are shown. The drawn parabola-like curve separates the heated front area which is due to the thermal stresses under compression from the rear region which is under tensile stresses. The zone of elastic unloading is located between the two areas. The cyclic plasticity at the shown locations in the base material, the heat affected zone and the weld during the heating and cooling phases show how the residual stresses develop. Point 1 undergoes elastic compressive stress, and at point 2, a plastic deformation occurs after reaching the compressive yield strength before this point is elastically relieved at point 3. The permanent elongation by compression at point 3 could lead to tensile residual stresses after cooling. Points 4 and 5 experienced tensile stresses during cooling due

Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures…

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31

The remaining strain at point 5 may indicate that after reaching room temperature, compressive residual stresses may be present. Point 6 would have a mechanical load cycle as point 5, if it would not have been so close to the heat source. Point 7 is on the weld center and is only subjected to elasto-plastic tensile stresses. It is understandable that the temperaturedependent spatial and temporal process and material modeling determine the accuracy of the

Computational welding mechanics is an engineering subject concerned with the mechanics and the material behavior during welding. In research and applications, the different welding processes, the microstructures resulting in the weld and their mechanical properties in terms of deformability, strength, and toughness and the structural behavior of welded components are to be considered for an advanced fitness-for-service assessment of welded

The accuracy of the predicted results in the calculation of residual stresses as a complex nonlinear problem is influenced by several assumptions and simplifications. Nevertheless, the experimental measurement of welding residual stresses involves a significant range of uncertainties. Since both numerical and experimental approaches involve inevitably their own limi-

**Figure 1.** Cyclic plasticity in the weld, heat-affected zone and the base material and the formation of welding residual

tations, it is necessary to apply these methods in combination with each other.

to the shrinkage restraint.

components.

stresses [6].

residual stress and distortion calculations.

The reliable characterization of welding residual stresses in structural components has been widely considered in many research communities. Tensile residual stresses which are present in welds could potentially decrease the tolerance of the component against applied external loads. In integrity assessments, the interaction between load and residual stresses is taken into account by using a couple of conservative approaches [1]. In order to predict the more realistic service life of welded components, it is necessary to be aware of the residual stress fields, particularly in the critical crack initiation sites. Over the past few decades, a large number of researches have been devoted to the experimental and numerical determination of welding residual stresses. Recent advances in both simulation and measurement of weld residual stresses have provided the possibility to describe the residual stresses. However, owing to the different thermal, metallurgical, and mechanical complexities and the interaction between them, there still exist a number of uncertainties in the accurate calculation and measurement of residual stresses. On the other hand, it is extremely difficult to quantify separately the effects of several variables and parameters.

#### **1.1. Computational welding mechanics**

Experimental analysis for the determination of the residual stress fields in welds by means of nondestructive methods requires complementary diffraction instruments [2]. Such studies are very costly, and because of the limitation of the volume and mass of the investigated object, they could just provide one in best case information about a portion of the whole residual stress field in a large structure. A scientific and engineering approach to solve this problem is the application of numerical methods for describing the development of residual stresses and studying their behavior under different mechanical and thermal loads.

Welding as a multi-physics problem is one of the most complicated processes from the modeling point of view. Different aspects, namely the arc physics, transient heat transfer, conductivity, fluid flow, phase transformations, grain size and deformations must be taken into account into the model. The first works on application of the numerical analysis of welds and the behavior of the material during welding are those of Boulton [3] and Rosenthal [4]. Since then, many models for the description of the heat source have been developed, which are all mentioned in the literature survey by Goldak [5].

In most models, which are used for the calculation of residual stress and distortion, the real heat input is simulated via an equivalent substitute heat source moving in the direction of welding. The fluid dynamics in the weld pool are almost always not included.

Residual stress and distortion are strongly influenced by the temperature-dependent plasticity. In **Figure 1**, the thermomechanical processes for the development of welding stresses are schematically illustrated. Here in this model from Radaj [6], the plastic zones in front and a linear heat source in a quasi-stationary temperature field are shown. The drawn parabola-like curve separates the heated front area which is due to the thermal stresses under compression from the rear region which is under tensile stresses. The zone of elastic unloading is located between the two areas. The cyclic plasticity at the shown locations in the base material, the heat affected zone and the weld during the heating and cooling phases show how the residual stresses develop. Point 1 undergoes elastic compressive stress, and at point 2, a plastic deformation occurs after reaching the compressive yield strength before this point is elastically relieved at point 3. The permanent elongation by compression at point 3 could lead to tensile residual stresses after cooling. Points 4 and 5 experienced tensile stresses during cooling due to the shrinkage restraint.

The maximum temperature in this time-dependent field reaches beyond the melting point in the weld pool, and the minimum value is the ambient temperature being reached after cooling down. Within this temperature field and due to the temperature-dependent physical and mechanical properties, an inhomogeneous thermal stress field is generated. The thermal stresses can either be accommodated elastically or lead to a stress state in which plastic deformations would be inevitable. There is another source of plastic deformation, which is induced during solid-state phase transformations if phase transformation occurs. As a result of the inhomogeneous plastic deformation during welding, some regions do not fit into the space

The reliable characterization of welding residual stresses in structural components has been widely considered in many research communities. Tensile residual stresses which are present in welds could potentially decrease the tolerance of the component against applied external loads. In integrity assessments, the interaction between load and residual stresses is taken into account by using a couple of conservative approaches [1]. In order to predict the more realistic service life of welded components, it is necessary to be aware of the residual stress fields, particularly in the critical crack initiation sites. Over the past few decades, a large number of researches have been devoted to the experimental and numerical determination of welding residual stresses. Recent advances in both simulation and measurement of weld residual stresses have provided the possibility to describe the residual stresses. However, owing to the different thermal, metallurgical, and mechanical complexities and the interaction between them, there still exist a number of uncertainties in the accurate calculation and measurement of residual stresses. On the other hand, it is extremely difficult to quantify separately the

Experimental analysis for the determination of the residual stress fields in welds by means of nondestructive methods requires complementary diffraction instruments [2]. Such studies are very costly, and because of the limitation of the volume and mass of the investigated object, they could just provide one in best case information about a portion of the whole residual stress field in a large structure. A scientific and engineering approach to solve this problem is the application of numerical methods for describing the development of residual stresses and

Welding as a multi-physics problem is one of the most complicated processes from the modeling point of view. Different aspects, namely the arc physics, transient heat transfer, conductivity, fluid flow, phase transformations, grain size and deformations must be taken into account into the model. The first works on application of the numerical analysis of welds and the behavior of the material during welding are those of Boulton [3] and Rosenthal [4]. Since then, many models for the description of the heat source have been developed, which are all

In most models, which are used for the calculation of residual stress and distortion, the real heat input is simulated via an equivalent substitute heat source moving in the direction of

welding. The fluid dynamics in the weld pool are almost always not included.

studying their behavior under different mechanical and thermal loads.

available, and due to geometrical compatibility, a residual stress field arises.

30 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

effects of several variables and parameters.

mentioned in the literature survey by Goldak [5].

**1.1. Computational welding mechanics**

The remaining strain at point 5 may indicate that after reaching room temperature, compressive residual stresses may be present. Point 6 would have a mechanical load cycle as point 5, if it would not have been so close to the heat source. Point 7 is on the weld center and is only subjected to elasto-plastic tensile stresses. It is understandable that the temperaturedependent spatial and temporal process and material modeling determine the accuracy of the residual stress and distortion calculations.

Computational welding mechanics is an engineering subject concerned with the mechanics and the material behavior during welding. In research and applications, the different welding processes, the microstructures resulting in the weld and their mechanical properties in terms of deformability, strength, and toughness and the structural behavior of welded components are to be considered for an advanced fitness-for-service assessment of welded components.

The accuracy of the predicted results in the calculation of residual stresses as a complex nonlinear problem is influenced by several assumptions and simplifications. Nevertheless, the experimental measurement of welding residual stresses involves a significant range of uncertainties. Since both numerical and experimental approaches involve inevitably their own limitations, it is necessary to apply these methods in combination with each other.

**Figure 1.** Cyclic plasticity in the weld, heat-affected zone and the base material and the formation of welding residual stresses [6].

With the development of modern high speed computers, process modeling has become a powerful tool for controlling and optimizing of different process parameters. Nowadays, finite element method has contributed in process simulation extensively. In the context of weld computational mechanics, modern software infrastructures, that is, the physics, mechanics, materials science, mathematics and numerical algorithms have been enriched enough to allow complex calculation of welded structures [7]. A proper FE model for welding simulation involves advanced aspects such as definition of the heat source, material phase transformations, temperature-dependent thermophysical and mechanical properties and material hardening behavior. But the key issue in this regard is to understand the underlying theory well enough. In the study described here, it has been tried to handle as much as possible the various assumptions and simplifications in the prediction of welding residual stresses.

In this chapter, three fusion weld case studies are described with focus on different geometries, single or multiple pass welds and finally different types of base materials particularly with regard to metallurgical behavior and hardening behavior. As the first case study [8], under the support of German Research Foundation (DFG) [9], a tubular specimen made of S355J2H structural steel was utilized for the weld residual stress assessments. The specimen was manufactured under closely controlled conditions. After the preparations, a single-pass dummy weld without filler material was created in the specimen. Appropriate material characterization was performed on the base metal under static and cyclic loading conditions. In the case studies two [10] and three [11], the results of a scientific community, the international *Network on Neutron Techniques standardization for Structural Integrity* (NeT) will be discussed. This network consists of 15 European-based member research institutes, universities and industries, which meet twice a year and discuss the results of defined round-robin tasks on welding simulation and experimental residual stress measurement techniques. Within the framework of NeT round robin, case study two focuses on a single bead on plate made of austenitic stainless steel and finally case study three deals with the multipass welding of Inconel.

phase, the transient temperature history during the welding process was calibrated by means of the measured thermocouple profiles. Furthermore, the fusion boundary of the weld bead was controlled by the cross-sectional macrograph of the specimen. Once an accurate thermo-metallurgical solution is obtained, one can study the mechanical aspect of the weld calculation. One of the most important focuses on the mechanical solution as the next step is to determine the best explanatory material hardening model. Since the predicted residual stresses are sensitive strongly to the high-temperature mechanical properties and especially to the cyclic hardening parameters, it is important to consider all the possible material-related simulation variables. The accuracy of calculated residual stresses was then controlled with measured data in order to optimize the choices for different variables. Since it is preferred to make use of through-thickness stress profiles for structural integrity and defect tolerance assessments [1], both X-ray and neutron diffraction measurement techniques were used in order to describe the surface and depth profile of welding

**Figure 2.** Simulation studies and residual stress measurements: cooperation in NeT (left), investigations within the

Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures…

http://dx.doi.org/10.5772/intechopen.74466

33

For all the calculations, the FEM weld-specific program SYSWELD was used as simulation

The accurate structural integrity assessment of welded structures or components requires the designers to be aware of the existing welding residual stress field within the material. A complex process such as welding could be described by means of both numerical and experi-

**2. Numerical studies of welding residual stresses**

residual stresses.

project by German Research Foundation (DFG) (right).

tools (**Figure 2**).

mental techniques.

Nickel alloy similar to stainless steel is a face-centered cubic, which shows no phase transformation during cooling from its melting temperature down to the room temperature. Thus, cooling rate for both stainless steel and nickel alloy is of less importance. However, for nickel alloys, particularly the precipitation hardened alloys, the composition-related metallurgical effects should be taken into account. Nickel alloys compared with stainless steels have lower thermal expansion coefficient, which may cause less distortion problems. The procedures for welding of stainless steels and nickel alloys are relatively similar. Sequentially, coupled thermal-mechanical analyses were performed in both task groups. The accuracy of predictions for the transient temperature field, welding residual stresses, equivalent plastic strains, and so on was then calibrated based on experimental measurements. The achievements and results could be then used as lessons for further numerical simulation. This involves the global calibration of the heat input on the basis of the thermocouple responses and detailed determination of the heat source parameters by matching the weld fusion boundaries to real weld cross sections.

Different stages of calculation were compared with experimental tests by taking into account the limitations and uncertainties of the measurements. In the thermo-metallurgical Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures… http://dx.doi.org/10.5772/intechopen.74466 33

With the development of modern high speed computers, process modeling has become a powerful tool for controlling and optimizing of different process parameters. Nowadays, finite element method has contributed in process simulation extensively. In the context of weld computational mechanics, modern software infrastructures, that is, the physics, mechanics, materials science, mathematics and numerical algorithms have been enriched enough to allow complex calculation of welded structures [7]. A proper FE model for welding simulation involves advanced aspects such as definition of the heat source, material phase transformations, temperature-dependent thermophysical and mechanical properties and material hardening behavior. But the key issue in this regard is to understand the underlying theory well enough. In the study described here, it has been tried to handle as much as possible the various assumptions and simplifications in the

32 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

In this chapter, three fusion weld case studies are described with focus on different geometries, single or multiple pass welds and finally different types of base materials particularly with regard to metallurgical behavior and hardening behavior. As the first case study [8], under the support of German Research Foundation (DFG) [9], a tubular specimen made of S355J2H structural steel was utilized for the weld residual stress assessments. The specimen was manufactured under closely controlled conditions. After the preparations, a single-pass dummy weld without filler material was created in the specimen. Appropriate material characterization was performed on the base metal under static and cyclic loading conditions. In the case studies two [10] and three [11], the results of a scientific community, the international *Network on Neutron Techniques standardization for Structural Integrity* (NeT) will be discussed. This network consists of 15 European-based member research institutes, universities and industries, which meet twice a year and discuss the results of defined round-robin tasks on welding simulation and experimental residual stress measurement techniques. Within the framework of NeT round robin, case study two focuses on a single bead on plate made of austenitic stainless steel and finally case study three deals with the

Nickel alloy similar to stainless steel is a face-centered cubic, which shows no phase transformation during cooling from its melting temperature down to the room temperature. Thus, cooling rate for both stainless steel and nickel alloy is of less importance. However, for nickel alloys, particularly the precipitation hardened alloys, the composition-related metallurgical effects should be taken into account. Nickel alloys compared with stainless steels have lower thermal expansion coefficient, which may cause less distortion problems. The procedures for welding of stainless steels and nickel alloys are relatively similar. Sequentially, coupled thermal-mechanical analyses were performed in both task groups. The accuracy of predictions for the transient temperature field, welding residual stresses, equivalent plastic strains, and so on was then calibrated based on experimental measurements. The achievements and results could be then used as lessons for further numerical simulation. This involves the global calibration of the heat input on the basis of the thermocouple responses and detailed determination of the heat source parameters by matching the weld fusion boundaries to real weld cross sections.

Different stages of calculation were compared with experimental tests by taking into account the limitations and uncertainties of the measurements. In the thermo-metallurgical

prediction of welding residual stresses.

multipass welding of Inconel.

**Figure 2.** Simulation studies and residual stress measurements: cooperation in NeT (left), investigations within the project by German Research Foundation (DFG) (right).

phase, the transient temperature history during the welding process was calibrated by means of the measured thermocouple profiles. Furthermore, the fusion boundary of the weld bead was controlled by the cross-sectional macrograph of the specimen. Once an accurate thermo-metallurgical solution is obtained, one can study the mechanical aspect of the weld calculation. One of the most important focuses on the mechanical solution as the next step is to determine the best explanatory material hardening model. Since the predicted residual stresses are sensitive strongly to the high-temperature mechanical properties and especially to the cyclic hardening parameters, it is important to consider all the possible material-related simulation variables. The accuracy of calculated residual stresses was then controlled with measured data in order to optimize the choices for different variables. Since it is preferred to make use of through-thickness stress profiles for structural integrity and defect tolerance assessments [1], both X-ray and neutron diffraction measurement techniques were used in order to describe the surface and depth profile of welding residual stresses.

For all the calculations, the FEM weld-specific program SYSWELD was used as simulation tools (**Figure 2**).

### **2. Numerical studies of welding residual stresses**

The accurate structural integrity assessment of welded structures or components requires the designers to be aware of the existing welding residual stress field within the material. A complex process such as welding could be described by means of both numerical and experimental techniques.

In this chapter, the applicability of FEM to the simulation of welding process is being examined. Three-dimensional models were applied within the commercial software package SYSWELD 8.5 to calculate numerically the inevitable residual stress field, which is produced as a consequence of nonuniform heating and cooling. A coupled thermo-metallurgical simulation was then conducted and the results of which included temperature history and phase proportions. These were then used as the input for further mechanical analyses within the uncoupled simulation technique. Using this technique, though the insignificant dimensional changes as well as the mechanical work are neglected, the accuracy of the results is kept to a high level. Different aspects of numerical welding simulation are explained in detail in Ref. [8].

#### **2.1. Case study 1: S355J2H single bead on tube**

On the basis of the well-documented experimental results on tubular specimens made of S355J2H in the project DFG FA992/1–1 [9], extensive numerical studies on welding simulation were performed on this material. The key modeling issues were as follows: heat source representation, solid-state phase transformation kinetic, material hardening laws and temperature-dependent material behavior. In the thermo-metallurgical phase, the transient temperature history during the welding process was calibrated according to the measured responses from the thermocouples along with the cross-sectional macrographs from the weld fusion boundaries. Once an accurate thermo-metallurgical solution was obtained, the mechanical aspects of the welding simulation were considered. Temperature dependent material properties together with cyclic hardening parameters are two important material related simulation variables which must be taken into account since they may affect strongly the predicted residual stresses. The accuracy of the calculated residual stress field was then validated by means of X-ray and neutron diffraction measurements.

#### *2.1.1. Welded specimens*

The tubular specimens out of structural steel S355J2H had a length of 250 mm with the outside and inside diameter of 56 and 36 mm, respectively. The base metal before welding had been heat treated for 30 min at 600°C under shielding gas in order to relieve the existing machining-induced residual stresses. The samples were produced by means of Tungsten Inert Gas (TIG) welding without filler material (**Figure 3**). The arc voltage, welding current and welding speed were set to 12 V, 250A and 15 cm/min, respectively, providing a total input energy of 7.2 kJ/cm. In this way, a 10 mm wide and 2.5 mm deep weld bead was produced on every tube. NiCr-Ni thermocouples were used to measure the temperature history at every 90o around the weld toe (Q1–Q4) [12].

#### *2.1.2. Plasticity and material hardening model*

Von Mises yield function is considered in this work as the criterion to describe where the plastic deformation begins. Besides that, the constitutive behavior of the material and the respective hardening model must be defined properly in order to preserve the accuracy of the calculated residual stresses. For simplicity, a single-element FE analysis technique was then applied in order to investigate the influence of the chosen hardening model on the predicted stress-strain responses of the material under mechanical loading conditions. In this regard, the calculation results under symmetric strain-controlled cyclic loading were compared with the obtained stress-strain responses from the isothermal low cyclic fatigue tests at constant amplitude. Three process-related strain ranges, namely 6%, 10% and 14% were chosen for the LCF tests as shown

**Figure 4.** Low cycle fatigue test results of S355J2H at Δε = 0.06, 0.1 and 0.14 (left), different types of hardening model [8].

**Figure 3.** TIG welding of the tubular specimens with temperature measurements [8].

Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures…

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35

SYSWLED supports the modeling of the nonlinear kinematic hardening behavior in the form of Armstrong-Frederick combined hardening model [13] under the isothermal and monopha-

in **Figure 4**.

sic condition:

Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures… http://dx.doi.org/10.5772/intechopen.74466 35

**Figure 3.** TIG welding of the tubular specimens with temperature measurements [8].

In this chapter, the applicability of FEM to the simulation of welding process is being examined. Three-dimensional models were applied within the commercial software package SYSWELD 8.5 to calculate numerically the inevitable residual stress field, which is produced as a consequence of nonuniform heating and cooling. A coupled thermo-metallurgical simulation was then conducted and the results of which included temperature history and phase proportions. These were then used as the input for further mechanical analyses within the uncoupled simulation technique. Using this technique, though the insignificant dimensional changes as well as the mechanical work are neglected, the accuracy of the results is kept to a high level. Different

On the basis of the well-documented experimental results on tubular specimens made of S355J2H in the project DFG FA992/1–1 [9], extensive numerical studies on welding simulation were performed on this material. The key modeling issues were as follows: heat source representation, solid-state phase transformation kinetic, material hardening laws and temperature-dependent material behavior. In the thermo-metallurgical phase, the transient temperature history during the welding process was calibrated according to the measured responses from the thermocouples along with the cross-sectional macrographs from the weld fusion boundaries. Once an accurate thermo-metallurgical solution was obtained, the mechanical aspects of the welding simulation were considered. Temperature dependent material properties together with cyclic hardening parameters are two important material related simulation variables which must be taken into account since they may affect strongly the predicted residual stresses. The accuracy of the calculated residual stress field was then validated by

The tubular specimens out of structural steel S355J2H had a length of 250 mm with the outside and inside diameter of 56 and 36 mm, respectively. The base metal before welding had been heat treated for 30 min at 600°C under shielding gas in order to relieve the existing machining-induced residual stresses. The samples were produced by means of Tungsten Inert Gas (TIG) welding without filler material (**Figure 3**). The arc voltage, welding current and welding speed were set to 12 V, 250A and 15 cm/min, respectively, providing a total input energy of 7.2 kJ/cm. In this way, a 10 mm wide and 2.5 mm deep weld bead was produced on every tube. NiCr-Ni thermocouples were used to measure the temperature history at every

Von Mises yield function is considered in this work as the criterion to describe where the plastic deformation begins. Besides that, the constitutive behavior of the material and the respective hardening model must be defined properly in order to preserve the accuracy of the calculated residual stresses. For simplicity, a single-element FE analysis technique was then applied in order to investigate the influence of the chosen hardening model on the predicted stress-strain responses of the material under mechanical loading conditions. In this regard, the calculation

aspects of numerical welding simulation are explained in detail in Ref. [8].

34 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**2.1. Case study 1: S355J2H single bead on tube**

means of X-ray and neutron diffraction measurements.

around the weld toe (Q1–Q4) [12].

*2.1.2. Plasticity and material hardening model*

*2.1.1. Welded specimens*

90o

**Figure 4.** Low cycle fatigue test results of S355J2H at Δε = 0.06, 0.1 and 0.14 (left), different types of hardening model [8].

results under symmetric strain-controlled cyclic loading were compared with the obtained stress-strain responses from the isothermal low cyclic fatigue tests at constant amplitude. Three process-related strain ranges, namely 6%, 10% and 14% were chosen for the LCF tests as shown in **Figure 4**.

SYSWLED supports the modeling of the nonlinear kinematic hardening behavior in the form of Armstrong-Frederick combined hardening model [13] under the isothermal and monophasic condition:

$$
\sigma(\varepsilon\_{\alpha}^{p}) = \sigma\_{\vartheta}(\varepsilon\_{\alpha}^{p}) + \frac{\zeta}{\mathcal{V}}(1 - e^{-\gamma \varepsilon\_{\eta}^{\nu}}) \tag{1}
$$

parameters through the fitting procedure. The total strain range in the respective LCF test was set to 14%. Being a one-pass weld is the cause for choosing the first load reversal as for the fitting procedure. In this case, any extra cyclic hardening is ignored. **Figure 5** shows the predicted responses at two of the strain ranges (6 and 14%) for simple isotropic, pure kinematic and combined isotropic-kinematic hardening models. Red and blue plots in **Figure 5** represent the measured and predicted responses, respectively. The dashed or continuous blue plots refer back to the used fitting approaches for defining the kinematic hardening parameters. In this regard, dashed blue lines and continuous blue line represent case 1 and case 2, respectively. As can be seen in **Figure 5** using the pure isotropic hardening model, though the Bauschinger effect is neglected, the predicted and measured monotonic responses as well as the peak stress values of the cyclic responses agree reasonably well except that the predicted yielding points during the cyclic responses are sharper than the measured ones. In case of using a pure kinematic hardening model, the reversed yielding points were predicted to be much lower than the measured ones due to the incorporation of the Bauschinger effect. In this regard, the nonlinear kinematic hardening model gives obviously better results in predicting the shape and peaks of the hysteresis loops but poorer results in predicting the monotonic stress-strain responses of the material rather than linear one. It should be noted that the level of peak stresses predicted by the linear kinematic hardening model depends strongly on the predefined maximum plastic strain in the monotonic mechanical property. By using the combined isotropic-kinematic hardening model with a 50% isotropic proportion, the reversed yielding points were improved significantly comparing with the pure kinematic cases. Even in the case of combined hardening, if the kinematic model parameters are obtained by fitting to the cyclic stress-strain curves, the predicted monotonic responses do not conform to the experimental curves though the cyclic responses match well enough. Indeed, matching both monotonic and cyclic responses is difficult, which

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could influence the final results differently depending on the case of study.

maximum temperature exceeds the austenitization finish temperature (Ac3).

The calculated and measured residual stress fields in the axial and hoop directions at 180º from the weld start point (Q3) are shown in **Figure 6**. As can be seen, the numerical results conform very well the experimentally measured data. Residual stress measurements by means of neutron diffraction (ND) were conducted at Helmholtz-Zentrum Berlin (HZB).

To be able to interpret the formation of welding residual stresses numerically, different aspects of the simulation need to be explained in detail. It is obvious that during welding every material point in the specimen is experiencing different thermal history depending on its location relative to the welded area. In this regard, the evolution of different material phases, cumulative and equivalent plastic strains and finally the welding residual stresses are investigated through the numerical analysis at different positions with respect to the welded area (**Figure 7**). For instance, at node-1, which is located within the welded area, the temperature goes beyond the melting point during heating and thus austenite transformation occurs substantially since the

Then, the material cools down from the maximum temperature and the austenite starts to transform into bainite and martensite depending on the cooling rate. The evolution of different

*2.1.3. Residual stress results*

where *σ*´ represents *<sup>σ</sup>* <sup>−</sup> *<sup>σ</sup>*<sup>0</sup> and *σ*<sup>0</sup> is the yield stress at zero plastic strain, *εeq p* is the equivalent plastic strain and *C* and *γ* are material kinematic hardening parameters (supported only as a single pair for this model). Isotropic hardening component that defines the expansion of the yield surface as a function of accumulated plastic strain is represented through the σ'<sup>0</sup> term. Meanwhile, the kinematic hardening component is introduced to the model to describe the translation of the yield surface in the stress space.

In order to define the kinematic hardening parameters, the model could be fitted in different ways to either monotonic or uniaxial cyclic stress-strain curves. Two case studies were considered in this work. In case 1, whether a pure kinematic or a combined isotropic-kinematic hardening model is implemented, the kinematic behavior is assumed to be linear. In this regard, the maximum plastic strain for defining the monotonic true stress versus plastic strain response was set to 100%. In case 2, a nonlinear kinematic hardening behavior was taken into account for both pure kinematic or combined hardening models. In this case, the first cyclic response of the material taken from the LCF test data was used in order to calibrate the respective model

**Figure 5.** Comparison between the measured and predicted stress-strain responses of S355J2H during the first load reversal at room temperature for strain ranges Δε=0.14 (top) and Δε=0.06 (bottom). Continuous and dashed lines are related to case studies 1 and 2 for finding the kinematic parameters [8].

parameters through the fitting procedure. The total strain range in the respective LCF test was set to 14%. Being a one-pass weld is the cause for choosing the first load reversal as for the fitting procedure. In this case, any extra cyclic hardening is ignored. **Figure 5** shows the predicted responses at two of the strain ranges (6 and 14%) for simple isotropic, pure kinematic and combined isotropic-kinematic hardening models. Red and blue plots in **Figure 5** represent the measured and predicted responses, respectively. The dashed or continuous blue plots refer back to the used fitting approaches for defining the kinematic hardening parameters. In this regard, dashed blue lines and continuous blue line represent case 1 and case 2, respectively. As can be seen in **Figure 5** using the pure isotropic hardening model, though the Bauschinger effect is neglected, the predicted and measured monotonic responses as well as the peak stress values of the cyclic responses agree reasonably well except that the predicted yielding points during the cyclic responses are sharper than the measured ones. In case of using a pure kinematic hardening model, the reversed yielding points were predicted to be much lower than the measured ones due to the incorporation of the Bauschinger effect. In this regard, the nonlinear kinematic hardening model gives obviously better results in predicting the shape and peaks of the hysteresis loops but poorer results in predicting the monotonic stress-strain responses of the material rather than linear one. It should be noted that the level of peak stresses predicted by the linear kinematic hardening model depends strongly on the predefined maximum plastic strain in the monotonic mechanical property. By using the combined isotropic-kinematic hardening model with a 50% isotropic proportion, the reversed yielding points were improved significantly comparing with the pure kinematic cases. Even in the case of combined hardening, if the kinematic model parameters are obtained by fitting to the cyclic stress-strain curves, the predicted monotonic responses do not conform to the experimental curves though the cyclic responses match well enough. Indeed, matching both monotonic and cyclic responses is difficult, which could influence the final results differently depending on the case of study.

#### *2.1.3. Residual stress results*

*σ*´(*εeq*

and *σ*<sup>0</sup>

where *σ*´ represents *<sup>σ</sup>* <sup>−</sup> *<sup>σ</sup>*<sup>0</sup>

yield surface in the stress space.

*p*

36 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

) = *σ*´ <sup>0</sup>(*εeq p* ) + \_\_ *C <sup>γ</sup>*(1 − *e* <sup>−</sup>*γεeq p*

is the yield stress at zero plastic strain, *εeq*

strain and *C* and *γ* are material kinematic hardening parameters (supported only as a single pair for this model). Isotropic hardening component that defines the expansion of the yield surface as a function of accumulated plastic strain is represented through the σ'<sup>0</sup> term. Meanwhile, the kinematic hardening component is introduced to the model to describe the translation of the

In order to define the kinematic hardening parameters, the model could be fitted in different ways to either monotonic or uniaxial cyclic stress-strain curves. Two case studies were considered in this work. In case 1, whether a pure kinematic or a combined isotropic-kinematic hardening model is implemented, the kinematic behavior is assumed to be linear. In this regard, the maximum plastic strain for defining the monotonic true stress versus plastic strain response was set to 100%. In case 2, a nonlinear kinematic hardening behavior was taken into account for both pure kinematic or combined hardening models. In this case, the first cyclic response of the material taken from the LCF test data was used in order to calibrate the respective model

**Figure 5.** Comparison between the measured and predicted stress-strain responses of S355J2H during the first load reversal at room temperature for strain ranges Δε=0.14 (top) and Δε=0.06 (bottom). Continuous and dashed lines are

related to case studies 1 and 2 for finding the kinematic parameters [8].

) (1)

is the equivalent plastic

*p*

The calculated and measured residual stress fields in the axial and hoop directions at 180º from the weld start point (Q3) are shown in **Figure 6**. As can be seen, the numerical results conform very well the experimentally measured data. Residual stress measurements by means of neutron diffraction (ND) were conducted at Helmholtz-Zentrum Berlin (HZB).

To be able to interpret the formation of welding residual stresses numerically, different aspects of the simulation need to be explained in detail. It is obvious that during welding every material point in the specimen is experiencing different thermal history depending on its location relative to the welded area. In this regard, the evolution of different material phases, cumulative and equivalent plastic strains and finally the welding residual stresses are investigated through the numerical analysis at different positions with respect to the welded area (**Figure 7**). For instance, at node-1, which is located within the welded area, the temperature goes beyond the melting point during heating and thus austenite transformation occurs substantially since the maximum temperature exceeds the austenitization finish temperature (Ac3).

Then, the material cools down from the maximum temperature and the austenite starts to transform into bainite and martensite depending on the cooling rate. The evolution of different phases during heating and cooling is shown in **Figure 8a**. In **Figure 8b**, the evolution of the axial and hoop residual stresses, the cumulative plastic strain and the equivalent plastic strain are shown by dividing the total process time into seven smaller time intervals. During time intervals 1 and 2, the moving torch does not yet reach Q3; thus, the material at node-1 undergoes some tension and compression elastically. Once the welding torch reaches Q3, the local temperature starts to increase during the time interval 3 and the material undergoes expansioninduced compressive stresses. Since yielding occurs in this period, plastic strain begins to accumulate in the material. In the interval 4 during which the temperature goes beyond 1300°C, the stress components and the cumulative plastic strains disappear since the temperature exceeds the material annealing temperature, which was previously set to 1300°C. Unexpectedly, the equivalent plastic strain is retained as can be seen in **Figure 8b**. Time interval 5 represents the cooling phase from annealing temperature down to bainitic transformation temperature. In this period, tensile stresses appear due to the shrinkage of the material at the point of interest. Meantime, plastic strains start to accumulate again in this period. By further cooling in the time interval 6, austenite starts to transform to bainite since the temperature has dropped below the bainitic transformation temperature. This type of transformation is associated with the decrease of density, which causes volume expansion and thus local compression in the material. Below 420°C in the time interval 7, rest of the austenite phase transforms into martensite, which is associated with more volume increase and consequently the compressive stresses increase. During the time intervals 6 and 7, the strain hardening of the material vanishes gradually due to the hardening recovery phenomena caused by austenite to ferrite transformation.

The situation at nodes 2 to 4 differs from what is explained at node-1 regarding the formation of

**Figure 8.** Evolution of different material phases (a) and residual stresses, cumulative and equivalent plastic strains (b) at

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A single weld bead on plate made of austenitic stainless steel was chosen as the benchmark problem for NeT Task Group 1 (TG1) in order to examine the influence of different simulation variables on the accuracy of predicted residual stresses. The specimen geometry and its boundary condition during welding are shown in **Figure 9**. The plate was 17 mm thick and was 200 mm and 150 mm in length and width, respectively. A single TIG weld bead with the same material as the base metal and a width of 7 mm was laid on the surface of the plate. The heat input and welding speed were set to 633 J/mm and 2.27 mm/s, respectively. Both base material and weld metal were characterized using temperature-dependent monotonic and cyclic mechanical tests. For calibration reason, a number of thermocouples were applied to the specimen top and bottom surfaces, along the weld line and as close as possible to the weld. After welding, residual stress measurements were also performed at different locations of the plate by using different techniques such as hole-drilling, contour method and neutron diffraction technique [10]. In TG1, the Bayesian average of the residual stress results from different measurements was used for the calibrations.

A three-dimensional finite element model was developed, and the welding simulations were conducted through sequentially coupled thermal-mechanical solutions. A moving heat source with the Goldak [14] formulation was applied to the model in order to simulate the movement of the welding torch. The gradual material deposition was also included in the model. The annealing scheme was incorporated in the model by considering a melting temperature of 1400°C. In this way, the material history including stress and strain as well as the strain

The heat input energy was calibrated first according to the responses of nine thermocouples [10]. After that, parameters of the heat source were adjusted according to the cross-sectional macro-graphs of the weld in order to match the boundaries of the calculated melted area with

hardening would be eliminated above the annealing temperature.

thermal stresses or plastic strains, which is discussed in detail in Ref. [8].

**2.2. Case study 2: 316 L single bead on plate**

node-1 with respect to the relevant temperature history [8].

*2.2.1. NeT TG1 simulation results*

the real condition (**Figure 10**).

**Figure 6.** Comparison of the calculated axial (left) and hoop (right) residual stress fields at Q3 with the ND-measurements [8].

**Figure 7.** Different representative material zones in the weld cross-section from the FE model at Q3 [8].

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**Figure 8.** Evolution of different material phases (a) and residual stresses, cumulative and equivalent plastic strains (b) at node-1 with respect to the relevant temperature history [8].

The situation at nodes 2 to 4 differs from what is explained at node-1 regarding the formation of thermal stresses or plastic strains, which is discussed in detail in Ref. [8].

#### **2.2. Case study 2: 316 L single bead on plate**

phases during heating and cooling is shown in **Figure 8a**. In **Figure 8b**, the evolution of the axial and hoop residual stresses, the cumulative plastic strain and the equivalent plastic strain are shown by dividing the total process time into seven smaller time intervals. During time intervals 1 and 2, the moving torch does not yet reach Q3; thus, the material at node-1 undergoes some tension and compression elastically. Once the welding torch reaches Q3, the local temperature starts to increase during the time interval 3 and the material undergoes expansioninduced compressive stresses. Since yielding occurs in this period, plastic strain begins to accumulate in the material. In the interval 4 during which the temperature goes beyond 1300°C, the stress components and the cumulative plastic strains disappear since the temperature exceeds the material annealing temperature, which was previously set to 1300°C. Unexpectedly, the equivalent plastic strain is retained as can be seen in **Figure 8b**. Time interval 5 represents the cooling phase from annealing temperature down to bainitic transformation temperature. In this period, tensile stresses appear due to the shrinkage of the material at the point of interest. Meantime, plastic strains start to accumulate again in this period. By further cooling in the time interval 6, austenite starts to transform to bainite since the temperature has dropped below the bainitic transformation temperature. This type of transformation is associated with the decrease of density, which causes volume expansion and thus local compression in the material. Below 420°C in the time interval 7, rest of the austenite phase transforms into martensite, which is associated with more volume increase and consequently the compressive stresses increase. During the time intervals 6 and 7, the strain hardening of the material vanishes gradually due to the hardening recovery phenomena caused by austenite to ferrite transformation.

38 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 6.** Comparison of the calculated axial (left) and hoop (right) residual stress fields at Q3 with the ND-measurements [8].

**Figure 7.** Different representative material zones in the weld cross-section from the FE model at Q3 [8].

A single weld bead on plate made of austenitic stainless steel was chosen as the benchmark problem for NeT Task Group 1 (TG1) in order to examine the influence of different simulation variables on the accuracy of predicted residual stresses. The specimen geometry and its boundary condition during welding are shown in **Figure 9**. The plate was 17 mm thick and was 200 mm and 150 mm in length and width, respectively. A single TIG weld bead with the same material as the base metal and a width of 7 mm was laid on the surface of the plate. The heat input and welding speed were set to 633 J/mm and 2.27 mm/s, respectively. Both base material and weld metal were characterized using temperature-dependent monotonic and cyclic mechanical tests. For calibration reason, a number of thermocouples were applied to the specimen top and bottom surfaces, along the weld line and as close as possible to the weld. After welding, residual stress measurements were also performed at different locations of the plate by using different techniques such as hole-drilling, contour method and neutron diffraction technique [10]. In TG1, the Bayesian average of the residual stress results from different measurements was used for the calibrations.

#### *2.2.1. NeT TG1 simulation results*

A three-dimensional finite element model was developed, and the welding simulations were conducted through sequentially coupled thermal-mechanical solutions. A moving heat source with the Goldak [14] formulation was applied to the model in order to simulate the movement of the welding torch. The gradual material deposition was also included in the model. The annealing scheme was incorporated in the model by considering a melting temperature of 1400°C. In this way, the material history including stress and strain as well as the strain hardening would be eliminated above the annealing temperature.

The heat input energy was calibrated first according to the responses of nine thermocouples [10]. After that, parameters of the heat source were adjusted according to the cross-sectional macro-graphs of the weld in order to match the boundaries of the calculated melted area with the real condition (**Figure 10**).

**Figure 9.** NeT TG1 specimen.

It should be noted that the yellow curve in **Figure 11** is representative of the Bayesian average of different measured data obtained from different techniques, which were comparable to each other. The combined hardening model in this case is optimized by matching to the saturated cyclic response of the material. In this project, it was observed that other mechanical solution variables than temperature-dependent material properties and material hardening behavior have minor influence on the finial simulation results. Experiences and lessons of NeT TG1 were then collected together as a simulation strategy for the future works and task groups.

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**Figure 11.** Comparison between the residual stress results using different material hardening models [11].

• In welding simulation, before proceeding to mechanical simulation, a verified global heat

• The use of kinematic and combined hardening models or preferably elasto-viscoplastic

• The used material constitutive model for the weld metal could differ from that of base material.

A three-pass slot weld in nickel alloy 600 plate has been chosen as the case study of NeT Task Group 6 (TG6). The dimensions of the plate are 200 mm × 150 mm × 12 mm. The slot is 76 mm

material constitutive behavior is recommended for the welding simulations.

These lessons are summarized as follows:

input and a calibrated heat source are absolutely necessary.

**2.3. Case study 3: nickel alloy three-pass bead-in-slot**

**Figure 10.** NeT TG1 weld bead on plate simulation.

One of the most important features of NeT TG1 was to comprehensively investigate the influence of material hardening model on the final field of predicted residual stresses. Of course the choice of the hardening model depends strongly on the used material. In this study, isotropic, kinematic and combined isotropic-kinematic hardening models were examined for the welding simulations. For determining the material kinematic hardening parameters, different fitting strategies were adopted, which have been described comprehensively in Ref. [10]. **Figure 11** shows the through thickness variation of transverse residual stresses in the mid-plane. As can be seen, the use of the isotropic hardening model in the welding simulation of the austenitic stainless steel has caused over conservatism in the predicted residual stresses. Combined isotropic-kinematic hardening model has given the best agreement with the experimental results. Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures… http://dx.doi.org/10.5772/intechopen.74466 41

**Figure 11.** Comparison between the residual stress results using different material hardening models [11].

It should be noted that the yellow curve in **Figure 11** is representative of the Bayesian average of different measured data obtained from different techniques, which were comparable to each other. The combined hardening model in this case is optimized by matching to the saturated cyclic response of the material. In this project, it was observed that other mechanical solution variables than temperature-dependent material properties and material hardening behavior have minor influence on the finial simulation results. Experiences and lessons of NeT TG1 were then collected together as a simulation strategy for the future works and task groups. These lessons are summarized as follows:


#### **2.3. Case study 3: nickel alloy three-pass bead-in-slot**

One of the most important features of NeT TG1 was to comprehensively investigate the influence of material hardening model on the final field of predicted residual stresses. Of course the choice of the hardening model depends strongly on the used material. In this study, isotropic, kinematic and combined isotropic-kinematic hardening models were examined for the welding simulations. For determining the material kinematic hardening parameters, different fitting strategies were adopted, which have been described comprehensively in Ref. [10]. **Figure 11** shows the through thickness variation of transverse residual stresses in the mid-plane. As can be seen, the use of the isotropic hardening model in the welding simulation of the austenitic stainless steel has caused over conservatism in the predicted residual stresses. Combined isotropic-kinematic hardening model has given the best agreement with the experimental results.

**Figure 9.** NeT TG1 specimen.

40 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 10.** NeT TG1 weld bead on plate simulation.

A three-pass slot weld in nickel alloy 600 plate has been chosen as the case study of NeT Task Group 6 (TG6). The dimensions of the plate are 200 mm × 150 mm × 12 mm. The slot is 76 mm long and 5 mm deep, which was filled with filler material made of alloy 82 (or 182) using the TIG welding process. The welding voltage ranges from 10 to 13 V depending on the weld pass number. Welding current and speed were set to 220 A and 70 mm/min for every pass. The specimen was constrained weakly to allow for free deformations. The multipass welding condition in this study provides complex thermomechanical loading condition, which requires more detailed assumptions and considerations regarding the cyclic behavior of the material. As noted in the NeT TG6 simulation protocol [11], the residual stress measurement is more challenging for the nickel-based alloys as compared with the stainless steel AISI 316. The objective of the NeT TG6 round robin is to promote parallel simulations and measurements in order to accurately predict the welding residual stresses in the slot welds.

metal are similar, their work hardening rates are different. Combined hardening (Lemaitre-Chaboche) or pure nonlinear kinematic hardening models were then fitted to the available

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Transverse hardness mapping after producing every single pass is shown in **Figure 13**. As can

A total number of 10 thermocouples were attached to the specimen top and bottom surfaces and close to the weld line. The global heat input and dwell times could be then calibrated on the basis of thermocouples responses. The specimen geometry and the configuration of ther-

Three sets of neutron diffraction measurements, one set of X-ray diffraction as well as one set of contour method measurements were planned in order to define experimentally the residual stress field in the material. Different sets of measured residual stresses agree well with each other.

The simulation methodology used for the welding simulation of nickel alloys is similar to that of AISI 316 L. Lessons and recommendations of NeT TG1 are supposed to be applied in the

experimental data in order to determine the model parameters.

be seen, the hardness of the weld area is lower than base material.

*2.3.1.2. Hardness measurement*

*2.3.1.3. Temperature measurement*

mocouples are shown in **Figure 14**.

*2.3.1.4. Residual stress measurement*

**Figure 13.** Measured hardness field after finishing each pass.

**Figure 14.** Specimen geometry and location of the thermocouples close to the slot.

*2.3.2. Numerical simulations*

#### *2.3.1. Experimental work*

A wide range of experiments were performed within the activities of NeT TG6 to support the numerical simulations:

#### *2.3.1.1. Material characterization*

The chemical composition, temperature-dependent tensile monotonic and uniaxial cyclic properties of alloy 600 and alloy 82 were determined in the NeT TG6 measurement round robin. Thermomechanical tests using the Gleeble testing machine were performed to determine the properties of the material in the heat-affected zone. LCF test results for alloy 600 at room temperature and 700°C are shown in **Figure 12**. For alloy 182 (weld metal), it was observed that the cyclic hardening rate is lower than the AISI 316 L. Thus, the combined isotropic-kinematic hardening model could be replaced simply with the pure kinematic one. Based on the test results, although the 0.2% proof stresses for the base material and the weld

**Figure 12.** LCF test results for alloy 600 at room temperature and 700°C (Δεtot = 1.5%).

metal are similar, their work hardening rates are different. Combined hardening (Lemaitre-Chaboche) or pure nonlinear kinematic hardening models were then fitted to the available experimental data in order to determine the model parameters.

#### *2.3.1.2. Hardness measurement*

long and 5 mm deep, which was filled with filler material made of alloy 82 (or 182) using the TIG welding process. The welding voltage ranges from 10 to 13 V depending on the weld pass number. Welding current and speed were set to 220 A and 70 mm/min for every pass. The specimen was constrained weakly to allow for free deformations. The multipass welding condition in this study provides complex thermomechanical loading condition, which requires more detailed assumptions and considerations regarding the cyclic behavior of the material. As noted in the NeT TG6 simulation protocol [11], the residual stress measurement is more challenging for the nickel-based alloys as compared with the stainless steel AISI 316. The objective of the NeT TG6 round robin is to promote parallel simulations and measure-

42 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

ments in order to accurately predict the welding residual stresses in the slot welds.

A wide range of experiments were performed within the activities of NeT TG6 to support the

The chemical composition, temperature-dependent tensile monotonic and uniaxial cyclic properties of alloy 600 and alloy 82 were determined in the NeT TG6 measurement round robin. Thermomechanical tests using the Gleeble testing machine were performed to determine the properties of the material in the heat-affected zone. LCF test results for alloy 600 at room temperature and 700°C are shown in **Figure 12**. For alloy 182 (weld metal), it was observed that the cyclic hardening rate is lower than the AISI 316 L. Thus, the combined isotropic-kinematic hardening model could be replaced simply with the pure kinematic one. Based on the test results, although the 0.2% proof stresses for the base material and the weld

**Figure 12.** LCF test results for alloy 600 at room temperature and 700°C (Δεtot = 1.5%).

*2.3.1. Experimental work*

numerical simulations:

*2.3.1.1. Material characterization*

Transverse hardness mapping after producing every single pass is shown in **Figure 13**. As can be seen, the hardness of the weld area is lower than base material.

#### *2.3.1.3. Temperature measurement*

A total number of 10 thermocouples were attached to the specimen top and bottom surfaces and close to the weld line. The global heat input and dwell times could be then calibrated on the basis of thermocouples responses. The specimen geometry and the configuration of thermocouples are shown in **Figure 14**.

#### *2.3.1.4. Residual stress measurement*

Three sets of neutron diffraction measurements, one set of X-ray diffraction as well as one set of contour method measurements were planned in order to define experimentally the residual stress field in the material. Different sets of measured residual stresses agree well with each other.

#### *2.3.2. Numerical simulations*

The simulation methodology used for the welding simulation of nickel alloys is similar to that of AISI 316 L. Lessons and recommendations of NeT TG1 are supposed to be applied in the

**Figure 13.** Measured hardness field after finishing each pass.

**Figure 14.** Specimen geometry and location of the thermocouples close to the slot.

TG6 solutions. Some of these recommendations were mentioned in Section 2.2.1. A preliminary finite element thermal calculation has been performed in Fraunhofer IWM as one of the simulation partners in NeT TG6 round robin. **Figure 15** depicts the comparison between the calculated temperature history and the response of a mid-length thermocouple called TC2.

The agreement between the results is quite well. The criterion for an accurate thermal simulation (as the basic prerequisite for residual stress calculation) is to achieve an agreement with the mid-length thermocouple response within 10%. On the other hand, the calculated melting boundaries including the cross-sectional area and shape of the fusion zone should match the real condition within ±20%. According to **Figure 16**, the calculated fusion boundaries match quite well to the real weld cross section illustrated in the macrographs.

The variation of calculated residual stress components along line BD (through the thickness) and B2 (across to the weld) are shown in **Figure 17** in comparison with the measured results. These results are obtained from neutron diffraction measurements. As can be seen, there exists a reasonable agreement between the calculations and measured results. The existing discrepancy might be attributed to the high-temperature annealing behavior, which is neglected in this study.

As shown in **Figure 17** (top), the maximum amount of longitudinal residual stress along line BD is predicted to be close to the bottom surfaces. According to **Figure 17** (bottom), relatively high tensile residual stresses exist in the weld area and HAZ. A peak value of 500 MPa in the longitudinal direction was observed at the weld toe, which could increase the probability of crack formation at the stress concentration sites, particularly because the most serious cracking problem with nickel alloys is hot cracking in either the weld metal or close to the fusion line in the HAZ with the latter being the more frequent [11].

**3. Conclusions**

In this chapter, three welding simulation case studies were reviewed. As the first case study, the numerical analysis of welding residual stresses in single bead tubular specimens made of structural steel S355J2H was studied. In case study 2, the NeT Task Group 1 was reviewed which focuses on single-pass weld bead on plate made of AISI 316 L and for case study 3, the NeT Task Group 6 was considered which is about the three-pass slot welds of nickel alloys. There exist very well documented experimental results on tubular specimens made of S355J2H in the project DFG FA992/1–1. On the other hand, NeT projects include a

**Figure 17.** Comparison between the measured and calculated residual stress components on lines BD (top) and B2 (bottom).

**Figure 16.** Calculated temperature contour plots of three weld passes compared with the real fusion boundaries.

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**Figure 15.** Experimental and numerical temperature histories for three-pass slot weld at mid-length thermocouple TC2.

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**Figure 16.** Calculated temperature contour plots of three weld passes compared with the real fusion boundaries.

**Figure 17.** Comparison between the measured and calculated residual stress components on lines BD (top) and B2 (bottom).

#### **3. Conclusions**

TG6 solutions. Some of these recommendations were mentioned in Section 2.2.1. A preliminary finite element thermal calculation has been performed in Fraunhofer IWM as one of the simulation partners in NeT TG6 round robin. **Figure 15** depicts the comparison between the calculated temperature history and the response of a mid-length thermocouple called TC2. The agreement between the results is quite well. The criterion for an accurate thermal simulation (as the basic prerequisite for residual stress calculation) is to achieve an agreement with the mid-length thermocouple response within 10%. On the other hand, the calculated melting boundaries including the cross-sectional area and shape of the fusion zone should match the real condition within ±20%. According to **Figure 16**, the calculated fusion boundaries match

The variation of calculated residual stress components along line BD (through the thickness) and B2 (across to the weld) are shown in **Figure 17** in comparison with the measured results. These results are obtained from neutron diffraction measurements. As can be seen, there exists a reasonable agreement between the calculations and measured results. The existing discrepancy might be attributed to the high-temperature annealing behavior, which is neglected in this study. As shown in **Figure 17** (top), the maximum amount of longitudinal residual stress along line BD is predicted to be close to the bottom surfaces. According to **Figure 17** (bottom), relatively high tensile residual stresses exist in the weld area and HAZ. A peak value of 500 MPa in the longitudinal direction was observed at the weld toe, which could increase the probability of crack formation at the stress concentration sites, particularly because the most serious cracking problem with nickel alloys is hot cracking in either the weld metal or close to the fusion

**Figure 15.** Experimental and numerical temperature histories for three-pass slot weld at mid-length thermocouple TC2.

quite well to the real weld cross section illustrated in the macrographs.

44 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

line in the HAZ with the latter being the more frequent [11].

In this chapter, three welding simulation case studies were reviewed. As the first case study, the numerical analysis of welding residual stresses in single bead tubular specimens made of structural steel S355J2H was studied. In case study 2, the NeT Task Group 1 was reviewed which focuses on single-pass weld bead on plate made of AISI 316 L and for case study 3, the NeT Task Group 6 was considered which is about the three-pass slot welds of nickel alloys. There exist very well documented experimental results on tubular specimens made of S355J2H in the project DFG FA992/1–1. On the other hand, NeT projects include a wide range of experimental measurements parallel to its advanced simulation programs. The goal is to develop a comprehensive simulation methodology for the prediction of residual stresses under the assistance of precise measurement techniques. Based on the results and achievements, FE simulation could be applied as a powerful tool for predicting the welding residual stresses required for the integrity assessments. The summaries of all these efforts have been already released in terms of a couple of recommendations. Exact thermal solutions, use of advanced material hardening models and including high-temperature annealing effects are some of the most important items out of those recommendations.

**Author details**

**References**

Kimiya Hemmesi and Majid Farajian\*

\*Address all correspondence to: majid.farajian@iwm.fraunhofer.de

[1] R6. Assessment of the Integrity of Structures Containing Defects. Br. Energy. Revision 4; 2013 [2] Farajian M, Nitschke-Pagel T, Wimpory RC, Hofmann M, Klaus M. Residual stress field measurements in welds by means of X-ray, synchrotron and neutron diffraction. Journal

Numerical Welding Simulation as a Basis for Structural Integrity Assessment of Structures…

http://dx.doi.org/10.5772/intechopen.74466

47

[3] Boulton NS, Lance Martin HE. Residual stresses in arc-welded plates. Proceedings of the

[4] Rosenthal D. Mathematical theory and heat distribution during welding and cutting.

[5] Goldak JA, Akhlaghi M. Computational Welding Mechanics. New York, USA: Springer;

[6] Radaj D. Eigenspannungen und Verzug beim Schweißen, Rechen- und Messverfahren.

[7] Goldak J. Web based simulation of welding and welded structures. CWA Conference. 2013 [8] Hemmesi K, Farajian M, Boin M. Numerical studies of welding residual stress field in tubular joints and the related experimental investigations by means of X-ray and neu-

[9] Farajian M. Residual stress relaxation in high strength steel welded joints under multi-

[10] Smith MC, Smith AC, Wimpory R, Ohms C. A review of the NeT Task Group 1 residual stress measurement and analysis round robin on a single weld bead-on-plate specimen.

[11] Smith MC. NeT TG6 Finite Element Simulation Protocol, Issue 1 for Phase 1 Simulations, 2016 [12] Farajian M. Stability and relaxation of welding residual stresses [PhD dissertation].

[13] Armstrong PJ, Frederick CO. A mathematical representation of the multiaxial bausch-

[14] Goldak J, Chakravariti A, Bibby M. A new finite element model for welding heat sources.

International Journal of Pressure Vessels and Piping. 2014;**120-121**:93-140

of Materials Science and Engineering Technology. 2011;**42**(11):996-1001

Fachbuchreihe Schweißtechnik. Düsseldorf: DVS-Verlag GmbH; 2000

tron diffraction analysis. Materials and Design. 2017;**126**:339-350

axial loading. DFG-FA992/1-1 Final Report. 2015

Braunschweig, Germany: Shaker Verlag; 2011

inger effect. CEGB Report RD/B/N731. 1966

Metallurgical Transactions. 1984;**15B**:299-305

Fraunhofer Institute for Mechanics of Materials IWM, Germany

Institution of Mechanical Engineers. 1936;**133**:295-347

Welding Journal. 1941;**20**(5):220-234

2005. ISBN-10:0-387-23287-7

The key conclusions and findings in this period are listed as follows:


### **Acknowledgements**

This contribution was partially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft – DFG) as part of the projects DFG FA992/2-1 "Numerical description of the behavior of welding residual stress field under multiaxial mechanical loading" and DFG FA992/2-2 "Numerical Incorporation of the Damaging Effects of Residual Stresses in the Multiaxial Fatigue Assessment of Welded Components and Structures". The respective residual stress measurements were done at the Helmholtz-Zentrum Berlin (HZB) and the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II) in Munich, Germany. The authors would like to thank deeply for the support. For those experiments conducted within the activities of NeT (Network on Neutron Techniques standardization for Structural Integrity) round robin, the authors would like to use the opportunity to express their gratitude to everyone who was involved in this fruitful collaboration.

## **Author details**

wide range of experimental measurements parallel to its advanced simulation programs. The goal is to develop a comprehensive simulation methodology for the prediction of residual stresses under the assistance of precise measurement techniques. Based on the results and achievements, FE simulation could be applied as a powerful tool for predicting the welding residual stresses required for the integrity assessments. The summaries of all these efforts have been already released in terms of a couple of recommendations. Exact thermal solutions, use of advanced material hardening models and including high-temperature annealing effects are some of the most important items out of those recommendations.

**1.** Welding residual stresses within the tubular welded joint could be accurately determined by means of the numerical simulation approach considering the phase transformations, microstructure- and temperature-dependent mechanical properties, transformation-

**2.** Combining the residual stress measurement results from X-ray and neutron diffraction over the whole cross section of welds showed a sharp gradient in the welding residual

**3.** Based on the simulations of the tubular welds, the material in the weld area undergoes compressive stresses due to the *γ* → *α* transformation-induced expansions during cooling. **4.** For the material S355J2H, isotropic hardening model seems to be suitable for predicting

**5.** In welding simulation, before proceeding to mechanical simulation, a verified global heat

**6.** The use of kinematic and combined hardening models or preferably elasto-viscoplastic material constitutive behavior is recommended for the welding simulation of stainless

**7.** The used material constitutive model for the weld metal could differ from that of base material.

This contribution was partially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft – DFG) as part of the projects DFG FA992/2-1 "Numerical description of the behavior of welding residual stress field under multiaxial mechanical loading" and DFG FA992/2-2 "Numerical Incorporation of the Damaging Effects of Residual Stresses in the Multiaxial Fatigue Assessment of Welded Components and Structures". The respective residual stress measurements were done at the Helmholtz-Zentrum Berlin (HZB) and the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II) in Munich, Germany. The authors would like to thank deeply for the support. For those experiments conducted within the activities of NeT (Network on Neutron Techniques standardization for Structural Integrity) round robin, the authors would like to use the opportunity to express their grati-

induced plasticity and recovering of strain hardening during transformation.

The key conclusions and findings in this period are listed as follows:

46 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

stress profile from top surface toward the material bulk.

input and a calibrated heat source is absolutely necessary.

tude to everyone who was involved in this fruitful collaboration.

welding residual stresses.

steel and Inconel.

**Acknowledgements**

Kimiya Hemmesi and Majid Farajian\*

\*Address all correspondence to: majid.farajian@iwm.fraunhofer.de

Fraunhofer Institute for Mechanics of Materials IWM, Germany

## **References**


**Chapter 3**

Provisional chapter

**Residual Stress Analysis of Laser Remanufacturing**

DOI: 10.5772/intechopen.72749

Residual Stress Analysis of Laser Remanufacturing

Laser remanufacturing is an advanced repairing method to remanufacture damaged parts based on laser processing, such as laser cladding and laser welding. As a critical factor in determining the remanufacturing quality, residual stress of different laserremanufactured parts was analysed by numerical methods based on deactivating and reactivating element theory, as well as experimental methods such as X-ray diffraction and hole drilling measurements. The distributions and evolution law of residual stress during multipass laser welding of 7A52 high-strength aluminium alloy, and the effects of forming strategy, heat input and solid-state phase transition on residual stress in the laser cladding forming layers of QT 500 cast iron and FV520B high strength steel, were emphatically studied. The simulation results of residual stress fit well with the experimental results, indicating that both residual stress and its accumulation phenomenon would occur during the laser welding and laser cladding forming, and were affected by factors such as welding pass, heat input and phase transition. It is feasible to control residual stress by using cross path forming strategy, less heat input and alloying power

Keywords: residual stress, phase transition, laser remanufacturing, finite element

Remanufacturing was defined as a process of returning the used product to its original performance. And, it is required that performance specification of the remanufactured product should be equivalent to or even better than that of the new one. Remanufacturing engineering generally refers to the related techniques or engineering activities to remanufacture the waste products, which regards product life cycle theory as instructions and performance upgrading

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Shi-yun Dong, Chao-qun Song, Xiang-yi Feng,

Shi-yun Dong, Chao-qun Song, Xiang-yi Feng,

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

materials with low martensite transition point (Ms).

Yong-jian Li and Shi-xing Yan

Yong-jian Li and Shi-xing Yan

Abstract

analysis

1. Introduction

http://dx.doi.org/10.5772/intechopen.72749

Provisional chapter

## **Residual Stress Analysis of Laser Remanufacturing**

DOI: 10.5772/intechopen.72749

Residual Stress Analysis of Laser Remanufacturing

Shi-yun Dong, Chao-qun Song, Xiang-yi Feng, Yong-jian Li and Shi-xing Yan Shi-yun Dong, Chao-qun Song, Xiang-yi Feng,

Additional information is available at the end of the chapter Yong-jian Li and Shi-xing Yan

http://dx.doi.org/10.5772/intechopen.72749 Additional information is available at the end of the chapter

#### Abstract

Laser remanufacturing is an advanced repairing method to remanufacture damaged parts based on laser processing, such as laser cladding and laser welding. As a critical factor in determining the remanufacturing quality, residual stress of different laserremanufactured parts was analysed by numerical methods based on deactivating and reactivating element theory, as well as experimental methods such as X-ray diffraction and hole drilling measurements. The distributions and evolution law of residual stress during multipass laser welding of 7A52 high-strength aluminium alloy, and the effects of forming strategy, heat input and solid-state phase transition on residual stress in the laser cladding forming layers of QT 500 cast iron and FV520B high strength steel, were emphatically studied. The simulation results of residual stress fit well with the experimental results, indicating that both residual stress and its accumulation phenomenon would occur during the laser welding and laser cladding forming, and were affected by factors such as welding pass, heat input and phase transition. It is feasible to control residual stress by using cross path forming strategy, less heat input and alloying power materials with low martensite transition point (Ms).

Keywords: residual stress, phase transition, laser remanufacturing, finite element analysis

### 1. Introduction

Remanufacturing was defined as a process of returning the used product to its original performance. And, it is required that performance specification of the remanufactured product should be equivalent to or even better than that of the new one. Remanufacturing engineering generally refers to the related techniques or engineering activities to remanufacture the waste products, which regards product life cycle theory as instructions and performance upgrading

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

as goals, with rules of energy-saving environment conservation-good quality-high efficiency by using advanced processing techniques [1]. It can bring great economic and social benefits on sources and environment to the world and has become an important way for sustainable society development [1–3].

2. Residual stress analysis of high-strength aluminium alloy pieces

Solidification cracking and stress corrosion cracking frequently occur in high-strength aluminium alloys, on the account of their relatively large linear expansion coefficients and high stress corrosion cracking susceptibility [7, 8]. Narrow gap laser welding (NGLW) is considered as one of the most effective ways to repair the cracks, for its lower heat input, less repairing deformation and better repairing quality, comparing with the conventional electric arc or plasma arc welding method [9–12]. However, residual stress of NGLW is also a vital factor for repairing quality of cracks and has been one of the research focuses of NGLW [13–15]. The aim of this work is to present distributions and evolution of residual stress during multipass

The base material sample in this case was 7A52 aluminium alloy plates with dimensions of

The six-pass NGLW was conducted by a 4 kW IPG fibre laser system with welding parameters: laser power 3.20 kW, welding speed 0.48 m/min and wire feed speed 2.15 m/min. A Ktype thermocouple was used to detect temperatures during the six-pass NGLW processing, which was located in the heat-affected zone (HAZ) about 5 mm from the groove sidewall and

MSC.Marc 2016.0.0 software was exploited to simulate the six-pass NGLW processing without regard to the molten pool flow and droplet transfer behaviour. One-half of the symmetric geometric model was adopted as shown in Figure 2b. The values of material thermo-physical

applied, with gap width 3 mm and groove depth 18 mm, as shown in Figure 2a.

Figure 2. Sketch of the geometric model: (a) narrow gap groove and (b) mesh generation.

, and the filler wire was ER 5356 feed wire. A parallel I-type groove was

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 51

remanufactured by laser welding

NGLW processing.

<sup>50</sup> <sup>50</sup> 20 mm3

2.1. Experimental procedure

9 mm from the plate top surface.

2.2. Numerical simulation procedure

Figure 1 shows the main procedures of used equipment remanufacturing process, which generally involves many steps such as disassembling, cleaning, detecting and assessing of the used components, remanufacturing, examining and reassembling of the remanufactured equipment. It also reveals that remanufacturing is supported by a series of relevant techniques during the whole process.

The remanufacturing forming procedure is of great importance to the quality of the remanufactured parts, which is also an obvious characteristic to distinguish remanufacturing production from manufacturing. As an advanced remanufacturing technology, laser remanufacturing can restore geometrical size and upgrade performance of the worn components with high productivity and little distortion, using laser cladding, laser welding, laser sintering or other laser-related processing methods [4, 5]. It has shown great benefits to the society for its successful applications over the last decade. More and more institutes, enterprises and industry sectors show great attentions to laser remanufacturing.

However, there are still some challenges for application of laser remanufacturing, especially residual stress-related problems such as brittle fracture, fatigue failure, stress corrosion cracking and buckling deformation [6]. As a research focus in recent years, residual stress has been experimentally measured by various damage detection methods such as hole drilling and indentation strain, as well as several non-destructive detection methods such as ultrasonic, Xray diffraction and neutron diffraction methods. However, the experimental data are limited to thoroughly characterize the region distribution of residual stress. Hence, simulation method based on finite element model (FEM) is necessary to estimate the 3D residual stress field of the laser-remanufactured pieces. In this chapter, it introduces some researches on residual stress of laser remanufacturing metal pieces with cases of high-strength aluminium alloy, cast iron and high-strength steel, respectively.

Figure 1. General procedures of mechanism remanufacturing.

## 2. Residual stress analysis of high-strength aluminium alloy pieces remanufactured by laser welding

Solidification cracking and stress corrosion cracking frequently occur in high-strength aluminium alloys, on the account of their relatively large linear expansion coefficients and high stress corrosion cracking susceptibility [7, 8]. Narrow gap laser welding (NGLW) is considered as one of the most effective ways to repair the cracks, for its lower heat input, less repairing deformation and better repairing quality, comparing with the conventional electric arc or plasma arc welding method [9–12]. However, residual stress of NGLW is also a vital factor for repairing quality of cracks and has been one of the research focuses of NGLW [13–15]. The aim of this work is to present distributions and evolution of residual stress during multipass NGLW processing.

#### 2.1. Experimental procedure

as goals, with rules of energy-saving environment conservation-good quality-high efficiency by using advanced processing techniques [1]. It can bring great economic and social benefits on sources and environment to the world and has become an important way for sustainable

50 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Figure 1 shows the main procedures of used equipment remanufacturing process, which generally involves many steps such as disassembling, cleaning, detecting and assessing of the used components, remanufacturing, examining and reassembling of the remanufactured equipment. It also reveals that remanufacturing is supported by a series of relevant techniques

The remanufacturing forming procedure is of great importance to the quality of the remanufactured parts, which is also an obvious characteristic to distinguish remanufacturing production from manufacturing. As an advanced remanufacturing technology, laser remanufacturing can restore geometrical size and upgrade performance of the worn components with high productivity and little distortion, using laser cladding, laser welding, laser sintering or other laser-related processing methods [4, 5]. It has shown great benefits to the society for its successful applications over the last decade. More and more institutes, enter-

However, there are still some challenges for application of laser remanufacturing, especially residual stress-related problems such as brittle fracture, fatigue failure, stress corrosion cracking and buckling deformation [6]. As a research focus in recent years, residual stress has been experimentally measured by various damage detection methods such as hole drilling and indentation strain, as well as several non-destructive detection methods such as ultrasonic, Xray diffraction and neutron diffraction methods. However, the experimental data are limited to thoroughly characterize the region distribution of residual stress. Hence, simulation method based on finite element model (FEM) is necessary to estimate the 3D residual stress field of the laser-remanufactured pieces. In this chapter, it introduces some researches on residual stress of laser remanufacturing metal pieces with cases of high-strength aluminium alloy, cast iron and

prises and industry sectors show great attentions to laser remanufacturing.

society development [1–3].

during the whole process.

high-strength steel, respectively.

Figure 1. General procedures of mechanism remanufacturing.

The base material sample in this case was 7A52 aluminium alloy plates with dimensions of <sup>50</sup> <sup>50</sup> 20 mm3 , and the filler wire was ER 5356 feed wire. A parallel I-type groove was applied, with gap width 3 mm and groove depth 18 mm, as shown in Figure 2a.

The six-pass NGLW was conducted by a 4 kW IPG fibre laser system with welding parameters: laser power 3.20 kW, welding speed 0.48 m/min and wire feed speed 2.15 m/min. A Ktype thermocouple was used to detect temperatures during the six-pass NGLW processing, which was located in the heat-affected zone (HAZ) about 5 mm from the groove sidewall and 9 mm from the plate top surface.

#### 2.2. Numerical simulation procedure

MSC.Marc 2016.0.0 software was exploited to simulate the six-pass NGLW processing without regard to the molten pool flow and droplet transfer behaviour. One-half of the symmetric geometric model was adopted as shown in Figure 2b. The values of material thermo-physical

Figure 2. Sketch of the geometric model: (a) narrow gap groove and (b) mesh generation.

where af, ar, b and c are the geometric parameters, vw and t are the welding velocity and time

Parameter af ar ff fr b c RH β Values 1.5 mm 4.0 mm 0.55 1.45 1.5 mm 2.5 mm 0.4 mm 4.0 mm 0.15

The heat flux values (qc) in Gauss cylindrical are characterized by Gaussian distribution in the

<sup>2</sup>πHR<sup>2</sup> <sup>þ</sup> βπRH<sup>2</sup> exp �3r<sup>2</sup>

where R and H are the effective radius and height of Gauss cylindrical, respectively, and β is

Here, the adopted values of heat source parameters are given in Table 1 on the basis of previous optimization by experimental observations to molten pool, measurements of joint

The heat transfer phenomena in NGLW process is governed by the three-dimensional heat

<sup>λ</sup> <sup>∂</sup><sup>T</sup> ∂y 

where r, λ and CP are the density, thermal conductivity and specific heat, T is the temperature, Qi is the internal heat source intensity and ΔH is the latent heat of fusion and crystallization. In this case, equivalent specific heat method was used to deal with ΔH, assuming that values of

The symmetrical plane was assumed as adiabatic condition, while on other planes, heat transfer from metal substrate to atmosphere or backing plate occurred by means of thermal

<sup>∂</sup><sup>n</sup> <sup>¼</sup> hcð Þþ <sup>T</sup> � <sup>T</sup><sup>0</sup> σε <sup>T</sup><sup>4</sup> � <sup>T</sup><sup>4</sup>

where λ is the thermal conductivity, T0 is the atmosphere temperature, hc is the convective heat

As for the mechanical boundary conditions, the y-direction displacement of all nodes was fixed on the symmetrical plane to keep the balance of joint, while the nodes on the bottom plane and

þ ∂ ∂z

<sup>λ</sup> <sup>∂</sup><sup>T</sup> ∂z 

0

(5)

on its cross section and comparisons between the simulated and experimental results.

R2

<sup>β</sup><sup>h</sup> <sup>þ</sup> <sup>R</sup>

R

(3)

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 53

þ Qi þ ΔH (4)

and ff and fr are the distribution coefficient of heat flux determined by af and ar.

radial direction and exponential decay along the depth, expressed as follows:

qcð Þ¼ <sup>r</sup>; <sup>h</sup> <sup>6</sup>Q<sup>2</sup>

<sup>λ</sup> <sup>∂</sup><sup>T</sup> ∂x 

CP had abrupt changes between the solidus and liquidus temperatures.

�<sup>λ</sup> <sup>∂</sup><sup>T</sup>

side edge were fixed in z direction to prevent rotational movement.

þ ∂ ∂y

convection and radiation, and the thermal boundary condition can be defined as

transfer coefficient, σ is the Stephan-Boltzmann constant and ε is the emissivity.

the energy attenuation coefficient.

Table 1. The values of heat source parameters.

conduction equation for unsteady state:

rCP ∂T <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>∂</sup> ∂x

2.2.2. Governing equations

2.2.3. Boundary conditions

Figure 3. Thermo-physical values of 7A52 and 5356 aluminium alloys: (a) specific heat and thermal conductivity and (b) elasticity modulus and thermal expansion coefficient.

Figure 4. Sketch of the hybrid heat source model for NGLW.

property such as thermal conductivity thermal expansion coefficient and specific heat were estimated by the thermodynamic software JMatPro as given in Figure 3.

#### 2.2.1. Heat source model

In order to more accurately describe the combined thermal effects of molten drop and laser irradiation on the base metal, a hybrid heat source model was adopted by combining doubleellipsoid heat source and Gauss cylindrical heat source, as shown in Figure 4.

The heat flux distribution in front half part (qf) and latter half part (qr) of the double ellipsoid could be, respectively, described as follows:

$$q\_f(x,y,z) = \frac{6\sqrt{3}Q\_1f\_f}{a\_fbc\pi\sqrt{\pi}}\exp\left\{-3\left[\frac{\left(x-v\_wt\right)^2}{a\_f^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2}\right]\right\}\tag{1}$$

$$q\_r(\mathbf{x}, y, z) = \frac{6\sqrt{3}Q\_1f\_r}{a\_r b c \pi \sqrt{\pi}} \exp\left\{-3\left[\frac{\left(\mathbf{x} - \boldsymbol{\upsilon}\_w \boldsymbol{t}\right)^2}{a\_r^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2}\right]\right\} \tag{2}$$


Table 1. The values of heat source parameters.

where af, ar, b and c are the geometric parameters, vw and t are the welding velocity and time and ff and fr are the distribution coefficient of heat flux determined by af and ar.

The heat flux values (qc) in Gauss cylindrical are characterized by Gaussian distribution in the radial direction and exponential decay along the depth, expressed as follows:

$$q\_c(r,h) = \frac{6Q\_2}{2\pi HR^2 + \beta\pi RH^2} \exp\left[\frac{-3r^2}{R^2}\right] \left[\frac{\beta h + R}{R}\right] \tag{3}$$

where R and H are the effective radius and height of Gauss cylindrical, respectively, and β is the energy attenuation coefficient.

Here, the adopted values of heat source parameters are given in Table 1 on the basis of previous optimization by experimental observations to molten pool, measurements of joint on its cross section and comparisons between the simulated and experimental results.

#### 2.2.2. Governing equations

The heat transfer phenomena in NGLW process is governed by the three-dimensional heat conduction equation for unsteady state:

$$
\rho \mathcal{L}\_P \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( \lambda \frac{\partial T}{\partial x} \right) + \frac{\partial}{\partial y} \left( \lambda \frac{\partial T}{\partial y} \right) + \frac{\partial}{\partial z} \left( \lambda \frac{\partial T}{\partial z} \right) + Q\_i + \Delta H \tag{4}
$$

where r, λ and CP are the density, thermal conductivity and specific heat, T is the temperature, Qi is the internal heat source intensity and ΔH is the latent heat of fusion and crystallization. In this case, equivalent specific heat method was used to deal with ΔH, assuming that values of CP had abrupt changes between the solidus and liquidus temperatures.

#### 2.2.3. Boundary conditions

property such as thermal conductivity thermal expansion coefficient and specific heat were

Figure 3. Thermo-physical values of 7A52 and 5356 aluminium alloys: (a) specific heat and thermal conductivity and (b)

52 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

In order to more accurately describe the combined thermal effects of molten drop and laser irradiation on the base metal, a hybrid heat source model was adopted by combining double-

The heat flux distribution in front half part (qf) and latter half part (qr) of the double ellipsoid

<sup>π</sup> <sup>p</sup> exp �<sup>3</sup> ð Þ <sup>x</sup> � vwt <sup>2</sup>

<sup>π</sup> <sup>p</sup> exp �<sup>3</sup> ð Þ <sup>x</sup> � vwt <sup>2</sup>

a2 f

a2 r

( ) " #

( ) " #

þ y2 <sup>b</sup><sup>2</sup> <sup>þ</sup> z2 c2

þ y2 <sup>b</sup><sup>2</sup> <sup>þ</sup> z2 c2 (1)

(2)

estimated by the thermodynamic software JMatPro as given in Figure 3.

ellipsoid heat source and Gauss cylindrical heat source, as shown in Figure 4.

6 ffiffiffi 3 <sup>p</sup> <sup>Q</sup>1<sup>f</sup> <sup>f</sup> af bcπ ffiffiffi

6 ffiffiffi 3 <sup>p</sup> <sup>Q</sup>1<sup>f</sup> <sup>r</sup> arbcπ ffiffiffi

2.2.1. Heat source model

could be, respectively, described as follows:

Figure 4. Sketch of the hybrid heat source model for NGLW.

elasticity modulus and thermal expansion coefficient.

qfð Þ¼ x; y; z

qrð Þ¼ x; y; z

The symmetrical plane was assumed as adiabatic condition, while on other planes, heat transfer from metal substrate to atmosphere or backing plate occurred by means of thermal convection and radiation, and the thermal boundary condition can be defined as

$$-\lambda \frac{\partial T}{\partial \mathbf{n}} = h\_c (T - T\_0) + \sigma \varepsilon \left(T^4 - T\_0^4\right) \tag{5}$$

where λ is the thermal conductivity, T0 is the atmosphere temperature, hc is the convective heat transfer coefficient, σ is the Stephan-Boltzmann constant and ε is the emissivity.

As for the mechanical boundary conditions, the y-direction displacement of all nodes was fixed on the symmetrical plane to keep the balance of joint, while the nodes on the bottom plane and side edge were fixed in z direction to prevent rotational movement.

#### 2.3. Result and discussions

#### 2.3.1. Validation of the model

Figure 5 shows the comparison of calculated and measured temperature curves from the third pass during NGLW processing, which presents good agreement between them. The peak temperature of the calculated curve was 308.2C, which was close to the measured 301.5C. And the heating or cooling rates of the measured curve are slightly lower due to thermal inertia of thermocouple.

#### 2.3.2. Evolution of transient stress field

Figure 6 shows the evolution of calculated transverse stress σ<sup>y</sup> distribution in the middle of the first, third and fifth pass during NGLW processing. There is almost no stress existing in molten pool for melting of metal substrate. However, stress of its vicinity appears as compressive stress as a result of thermal expansion effect, which in turn leads to a tensile transverse stress at its distant zone. By comparing absolute value of the transverse stress and its concentration region in different weld passes, the existence of stress accumulation phenomenon can be confirmed during the multipass NGLW process.

#### 2.3.3. Residual stress analysis

Figure 7 shows the 3D distributions of the numerically predicted transverse residual stress, longitudinal residual stress, vertical residual stress and von Mises equivalent residual stress in the joint. The concentration region of high residual stress is predominately presented in the weld zone or HAZ near the fusion line, where the latter part has higher values of von Mises equivalent stress than the front part for the gradual accumulations of distortion and stress, as shown in Figure 7d.

The residual stress distributions along the weld centre line EF and its vertical line BC, as marked in Figure 1b, are shown in Figure 8. Along the centre line of weld, both the transverse and longitudinal residual stresses show stable tensile stress characteristics with average values of 45.5 and 141.4 MPa, without regard to its unstable front and latter part. During the welding, rapid fusion and solidification appear along welding direction, accompanied by unbalanced

expansion and shrinkage behaviours, resulting in higher longitudinal residual stress than the transverse residual stress. Nevertheless, the distribution of residual stress in its vertical direction is more complicated, as presented in Figure 8b. With increase of distance from the weld centre, values of transverse and longitudinal residual stress rapidly decline at the fusion line, and then the longitudinal residual stress decreases gradually until it turns into compressive residual stress from tensile stress, while the transverse residual stress begins to increase and

Figure 7. 3D residual stress distributions: (a) transverse residual stress σy, (b) longitudinal residual stress σx, (c) vertical

Figure 6. Distribution of transverse stress during the (a) first pass, (b) fifth pass, (c) and (d) third pass NGLW.

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 55

then descends again, maintaining tensile residual stress all through.

residual stress σ<sup>z</sup> and (d) von Mises equivalent stress.

Figure 5. Calculated and measured temperature curves from the third pass.

2.3. Result and discussions 2.3.1. Validation of the model

inertia of thermocouple.

2.3.3. Residual stress analysis

2.3.2. Evolution of transient stress field

confirmed during the multipass NGLW process.

Figure 5. Calculated and measured temperature curves from the third pass.

Figure 5 shows the comparison of calculated and measured temperature curves from the third pass during NGLW processing, which presents good agreement between them. The peak temperature of the calculated curve was 308.2C, which was close to the measured 301.5C. And the heating or cooling rates of the measured curve are slightly lower due to thermal

54 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Figure 6 shows the evolution of calculated transverse stress σ<sup>y</sup> distribution in the middle of the first, third and fifth pass during NGLW processing. There is almost no stress existing in molten pool for melting of metal substrate. However, stress of its vicinity appears as compressive stress as a result of thermal expansion effect, which in turn leads to a tensile transverse stress at its distant zone. By comparing absolute value of the transverse stress and its concentration region in different weld passes, the existence of stress accumulation phenomenon can be

Figure 7 shows the 3D distributions of the numerically predicted transverse residual stress, longitudinal residual stress, vertical residual stress and von Mises equivalent residual stress in the joint. The concentration region of high residual stress is predominately presented in the weld zone or HAZ near the fusion line, where the latter part has higher values of von Mises equivalent stress than the front part for the gradual accumulations of distortion and stress, as shown in Figure 7d. The residual stress distributions along the weld centre line EF and its vertical line BC, as marked in Figure 1b, are shown in Figure 8. Along the centre line of weld, both the transverse and longitudinal residual stresses show stable tensile stress characteristics with average values of 45.5 and 141.4 MPa, without regard to its unstable front and latter part. During the welding, rapid fusion and solidification appear along welding direction, accompanied by unbalanced

Figure 6. Distribution of transverse stress during the (a) first pass, (b) fifth pass, (c) and (d) third pass NGLW.

Figure 7. 3D residual stress distributions: (a) transverse residual stress σy, (b) longitudinal residual stress σx, (c) vertical residual stress σ<sup>z</sup> and (d) von Mises equivalent stress.

expansion and shrinkage behaviours, resulting in higher longitudinal residual stress than the transverse residual stress. Nevertheless, the distribution of residual stress in its vertical direction is more complicated, as presented in Figure 8b. With increase of distance from the weld centre, values of transverse and longitudinal residual stress rapidly decline at the fusion line, and then the longitudinal residual stress decreases gradually until it turns into compressive residual stress from tensile stress, while the transverse residual stress begins to increase and then descends again, maintaining tensile residual stress all through.

Double-ellipsoid heat source model and Gauss body heat source model are often used to simulate the welding process, but the process of laser cladding is different with welding process; these heat source models are not suitable for simulating the cladding. Coupling of uniform body heat source (the energy density is same in different points of the heat source) and Gauss surface heat source was adopted in this experiment simulation process. The simulation uses ANSYS finite element software. Firstly, the stress evolution process under parallel stacking forming and cross stacking forming passes was simulated. Considering the actual remanufacturing process, the model is under one side constraint or fully constrained state. Figure 10 is the temperature distribution at 2 and 5 s after multilayer laser cladding process, and Figure 11 shows the temperature cycle curve of the fusion zone and the heat-affected zone. It can be seen that the clad layer and the heat-affected zone undergo repeated thermal cycles,

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 57

Figure 12 shows the nephogram of the longitudinal stress, the deformation and macroscopic stress state in remanufacturing process. Ends of the sample in x direction are restrained. It can be seen that the stress is mainly concentrated around the constraint parts and the layers. Figure 13 is the curve of the longitudinal stress of a node in the layer and a node in the substrate, and the node's location can be seen in Figure 12. The layer mainly presents the tensile stress state, while the substrate is mainly in the state of compressive stress. For the actual remanufacturing process, the constraints should be avoided or removed as far as

In order to obtain the residual stress distribution in the surface and interior of the clad layer, X-ray diffraction method was used for measuring the accumulation of residual stress in the clad layer. The electrolytic etching method was used to peel clad layer from the top surface to the internal layer, and the thickness of the peeling layer is 60 μm. Residual stress parallel or vertical to the cladding line was tested, respectively, at a certain point, and the schematic

which easily results in stress concentration.

possible.

3.2. Experimental procedure

diagram of the test is shown in Figure 14.

Figure 10. Temperature distribution at (a) 2 and (b) 5 s.

Figure 8. Residual stress distributions along (a) line EF and (b) line BC marked in Figure 1b.

## 3. Residual stress analysis of cast iron pieces remanufactured by laser cladding

QT 500 nodular casts iron as an industrial basic material is widely used in ship engines, crankshafts and machine tools [16–18]. As for laser cladding remanufacturing the cast iron pieces, due to the high carbon content, brittle phases are easily generated near the interface between the clad and substrate which causes residual stress during remanufacturing process. Therefore, study on residual stress and its control measures is vital to successful remanufacturing of cast iron components [19–21]. Two common laser pass-forming methods, parallel stacking forming and cross stacking forming, are chosen for the laser cladding process, as shown in Figure 9. A kind of Ni-Cu alloy power with element content of 0.03 wt.%C, 2.0 wt.%Si, 1.1wt.% B, 0.5wt.%Fe and 20.0 wt.%Cu and the balance Ni was selected as the cladding material, whose particle size scale was 20–106 μm.

#### 3.1. Numerical simulation procedures

Thermal stress after cast iron laser cladding mainly comes from shrinkage of the clad layers during cooling process. Larger expansion coefficient difference between the substrate and the clad always caused larger residual stress after processing, which is usually a direct reason to the layer cracking. The cast iron parts are often large-scale castings, which can be considered as a fully constrained state around the forming layer.

Figure 9. Sketch of the laser passes: (a) parallel stacking and (b) cross stacking.

Double-ellipsoid heat source model and Gauss body heat source model are often used to simulate the welding process, but the process of laser cladding is different with welding process; these heat source models are not suitable for simulating the cladding. Coupling of uniform body heat source (the energy density is same in different points of the heat source) and Gauss surface heat source was adopted in this experiment simulation process. The simulation uses ANSYS finite element software. Firstly, the stress evolution process under parallel stacking forming and cross stacking forming passes was simulated. Considering the actual remanufacturing process, the model is under one side constraint or fully constrained state. Figure 10 is the temperature distribution at 2 and 5 s after multilayer laser cladding process, and Figure 11 shows the temperature cycle curve of the fusion zone and the heat-affected zone. It can be seen that the clad layer and the heat-affected zone undergo repeated thermal cycles, which easily results in stress concentration.

Figure 12 shows the nephogram of the longitudinal stress, the deformation and macroscopic stress state in remanufacturing process. Ends of the sample in x direction are restrained. It can be seen that the stress is mainly concentrated around the constraint parts and the layers. Figure 13 is the curve of the longitudinal stress of a node in the layer and a node in the substrate, and the node's location can be seen in Figure 12. The layer mainly presents the tensile stress state, while the substrate is mainly in the state of compressive stress. For the actual remanufacturing process, the constraints should be avoided or removed as far as possible.

#### 3.2. Experimental procedure

3. Residual stress analysis of cast iron pieces remanufactured by laser

Figure 8. Residual stress distributions along (a) line EF and (b) line BC marked in Figure 1b.

56 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

QT 500 nodular casts iron as an industrial basic material is widely used in ship engines, crankshafts and machine tools [16–18]. As for laser cladding remanufacturing the cast iron pieces, due to the high carbon content, brittle phases are easily generated near the interface between the clad and substrate which causes residual stress during remanufacturing process. Therefore, study on residual stress and its control measures is vital to successful remanufacturing of cast iron components [19–21]. Two common laser pass-forming methods, parallel stacking forming and cross stacking forming, are chosen for the laser cladding process, as shown in Figure 9. A kind of Ni-Cu alloy power with element content of 0.03 wt.%C, 2.0 wt.%Si, 1.1wt.% B, 0.5wt.%Fe and 20.0 wt.%Cu and the balance Ni was selected as the cladding material, whose

Thermal stress after cast iron laser cladding mainly comes from shrinkage of the clad layers during cooling process. Larger expansion coefficient difference between the substrate and the clad always caused larger residual stress after processing, which is usually a direct reason to the layer cracking. The cast iron parts are often large-scale castings, which can be considered as

cladding

particle size scale was 20–106 μm.

3.1. Numerical simulation procedures

a fully constrained state around the forming layer.

Figure 9. Sketch of the laser passes: (a) parallel stacking and (b) cross stacking.

In order to obtain the residual stress distribution in the surface and interior of the clad layer, X-ray diffraction method was used for measuring the accumulation of residual stress in the clad layer. The electrolytic etching method was used to peel clad layer from the top surface to the internal layer, and the thickness of the peeling layer is 60 μm. Residual stress parallel or vertical to the cladding line was tested, respectively, at a certain point, and the schematic diagram of the test is shown in Figure 14.

Figure 11. Temperature distribution of different zones: (a) the fusion zone and (b) the HAZ (c) location of the selected nodes.

#### 3.3. Results and discussions

Figure 15 shows residual stress distribution in different scanning passes in the clad layer. It can be found that residual stress increases slowly from the surface to inside of the layers formed by cross stacking method. The state of stress is tensile stress with the highest value +300 MPa. The residual stress of the clad layer formed by the parallel path is fluctuated from the surface to the interior, and the fitting curve shows a downward trend. The residual stress at the top of the clad layer reaches the highest tensile stress, reaching +380 MPa, and the lowest residual stress is 50 MPa inside the clad layer. It can be seen that the residual stress of the cross path cladding is smaller than that of the parallel path in the range of 340 μm depth from the surface, and beyond this range, residual stress changes in opposite direction. Residual stress distribution vertical to cladding line direction of the cladding is shown in Figure 15b. It can be found that residual stress from the surface to the interior in the clad layer in two kinds of forming methods is increased, but the residual stress in the layers formed in cross path is smaller than that of parallel path at different depths. It can be seen that the cross path forming is beneficial to reduce the thermal stress of the clad layer in the vertical direction.

The thermal cycle curve of the cross stacking forming shows irregular and overlapping effect, and the interval between two adjacent temperature peaks is relatively large. Therefore, there is no apparent periodic heat accumulation in the clad layer, and the heat dispersion effect is obvious. Therefore, characteristics of the temperature field with relatively small temperature gradient caused smaller shrinkage difference of the clad layer, and the thermal stress in the clad layer decreased. The thermal cycling curves of parallel path forming show apparent

Figure 12. Nephogram of stress and deformation: (a) longitudinal stress, (b) deformation and (c) macroscopic stress.

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Figure 13. Stress curves of the (a) selected node in the layer and (b) selected node in the substrate.

Figure 12. Nephogram of stress and deformation: (a) longitudinal stress, (b) deformation and (c) macroscopic stress.

Figure 13. Stress curves of the (a) selected node in the layer and (b) selected node in the substrate.

3.3. Results and discussions

nodes.

Figure 15 shows residual stress distribution in different scanning passes in the clad layer. It can be found that residual stress increases slowly from the surface to inside of the layers formed by cross stacking method. The state of stress is tensile stress with the highest value +300 MPa. The residual stress of the clad layer formed by the parallel path is fluctuated from the surface to the interior, and the fitting curve shows a downward trend. The residual stress at the top of the clad layer reaches the highest tensile stress, reaching +380 MPa, and the lowest residual stress is 50 MPa inside the clad layer. It can be seen that the residual stress of the cross path cladding is smaller than that of the parallel path in the range of 340 μm depth from the surface, and beyond this range, residual stress changes in opposite direction. Residual stress distribution vertical to cladding line direction of the cladding is shown in Figure 15b. It can be found that residual stress from the surface to the interior in the clad layer in two kinds of forming methods is increased, but the residual stress in the layers formed in cross path is smaller than that of parallel path at different depths. It can be seen that the cross path forming is beneficial

Figure 11. Temperature distribution of different zones: (a) the fusion zone and (b) the HAZ (c) location of the selected

The thermal cycle curve of the cross stacking forming shows irregular and overlapping effect, and the interval between two adjacent temperature peaks is relatively large. Therefore, there is

to reduce the thermal stress of the clad layer in the vertical direction.

58 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

no apparent periodic heat accumulation in the clad layer, and the heat dispersion effect is obvious. Therefore, characteristics of the temperature field with relatively small temperature gradient caused smaller shrinkage difference of the clad layer, and the thermal stress in the clad layer decreased. The thermal cycling curves of parallel path forming show apparent

Figure 14. Schematic diagram of residual stress tests.

increase of the depth. At the depth of 600 μm, the residual tensile stress of the clad layer reaches 600 MPa, approaching the tensile strength of the clad layer, and the cracking tendency of the deposited clad layer increases. Therefore, the stress distribution characteristics of the clad layer under 1200 W are poor, and the cracks may exist in the clad layer. This also verifies that the low-power cladding process has good quality control effect on the remanufacturing of

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 61

Figure 16. Residual stress curves in different laser powers: (a) parallel and (b) vertical to cladding line.

According to the analysis of temperature field at the laser power of 800 and 1200 W, with the increase of laser power, the peak temperature of the thermal cycle curve increases significantly, and the temperature gradient of molten pool and gradient around the area increases. Reduction of cooling time causes cooling velocity to increase rapidly and results in the increasing of elastic-plastic deformation of cladding under residual stress. After solidification, the residual

To sum up, temperature field of laser cladding during cladding process has an important influence on the residual stress of the laser cladding. The results of the simulation and the actual test show that for the remanufacturing process of cast iron, it can be to helpful to reduce the overall residual stress by using cross path method, and lower heat input causes lower residual stress. These two methods result in the homogenization of the expansion and contraction of the layers during cladding process; therefore, the deformation is smaller, and the residual stress is relatively low. Therefore, from the point of view of controlling the residual stress of the clad layer, using low power and cross path method are used to control the residual

4. Residual stress analysis of high-strength steel pieces remanufactured by

During the complex thermal cycling of laser cladding, the high-strength steel, solid phase transition, such as eutectoid reaction, solid solution reaction, austenite transition and martensitic transition usually take place. Solid-state phase transition, which is accompanied by specific

stress distribution along different directions is shown in Figure 16.

cast iron castings.

stress of the clad layer.

laser cladding

Figure 15. Residual stress in different scanning passes: (a) parallel and (b) vertical to cladding line.

periodic thermal cumulative effect and heat accumulation of the clad layers, then large temperature gradient exists between high-temperature area of molten pool and the ambient clad layer and the shrinkage deformation and the stress of layers increases. Therefore, the cross path forming is beneficial to the thermal stress control of the clad layer.

Figure 16 shows residual stress distribution in the clad layer with different laser powers. It shows that the residual stress differs obviously in the parallel direction and vertical direction when the power increased from 800 to 1200 W. The residual stress decreases apparently in the layers parallel to cladding direction when depth increases. The residual stress in the surface reaches 120 MPa. In depth of 60 μm layer, the tensile stress begins to change into the compressive stress, and in depth of 600 μm, the residual stress reached 300 MPa in the clad layer. In contrast, stress decreases slowly when the power is 800 W.

In the vertical direction of the cladding line, with the increase of layer depth, residual tensile stress of clad layer increases from the surface to the interior when the power reaches 1200 W. The curve slope becomes larger, which means that the stress increases persistently with the

Figure 16. Residual stress curves in different laser powers: (a) parallel and (b) vertical to cladding line.

increase of the depth. At the depth of 600 μm, the residual tensile stress of the clad layer reaches 600 MPa, approaching the tensile strength of the clad layer, and the cracking tendency of the deposited clad layer increases. Therefore, the stress distribution characteristics of the clad layer under 1200 W are poor, and the cracks may exist in the clad layer. This also verifies that the low-power cladding process has good quality control effect on the remanufacturing of cast iron castings.

According to the analysis of temperature field at the laser power of 800 and 1200 W, with the increase of laser power, the peak temperature of the thermal cycle curve increases significantly, and the temperature gradient of molten pool and gradient around the area increases. Reduction of cooling time causes cooling velocity to increase rapidly and results in the increasing of elastic-plastic deformation of cladding under residual stress. After solidification, the residual stress distribution along different directions is shown in Figure 16.

To sum up, temperature field of laser cladding during cladding process has an important influence on the residual stress of the laser cladding. The results of the simulation and the actual test show that for the remanufacturing process of cast iron, it can be to helpful to reduce the overall residual stress by using cross path method, and lower heat input causes lower residual stress. These two methods result in the homogenization of the expansion and contraction of the layers during cladding process; therefore, the deformation is smaller, and the residual stress is relatively low. Therefore, from the point of view of controlling the residual stress of the clad layer, using low power and cross path method are used to control the residual stress of the clad layer.

periodic thermal cumulative effect and heat accumulation of the clad layers, then large temperature gradient exists between high-temperature area of molten pool and the ambient clad layer and the shrinkage deformation and the stress of layers increases. Therefore, the cross

Figure 16 shows residual stress distribution in the clad layer with different laser powers. It shows that the residual stress differs obviously in the parallel direction and vertical direction when the power increased from 800 to 1200 W. The residual stress decreases apparently in the layers parallel to cladding direction when depth increases. The residual stress in the surface reaches 120 MPa. In depth of 60 μm layer, the tensile stress begins to change into the compressive stress, and in depth of 600 μm, the residual stress reached 300 MPa in the clad layer. In

In the vertical direction of the cladding line, with the increase of layer depth, residual tensile stress of clad layer increases from the surface to the interior when the power reaches 1200 W. The curve slope becomes larger, which means that the stress increases persistently with the

path forming is beneficial to the thermal stress control of the clad layer.

Figure 15. Residual stress in different scanning passes: (a) parallel and (b) vertical to cladding line.

60 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

contrast, stress decreases slowly when the power is 800 W.

Figure 14. Schematic diagram of residual stress tests.

## 4. Residual stress analysis of high-strength steel pieces remanufactured by laser cladding

During the complex thermal cycling of laser cladding, the high-strength steel, solid phase transition, such as eutectoid reaction, solid solution reaction, austenite transition and martensitic transition usually take place. Solid-state phase transition, which is accompanied by specific volume change, transition plasticity and some other effects, will affect the stress field and final residual stress distribution.

Phase transition plasticity refers to the plastic strain of the material under the external load which is much less than yield strength. It mainly comes from the Greenwood-Johnson mechanism and the Magee mechanism. According to the classic work of Inoue, Leblond and Fisher, considering that during the laser cladding processing the longitudinal residual stress value is close to that of yield strength, the expression of the stress increment should be

where Δεαγ is the strain difference between austenite and martensite considering the volume

account the hardening effect), Sij is the deviatoric stress tensor and f <sup>M</sup> is the volume fraction of

The expression above is complex, and in practice the related parameters are difficult to obtain.

It is assumed that the initial and final austenitic ratio is f'γ<sup>0</sup> and 100% when the temperature rises to Ac1 and Ac3, respectively; the percentage of austenite phase increases linearly as temperature rises. Once the temperature is lower than Ms, austenite will partially or totally transform into martensite during the subsequent cooling period. The martensite tempering

In this work, under the condition of single-pass deposition, three kinds of situations are analysed in comparison: the two are phase transition (one considering stress influence) and the other one without phase transition. We obtained the following characteristics by experi-

and rises up to ~19 � <sup>10</sup>�6�C (at above 600�C); Ms = 160�C, Ac1 = 600�C and Ac3 = 900�C; the volumetric change strain is 0.0067352; kinetic coefficient of the phase transition during the

convection is simulated indirectly by elevated thermal conductivity coefficient (twice as large as that of room temperature) and the double-ellipsoid heat source. Latent heat (283 J/g) is taken into consideration when melting and solidification take place. The emissivity (ε) is defined to be 0.5, and the convection coefficient (hc) is 30 W/m<sup>2</sup> K. Initial temperature is set at 25�C (room temperature). Finally, the deposition process is regarded as quasi-steady process, and the

In the same piece of substrate, under the same experimental conditions, technological parameters and using different material powders (with phase transition and without phase transition,

<sup>Δ</sup>εTrp <sup>¼</sup> <sup>3</sup><sup>k</sup> <sup>1</sup> � <sup>f</sup> <sup>M</sup>

and formation of interdendritic eutectic phase during solidification are neglected.

cooling period is ~0.02347; and parameter of transition plasticity is 1.165 � <sup>10</sup>�<sup>4</sup>

ments: expansion coefficient of martensite state is about 18.75 � <sup>10</sup>�<sup>6</sup>

<sup>Δ</sup><sup>f</sup> <sup>M</sup> � <sup>h</sup> <sup>σ</sup>eq

σy 

is the yield strength of high-temperature phase (taking into

<sup>Δ</sup><sup>f</sup> <sup>M</sup> � Sij (9)

/

�C (room temperature)

. Molten pool

� Sij (8)

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 63

<sup>Δ</sup>εTrp ¼ � <sup>2</sup>Δεαγ σy <sup>γ</sup> ε eff γ ln <sup>f</sup> <sup>M</sup>

<sup>γ</sup> ε eff γ

revised to

martensite.

effects of phase transition, σ<sup>y</sup>

A simplified equation is put forward [25]:

where k is easily obtained by experiments.

materials are assumed isotropic [25].

4.2. Experimental measuring procedure

The occurrence of solid-state phase transition may have a certain impact on laser cladding or other welding processes under certain conditions. In some cases, the effect is even dominant. Since transition-induced plasticity increases the martensitic transition temperature, the martensitic transition has a significant effect on distribution of residual stress [22]. Ohta [23] studied the effect of solid phase transition on the evolution of residual stress and analysed the influence of diffusion phase transition and non-diffusion phase transition on residual stress. Materials with low phase transition point will result in lower residual stresses; the effect of solid-state phase transition on mechanical properties, solid phase transition volume effect and solid-state phase transition plasticity is the main factors affecting the stress evolution [24].

For steel, it is a hotspot to consider the solid-state phase transition effect in the process of laser cladding thermal-machine simulation. However, the actual situation is complex and still has some work to be done [25]. Firstly, the coupling interaction is very complicated since the stress has a great effect on the phase transition temperature and phase transition kinetics, which in turn affects the evolution of stress. Secondly, the tempering effect accompanying the thermal cycling will affect the physical properties and phase transition properties of the material. Then, many work lacks systematic and reliable physical data, especially computer simulation, in which the systematic and reliability of the data is a very important factor. Moreover, the research results are mostly limited to the welding process [25, 26].

#### 4.1. Numerical simulation procedure

The laser cladding is a processing with multi-parameter, complex nonlinearity and strong coupling and has a wide variety of scanning strategies; the scanning strategy is in direct relation to the thermal cycle of the laser cladding process, which has great influence on the stress, strain and microstructure of the remanufacturing part. Based on a few simplification and assumptions, computer simulation can try all kinds of process parameters and provides the temperature and stress data of remanufacturing part at any point and any time for the analysis of stress, microstructure and properties evolution.

Austenite is set as the initial phase in the solidification process. As temperature decreases, the martensitic phase transition starts at Ms (the martensite starting temperature) and finishes at Mf (the martensite finishing temperature). The volume fraction of martensite phase (fM) can be shown as [27]

$$f\_M = 1 - f\_{\gamma 0} \Phi(T) \tag{6}$$

$$\Phi(T) = \begin{cases} 1 & T \ge M\_s \\ \exp(-\alpha (M\_s - T)) T < M\_s \end{cases} \tag{7}$$

where fγ<sup>0</sup> is the initial austenitic volume percentage and fγ0Φ(T) is the ratio of austenite at a specific temperatures α is the kinetics coefficient of phase change, and can be obtained by experiments.

Phase transition plasticity refers to the plastic strain of the material under the external load which is much less than yield strength. It mainly comes from the Greenwood-Johnson mechanism and the Magee mechanism. According to the classic work of Inoue, Leblond and Fisher, considering that during the laser cladding processing the longitudinal residual stress value is close to that of yield strength, the expression of the stress increment should be revised to

$$
\Delta \varepsilon^{Trp} = -\frac{2\Delta \varepsilon\_{a\underline{\gamma}}}{\sigma\_{\underline{\gamma}}^{\underline{\v}} \left(\varepsilon\_{\underline{\gamma}}^{\underline{\omega}\underline{\gamma}}\right)} \ln \langle f\_M \rangle \Delta f\_M \cdot h \left(\frac{\sigma^{eq}}{\sigma^y}\right) \cdot S\_{\vec{\imath}\underline{\gamma}} \tag{8}
$$

where Δεαγ is the strain difference between austenite and martensite considering the volume effects of phase transition, σ<sup>y</sup> <sup>γ</sup> ε eff γ is the yield strength of high-temperature phase (taking into account the hardening effect), Sij is the deviatoric stress tensor and f <sup>M</sup> is the volume fraction of martensite.

The expression above is complex, and in practice the related parameters are difficult to obtain. A simplified equation is put forward [25]:

$$
\Delta \varepsilon^{Trp} = \mathfrak{B} \mathfrak{k} \{ \mathbf{1} - f\_M \} \Delta f\_M \cdot \mathfrak{S}\_{\vec{\eta}} \tag{9}
$$

where k is easily obtained by experiments.

volume change, transition plasticity and some other effects, will affect the stress field and final

62 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

The occurrence of solid-state phase transition may have a certain impact on laser cladding or other welding processes under certain conditions. In some cases, the effect is even dominant. Since transition-induced plasticity increases the martensitic transition temperature, the martensitic transition has a significant effect on distribution of residual stress [22]. Ohta [23] studied the effect of solid phase transition on the evolution of residual stress and analysed the influence of diffusion phase transition and non-diffusion phase transition on residual stress. Materials with low phase transition point will result in lower residual stresses; the effect of solid-state phase transition on mechanical properties, solid phase transition volume effect and solid-state phase transition plasticity is the main factors affecting the stress evolu-

For steel, it is a hotspot to consider the solid-state phase transition effect in the process of laser cladding thermal-machine simulation. However, the actual situation is complex and still has some work to be done [25]. Firstly, the coupling interaction is very complicated since the stress has a great effect on the phase transition temperature and phase transition kinetics, which in turn affects the evolution of stress. Secondly, the tempering effect accompanying the thermal cycling will affect the physical properties and phase transition properties of the material. Then, many work lacks systematic and reliable physical data, especially computer simulation, in which the systematic and reliability of the data is a very important factor. Moreover, the

The laser cladding is a processing with multi-parameter, complex nonlinearity and strong coupling and has a wide variety of scanning strategies; the scanning strategy is in direct relation to the thermal cycle of the laser cladding process, which has great influence on the stress, strain and microstructure of the remanufacturing part. Based on a few simplification and assumptions, computer simulation can try all kinds of process parameters and provides the temperature and stress data of remanufacturing part at any point and any time for the

Austenite is set as the initial phase in the solidification process. As temperature decreases, the martensitic phase transition starts at Ms (the martensite starting temperature) and finishes at Mf (the martensite finishing temperature). The volume fraction of martensite phase (fM) can be

1 T ≥ Ms

expð Þ �αð Þ Ms � T T < Ms 

where fγ<sup>0</sup> is the initial austenitic volume percentage and fγ0Φ(T) is the ratio of austenite at a specific temperatures α is the kinetics coefficient of phase change, and can be obtained by

f <sup>M</sup> ¼ 1 � f <sup>γ</sup><sup>0</sup>Φð Þ T (6)

(7)

research results are mostly limited to the welding process [25, 26].

analysis of stress, microstructure and properties evolution.

Φð Þ¼ T

4.1. Numerical simulation procedure

residual stress distribution.

tion [24].

shown as [27]

experiments.

It is assumed that the initial and final austenitic ratio is f'γ<sup>0</sup> and 100% when the temperature rises to Ac1 and Ac3, respectively; the percentage of austenite phase increases linearly as temperature rises. Once the temperature is lower than Ms, austenite will partially or totally transform into martensite during the subsequent cooling period. The martensite tempering and formation of interdendritic eutectic phase during solidification are neglected.

In this work, under the condition of single-pass deposition, three kinds of situations are analysed in comparison: the two are phase transition (one considering stress influence) and the other one without phase transition. We obtained the following characteristics by experiments: expansion coefficient of martensite state is about 18.75 � <sup>10</sup>�<sup>6</sup> / �C (room temperature) and rises up to ~19 � <sup>10</sup>�6�C (at above 600�C); Ms = 160�C, Ac1 = 600�C and Ac3 = 900�C; the volumetric change strain is 0.0067352; kinetic coefficient of the phase transition during the cooling period is ~0.02347; and parameter of transition plasticity is 1.165 � <sup>10</sup>�<sup>4</sup> . Molten pool convection is simulated indirectly by elevated thermal conductivity coefficient (twice as large as that of room temperature) and the double-ellipsoid heat source. Latent heat (283 J/g) is taken into consideration when melting and solidification take place. The emissivity (ε) is defined to be 0.5, and the convection coefficient (hc) is 30 W/m<sup>2</sup> K. Initial temperature is set at 25�C (room temperature). Finally, the deposition process is regarded as quasi-steady process, and the materials are assumed isotropic [25].

#### 4.2. Experimental measuring procedure

In the same piece of substrate, under the same experimental conditions, technological parameters and using different material powders (with phase transition and without phase transition,


The technology parameters of the laser cladding process are as follows: energy power is 1.8 kW; scanning rate is 8 mm/s; width of a single track is 3 mm; and lapping rate is 0.5.

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 65

1. For samples with solid-state phase transition, the first principal stress values are both low; #5 and #6 samples show compressive stress, and #1 sample is in tension stress state, whose

2. For most samples with no solid-state phase transition, the first principal stress of tension

3. For materials with solid-state phase transition, the higher solid-state phase transition

Figure 18 shows the residual stress distribution under the condition of single-pass deposition. Firstly, the stress distribution is nearly the same in the area away from the cladding bead. For the case with phase transition considered (Figure 18b), it is obvious that the stresses are lower in the clad bead as well as the adjacent region. Moreover, the interface between the cladding and substrate shows a lower stress level than that of the clad layer and substrate. The maximum tensile stress is observed at about a few millimetres from the surface of the clad layer. Nonetheless, when the phase transition is ignored (Figure 18a), the residual stresses in the cladding bead increase obviously, which are near the yield strength; the maximum tensile stress is found in the interface between the substrate and the clad layer. When phase transition is taken into account, the cases with and without considering the stress effect on phase transition temperature (Figure 18c and d,

Figure 18. Stress distribution of single-layer laser clad sample: (a) ignore phase transition (b) considering phase transition, and ignore the stress effect on phase transition temperature (c) considering both phase transition and stress effect on

The residual stress results are shown in Table 3; it can be seen that:

stress state and the stress value are high.

4.3. Result and discussions

phase transition temperature.

temperature means higher residual stress obtained.

respectively) show a similar residual stress level and distribution [25].

value is at about 12.7% of the yield stress in the room temperature.

Table 2. The ingredients of the used laser cladding alloying powders.

Figure 17. The laser cladding samples of different alloying powders.


Table 3. The result of the residual stress (RT, room temperature).

respectively) as shown in Table 2, the hole drilling method is used for measurement of residual stress of different powders in one position.

In this case, FV520B is martensitic precipitation-hardening steel with excellent strength and good welding performance and is used as the substrate. These samples (Figure 17) are clad layers of different materials, and the scanning strategy is arch deposition (as shown in Table 2). The technology parameters of the laser cladding process are as follows: energy power is 1.8 kW; scanning rate is 8 mm/s; width of a single track is 3 mm; and lapping rate is 0.5.

The residual stress results are shown in Table 3; it can be seen that:


#### 4.3. Result and discussions

respectively) as shown in Table 2, the hole drilling method is used for measurement of residual

 250 1280 163.44 32.06 181.60 None — 88.86 8.11 73.26 Below RT ———— Below RT 720 430.07 111.04 386.69 158 920 196.91 307.47 269.75 190 1150 67.52 169.83 148.11 None 530 349.26 187.61 302.75

C) Y<sup>s</sup> (MPa) σ<sup>1</sup> (MPa) σ<sup>2</sup> (MPa) σ<sup>e</sup> (MPa)

C Cr Ni Mo Mn Nb Si B Cu Fe

1 0.13 12.8 4.7 ——— 1.0 1.4 — Bal 2 0.03 — Bal ——— 2 1.1 20 0.5 3 0.03 17.5 14 2.3 2.0 — 1.0 — — Bal 4 0.1 15 10 ——— 1.0 1.0 — Bal 5 0.03 13.8 4.5 1.0 0.7 0.35 0.5 — — Bal 6 0.12 15.4 4.2 1.4 0.6 — 1.4 0.8 — Bal 7 0.05 — Bal ——— 2.7 1.8 — 0.4

64 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Table 2. The ingredients of the used laser cladding alloying powders.

Figure 17. The laser cladding samples of different alloying powders.

Ms (

In this case, FV520B is martensitic precipitation-hardening steel with excellent strength and good welding performance and is used as the substrate. These samples (Figure 17) are clad layers of different materials, and the scanning strategy is arch deposition (as shown in Table 2).

stress of different powders in one position.

Table 3. The result of the residual stress (RT, room temperature).

Figure 18 shows the residual stress distribution under the condition of single-pass deposition. Firstly, the stress distribution is nearly the same in the area away from the cladding bead. For the case with phase transition considered (Figure 18b), it is obvious that the stresses are lower in the clad bead as well as the adjacent region. Moreover, the interface between the cladding and substrate shows a lower stress level than that of the clad layer and substrate. The maximum tensile stress is observed at about a few millimetres from the surface of the clad layer. Nonetheless, when the phase transition is ignored (Figure 18a), the residual stresses in the cladding bead increase obviously, which are near the yield strength; the maximum tensile stress is found in the interface between the substrate and the clad layer. When phase transition is taken into account, the cases with and without considering the stress effect on phase transition temperature (Figure 18c and d, respectively) show a similar residual stress level and distribution [25].

Figure 18. Stress distribution of single-layer laser clad sample: (a) ignore phase transition (b) considering phase transition, and ignore the stress effect on phase transition temperature (c) considering both phase transition and stress effect on phase transition temperature.

Acknowledgements

1516007).

Author details

References

The work was supported by the key programme of the National Key Research and Development of China (Grant No. 2016YFB1100205), NSFC programme (Grant No.51705532) and Beijing Science and Technology projects (Grant No. Z161100004916009, Z16110000

Residual Stress Analysis of Laser Remanufacturing http://dx.doi.org/10.5772/intechopen.72749 67

[1] Xu BS. Theory and technology of equipment remanufacturing engineering. National

[2] Xu Bs, Dong sy, Zhu S, et al. Prospects and developing of remanufacture forming technology [J]. Journal of Mechanical Engineering. 2012;48(15):96-105. DOI: 10.3901/JME.2012.15.096

[3] Cunha JO, Konstantaras I, Melo RA, et al. On multi-item economic lot-sizing with remanufacturing and uncapacitated production. Applied Mathematical Modelling. 2017;50:

[4] Xu BS, Dong SY. Laser Remanufacturing Technology. Beijing, China: National Defense

[5] Dong SY, Xu BS, Wang ZJ, et al. Laser remanufacturing technology and its applications. Lasers in Material Processing and Manufacturing III. 2007;6825:68251N. DOI: 10.1117/

[6] De A, DebRoy T. A perspective on residual stresses in welding. Science and Technology of Welding and Joining. 2011;16(3):204-208. DOI: 10.1179/136217111X12978476537783

[7] Hu B, Richardson IM. Mechanism and possible solution for transverse solidification cracking in laser welding of high strength aluminium alloys. Materials Science and Engineering:

[8] Sheikhi M, Ghaini FM, Assadi H. Prediction of solidification cracking in pulsed laser welding of 2024 aluminum alloy. Acta Materialia. 2015;82:491-502. DOI: 10.1016/j.actamat.

Shi-yun Dong\*, Chao-qun Song, Xiang-yi Feng, Yong-jian Li and Shi-xing Yan

\*Address all correspondence to: syd422@sohu.com

National Key Laboratory for Remanufacturing, Beijing, China

Defense Industrial Press, Beijing, China; 2007

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Figure 19. Longitudinal stress of a single-pass laser clad from calculation and experiment determination.

Figure 19 shows longitudinal residual stress evolution (z direction, along the laser travel) of the midpoint in a clad layer. The simulation results are in contrast to the results obtained by experimental determination. When the phase transition is ignored, the residual longitudinal stress is close to the yield strength (around 1200 MPa). When considering the phase transition, as the temperature decreases, the maximum longitudinal stress is around 600 MPa and finally stabilized at around 200 MPa. When the stress influence on phase transition temperature is considered, the residual longitudinal stress is closer to the experimental results (394 MPa) than the other two cases. Generally speaking, phase transition has an obvious effect on the residual stresses, making it a more accurate simulation result.

#### 5. Conclusions

Laser remanufacturing is an advanced repairing method to restore the damaged parts based on laser processing, such as laser cladding and laser welding. To avoid obvious distortion and severe residual stress concentration, it is necessary to carry out residual stress analysis by numerical simulation and experimental methods. For high-strength aluminium alloy parts remanufactured by multipass NGLW process, welding passes have obvious effects on the distribution of residual stress, and its accumulation phenomenon would be exacerbated with the increase of welding passes. From the point of view of controlling the residual stress, low laser power and cross path forming strategies were suggested for their important influences on the residual stress in the laser clad layer of nodular cast iron pieces. For high-strength steel with solid-state phase transition remanufactured by laser cladding, the phase transition from austenite to martensite during the cooling process had a positive influence to reduce the magnitude of residual stresses, and a lower residual stress can be obtained using alloying powder materials with lower solid-state phase transition temperature.

## Acknowledgements

The work was supported by the key programme of the National Key Research and Development of China (Grant No. 2016YFB1100205), NSFC programme (Grant No.51705532) and Beijing Science and Technology projects (Grant No. Z161100004916009, Z16110000 1516007).

## Author details

Shi-yun Dong\*, Chao-qun Song, Xiang-yi Feng, Yong-jian Li and Shi-xing Yan

\*Address all correspondence to: syd422@sohu.com

National Key Laboratory for Remanufacturing, Beijing, China

## References

Figure 19 shows longitudinal residual stress evolution (z direction, along the laser travel) of the midpoint in a clad layer. The simulation results are in contrast to the results obtained by experimental determination. When the phase transition is ignored, the residual longitudinal stress is close to the yield strength (around 1200 MPa). When considering the phase transition, as the temperature decreases, the maximum longitudinal stress is around 600 MPa and finally stabilized at around 200 MPa. When the stress influence on phase transition temperature is considered, the residual longitudinal stress is closer to the experimental results (394 MPa) than the other two cases. Generally speaking, phase transition has an obvious effect on the residual

Figure 19. Longitudinal stress of a single-pass laser clad from calculation and experiment determination.

66 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Laser remanufacturing is an advanced repairing method to restore the damaged parts based on laser processing, such as laser cladding and laser welding. To avoid obvious distortion and severe residual stress concentration, it is necessary to carry out residual stress analysis by numerical simulation and experimental methods. For high-strength aluminium alloy parts remanufactured by multipass NGLW process, welding passes have obvious effects on the distribution of residual stress, and its accumulation phenomenon would be exacerbated with the increase of welding passes. From the point of view of controlling the residual stress, low laser power and cross path forming strategies were suggested for their important influences on the residual stress in the laser clad layer of nodular cast iron pieces. For high-strength steel with solid-state phase transition remanufactured by laser cladding, the phase transition from austenite to martensite during the cooling process had a positive influence to reduce the magnitude of residual stresses, and a lower residual stress can be obtained using alloying powder materials

stresses, making it a more accurate simulation result.

with lower solid-state phase transition temperature.

5. Conclusions


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[21] Ghaini FM, Ebrahimnia M, Gholizade S. Characteristics of cracks in heat affected zone of ductile cast iron in powder welding process. Engineering Failure Analysis. 2011;18(1):47-51.

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[22] Bhadeshia H. Phase transformations contributing to the properties of modern steels. Bulletin of the Polish Academy of Sciences Technical Sciences. 2010;58(2):255-265. DOI:

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[24] Hu LX, Dongpo W, Wenxian W, et al. Ultrasonic peening and low transition temperature electrodes used for improving the fatigue strength of welded joints. Welding in the

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[26] Francis JA, Bhadeshia H, Withers PJ. Welding residual stresses in ferritic power plant steels. Materials Science and Technology. 2007;23(9):1009-1020. DOI: 10.1179/174328407X213116

[27] Koistinen DP, Marburger RE. A general equation prescribing the extent of the austenitemartensite transition in pure iron-carbon alloys and plain carbon steels. Acta Metallurgica.

Welding in the World. 2003;47(3–4):38-43. DOI: 10.1533/weli.18.2.112.27124

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10.1016/j.matdes.2015.08.061


[21] Ghaini FM, Ebrahimnia M, Gholizade S. Characteristics of cracks in heat affected zone of ductile cast iron in powder welding process. Engineering Failure Analysis. 2011;18(1):47-51. DOI: 10.1016/j.engfailanal.2010.08.002

[9] Guo W, Li L, Dong SY, et al. Comparison of microstructure and mechanical properties of ultra-narrow gap laser and gas-metal-arc welded S960 high strength steel. Optics and

[10] Dittrich D, Schedewy R, Brenner B, et al. Laser-multi-pass-narrow-gap-welding of hot crack sensitive thick aluminum plates. Physics Procedia. 2013;41:225-233. DOI: 10.1016/j.

[11] Zhang ZH, Dong SY, Wang YJ, et al. Microstructure characteristics of thick aluminum alloy plate joints welded by fiber laser. Materials & Design. 2015;84:173-177. DOI:

[12] Zhang ZH, Dong SY, Wang YJ, et al. Study on microstructures and mechanical properties of super narrow gap joints of thick and high strength aluminum alloy plates welded by fiber laser. The International Journal of Advanced Manufacturing Technology. 2016;82(1–4):

[13] Guo W, Francis JA, Li L, et al. Residual stress distributions in laser and gas-metal-arc welded high-strength steel plates. Materials Science and Technology. 2016;32(14):1449-

[14] Elmesalamy A, Francis JA, Li L. A comparison of residual stresses in multi pass narrow gap laser welds and gas-tungsten arc welds in AISI 316L stainless steel. International Journal of Pressure Vessels and Piping. 2014;113:49-59. DOI: 10.1016/j.ijpvp.2013.11.002

[15] Phaoniam R, Shinozaki K, Yamamoto M, et al. Solidification cracking susceptibility of modified 9Cr1Mo steel weld metal during hot-wire laser welding with a narrow gap groove. Welding in the World. 2014;58(4):469-476. DOI: 10.1007/s40194-014-0130-2 [16] Jeshvaghani RA, Harati E, Shamanian M. Effects of surface alloying on microstructure and wear behavior of ductile iron surface-modified with a nickel-based alloy using shielded metal arc welding. Materials and Design. 2011;32(3):1531-1536. DOI: 10.1016/j.

[17] Pouranvari M. On the weldability of grey cast iron using nickel based filler metal. Materials & Design. 2010;31(7):3253-3258. DOI: 10.1016/j.matdes.2010.02.034

[18] Cheng X, Hu SB, Song WL, et al. Improvement in corrosion resistance of a nodular cast iron surface modified by plasma beam treatment. Applied Surface Science. 2013;286(4):

[19] Abboud JH. Microstructure and erosion characteristic of nodular cast iron surface modified by tungsten inert gas. Materials & Design. 2012;35:677-684. DOI: 10.1016/j.matdes.2011.09.029

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**Chapter 4**

**Provisional chapter**

**Residual Stress in Friction Stir Welding and Laser-**

**Residual Stress in Friction Stir Welding and Laser-**

**and Experiments**

**and Experiments**

Vincenzo Moramarco

**Abstract**

**1. Introduction**

Vincenzo Moramarco

Caterina Casavola, Alberto Cazzato and

Caterina Casavola, Alberto Cazzato and

http://dx.doi.org/10.5772/intechopen.72271

thermography, X-ray diffraction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Assisted Friction Stir Welding by Numerical Simulation**

The friction stir welding (FSW) has become an important welding technique to join materials that are difficult to weld by traditional fusion welding technology. In this technique, the material is not led to fusion, and the joint is the result of the rotation and movement along the welding line of the tool that causes softening of material due to frictional heat and the stirring of the same. In FSW, the temperature does not reach the fusion value of the materials, and this helps to decrease the residual stress values. However, due to the higher force involved in the weld and, thus, the rigid clamping used, the residual stresses are not low in general in this technique. As the presence of high residual stress values influences the post-weld mechanical properties, e.g. fatigue properties, it is important to investigate the residual stress distribution in the FSW welds. In this chapter, two numerical models that predict temperatures and residual stresses in friction stir welding and laser-assisted friction stir welding will be described. Experimental measurements of temperatures and residual stress will be carried out to validate the prediction of the models.

**Keywords:** friction stir welding, laser-assisted friction stir welding, residual stress,

**Assisted Friction Stir Welding by Numerical Simulation** 

DOI: 10.5772/intechopen.72271

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Since 1991, when the process was initially developed, friction stir welding (FSW) has become a promising welding method for joining materials that would otherwise be hardly weldable by means of the conventional welding technology [1]. This important advantage is mainly due to the FSW nature of being a solid-state welding process. In fact, the material is not

**Provisional chapter**

#### **Residual Stress in Friction Stir Welding and Laser-Assisted Friction Stir Welding by Numerical Simulation and Experiments Assisted Friction Stir Welding by Numerical Simulation and Experiments**

**Residual Stress in Friction Stir Welding and Laser-**

DOI: 10.5772/intechopen.72271

Caterina Casavola, Alberto Cazzato and Vincenzo Moramarco Vincenzo Moramarco Additional information is available at the end of the chapter

Caterina Casavola, Alberto Cazzato and

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72271

#### **Abstract**

The friction stir welding (FSW) has become an important welding technique to join materials that are difficult to weld by traditional fusion welding technology. In this technique, the material is not led to fusion, and the joint is the result of the rotation and movement along the welding line of the tool that causes softening of material due to frictional heat and the stirring of the same. In FSW, the temperature does not reach the fusion value of the materials, and this helps to decrease the residual stress values. However, due to the higher force involved in the weld and, thus, the rigid clamping used, the residual stresses are not low in general in this technique. As the presence of high residual stress values influences the post-weld mechanical properties, e.g. fatigue properties, it is important to investigate the residual stress distribution in the FSW welds. In this chapter, two numerical models that predict temperatures and residual stresses in friction stir welding and laser-assisted friction stir welding will be described. Experimental measurements of temperatures and residual stress will be carried out to validate the prediction of the models.

**Keywords:** friction stir welding, laser-assisted friction stir welding, residual stress, thermography, X-ray diffraction

### **1. Introduction**

Since 1991, when the process was initially developed, friction stir welding (FSW) has become a promising welding method for joining materials that would otherwise be hardly weldable by means of the conventional welding technology [1]. This important advantage is mainly due to the FSW nature of being a solid-state welding process. In fact, the material is not

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

fused, and the welding process is the result of the tool rotation and movement along the welding line that causes softening of material due to frictional heat and the stirring of the same. In FSW, the temperature does not reach the fusion value of the materials, and this helps to decrease the residual stress values. However, due to the higher force involved in the weld and, thus, the rigid clamping used, the residual stresses are not low in general in this technique. The constraints avoid the contraction of the materials during cooling in both longitudinal and transverse directions, thereby resulting in generation of longitudinal (parallel to welding direction) and transverse stresses (normal to welding direction). As the presence of high residual stress values influences the post-weld mechanical properties, e.g. fatigue properties, it is important to investigate the residual stress distribution in the FSW welds. Some studies have been carried out on residual stresses in FSW [1, 2–5]. In most of these, some similar conclusions can be highlighted. First, the residual stresses in FSW welds are lower than those generated during fusion welding, but they are not negligible at all. The low residual stress in the FSW welds has been attributed to the lower heat input during FSW and recrystallization accommodation of these stresses. Second, the transverse stresses are lower than the longitudinal ones, independent on tool rotation rate, traverse speed and pin diameter. Third, the distributions of the transverse and longitudinal residual stresses show an "M"-like trend across the welded joint. Moreover, in the advancing side, there is a higher residual stress peak [1].

This chapter will describe the temperature fields and residual stresses in both FSW and laserassisted friction stir welding (LAFSW), evaluated by means of experimental measurements and finite element analysis. Two numerical models will be developed and validated on the experimental results of temperatures and residual stresses. Furthermore, besides a deeper knowledge of FSW, these numerical simulations have also the aim to guide the development of the process through the research of optimal parameters minimising the amount of trial and error.

## **2. The friction stir welding process**

The FSW main idea is very simple. A rotating tool is inserted into the plates to be welded, and while rotating, it is moved along the welding line (**Figure 1**).

The tool (**Figure 1**) has two main functions: heat the workpiece and move the material to produce the joint. The heat is produced mainly by the shoulder friction with the top surface of the workpiece. This softens the material to be welded. Moreover, the shoulder prevents expulsion of the material and guides the flow of the material during welding. The tool pin, in addition to being the secondary source of heat generation, provides the stirring action to the materials of the two plates to be joined [1]. FSW is mainly a mechanical process, and the forces involved in this type of work are relevant. Thus, the workpiece is placed on a thick backing plate and is

**Figure 2.** Scheme of FSW process steps: (a) rotating tool before plunging, (b) plunging and then tool shoulder touches the work piece surface producing frictional heat, (c) rotating tool traverses along the work piece and (d) pulling out from

Residual Stress in Friction Stir Welding and Laser-Assisted Friction Stir Welding by Numerical…

http://dx.doi.org/10.5772/intechopen.72271

73

Two are the main parameters in FSW: tool rotation rate [rpm] and tool traverse speed [mm/ min]. The rotation of tool controls the stirring and mixing action of the material, and the tool translation moves the stirred material from the front to the back of the pin. Higher tool rotation rates generate an increase of temperature due of higher friction heating and result in more intense stirring and mixing of material, but the frictional coupling of tool surface with

clamped rigidly by strong fixture to eliminate any degrees of freedom.

**2.2. Welding parameters**

the workpiece.

**Figure 1.** Scheme of friction stir welding process.

During the FSW process, the material undergoes a severe plastic deformation at elevated temperature. This generates a fine and equiaxed recrystallized grain structure that produces good mechanical properties [1, 6].

#### **2.1. Process**

The welding process is divided into four main steps: rotating, plunge and dwell, translation and exit. The tool starts to rotate before the plunge phase (**Figure 2a**). During the plunge phase, the tool penetrates the material, and subsequently, it is held in position for a few seconds while still rotating (**Figure 2b**). This phase is called dwell time, and the aim of this step is to heat and thus soften the material before welding. Then the tool moves along the joint line carrying out the weld (**Figure 2c**). Finally, the tool is pulled out from the material (**Figure 2d**).

Residual Stress in Friction Stir Welding and Laser-Assisted Friction Stir Welding by Numerical… http://dx.doi.org/10.5772/intechopen.72271 73

**Figure 1.** Scheme of friction stir welding process.

fused, and the welding process is the result of the tool rotation and movement along the welding line that causes softening of material due to frictional heat and the stirring of the same. In FSW, the temperature does not reach the fusion value of the materials, and this helps to decrease the residual stress values. However, due to the higher force involved in the weld and, thus, the rigid clamping used, the residual stresses are not low in general in this technique. The constraints avoid the contraction of the materials during cooling in both longitudinal and transverse directions, thereby resulting in generation of longitudinal (parallel to welding direction) and transverse stresses (normal to welding direction). As the presence of high residual stress values influences the post-weld mechanical properties, e.g. fatigue properties, it is important to investigate the residual stress distribution in the FSW welds. Some studies have been carried out on residual stresses in FSW [1, 2–5]. In most of these, some similar conclusions can be highlighted. First, the residual stresses in FSW welds are lower than those generated during fusion welding, but they are not negligible at all. The low residual stress in the FSW welds has been attributed to the lower heat input during FSW and recrystallization accommodation of these stresses. Second, the transverse stresses are lower than the longitudinal ones, independent on tool rotation rate, traverse speed and pin diameter. Third, the distributions of the transverse and longitudinal residual stresses show an "M"-like trend across the welded joint. Moreover, in the advancing side, there is a higher

72 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

This chapter will describe the temperature fields and residual stresses in both FSW and laserassisted friction stir welding (LAFSW), evaluated by means of experimental measurements and finite element analysis. Two numerical models will be developed and validated on the experimental results of temperatures and residual stresses. Furthermore, besides a deeper knowledge of FSW, these numerical simulations have also the aim to guide the development of the process

The FSW main idea is very simple. A rotating tool is inserted into the plates to be welded, and

During the FSW process, the material undergoes a severe plastic deformation at elevated temperature. This generates a fine and equiaxed recrystallized grain structure that produces

The welding process is divided into four main steps: rotating, plunge and dwell, translation and exit. The tool starts to rotate before the plunge phase (**Figure 2a**). During the plunge phase, the tool penetrates the material, and subsequently, it is held in position for a few seconds while still rotating (**Figure 2b**). This phase is called dwell time, and the aim of this step is to heat and thus soften the material before welding. Then the tool moves along the joint line carrying out the weld (**Figure 2c**). Finally, the tool is pulled out from the material (**Figure 2d**).

through the research of optimal parameters minimising the amount of trial and error.

residual stress peak [1].

**2. The friction stir welding process**

good mechanical properties [1, 6].

**2.1. Process**

while rotating, it is moved along the welding line (**Figure 1**).

**Figure 2.** Scheme of FSW process steps: (a) rotating tool before plunging, (b) plunging and then tool shoulder touches the work piece surface producing frictional heat, (c) rotating tool traverses along the work piece and (d) pulling out from the workpiece.

The tool (**Figure 1**) has two main functions: heat the workpiece and move the material to produce the joint. The heat is produced mainly by the shoulder friction with the top surface of the workpiece. This softens the material to be welded. Moreover, the shoulder prevents expulsion of the material and guides the flow of the material during welding. The tool pin, in addition to being the secondary source of heat generation, provides the stirring action to the materials of the two plates to be joined [1]. FSW is mainly a mechanical process, and the forces involved in this type of work are relevant. Thus, the workpiece is placed on a thick backing plate and is clamped rigidly by strong fixture to eliminate any degrees of freedom.

#### **2.2. Welding parameters**

Two are the main parameters in FSW: tool rotation rate [rpm] and tool traverse speed [mm/ min]. The rotation of tool controls the stirring and mixing action of the material, and the tool translation moves the stirred material from the front to the back of the pin. Higher tool rotation rates generate an increase of temperature due of higher friction heating and result in more intense stirring and mixing of material, but the frictional coupling of tool surface with workpiece controls and governs the heating. Consequently, there is not a monotonic increase in heating with increasing tool rotation rate because the coefficient of friction at interface will change with the tool rotation rate.

**3. Temperature field in FSW and laser-assisted FSW processes**

the advancing side and the retreating side.

the numerical models that will be described later.

**3.1. Thermographic analysis of FSW and laser-assisted FSW**

trials and errors.

thermal camera.

The temperature distributions and the thermal histories have a key role in FSW and LAFSW. They determine whether the welding process will produce a good weld, influencing the residual stresses, the microstructure and the strength of welds. Several studies have measured temperatures in FSW using thermocouples [8–10], but only a few have been involved in experimental analysis using thermography [9] and still less on laser-assisted friction stir welding. Employing thermocouples, Xu et al. [8] showed that the temperature decreases with decreasing the transverse speed and increases with increasing the rotational speed. Moreover, they noted that the distribution of the temperatures in the plunge phase is correlated only to the rotational tool speed. Finally, they showed that mechanical properties such as the yield and tensile strengths of the welded plate are related to the process parameters. Increasing the rotational tool speed increases yield and tensile strengths, while the elongation decreases. Hwang et al. [9] conducted a study on temperature distribution using thermocouples and find out that the temperatures on the advancing side are slightly higher than those on the retreating side. Also, Maeda et al. [10] have applied thermocouples on both top and bottom surfaces of the work plates and have found an asymmetric temperature distribution between

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Although experimental measures are fundamental to understand the thermal phenomenon in the FSW process and LAFSW, they present some limitations, (e.g. economic costs or internal temperature measurements). For this reason, the implementation of numerical models that can predict the temperature distributions has a significant role to estimate the correct weld parameters, to improve mechanical properties of the welded joints and reduce the amount of

In the next section, the experimental setup employed to measure the temperature field on both FSW and LAFSW will be described. These experiments will be used for the validation of

A NEC H2640 infrared camera with configurable ranges between −40 and 2000°C, a resolution of 0.06°C, an accuracy of ±2°C and a spectral range of 8–13 μm has been used to acquire the temperature during the welding process. **Figure 4** shows the experimental setup of the

The angle between the FSW tool axis and the camera has been set to 30°. In order to reduce problems related to the low emissivity of aluminium and reflection, the specimen has been painted with matte black acrylic spray paint. An emissivity ε = 0.95 has been set on the camera. When the specimens have to be mechanically tested after the welding process, the central zone of the specimen has not been painted to avoid paint inclusion into the welded joint. This allows to acquire correctly the temperature near the tool, but not influencing the mechanical characteristics of the joints. However, when there is the necessity to acquire the temperatures in front of the tool, e.g. in LAFSW, the specimens have been completely painted, and bead-on-plate welds have been done. Consequently, no mechanical tests have been done on this typology

Further, the insertion depth of pin into the workpieces (in position control mode) or the downward force on the tool (in force control mode) is important for producing good welds. When these parameters are not correct, the shoulder of tool may not contact the workpiece surface or create excessive flash around the welds.

In addition, preheating or cooling can also be important for some FSW processes. For example, in materials with high melting point such as steel or titanium, the heat produced by friction and stirring may be not sufficient to soften and plasticize the material around the tool. In these cases, preheating or an additional external heating source, e.g. laser, can help the material flow and widen the process window [1].

#### **2.3. Laser-assisted friction stir welding**

In this technique, a defocused laser beam precedes the FSW tool during welding at a distance between 10 and 40 mm, increasing the temperatures reached in front of the tool and allowing an easier advancement of the same. In **Figure 3**, a scheme of the LAFSW setup has been reported.

The commonly used laser sources are diode laser, Nd:YAG fibre optic laser and CO<sup>2</sup> laser. The laser spot is activated just before the plunging stage or at the start of the welding phase of FSW [7]. The assistance of the laser in FSW is an attractive way to preheat the material with a conventional FSW setup. This technique has been employed to weld a variety of light alloys, high-strength alloys and dissimilar alloys. The higher heat input allows a better material plasticisation and grain refinements that improve the material flow and the mechanical properties. The better plasticisation should help also to reduce the downward axial force, the tool wear and increase welding speed [7].

**Figure 3.** Scheme of the LAFSW setup.

## **3. Temperature field in FSW and laser-assisted FSW processes**

workpiece controls and governs the heating. Consequently, there is not a monotonic increase in heating with increasing tool rotation rate because the coefficient of friction at interface will

74 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Further, the insertion depth of pin into the workpieces (in position control mode) or the downward force on the tool (in force control mode) is important for producing good welds. When these parameters are not correct, the shoulder of tool may not contact the workpiece

In addition, preheating or cooling can also be important for some FSW processes. For example, in materials with high melting point such as steel or titanium, the heat produced by friction and stirring may be not sufficient to soften and plasticize the material around the tool. In these cases, preheating or an additional external heating source, e.g. laser, can help the

In this technique, a defocused laser beam precedes the FSW tool during welding at a distance between 10 and 40 mm, increasing the temperatures reached in front of the tool and allowing an easier advancement of the same. In **Figure 3**, a scheme of the LAFSW setup has been

The laser spot is activated just before the plunging stage or at the start of the welding phase of FSW [7]. The assistance of the laser in FSW is an attractive way to preheat the material with a conventional FSW setup. This technique has been employed to weld a variety of light alloys, high-strength alloys and dissimilar alloys. The higher heat input allows a better material plasticisation and grain refinements that improve the material flow and the mechanical properties. The better plasticisation should help also to reduce the downward axial force, the

laser.

The commonly used laser sources are diode laser, Nd:YAG fibre optic laser and CO<sup>2</sup>

change with the tool rotation rate.

surface or create excessive flash around the welds.

material flow and widen the process window [1].

**2.3. Laser-assisted friction stir welding**

tool wear and increase welding speed [7].

**Figure 3.** Scheme of the LAFSW setup.

reported.

The temperature distributions and the thermal histories have a key role in FSW and LAFSW. They determine whether the welding process will produce a good weld, influencing the residual stresses, the microstructure and the strength of welds. Several studies have measured temperatures in FSW using thermocouples [8–10], but only a few have been involved in experimental analysis using thermography [9] and still less on laser-assisted friction stir welding. Employing thermocouples, Xu et al. [8] showed that the temperature decreases with decreasing the transverse speed and increases with increasing the rotational speed. Moreover, they noted that the distribution of the temperatures in the plunge phase is correlated only to the rotational tool speed. Finally, they showed that mechanical properties such as the yield and tensile strengths of the welded plate are related to the process parameters. Increasing the rotational tool speed increases yield and tensile strengths, while the elongation decreases. Hwang et al. [9] conducted a study on temperature distribution using thermocouples and find out that the temperatures on the advancing side are slightly higher than those on the retreating side. Also, Maeda et al. [10] have applied thermocouples on both top and bottom surfaces of the work plates and have found an asymmetric temperature distribution between the advancing side and the retreating side.

Although experimental measures are fundamental to understand the thermal phenomenon in the FSW process and LAFSW, they present some limitations, (e.g. economic costs or internal temperature measurements). For this reason, the implementation of numerical models that can predict the temperature distributions has a significant role to estimate the correct weld parameters, to improve mechanical properties of the welded joints and reduce the amount of trials and errors.

In the next section, the experimental setup employed to measure the temperature field on both FSW and LAFSW will be described. These experiments will be used for the validation of the numerical models that will be described later.

#### **3.1. Thermographic analysis of FSW and laser-assisted FSW**

A NEC H2640 infrared camera with configurable ranges between −40 and 2000°C, a resolution of 0.06°C, an accuracy of ±2°C and a spectral range of 8–13 μm has been used to acquire the temperature during the welding process. **Figure 4** shows the experimental setup of the thermal camera.

The angle between the FSW tool axis and the camera has been set to 30°. In order to reduce problems related to the low emissivity of aluminium and reflection, the specimen has been painted with matte black acrylic spray paint. An emissivity ε = 0.95 has been set on the camera.

When the specimens have to be mechanically tested after the welding process, the central zone of the specimen has not been painted to avoid paint inclusion into the welded joint. This allows to acquire correctly the temperature near the tool, but not influencing the mechanical characteristics of the joints. However, when there is the necessity to acquire the temperatures in front of the tool, e.g. in LAFSW, the specimens have been completely painted, and bead-on-plate welds have been done. Consequently, no mechanical tests have been done on this typology

In the numerical model, as the temperature does not exceed 500°C, the heat lost by radiation

The AA5754 thermo-physical material properties (i.e. thermal conductivity and specific heat) have been implemented as a function of temperature [12]. Due to a lack of literature data, the

The welding process has been simulated by a moving thermal source along the welded zone. According to Schmidt et al. [13, 14], the analytical expression used for simulating FSW tool

The *Rprobe* and *Rshoulder* are the pin and shoulder radius of the tool (Eq. (1), **Figure 6**). *Hprobe* and

plunge force, the rotational speed and the friction coefficient, respectively. The μ coefficient has been set to 0.3 according with Schmidt et al. papers [13, 14]. The remaining terms in the equation are *Rshoulder* 10.75 mm, *Rprobe* 3 mm, α = 0° and *Hprobe* 5.8 mm. The traverse speed has

The verification and validation of the previously described FSW model have been carried out on bead-on-plate welds. The studies have been regarded three steps (**Figure 7**) of the welding process. During each step, the numerical and experimental temperature data have been acquired and compared. In particular, the start phase is the welding initial step where the

)(1 <sup>+</sup> tan*α*) <sup>+</sup> *Rprobe*

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<sup>3</sup> + 3 *Rprobe*

<sup>2</sup> *Hprobe*) (1)

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, ω and μ are the normal

to 20,000 N in

density of the material has been kept constant with the temperature.

<sup>2</sup> ((*Rshoulder*

α are the pin height and the shoulder concavity angle. Moreover, *Fn*

<sup>3</sup> − *Rprobe* 3

been set to 20 cm/min, the rotational speed to 500 RPM and the normal force *Fn*

has not been considered [11].

heat generation is reported in Eq. (1):

<sup>3</sup>

accordance with the process parameters.

*3.2.2. Results and discussion for FSW model*

**Figure 6.** Tool geometry scheme.

*F* \_\_\_\_\_\_ *<sup>n</sup> Rshoulder*

*Q* = \_\_2

**Figure 4.** Thermographic experimental setup.

of specimens. Temperature measurements have been carried out on the retreating side of the welded plate because the configuration of the FSW machine prevents access to both sides.

#### **3.2. Numerical prediction of temperature fields in FSW and LAFSW**

#### *3.2.1. FSW model description*

Finite element analysis, by means of software ANSYS 14.5, has been implemented to develop a 3D transient thermal model and simulate the FSW thermal history. Due to the symmetry of the problem, a half plate model has been simulated to decrease the element number and reduce the computational time. The model has been meshed using 6000 SOLID90 elements. A thicker mesh has been employed near the welding line (**Figure 5**) to describe in a more accurate way the thermal behaviour near the tool area and to consider the higher gradient of temperature. The natural convection on the top surface and on the lateral side of the specimen has been set to 20 W/m<sup>2</sup> °C. Moreover, a convection coefficient of 300 W/m<sup>2</sup> °C has been employed to simulate the conduction between the backing plate and bottom surface of the specimen. The specific value of the convection coefficient has been employed to match the maximum temperature, reached during the weld process, between the experimental data and the numerical model.

**Figure 5.** FSW model mesh and convection coefficient.

In the numerical model, as the temperature does not exceed 500°C, the heat lost by radiation has not been considered [11].

The AA5754 thermo-physical material properties (i.e. thermal conductivity and specific heat) have been implemented as a function of temperature [12]. Due to a lack of literature data, the density of the material has been kept constant with the temperature.

The welding process has been simulated by a moving thermal source along the welded zone. According to Schmidt et al. [13, 14], the analytical expression used for simulating FSW tool heat generation is reported in Eq. (1):

$$Q = \frac{2}{3} \,\mu a \,\nu \frac{F\_v}{R\_{shudir}^2} \left( (R\_{shudir}^3 - R\_{pub}^3)(1 + \tan a) + R\_{pub}^3 + 3 \, R\_{pub}^2 \, H\_{pub} \right) \tag{1}$$

The *Rprobe* and *Rshoulder* are the pin and shoulder radius of the tool (Eq. (1), **Figure 6**). *Hprobe* and α are the pin height and the shoulder concavity angle. Moreover, *Fn* , ω and μ are the normal plunge force, the rotational speed and the friction coefficient, respectively. The μ coefficient has been set to 0.3 according with Schmidt et al. papers [13, 14]. The remaining terms in the equation are *Rshoulder* 10.75 mm, *Rprobe* 3 mm, α = 0° and *Hprobe* 5.8 mm. The traverse speed has been set to 20 cm/min, the rotational speed to 500 RPM and the normal force *Fn* to 20,000 N in accordance with the process parameters.

#### *3.2.2. Results and discussion for FSW model*

of specimens. Temperature measurements have been carried out on the retreating side of the welded plate because the configuration of the FSW machine prevents access to both sides.

Finite element analysis, by means of software ANSYS 14.5, has been implemented to develop a 3D transient thermal model and simulate the FSW thermal history. Due to the symmetry of the problem, a half plate model has been simulated to decrease the element number and reduce the computational time. The model has been meshed using 6000 SOLID90 elements. A thicker mesh has been employed near the welding line (**Figure 5**) to describe in a more accurate way the thermal behaviour near the tool area and to consider the higher gradient of temperature. The natural convection on the top surface and on the lateral side of the specimen has been set to 20 W/m<sup>2</sup> °C. Moreover, a convection coefficient of 300 W/m<sup>2</sup> °C has been employed to simulate the conduction between the backing plate and bottom surface of the specimen. The specific value of the convection coefficient has been employed to match the maximum temperature, reached during the weld process, between the experimental data and the numerical model.

**3.2. Numerical prediction of temperature fields in FSW and LAFSW**

76 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

*3.2.1. FSW model description*

**Figure 4.** Thermographic experimental setup.

**Figure 5.** FSW model mesh and convection coefficient.

The verification and validation of the previously described FSW model have been carried out on bead-on-plate welds. The studies have been regarded three steps (**Figure 7**) of the welding process. During each step, the numerical and experimental temperature data have been acquired and compared. In particular, the start phase is the welding initial step where the

**Figure 6.** Tool geometry scheme.

**Figure 7.** Location scheme of experimental measured points.

FSW tool is at about 30 mm from the edge of the plate. The middle step is in the half of the specimen, and finally, the end phase is at 30 mm from the left edge of the plate.

The graphs of the maximum temperatures versus distance from the weld line, for both experimental and numerical data, have been plotted in **Figure 8a**–**c**. The trends highlight that the estimation of the numerical model agrees with the experimental data. Indeed, in the start phase (**Figure 8a**), the maximum error between experimental and numerical data is 5.9%; in the middle step, it is 6.2% (**Figure 8b**) and in the end step (**Figure 8c**), the error is 6.3%. In order to accurately validate the numerical model, in **Figure 8d**, the temperature vs. time of the numerical model and experimental data for the point A in **Figure 7** has been reported. The trends are in good agreement though there are some small differences in the cooling phase. These differences are due to the use of heat convection instead of conduction in the numerical simulation of the contact between backing plate and specimen. Finally, the model is validated, and its results are good (37.1% of maximum error) considering all the parameters, such as coefficient of convection, friction coefficient and variability of normal force, that are difficult to consider.

**Figure 9** shows the comparison between the numerical isothermals at the top surface of the specimen and the image of the surface temperature distribution taken by the infrared camera.

The white area in this figure describes the zone of the plate where the temperature exceeds 250°C. Overall, there is a good agreement between the numerical and experimental data on the whole plate. Only in the area near the clamping system, not implemented in the FEM model, the surface temperature is slightly different.

used [12], and also in this case, only half plate has been simulated to reduce the computational time. The process parameters for the FSW are the same of the previous models. The laser power has been set to 500 W, and the distance of FSW tool-laser spot is 40 mm. A gradual thicker mesh of SOLID90 elements has been adopted near the welding line to describe more accurately the thermal behaviour where the temperature gradient is higher (**Figure 10**). The

**Figure 8.** Temperature trend in the start phase (a), in the middle phase (b) and in the end phase (c) and temperature vs.

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time of a middle point distant 16 mm from the centre line (d) for FSW.

and on the lateral side of the specimen. In this model, in different manners of the previous model, the interface between the backing plate and the specimen has been simulated

°C on the top surface

natural convection between aluminium and air has been set to 20 W/m<sup>2</sup>

**Figure 9.** Graphical comparison between numerical data and the experimental ones for FSW.

#### *3.2.3. Laser-assisted FSW model description*

The LAFSW numerical simulation is based on the previously described FSW model. However, beyond the adding of the laser source, some other improvements have been done, e.g. the adding of a backing plate to simulate in a better way the cooling phase. The same temperature-dependent thermo-physical properties of the previously described model have been

**Figure 8.** Temperature trend in the start phase (a), in the middle phase (b) and in the end phase (c) and temperature vs. time of a middle point distant 16 mm from the centre line (d) for FSW.

**Figure 9.** Graphical comparison between numerical data and the experimental ones for FSW.

FSW tool is at about 30 mm from the edge of the plate. The middle step is in the half of the

The graphs of the maximum temperatures versus distance from the weld line, for both experimental and numerical data, have been plotted in **Figure 8a**–**c**. The trends highlight that the estimation of the numerical model agrees with the experimental data. Indeed, in the start phase (**Figure 8a**), the maximum error between experimental and numerical data is 5.9%; in the middle step, it is 6.2% (**Figure 8b**) and in the end step (**Figure 8c**), the error is 6.3%. In order to accurately validate the numerical model, in **Figure 8d**, the temperature vs. time of the numerical model and experimental data for the point A in **Figure 7** has been reported. The trends are in good agreement though there are some small differences in the cooling phase. These differences are due to the use of heat convection instead of conduction in the numerical simulation of the contact between backing plate and specimen. Finally, the model is validated, and its results are good (37.1% of maximum error) considering all the parameters, such as coefficient of convection, friction coefficient and variability of normal force, that are difficult

**Figure 9** shows the comparison between the numerical isothermals at the top surface of the specimen and the image of the surface temperature distribution taken by the infrared camera. The white area in this figure describes the zone of the plate where the temperature exceeds 250°C. Overall, there is a good agreement between the numerical and experimental data on the whole plate. Only in the area near the clamping system, not implemented in the FEM

The LAFSW numerical simulation is based on the previously described FSW model. However, beyond the adding of the laser source, some other improvements have been done, e.g. the adding of a backing plate to simulate in a better way the cooling phase. The same temperature-dependent thermo-physical properties of the previously described model have been

specimen, and finally, the end phase is at 30 mm from the left edge of the plate.

78 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

to consider.

model, the surface temperature is slightly different.

**Figure 7.** Location scheme of experimental measured points.

*3.2.3. Laser-assisted FSW model description*

used [12], and also in this case, only half plate has been simulated to reduce the computational time. The process parameters for the FSW are the same of the previous models. The laser power has been set to 500 W, and the distance of FSW tool-laser spot is 40 mm. A gradual thicker mesh of SOLID90 elements has been adopted near the welding line to describe more accurately the thermal behaviour where the temperature gradient is higher (**Figure 10**). The natural convection between aluminium and air has been set to 20 W/m<sup>2</sup> °C on the top surface and on the lateral side of the specimen. In this model, in different manners of the previous model, the interface between the backing plate and the specimen has been simulated employing the conduction (**Figure 10**). A coefficient of 450 W/m<sup>2</sup> °C has been used to simulate the conduction between the backing plate (a 400 mm × 400 mm × 10 mm FE360 steel plate) and bottom surface of the specimen. The specific value of the conduction coefficient has been employed to match the maximum temperature, reached during the weld process, between the experimental data and the numerical model.

As in the previous FSW model, the welding process has been modelled as a uniform thermal source. However, while Fn is the same as the previous model, the friction coefficient μ has been set equal to 0.237 according to the experimental tests. Finally, the laser source has been simulated as a uniform heat source of 2 mm radius that moves together to FSW tool.

#### *3.2.4. Result and discussion for laser-assisted FSW model*

As in the previously shown results for FSW, also in this case, three different steps have been studied and reported in the later graphs. As in the previous model, the middle step is in the middle of the plate; instead, the start position and the end position are at 65 mm from the right and left plate edges, respectively. The temperature has been acquired at 16, 26, 36 and 50 mm from the welding line for each of the three steps. The trends of the temperature versus distance from the weld line have been plotted for numerical and experimental data in the start (**Figure 11a**), middle (**Figure 11b**) and end (**Figure 11c**) phases. Generally, these graphs show that the numerical model fits the experimental data with low errors. This is confirmed by R<sup>2</sup> value that is 0.992 in the start step, 0.999 in the middle phase and, finally, 0.999 in the end step. In **Figure 10d**, the temperature versus time of the experimental data and the numerical model has been reported. This graph represents the temperatures of a central point distant 16 mm from the welding line. In general, there is a good agreement between the numerical model and the experimental data, and compared to the previous model, the adding of the baking plate improves the cooling phase prediction (**Figure 8d** vs. **Figure 11d**).

The value of the thermal contact conductance coefficient, between the aluminium specimens and the backing plate, has been selected to fit the numerical maximum temperature in the

**Figure 11.** Temperature trend in the start phase (a), in the middle phase (b) and in the end phase (c) and temperature vs.

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In **Figure 12**, a qualitative comparison of thermal field measured experimentally and that obtained numerically has been reported. Moreover, the temperature of welded area behind the FSW tool is not correct because there is a variation of the emissivity due to the paint

**Figure 12.** Graphical comparison between the experimental data (a) and numerical results (b) for LAFSW.

point A with the experimental data.

removal and change of roughness after the transit of FSW tool.

time of a middle point distant 16 mm from the centre line (d) for LAFSW.

**Figure 10.** LAFSW scheme of model mesh.

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employing the conduction (**Figure 10**). A coefficient of 450 W/m<sup>2</sup> °C has been used to simulate the conduction between the backing plate (a 400 mm × 400 mm × 10 mm FE360 steel plate) and bottom surface of the specimen. The specific value of the conduction coefficient has been employed to match the maximum temperature, reached during the weld process, between the

80 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

As in the previous FSW model, the welding process has been modelled as a uniform thermal source. However, while Fn is the same as the previous model, the friction coefficient μ has been set equal to 0.237 according to the experimental tests. Finally, the laser source has been

As in the previously shown results for FSW, also in this case, three different steps have been studied and reported in the later graphs. As in the previous model, the middle step is in the middle of the plate; instead, the start position and the end position are at 65 mm from the right and left plate edges, respectively. The temperature has been acquired at 16, 26, 36 and 50 mm from the welding line for each of the three steps. The trends of the temperature versus distance from the weld line have been plotted for numerical and experimental data in the start (**Figure 11a**), middle (**Figure 11b**) and end (**Figure 11c**) phases. Generally, these graphs show that the numerical model fits the experimental data with low errors. This is

0.999 in the end step. In **Figure 10d**, the temperature versus time of the experimental data and the numerical model has been reported. This graph represents the temperatures of a central point distant 16 mm from the welding line. In general, there is a good agreement between the numerical model and the experimental data, and compared to the previous model, the adding of the baking plate improves the cooling phase prediction (**Figure 8d** vs.

value that is 0.992 in the start step, 0.999 in the middle phase and, finally,

simulated as a uniform heat source of 2 mm radius that moves together to FSW tool.

experimental data and the numerical model.

confirmed by R<sup>2</sup>

**Figure 11d**).

**Figure 10.** LAFSW scheme of model mesh.

*3.2.4. Result and discussion for laser-assisted FSW model*

**Figure 11.** Temperature trend in the start phase (a), in the middle phase (b) and in the end phase (c) and temperature vs. time of a middle point distant 16 mm from the centre line (d) for LAFSW.

The value of the thermal contact conductance coefficient, between the aluminium specimens and the backing plate, has been selected to fit the numerical maximum temperature in the point A with the experimental data.

In **Figure 12**, a qualitative comparison of thermal field measured experimentally and that obtained numerically has been reported. Moreover, the temperature of welded area behind the FSW tool is not correct because there is a variation of the emissivity due to the paint removal and change of roughness after the transit of FSW tool.

**Figure 12.** Graphical comparison between the experimental data (a) and numerical results (b) for LAFSW.

## **4. Residual stresses in FSW and LAFSW processes**

Residual stresses have a fundamental role in welded structures because they affect the mechanical response of parts (i.e. corrosion resistance, fatigue life and many other material characteristics). Residual stress distribution, also in FSW process where, though the heat input is lower than traditional welding techniques, the constraints applied to the parts to weld are more severe, should be deeply studied.

A Xstress 3000 G3R Stresstech X-ray diffractometer has been employed to measure the residual stresses. 30 kV and 8 mA of current have been used to power a Cr tube (λ = 0.2291 nm). An angle of 156.7° has been selected as 2θ diffraction angle, and five φ different angles (0, ±22.5, ±45°) with an oscillation of ±3° have been employed to increase the quality of the measures. The residual stresses, both longitudinal (x-axis direction) and transverse (y-axis direction), have been carried out along the centre line of the specimens, i.e. the line normal to the welding

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An uncoupled FE model has been carried out to calculate residual stress field. The first step has been to carry out a thermal analysis to simulate the temperature history related to the welding process. Then, the calculated temperature field has been used as thermal input to the mechanical model to predict the residual stresses and strains. This analysis has been implemented by means of FE software ANSYS 14.5. The thermal simulation is based on the previously presented model modified to describe the welding process of two 200 mm × 100 mm plates in butt-weld configuration. With the aim of an accurate simulation of residual thermal stresses, beyond the temperature-dependent thermophysical properties, also temperaturedependent thermomechanical properties have been used [13]. It is worth noting that enthalpy values are not considered in the simulation, as the FSW is a solid-state welding method and there is no material melting. Moreover, a multilinear isotropic hardening has been employed

In order to calculate the residual stresses, the thermal histories simulated by the FE thermal model have been inputted in the mechanical simulation. To this aim, the SOLID186 elements have been employed instead of the SOLID90 elements, keeping the same load step and mesh size. Moreover, to simulate the mechanical effect due to the compression force applied by the tool, a uniform axial pressure distributed on tool area has been included in the FE mechanical model. The mechanical constrains have been set according with experimental setup. Once that the welding simulation is concluded, the constraints are gradually released, and the

The FSW has been carried out perpendicular to the rolling direction of the AA5754 sheets. As the layout of the FSW machine does not allow an easy access to both side of the plate, the temperature measurement, residual stresses analysis and numerical simulation have been

Numerical model has been validated on both temperatures and stresses on the actual case in order to obtain reliable stress values in the simulated case. To reach this aim, the temperature field of the specimen has been measured during the FSW test by an infrared thermo-camera. In the same way, as in the Section 3.2.2, the recorded values have been compared with the data calculated by the numerical model in three different positions when maximum. The middle

line in the middle of the plate.

*4.2.1. Numerical model description*

to describe the material behaviour.

**4.2. Numerical prediction of residual stresses in FSW**

residual stresses due to FSW process have been evaluated.

executed in the retreating side of the plate.

*4.2.2. Results and discussion*

Technical literature reports numerous research papers that deal with the experimental evaluation of residual stress distribution in FSW joints. Dalle Donne et al. [15], employing different techniques, have measured residual stress distribution on FSW 2024Al-T3 and 6013Al-T6 joints. They have shown that longitudinal and transverse residual stresses have a "M"-like distribution across the weld. Moreover, the longitudinal residual stresses are higher than the transverse ones regardless on traverse speed, tool rotation speed and pin diameter. Peel et al. [3], employing synchrotron X-ray method, have measured the residual stress in FSW AA5083 welded joints. The results show that there is a tension state in the weld bead in both longitudinal and transverse residual stress directions. Furthermore, they have proven that the longitudinal stresses increase with increasing the traverse speed. Sutton et al. [16] and also Donne et al. have proven that the longitudinal is the most important component in the residual stresses analysis in FSW process and that the transverse is about 70% of the longitudinal component.

In order to have a wider understanding of the FSW process, some researchers have recently simulated the FSW process by numerical models. Moreover, these numerical models have also the aim to develop the process through the research of optimal parameters minimising the amount of trial and error. Khandkar et al. [17] have made an uncoupled thermomechanical model for some aluminium alloys and 304 L stainless steel based on torque input for calculating temperature and then residual stress. Chen et al. [18] have developed a 3D numerical model to study the thermal impact and evolution of the residual stresses in the welded joints. However, the previously described numerical simulations are only thermal or thermomechanical models in which, for example, the tool mechanical force is not considered. These effects are important and should be included into the thermomechanical simulations.

Though many works on measuring residual stresses in FSW have been done, few works have been carried out on measuring or simulating residual stresses in innovative techniques, such as LAFSW. In the next section, the measurement of residual stresses in FSW and LAFSW will be presented, and the results will be useful to validate the FSW and LAFSW numerical models.

#### **4.1. Residual stress measurements in FSW and LAFSW**

FSW and LAFSW tests were conducted on 6-mm thick 5754 H111 aluminium alloy plates, in butt joint configuration. Two rectangular plates, 200 mm × 100 mm, have been welded perpendicular to the rolling direction. The welding process is the same in the previous sections.

A Xstress 3000 G3R Stresstech X-ray diffractometer has been employed to measure the residual stresses. 30 kV and 8 mA of current have been used to power a Cr tube (λ = 0.2291 nm). An angle of 156.7° has been selected as 2θ diffraction angle, and five φ different angles (0, ±22.5, ±45°) with an oscillation of ±3° have been employed to increase the quality of the measures. The residual stresses, both longitudinal (x-axis direction) and transverse (y-axis direction), have been carried out along the centre line of the specimens, i.e. the line normal to the welding line in the middle of the plate.

#### **4.2. Numerical prediction of residual stresses in FSW**

#### *4.2.1. Numerical model description*

**4. Residual stresses in FSW and LAFSW processes**

82 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

more severe, should be deeply studied.

dinal component.

mechanical simulations.

numerical models.

sections.

**4.1. Residual stress measurements in FSW and LAFSW**

Residual stresses have a fundamental role in welded structures because they affect the mechanical response of parts (i.e. corrosion resistance, fatigue life and many other material characteristics). Residual stress distribution, also in FSW process where, though the heat input is lower than traditional welding techniques, the constraints applied to the parts to weld are

Technical literature reports numerous research papers that deal with the experimental evaluation of residual stress distribution in FSW joints. Dalle Donne et al. [15], employing different techniques, have measured residual stress distribution on FSW 2024Al-T3 and 6013Al-T6 joints. They have shown that longitudinal and transverse residual stresses have a "M"-like distribution across the weld. Moreover, the longitudinal residual stresses are higher than the transverse ones regardless on traverse speed, tool rotation speed and pin diameter. Peel et al. [3], employing synchrotron X-ray method, have measured the residual stress in FSW AA5083 welded joints. The results show that there is a tension state in the weld bead in both longitudinal and transverse residual stress directions. Furthermore, they have proven that the longitudinal stresses increase with increasing the traverse speed. Sutton et al. [16] and also Donne et al. have proven that the longitudinal is the most important component in the residual stresses analysis in FSW process and that the transverse is about 70% of the longitu-

In order to have a wider understanding of the FSW process, some researchers have recently simulated the FSW process by numerical models. Moreover, these numerical models have also the aim to develop the process through the research of optimal parameters minimising the amount of trial and error. Khandkar et al. [17] have made an uncoupled thermomechanical model for some aluminium alloys and 304 L stainless steel based on torque input for calculating temperature and then residual stress. Chen et al. [18] have developed a 3D numerical model to study the thermal impact and evolution of the residual stresses in the welded joints. However, the previously described numerical simulations are only thermal or thermomechanical models in which, for example, the tool mechanical force is not considered. These effects are important and should be included into the thermo-

Though many works on measuring residual stresses in FSW have been done, few works have been carried out on measuring or simulating residual stresses in innovative techniques, such as LAFSW. In the next section, the measurement of residual stresses in FSW and LAFSW will be presented, and the results will be useful to validate the FSW and LAFSW

FSW and LAFSW tests were conducted on 6-mm thick 5754 H111 aluminium alloy plates, in butt joint configuration. Two rectangular plates, 200 mm × 100 mm, have been welded perpendicular to the rolling direction. The welding process is the same in the previous An uncoupled FE model has been carried out to calculate residual stress field. The first step has been to carry out a thermal analysis to simulate the temperature history related to the welding process. Then, the calculated temperature field has been used as thermal input to the mechanical model to predict the residual stresses and strains. This analysis has been implemented by means of FE software ANSYS 14.5. The thermal simulation is based on the previously presented model modified to describe the welding process of two 200 mm × 100 mm plates in butt-weld configuration. With the aim of an accurate simulation of residual thermal stresses, beyond the temperature-dependent thermophysical properties, also temperaturedependent thermomechanical properties have been used [13]. It is worth noting that enthalpy values are not considered in the simulation, as the FSW is a solid-state welding method and there is no material melting. Moreover, a multilinear isotropic hardening has been employed to describe the material behaviour.

In order to calculate the residual stresses, the thermal histories simulated by the FE thermal model have been inputted in the mechanical simulation. To this aim, the SOLID186 elements have been employed instead of the SOLID90 elements, keeping the same load step and mesh size. Moreover, to simulate the mechanical effect due to the compression force applied by the tool, a uniform axial pressure distributed on tool area has been included in the FE mechanical model. The mechanical constrains have been set according with experimental setup. Once that the welding simulation is concluded, the constraints are gradually released, and the residual stresses due to FSW process have been evaluated.

The FSW has been carried out perpendicular to the rolling direction of the AA5754 sheets. As the layout of the FSW machine does not allow an easy access to both side of the plate, the temperature measurement, residual stresses analysis and numerical simulation have been executed in the retreating side of the plate.

#### *4.2.2. Results and discussion*

Numerical model has been validated on both temperatures and stresses on the actual case in order to obtain reliable stress values in the simulated case. To reach this aim, the temperature field of the specimen has been measured during the FSW test by an infrared thermo-camera. In the same way, as in the Section 3.2.2, the recorded values have been compared with the data calculated by the numerical model in three different positions when maximum. The middle step is in the half of the plate; instead, the start position and the end position are at 50 mm from the right and left plate edges, respectively. The temperature has been acquired at 16, 36, 80 and 100 mm from the welding line for each of the three steps. In **Figure 13**, the graphs of the temperature versus distance from the weld line have been plotted both for numerical and experimental data. Generally, the numerical results show a good agreement with the experimental measurements. This is confirmed by R<sup>2</sup> that is 0.997 in the start step (**Figure 13a**), 0.999 in the middle phase (**Figure 13b**) and, finally, 0.991 in the end step (**Figure 13c**). The graph of temperature vs. time for both experimental and numerical data (of the A point in **Figure 7**) has been reported in **Figure 13d**. In general, the trends of experimental and the numerical data are in good agreement with some small difference in the cooling phase as already explained previously.

The mechanical part of the model has been validated based on the X-ray diffraction stressmeasured data. In **Figure 14** the stress in the welding direction, i.e. the longitudinal stress, has been reported and compared with the numerical values. The longitudinal stress shows a "M"-like distribution across the weld, and moreover, the maximum stress value in a FSW weld is located on the edge of the bead described in **Figure 14** by the vertical grey line at 10.75 mm from the welding line.

The residual stresses in the transverse direction, for both experimental and numerical data, have been reported in **Figure 15**. The transverse residual stress values are roughly constant in the plate with a value of 60 MPa and, in agreement with Sutton et al. [16], are about 70% of the longitudinal one.

The residual stress results show a good agreement between experimental and numerical data, although some little discrepancies exist. These are located away from the welding line where the initial residual stresses of the plate are preponderant. In the numerical model, the initial

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The mechanical part of the LAFSW model is based on the thermal model described in Section 3.2.3, but to the previously described thermal model, it has been added the

state of the plate is difficult to consider and to simulate.

**Figure 14.** Numerical vs. experimental comparison of longitudinal stress in FSW.

**4.3. Numerical prediction of residual stresses in LAFSW**

**Figure 15.** Numerical vs. experimental comparison of transverse stress in FSW.

*4.3.1. Numerical model description*

**Figure 13.** Temperature trend in the start phase (a), in the middle phase (b) and in the end phase (c) and temperature vs. time of a middle point distant 16 mm from the centre line (d) for FSW.

Residual Stress in Friction Stir Welding and Laser-Assisted Friction Stir Welding by Numerical… http://dx.doi.org/10.5772/intechopen.72271 85

**Figure 14.** Numerical vs. experimental comparison of longitudinal stress in FSW.

The residual stress results show a good agreement between experimental and numerical data, although some little discrepancies exist. These are located away from the welding line where the initial residual stresses of the plate are preponderant. In the numerical model, the initial state of the plate is difficult to consider and to simulate.

#### **4.3. Numerical prediction of residual stresses in LAFSW**

#### *4.3.1. Numerical model description*

step is in the half of the plate; instead, the start position and the end position are at 50 mm from the right and left plate edges, respectively. The temperature has been acquired at 16, 36, 80 and 100 mm from the welding line for each of the three steps. In **Figure 13**, the graphs of the temperature versus distance from the weld line have been plotted both for numerical and experimental data. Generally, the numerical results show a good agreement with the experimental measure-

84 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

phase (**Figure 13b**) and, finally, 0.991 in the end step (**Figure 13c**). The graph of temperature vs. time for both experimental and numerical data (of the A point in **Figure 7**) has been reported in **Figure 13d**. In general, the trends of experimental and the numerical data are in good agree-

The mechanical part of the model has been validated based on the X-ray diffraction stressmeasured data. In **Figure 14** the stress in the welding direction, i.e. the longitudinal stress, has been reported and compared with the numerical values. The longitudinal stress shows a "M"-like distribution across the weld, and moreover, the maximum stress value in a FSW weld is located on the edge of the bead described in **Figure 14** by the vertical grey line at

The residual stresses in the transverse direction, for both experimental and numerical data, have been reported in **Figure 15**. The transverse residual stress values are roughly constant in the plate with a value of 60 MPa and, in agreement with Sutton et al. [16], are about 70% of

**Figure 13.** Temperature trend in the start phase (a), in the middle phase (b) and in the end phase (c) and temperature vs.

time of a middle point distant 16 mm from the centre line (d) for FSW.

ment with some small difference in the cooling phase as already explained previously.

that is 0.997 in the start step (**Figure 13a**), 0.999 in the middle

ments. This is confirmed by R<sup>2</sup>

10.75 mm from the welding line.

the longitudinal one.

The mechanical part of the LAFSW model is based on the thermal model described in Section 3.2.3, but to the previously described thermal model, it has been added the

**Figure 15.** Numerical vs. experimental comparison of transverse stress in FSW.

mechanical part which employs the thermal data as an input to the mechanical model. However, as explained previously, the LAFSW has been validated on a bead-on-plate configuration to capture also the temperature in front of the tool. To validate the residual stress model, it is necessary to carry out the measurements on real butt-weld configuration. In order to solve this problem, once the numerical model has been validated (see Section 3.2.4), it has been implemented on the basis of the actual welding setup simulating the joining of two 200 mm × 100 mm plates. The new temperature distribution has been inputted to the mechanical part of the model to simulate the residual stresses in the actual configuration. Finally, the experimental data have been compared to the numerical residual stress values.

The same procedure to pass the temperature data from the thermal model to the mechanical part as an input, explained in Section 4.2.1, has been also employed in this model. Also in this case, the mechanical constrains have been set according to experimental setup, and once that the welding simulation is concluded, the constraints are gradually released, and the residual stresses due to LAFSW process have been evaluated.

#### *4.3.2. Results and discussion*

In **Figure 16**, the numerical versus experimental longitudinal stress trend has been reported for the retreating side. Also in this case, the maximum stress value in the LAFSW welds is located on the edge of the bead as has been shown in **Figure 16** by a vertical grey line at 10.75 mm from the joining line.

**5. Summary and conclusions**

**Figure 17.** Numerical vs. experimental comparison of transverse stress for LAFSW.

thermally and mechanically.

trend should tend to the pre-weld value.

behaviour of the FSW joints should be considered.

In this chapter, two 3D thermo-mechanical models have been developed in order to predict temperatures and residual stresses in friction stir welding and laser-assisted FSW. These models include the mechanical action of the shoulder and the thermo-mechanical characteristic of AA5754 at different temperatures. Thermographic analysis of FSW and LAFSW process and residual stress measurement by X-ray diffraction has been carried out to validate the model

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The results for both the numerical models and experimental data show that the longitudinal stress presents a "M"-like distribution across the weld, and moreover, the maximum stress value in a FSW and LAFSW weld is located on the edge of the bead. The stress in the transverse direction is roughly constant with values between 50 and 60 MPa along all the transverse directions of the plate. Moreover, according to the observations reported by Sutton et al. [16], the transverse stress has lower values than longitudinal stress and it is about 70% of the this one. Although some little discrepancies exist between the simulated numerical values and the measured ones, the distribution of the residual stress, both longitudinal and transverse, shows a good agreement with the experimental results for both FSW and LAFSW models. However, away from the welding line, there is the maximum difference between numerical and experimental data for both longitudinal and transverse stresses. This could be explained considering that the initial residual stress in the numerical model is difficult to consider. Indeed, away from the welding line, the influence of the welding process is minimal, and the residual stress

In conclusion, the importance of the prediction and measurement of residual stress in FSW and LAFSW has been highlighted. Though the FSW is a solid-state welding process, the residual stresses are not low in general, and the influence of these stresses on the mechanical

The transverse residual stress trend has been reported in **Figure 17**. This trend shows, for both experimental and numerical data, that the transverse residual stress values are roughly constant in the plate and that there is a good agreement between numerical and experimental results. However, the effect of the laser is visible in the welded zone where there is a small increment of the residual stress values.

**Figure 16.** Numerical vs. experimental comparison of longitudinal stress for LAFSW.

Residual Stress in Friction Stir Welding and Laser-Assisted Friction Stir Welding by Numerical… http://dx.doi.org/10.5772/intechopen.72271 87

**Figure 17.** Numerical vs. experimental comparison of transverse stress for LAFSW.

#### **5. Summary and conclusions**

mechanical part which employs the thermal data as an input to the mechanical model. However, as explained previously, the LAFSW has been validated on a bead-on-plate configuration to capture also the temperature in front of the tool. To validate the residual stress model, it is necessary to carry out the measurements on real butt-weld configuration. In order to solve this problem, once the numerical model has been validated (see Section 3.2.4), it has been implemented on the basis of the actual welding setup simulating the joining of two 200 mm × 100 mm plates. The new temperature distribution has been inputted to the mechanical part of the model to simulate the residual stresses in the actual configuration. Finally, the experimental data have been compared to the numerical

86 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

The same procedure to pass the temperature data from the thermal model to the mechanical part as an input, explained in Section 4.2.1, has been also employed in this model. Also in this case, the mechanical constrains have been set according to experimental setup, and once that the welding simulation is concluded, the constraints are gradually released, and the residual

In **Figure 16**, the numerical versus experimental longitudinal stress trend has been reported for the retreating side. Also in this case, the maximum stress value in the LAFSW welds is located on the edge of the bead as has been shown in **Figure 16** by a vertical grey line at

The transverse residual stress trend has been reported in **Figure 17**. This trend shows, for both experimental and numerical data, that the transverse residual stress values are roughly constant in the plate and that there is a good agreement between numerical and experimental results. However, the effect of the laser is visible in the welded zone where there is a small

residual stress values.

*4.3.2. Results and discussion*

10.75 mm from the joining line.

increment of the residual stress values.

**Figure 16.** Numerical vs. experimental comparison of longitudinal stress for LAFSW.

stresses due to LAFSW process have been evaluated.

In this chapter, two 3D thermo-mechanical models have been developed in order to predict temperatures and residual stresses in friction stir welding and laser-assisted FSW. These models include the mechanical action of the shoulder and the thermo-mechanical characteristic of AA5754 at different temperatures. Thermographic analysis of FSW and LAFSW process and residual stress measurement by X-ray diffraction has been carried out to validate the model thermally and mechanically.

The results for both the numerical models and experimental data show that the longitudinal stress presents a "M"-like distribution across the weld, and moreover, the maximum stress value in a FSW and LAFSW weld is located on the edge of the bead. The stress in the transverse direction is roughly constant with values between 50 and 60 MPa along all the transverse directions of the plate. Moreover, according to the observations reported by Sutton et al. [16], the transverse stress has lower values than longitudinal stress and it is about 70% of the this one.

Although some little discrepancies exist between the simulated numerical values and the measured ones, the distribution of the residual stress, both longitudinal and transverse, shows a good agreement with the experimental results for both FSW and LAFSW models. However, away from the welding line, there is the maximum difference between numerical and experimental data for both longitudinal and transverse stresses. This could be explained considering that the initial residual stress in the numerical model is difficult to consider. Indeed, away from the welding line, the influence of the welding process is minimal, and the residual stress trend should tend to the pre-weld value.

In conclusion, the importance of the prediction and measurement of residual stress in FSW and LAFSW has been highlighted. Though the FSW is a solid-state welding process, the residual stresses are not low in general, and the influence of these stresses on the mechanical behaviour of the FSW joints should be considered.

As a future development of this work, the authors are improving the described models and Eq. (1) to consider and predict the differences in the temperatures and, thus, in the residual stresses between advancing and retreating sides. These differences change in accordance to the traverse and the rotating tool speeds due to the concordance and discordance between the travel and the rotating tool directions in, respectively, the advancing and the retreating sides.

[10] Maedaa M, Liub H, Fujiib H, Shibayanagib T. Temperature field in the vicinity of FSW-tool during friction stir welding of Aluminium alloys. Welding in the World.

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[11] Chao YJ, Qi X, Tang W. Heat transfer in friction stir welding—Experimental and numerical studies. Journal of Manufacturing Science and Engineering. 2003;**125**(1):138-145 [12] Khanna SK, Long X, Porter WD, Wang H, Liu CK, Radovic M, Lara-Curzio E. Residual stresses in spot welded new generation aluminium alloys part A–thermophysical and thermomechanical properties of 6111 and 5754 aluminium alloys. Science and

[13] Schmidt HB, Hattel JH. Thermal modelling of friction stir welding. Scripta Materialia.

[14] Schmidt H, Hattel J, Wert J. An analytical model for the heat generation in friction stir welding. Modelling and Simulation in Materials Science and Engineering. 2004;**12**(1):143

[15] Dalle Donne C, Lima E, Wegener J, Pyzalla A, Buslaps T. Investigations on residual stresses in friction stir welds. In: 3rd International Symposium on Friction Stir Welding;

[16] Sutton MA, Reynolds AP, Wang DQ, Hubbard CRA. Study of residual stresses and microstructure in 2024-T3 aluminum friction stir butt welds. Journal of Engineering

[17] Khandkar MZH, Khan JA, Reynolds AP, Sutton MA. Predicting residual thermal stresses in friction stir welded metals. Journal of Materials Processing Technology.

[18] Chen C, Kovacevic R. Finite element modeling of friction stir welding – Thermal and thermomechanical analysis. International Journal of Machine Tools and Manufacture.

27-28 September 2001; Kobe (Japan). TWI, Cambridge (UK); 2001. pp. 1-10

Technology of Welding & Joining. 2013;**10**(1):82-87

Materials and Technology. 2002;**124**(2):215-221

2005;**49**(3):69-75

2008;**58**(5):332-337

2006;**174**(1):195-203

2003;**43**(13):1319-1326

## **Author details**

Caterina Casavola\*, Alberto Cazzato and Vincenzo Moramarco

\*Address all correspondence to: casavola@poliba.it

Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Bari, Italy

## **References**


[10] Maedaa M, Liub H, Fujiib H, Shibayanagib T. Temperature field in the vicinity of FSW-tool during friction stir welding of Aluminium alloys. Welding in the World. 2005;**49**(3):69-75

As a future development of this work, the authors are improving the described models and Eq. (1) to consider and predict the differences in the temperatures and, thus, in the residual stresses between advancing and retreating sides. These differences change in accordance to the traverse and the rotating tool speeds due to the concordance and discordance between the travel and the rotating tool directions in, respectively, the advancing and the retreating sides.

Department of Mechanics, Mathematics and Management, Polytechnic University of Bari,

[1] Mishra RS, Ma ZY. Friction stir welding and processing. Materials Science and

[2] Reynolds AP, Tang W, Gnaupel-Herold T, Prask H. Structure, properties, and residual stress of 304L stainless steel friction stir welds. Scripta Materialia. 2003;**48**(9):1289-1294

[3] Peel M, Steuwer A, Preuss M, Withers PJ. Microstructure, mechanical properties and residual stresses as a function of welding speed in aluminium AA5083 friction stir welds.

[4] Prime MB, Gnäupel-Herold T, Baumann JA, Lederich RJ, Bowden DM, Sebring RJ. Residual stress measurements in a thick, dissimilar aluminum alloy friction stir weld.

[5] Darvazi AR, Iranmanesh M. Prediction of asymmetric transient temperature and longitudinal residual stress in friction stir welding of 304L stainless steel. Materials & Design.

[6] Rhodes CG, Mahoney MW, Bingel WH, Spurling RA, Bampton CC. Effects of friction stir welding on microstructure of 7075 aluminum. Scripta Materialia. 1997;**36**(1):69-75 [7] Padhy G, Wu C, Gao S. Auxiliary energy assisted friction stir welding – Status review.

[8] Xu W, Liu J, Luan G, Dong C. Temperature evolution, microstructure and mechanical properties of friction stir welded thick 2219-O aluminum alloy joints. Materials &

[9] Hwang YM, Kang ZW, Chiou YC, Hsu HH. Experimental study on temperature distributions within the workpiece during friction stir welding of aluminum alloys.

International Journal of Machine Tools and Manufacture. 2008;**48**(7-8):778-787

Science and Technology of Welding and Joining. 2015;**20**(8):631-649

Caterina Casavola\*, Alberto Cazzato and Vincenzo Moramarco

88 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

\*Address all correspondence to: casavola@poliba.it

Engineering: R: Reports. 2005;**50**(1-2):1-78

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**Author details**

Bari, Italy

**References**


**Chapter 5**

**Provisional chapter**

**Residual Stress Pattern Prediction in Spray Transfer**

**Residual Stress Pattern Prediction in Spray Transfer** 

Jon Ander Esnaola, Ibai Ulacia,

and Done Ugarte

**Abstract**

thick T-joint welds.

**1. Introduction**

http://dx.doi.org/10.5772/intechopen.72134

Arkaitz Lopez-Jauregi and Done Ugarte

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Jon Ander Esnaola, Ibai Ulacia, Arkaitz Lopez-Jauregi

**Multipass Welding by Means of Numerical Simulation**

One of the main problems of gas metal arc welding (GMAW) process is the generation of residual stresses (RS), which has a direct impact on the mechanical performance of welded components. Nevertheless, RS pattern prediction is complex and requires the simulation of the welding process. Consequently, most of the currently used dimensioning approaches do not consider RS, leading to design oversized structures. This fact is especially relevant in big structures since it generates high material, manufacturing and product transportation costs. Nowadays, there are different numerical methods to predict the RS generated in GMAW process, being Goldak's method one of the most widely used model. However, the use of these methods during the design process is limited, as they require experimentally defining many parameters. Alternatively, in this chapter, a new methodology to define the heat source energy based on the spray welding physics is exposed. The experimental validation of the methodology conducted for a multipass butt weld case shows good agreement in both the temperature pattern (9.16% deviation) and the RS pattern (42 MPa deviation). Finally, the proposed methodology is extended to analyse the influence of the thickness and the number of passes in the RS pattern of

**Keywords:** multipass welding, analytic procedure, finite element method, equivalent

Gas metal arc welding (GMAW, also referred as metal inert gas (MIG)), is one of the most extended welding techniques in metal manufacturing industry [1, 2]. Particularly, multipass

heat source, temperature distribution, residual stresses

**Multipass Welding by Means of Numerical Simulation**

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.72134

#### **Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical Simulation Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical Simulation**

DOI: 10.5772/intechopen.72134

Jon Ander Esnaola, Ibai Ulacia, Arkaitz Lopez-Jauregi and Done Ugarte Jon Ander Esnaola, Ibai Ulacia, Arkaitz Lopez-Jauregi and Done Ugarte

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72134

#### **Abstract**

One of the main problems of gas metal arc welding (GMAW) process is the generation of residual stresses (RS), which has a direct impact on the mechanical performance of welded components. Nevertheless, RS pattern prediction is complex and requires the simulation of the welding process. Consequently, most of the currently used dimensioning approaches do not consider RS, leading to design oversized structures. This fact is especially relevant in big structures since it generates high material, manufacturing and product transportation costs. Nowadays, there are different numerical methods to predict the RS generated in GMAW process, being Goldak's method one of the most widely used model. However, the use of these methods during the design process is limited, as they require experimentally defining many parameters. Alternatively, in this chapter, a new methodology to define the heat source energy based on the spray welding physics is exposed. The experimental validation of the methodology conducted for a multipass butt weld case shows good agreement in both the temperature pattern (9.16% deviation) and the RS pattern (42 MPa deviation). Finally, the proposed methodology is extended to analyse the influence of the thickness and the number of passes in the RS pattern of thick T-joint welds.

**Keywords:** multipass welding, analytic procedure, finite element method, equivalent heat source, temperature distribution, residual stresses

#### **1. Introduction**

Gas metal arc welding (GMAW, also referred as metal inert gas (MIG)), is one of the most extended welding techniques in metal manufacturing industry [1, 2]. Particularly, multipass

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

welding in spray transfer mode presents uniform metal transfer to workpiece at high rate, together with high arc stability and low weld spatter. For this reason, spray transfer mode is especially adequate to join thick plate structures [3, 4].

butt weld [12]. It can be observed that from instant *t*

Then, during the cooling down process from instant *t*

limit its expansion in *x* direction up to *ε<sup>T</sup>*

the selected parameters [13].

yielding at *σ<sup>1</sup>*

yields at *σ<sup>4</sup>*

RS pattern [22].

*0* to *t2*

Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical…

*2*

*2*

to instant *t*

.

welding torch passes nearby trying to expand. The constraints of the surrounding material

thermal expansion is limited by the surrounding material. Consequently, tensile stress that

**Figure 2** compares the RS pattern variation near the weld toe for a butt weld case depending on the plate size and welding deposition rate. It can be observed that the distribution and magnitude of tractive and compressive stresses completely changes when modifying any of

Due to the complexity of the multiphysics phenomena that take place in the RS generation of welded structures, the estimation of their magnitude and distribution is not straight forward [14, 15]. In addition, nowadays accurate experimental measurement of RS presents some limitations as experimental methods are not fully reliable and imply huge time and economic cost [9, 16, 17]. Consequently, most of the currently used welding dimensioning approaches do not consider RS. Therefore, current welded designs are in general conservative, leading to oversized structures. This fact is especially relevant in big structures since it generates high material, manufacturing and product transportation costs. As a simplified manner to take into

However, nowadays the RS distribution and magnitude can be estimated by means of numerical simulation [14, 21]. As already explained, the RS generation in welded plates is very dependent on the thermal pattern history along the whole component as well as the materials thermomechanical properties. Thus, the procedure used to model the moving heat source during the welding process simulation is determinant in the accuracy of the predicted

Different approaches to model the heat source energy can be found in the literature. In the early 1940s, Rosenthal presented an analytic model to consider heat source at a quasi-steady regime, concentrated in a moving point [23]. Although the model could be applied in simple geometries, it was not suitable to be used at plates over certain thickness [2, 6]. At the end of

**Figure 2.** Transversal RS distribution near the weld toe of a butt weld: (a) under high deposition speed in a big plate, (b)

high deposition speed in a short plate and (c) low deposition speed in a big plate [13].

account RS, some authors consider the yield stress value as RS magnitude [18–20].

*2*

and suffering elastic-plastic deformation *εep*

is generated suffering plastic deformation up to *σ<sup>5</sup>*

, the material is heated up as the

http://dx.doi.org/10.5772/intechopen.72134

, the elastic recovery from

up to *σ<sup>2</sup>*

.

93

, and the initially stress-free material is compressed

*5*

at high temperature *T2*

Nevertheless, one of the main drawbacks of welded structures is the generation of residual stresses (RS), which may compromise their mechanical performance. RS are generated due to high thermal cycles in the welding process where non-uniform heating and cooling occur [5, 6]. High thermal gradients generate inhomogeneous thermal expansion constrained by the surrounding material, which presents temperature-dependent mechanical properties. This way, the material at lower temperature suffers lower thermal expansion and presents higher strength. Thus, they also limit the expansion of adjacent areas at higher temperature which, in addition, present lower strength and, consequently, can suffer compressive plastic deformation. Finally, during the cooling down process, the areas yielded at high temperature constrain the elastic springback of not yielded areas generating internal stresses that remain on the welded component. This RS can be tractive or compressive depending on the constraints transmitted from the adjacent areas. As a result, tensile and compressive areas as well as the magnitude of the final RS pattern depend on several factors such as structural dimension, welding sequence, preparation of the weld groove, mechanical restraints or the number of weld passes [7–9]. In general, tensile residual stresses are considered detrimental because they increase the susceptibility of the welded joint to fatigue damage, stress-cracking corrosion (SCC), structural buckling and brittle fracture [6, 10, 11].

**Figure 1** shows an example of the RS evolution of a determined point (*dx, dy*) of a plate near the weld seam depending on the thermal history subjected during the welding process of a

**Figure 1.** Schematic of the RS generation in a generic point nearby the welded seam [12].

butt weld [12]. It can be observed that from instant *t 0* to *t2* , the material is heated up as the welding torch passes nearby trying to expand. The constraints of the surrounding material limit its expansion in *x* direction up to *ε<sup>T</sup> 2* , and the initially stress-free material is compressed yielding at *σ<sup>1</sup>* and suffering elastic-plastic deformation *εep 2* at high temperature *T2* up to *σ<sup>2</sup>* . Then, during the cooling down process from instant *t 2* to instant *t 5* , the elastic recovery from thermal expansion is limited by the surrounding material. Consequently, tensile stress that yields at *σ<sup>4</sup>* is generated suffering plastic deformation up to *σ<sup>5</sup>* .

welding in spray transfer mode presents uniform metal transfer to workpiece at high rate, together with high arc stability and low weld spatter. For this reason, spray transfer mode is

Nevertheless, one of the main drawbacks of welded structures is the generation of residual stresses (RS), which may compromise their mechanical performance. RS are generated due to high thermal cycles in the welding process where non-uniform heating and cooling occur [5, 6]. High thermal gradients generate inhomogeneous thermal expansion constrained by the surrounding material, which presents temperature-dependent mechanical properties. This way, the material at lower temperature suffers lower thermal expansion and presents higher strength. Thus, they also limit the expansion of adjacent areas at higher temperature which, in addition, present lower strength and, consequently, can suffer compressive plastic deformation. Finally, during the cooling down process, the areas yielded at high temperature constrain the elastic springback of not yielded areas generating internal stresses that remain on the welded component. This RS can be tractive or compressive depending on the constraints transmitted from the adjacent areas. As a result, tensile and compressive areas as well as the magnitude of the final RS pattern depend on several factors such as structural dimension, welding sequence, preparation of the weld groove, mechanical restraints or the number of weld passes [7–9]. In general, tensile residual stresses are considered detrimental because they increase the susceptibility of the welded joint to fatigue damage, stress-cracking corrosion (SCC), structural buckling

**Figure 1** shows an example of the RS evolution of a determined point (*dx, dy*) of a plate near the weld seam depending on the thermal history subjected during the welding process of a

**Figure 1.** Schematic of the RS generation in a generic point nearby the welded seam [12].

especially adequate to join thick plate structures [3, 4].

92 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

and brittle fracture [6, 10, 11].

**Figure 2** compares the RS pattern variation near the weld toe for a butt weld case depending on the plate size and welding deposition rate. It can be observed that the distribution and magnitude of tractive and compressive stresses completely changes when modifying any of the selected parameters [13].

Due to the complexity of the multiphysics phenomena that take place in the RS generation of welded structures, the estimation of their magnitude and distribution is not straight forward [14, 15]. In addition, nowadays accurate experimental measurement of RS presents some limitations as experimental methods are not fully reliable and imply huge time and economic cost [9, 16, 17]. Consequently, most of the currently used welding dimensioning approaches do not consider RS. Therefore, current welded designs are in general conservative, leading to oversized structures. This fact is especially relevant in big structures since it generates high material, manufacturing and product transportation costs. As a simplified manner to take into account RS, some authors consider the yield stress value as RS magnitude [18–20].

However, nowadays the RS distribution and magnitude can be estimated by means of numerical simulation [14, 21]. As already explained, the RS generation in welded plates is very dependent on the thermal pattern history along the whole component as well as the materials thermomechanical properties. Thus, the procedure used to model the moving heat source during the welding process simulation is determinant in the accuracy of the predicted RS pattern [22].

Different approaches to model the heat source energy can be found in the literature. In the early 1940s, Rosenthal presented an analytic model to consider heat source at a quasi-steady regime, concentrated in a moving point [23]. Although the model could be applied in simple geometries, it was not suitable to be used at plates over certain thickness [2, 6]. At the end of

**Figure 2.** Transversal RS distribution near the weld toe of a butt weld: (a) under high deposition speed in a big plate, (b) high deposition speed in a short plate and (c) low deposition speed in a big plate [13].

1960s, Pavelic et al. [24] proposed a procedure to model as a moving circular heat input area with a Gaussian distribution of the heat intensity. The model considers that all the heat supplies occur through the surface, which also limits its use over certain plate thickness.

order to solve accuracy limitations. This method, besides the computational cost, requires the definition of many parameters such as the arc plasma viscosity, the arc plasma temperature, the surface tension coefficient, etc. The complexity to determine those parameters together

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95

In general, the presented methods are sometimes imprecise or require defining experimentally many parameters, which limit their use during the design process. As an alternative, in this chapter an analytic procedure to calculate the welding process key parameters is presented. The procedure is based on the welding physics for spray transfer, and the key parameters are analytically estimated. Thus, the procedure feeds the FEM numerical model without the need to conduct experimental process measurements, which enables to be used as a predictive tool. The proposed procedure has been experimentally validated. First, the heat source model has been verified, and then the temperature pattern and the residual stress pattern predicted by the FEM model have been compared against experimental measurements. The main contribution of the presented procedure is that it provides an agreement between the accuracy of the model in the residual stress estimation, the computational cost and the model definition effort. In addition, the new procedure does not require any preliminary experimental welding

Finally, the proposed procedure is extended to a T-joint configuration with 70% penetration in a thickness range from 20 to 60 mm to determine the influence of the thickness and number

The proposed methodology to predict RS consists of two steps. First, the process key parameters, which are the heat source and the welding speed, are defined. For that purpose, an analytic procedure to determine the heat source and welding speed that ensure proper spray transfer welding is developed. Then, an uncoupled thermomechanical FEM model is used to simulate the welding process. This numerical model is fed from the previously defined

The multipass spray transfer welding numerical model requires the determination of the heat source energy and the welding speed as input data. Both parameters are estimated based on

**Figure 4** shows the detail of the configuration of the welding torch, where *Larc* is the arc length, *L*CTW is the contact to work distance and *L*SO is the wire extension or electrical stick-out length.

The heat source energy is the thermal energy provided to the weld bead along the welding process. This parameter is calculated considering the efficiency in the transformation of the

with the high computational cost limits the use of this technique.

test data, which make it suitable to be used in the design process.

of passes in the RS pattern.

process key parameters.

*2.1.1. Heat source energy*

**2. New methodology to predict RS**

**2.1. Determination of process key parameters**

the welding torch configuration and the cross section to weld.

In 1984, Goldak et al. presented an alternative heat source model, known as the double ellipsoidal method or Goldak's method, which is one of the most extended methods nowadays [25–30]. This method considers a double ellipsoidal power density distribution (**Figure 3**). This method presents good accuracy even though it requires experimental run trials to measure the weld pool. These measurements should be conducted during or after finishing the welding process, which limits its use as a predictive tool [31]. In addition, the measurement of the weld pool for certain configurations such as T-joints or L-joints is geometrically limited. In 1997, Wahab et al. [32] developed some analytical equations based on experimental measurements to predict the weld pool depending on the applied voltage, current intensity, welding speed and CO2 %. Nevertheless, even these analytical equations enable the use of Goldak's method as a predictive tool, it still presents a lack of precision with reported stress deviations higher than 100 MPa [10].

In 1998, Brickstad et al. [7] proposed a heat source modelling technique where the current and voltage applied in the welding process were used as input parameters. The technique was implemented to simulate a case study of a multipass butt weld of stainless steel pipes by means of a two-dimensional axisymmetric numeric model. The validity of the model was not evaluated against experimental data. In 2007, Barsoum et al. [33] implemented the same technique also in a three-dimensional model to simulate a multipass welding of a tubular joint. The results obtained in the experimental validation showed that even the temperature prediction for a single pass butt weld was accurate, the model presents a lack of precision for multipass cases. In addition, in this method the calculated temperature histories are set into agreement with experimental data measured by thermocouples. If there is no experimental data available, the welding parameters are adjusted to achieve a reasonable molten zone size and distance to the HAZ from the fusion zone boundary [30].

Finally, from 2007 to 2009, Hu et al. [34–36] presented several works were a 3D mathematical model was implemented to represent the physics of the plasma arc and the metal transfer in

**Figure 3.** Schematic of the heat source modelization with Goldak's double-ellipsoidal method [25].

order to solve accuracy limitations. This method, besides the computational cost, requires the definition of many parameters such as the arc plasma viscosity, the arc plasma temperature, the surface tension coefficient, etc. The complexity to determine those parameters together with the high computational cost limits the use of this technique.

In general, the presented methods are sometimes imprecise or require defining experimentally many parameters, which limit their use during the design process. As an alternative, in this chapter an analytic procedure to calculate the welding process key parameters is presented. The procedure is based on the welding physics for spray transfer, and the key parameters are analytically estimated. Thus, the procedure feeds the FEM numerical model without the need to conduct experimental process measurements, which enables to be used as a predictive tool. The proposed procedure has been experimentally validated. First, the heat source model has been verified, and then the temperature pattern and the residual stress pattern predicted by the FEM model have been compared against experimental measurements. The main contribution of the presented procedure is that it provides an agreement between the accuracy of the model in the residual stress estimation, the computational cost and the model definition effort. In addition, the new procedure does not require any preliminary experimental welding test data, which make it suitable to be used in the design process.

Finally, the proposed procedure is extended to a T-joint configuration with 70% penetration in a thickness range from 20 to 60 mm to determine the influence of the thickness and number of passes in the RS pattern.

## **2. New methodology to predict RS**

1960s, Pavelic et al. [24] proposed a procedure to model as a moving circular heat input area with a Gaussian distribution of the heat intensity. The model considers that all the heat sup-

In 1984, Goldak et al. presented an alternative heat source model, known as the double ellipsoidal method or Goldak's method, which is one of the most extended methods nowadays [25–30]. This method considers a double ellipsoidal power density distribution (**Figure 3**). This method presents good accuracy even though it requires experimental run trials to measure the weld pool. These measurements should be conducted during or after finishing the welding process, which limits its use as a predictive tool [31]. In addition, the measurement of the weld pool for certain configurations such as T-joints or L-joints is geometrically limited. In 1997, Wahab et al. [32] developed some analytical equations based on experimental measurements to predict the weld pool depending on the applied voltage, current intensity, welding speed and CO2

Nevertheless, even these analytical equations enable the use of Goldak's method as a predictive tool, it still presents a lack of precision with reported stress deviations higher than 100 MPa [10]. In 1998, Brickstad et al. [7] proposed a heat source modelling technique where the current and voltage applied in the welding process were used as input parameters. The technique was implemented to simulate a case study of a multipass butt weld of stainless steel pipes by means of a two-dimensional axisymmetric numeric model. The validity of the model was not evaluated against experimental data. In 2007, Barsoum et al. [33] implemented the same technique also in a three-dimensional model to simulate a multipass welding of a tubular joint. The results obtained in the experimental validation showed that even the temperature prediction for a single pass butt weld was accurate, the model presents a lack of precision for multipass cases. In addition, in this method the calculated temperature histories are set into agreement with experimental data measured by thermocouples. If there is no experimental data available, the welding parameters are adjusted to achieve a reasonable molten zone size

Finally, from 2007 to 2009, Hu et al. [34–36] presented several works were a 3D mathematical model was implemented to represent the physics of the plasma arc and the metal transfer in

**Figure 3.** Schematic of the heat source modelization with Goldak's double-ellipsoidal method [25].

and distance to the HAZ from the fusion zone boundary [30].

%.

plies occur through the surface, which also limits its use over certain plate thickness.

94 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

The proposed methodology to predict RS consists of two steps. First, the process key parameters, which are the heat source and the welding speed, are defined. For that purpose, an analytic procedure to determine the heat source and welding speed that ensure proper spray transfer welding is developed. Then, an uncoupled thermomechanical FEM model is used to simulate the welding process. This numerical model is fed from the previously defined process key parameters.

#### **2.1. Determination of process key parameters**

The multipass spray transfer welding numerical model requires the determination of the heat source energy and the welding speed as input data. Both parameters are estimated based on the welding torch configuration and the cross section to weld.

**Figure 4** shows the detail of the configuration of the welding torch, where *Larc* is the arc length, *L*CTW is the contact to work distance and *L*SO is the wire extension or electrical stick-out length.

#### *2.1.1. Heat source energy*

The heat source energy is the thermal energy provided to the weld bead along the welding process. This parameter is calculated considering the efficiency in the transformation of the

**Figure 4.** Schematic of the welding torch configuration (adapted from [1]).

consumed electric power into heat power. This energy lose is caused by the wire resistance, heat losses to the surrounding, the energy consumed in the gas or flux heating, etc. Thus, efficiency can vary between 0.66 and 0.85 depending on the used facility [1]. Therefore, the supplied heat power can be determined with Eq. (1):

$$P\_{\rm TH} = \eta \cdot I \cdot V\_{\rm tot} \tag{1}$$

where *R*arc is the arc electric resistance, *<sup>a</sup>*<sup>0</sup>

between 0.8 and 1.6 mm (adapted from [37]).

*Vso* = *ρ<sup>s</sup>*

welding speed can be determined by Eq. (6):

where *vW* is the wire feed speed, *As*

The voltage drop across the electrode is calculated with Eq. (4):

is the resistivity of the stick-out material and *Aso*

*Aso* <sup>⋅</sup> *<sup>v</sup>*<sup>W</sup> <sup>=</sup> *As* <sup>⋅</sup> *vs* <sup>→</sup> *vs* <sup>=</sup> *Aso* <sup>⋅</sup> *<sup>v</sup>* \_\_\_\_\_\_\_W

(**Figure 4**) is determined with Eq. (5):

*Lso* = *L*CTW − *L*arc (5)

The welding speed is the velocity the welding torch advances along the welding bead. It is assumed that GMAW process fulfils the mass conservation law. Thus, wire feed speed and

There are two approaches to model the wire feed rate for constant voltage welding used in GMAW, as suggested by Palani et al. (2007) [39]. The first approach consists in fitting the

*As*

is the weld pass cross section and *vs*

according to Lesnewich [48].

The stick-out length *Lso*

*2.1.2. Welding speed*

where *ρ<sup>s</sup>*

is the anode/cathode voltage drop and *a*<sup>1</sup>

Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical…

*I* (4)

is the cross-section area of the wire.

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97

potential gradient. The minimum *L*arc to ensure spray transfer has to be higher than 4.5 mm

**Figure 5.** Globular mode to spray mode transition current depending on the use of shielding gas for wire diameter range

*L* \_\_\_*so Aso* is the arc

(6)

is the welding speed.

where *P*TH is the supplied thermal power, *η* is the heat transformation efficiency, *I* is the current intensity and *V*Tot is the total voltage.

In order to ensure proper spray transfer, the transition welding intensity between globular and spray transfer modes is determined first. This parameter is dependent on the used shielding gas and filler wire diameter. Thus, using current intensity values higher than the transition current intensity limit value provides proper spray transfer. **Figure 5** represents the correlations proposed by Norrish [37] to determine the globular-to-spray mode transition current depending on the shielding gas for a wire diameter range between 0.8 and 1.6 mm.

The total voltage drop *V*Tot is approximately the addition of the voltage drop in the electric stick-out length *Vso* and the voltage drop across the arc *V*arc (2) [1].

$$V\_{\rm rot} = V\_{\rm av} + V\_{\rm so} \tag{2}$$

The arc voltage drop can be obtained with Eq. (3):

$$V\_{\rm acc} = \, I \cdot \mathbb{R}\_{\rm acc} + a\_0 + a\_1 \cdot L\_{\rm acc} \tag{3}$$

**Figure 5.** Globular mode to spray mode transition current depending on the use of shielding gas for wire diameter range between 0.8 and 1.6 mm (adapted from [37]).

where *R*arc is the arc electric resistance, *<sup>a</sup>*<sup>0</sup> is the anode/cathode voltage drop and *a*<sup>1</sup> is the arc potential gradient. The minimum *L*arc to ensure spray transfer has to be higher than 4.5 mm according to Lesnewich [48].

The voltage drop across the electrode is calculated with Eq. (4):

$$V\_{so} = \rho\_s \frac{L\_{ss}}{A\_{ss}} I \tag{4}$$

where *ρ<sup>s</sup>* is the resistivity of the stick-out material and *Aso* is the cross-section area of the wire.

The stick-out length *Lso* (**Figure 4**) is determined with Eq. (5):

$$L\_{\rm so} = L\_{\rm CTW} - L\_{\rm acc} \tag{5}$$

#### *2.1.2. Welding speed*

consumed electric power into heat power. This energy lose is caused by the wire resistance, heat losses to the surrounding, the energy consumed in the gas or flux heating, etc. Thus, efficiency can vary between 0.66 and 0.85 depending on the used facility [1]. Therefore, the

*P*TH = *η* ⋅ *I* ⋅ *V*Tot (1)

where *P*TH is the supplied thermal power, *η* is the heat transformation efficiency, *I* is the cur-

In order to ensure proper spray transfer, the transition welding intensity between globular and spray transfer modes is determined first. This parameter is dependent on the used shielding gas and filler wire diameter. Thus, using current intensity values higher than the transition current intensity limit value provides proper spray transfer. **Figure 5** represents the correlations proposed by Norrish [37] to determine the globular-to-spray mode transition current depending on the shielding gas for a wire diameter range between 0.8

The total voltage drop *V*Tot is approximately the addition of the voltage drop in the electric

*V*Tot = *V*arc + *V*so (2)

*V*arc = *I* ⋅ *R*arc + *a*<sup>0</sup> + *a*<sup>1</sup> ⋅ *L*arc (3)

and the voltage drop across the arc *V*arc (2) [1].

supplied heat power can be determined with Eq. (1):

**Figure 4.** Schematic of the welding torch configuration (adapted from [1]).

96 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

rent intensity and *V*Tot is the total voltage.

The arc voltage drop can be obtained with Eq. (3):

and 1.6 mm.

stick-out length *Vso*

The welding speed is the velocity the welding torch advances along the welding bead. It is assumed that GMAW process fulfils the mass conservation law. Thus, wire feed speed and welding speed can be determined by Eq. (6):

$$A\_{so} \cdot v\_W = A\_s \cdot v\_s \to v\_s = \frac{A\_w \cdot v\_W}{A\_s} \tag{6}$$

where *vW* is the wire feed speed, *As* is the weld pass cross section and *vs* is the welding speed.

There are two approaches to model the wire feed rate for constant voltage welding used in GMAW, as suggested by Palani et al. (2007) [39]. The first approach consists in fitting the equation relating welding current and wire feed rate with experimental data. The second approach consists in using the results of the experiments to determine the constants of proportionality for the arc heating and the electrical resistance heating.

In the methodology presented in this chapter, the second approach is used. Thus, the wire feed speed is calculated with Eq. (7) [37]:

$$v\_{\parallel W} = \alpha \cdot I + \frac{\beta \cdot L\_{\text{w}} \cdot I^2}{A\_{\text{w}}} \tag{7}$$

thermomechanical approach where the thermal domain is solved first. Then, the mechanical field is solved fed by the previously calculated thermal pattern history. Consequently, computational cost can be significantly reduced. Both equation systems are solved by using the

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99

Even though both models are solved separately, they share same geometric model where just

The geometric model has to include the geometry of each welding pass based on the calculated cross section for each pass. According to Teng et al. [44], the flank angle does not have significant effect in the residual stress value. For this reason, considering the real geometry of the plates to weld, a flank angle of 30° has been selected to define the bead radius (see **Figure 7**). The arcs for the bead in the rest of the passes are defined concentric with respect to the last pass by keeping the value of the initially calculated cross section for each pass.

The model is meshed by using full integration continuum hexahedral elements (recommended) where the proper formulation is selected, respectively, to solve the thermal domain and the mechanical domain (**Figure 8a**). The addition of filler material through each pass is modelled by using the kill/rebirth method [13, 22, 26] (**Figure 8b** and **c**). In this method, all the weld bead elements are initially inactive and, consequently, eliminated from the equation sys-

torch pass. In order to ensure sufficient resolution in the transient temperature evolution, a temporal discretization of one second is specified. Symmetry is not considered as an asymmetric clamping condition where just one plate end is fixed to avoid during the validation the influence of the boundary restrictions in the predicted RS pattern (in accordance with the

**Figure 7.** Schematic of the procedure to calculate the weld bead geometry for each pass for a three-pass weld case.

), simulating the welding

tem. Then, elements are activated in function of the welding speed (*vs*

implicit direct integration method.

*2.2.1. Geometric model*

used experimental set-up).

the element type and restrictions differ.

where *α* and *β* are constants dependent on the used wire properties.

Moreover, considering different values of the constants (*α* and *β*) from several studies for solid plain carbon steel wire analysed from literature (Norrish 1992 [37], Murray 2002 [40], Modenesi 2007 [41], Palani 2006 [42], Palani 2007 [39]), it is observed that their difference is negligible (**Figure 6**). Therefore, in the present work, it is decided to consider the values defined in [37], *α* ≈ 0.3 mmA-1 s-1 and *β* ≈ 5 ⋅ 1 0<sup>−</sup><sup>5</sup> A-2 s-1 for a 1.2 mm plain carbon steel wire.

#### **2.2. Uncoupled thermomechanical FEM modelling procedure**

Welding is a thermometallurgical process where the thermal field directly affects in the mechanical domain response, but the effect of the mechanical field on the thermal domain can be considered negligible as dimensional changes in the welding process are not representative and generated deformation energy is insignificant compared to the thermal energy from the welding arc [43]. Thus, the welding process can be modelled with an uncoupled

**Figure 6.** Comparison of different approaches to determine wire speed based on welding intensity for carbon steel filler (adapted from [37, 39–42]).

thermomechanical approach where the thermal domain is solved first. Then, the mechanical field is solved fed by the previously calculated thermal pattern history. Consequently, computational cost can be significantly reduced. Both equation systems are solved by using the implicit direct integration method.

Even though both models are solved separately, they share same geometric model where just the element type and restrictions differ.

#### *2.2.1. Geometric model*

equation relating welding current and wire feed rate with experimental data. The second approach consists in using the results of the experiments to determine the constants of pro-

In the methodology presented in this chapter, the second approach is used. Thus, the wire

Moreover, considering different values of the constants (*α* and *β*) from several studies for solid plain carbon steel wire analysed from literature (Norrish 1992 [37], Murray 2002 [40], Modenesi 2007 [41], Palani 2006 [42], Palani 2007 [39]), it is observed that their difference is negligible (**Figure 6**). Therefore, in the present work, it is decided to consider the values

Welding is a thermometallurgical process where the thermal field directly affects in the mechanical domain response, but the effect of the mechanical field on the thermal domain can be considered negligible as dimensional changes in the welding process are not representative and generated deformation energy is insignificant compared to the thermal energy from the welding arc [43]. Thus, the welding process can be modelled with an uncoupled

**Figure 6.** Comparison of different approaches to determine wire speed based on welding intensity for carbon steel filler

*β* ⋅ *Lso* ⋅ *I*<sup>2</sup> \_\_\_\_\_\_\_\_ *Aso*

A-2 s-1 for a 1.2 mm plain carbon steel wire.

(7)

portionality for the arc heating and the electrical resistance heating.

98 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

where *α* and *β* are constants dependent on the used wire properties.

**2.2. Uncoupled thermomechanical FEM modelling procedure**

feed speed is calculated with Eq. (7) [37]:

*vW* = *α* ⋅ *I* +

defined in [37], *α* ≈ 0.3 mmA-1 s-1 and *β* ≈ 5 ⋅ 1 0<sup>−</sup><sup>5</sup>

(adapted from [37, 39–42]).

The geometric model has to include the geometry of each welding pass based on the calculated cross section for each pass. According to Teng et al. [44], the flank angle does not have significant effect in the residual stress value. For this reason, considering the real geometry of the plates to weld, a flank angle of 30° has been selected to define the bead radius (see **Figure 7**). The arcs for the bead in the rest of the passes are defined concentric with respect to the last pass by keeping the value of the initially calculated cross section for each pass.

The model is meshed by using full integration continuum hexahedral elements (recommended) where the proper formulation is selected, respectively, to solve the thermal domain and the mechanical domain (**Figure 8a**). The addition of filler material through each pass is modelled by using the kill/rebirth method [13, 22, 26] (**Figure 8b** and **c**). In this method, all the weld bead elements are initially inactive and, consequently, eliminated from the equation system. Then, elements are activated in function of the welding speed (*vs* ), simulating the welding torch pass. In order to ensure sufficient resolution in the transient temperature evolution, a temporal discretization of one second is specified. Symmetry is not considered as an asymmetric clamping condition where just one plate end is fixed to avoid during the validation the influence of the boundary restrictions in the predicted RS pattern (in accordance with the used experimental set-up).

**Figure 7.** Schematic of the procedure to calculate the weld bead geometry for each pass for a three-pass weld case.

• **Modelization of mechanical field**: Clamping restraints have to be considered as boundary conditions. In addition, temperature pattern is fed from the previously calculated thermal model considering the rebirth speed corresponding to the welding speed. Once the welding process and cooling down process are completed, clamping restrains are deactivated

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The proposed procedure is implemented and validated for a case study of three-pass spray transfer butt weld of 10 mm thick and 200 mm length of two S275JR steel plates (see **Figure 9**). The used filler material is a 1.2 mm wire diameter PRAXAIR M-86 according to the AWS/ASME SFA 5.18 ER70S-6 standard. Stargon 82, with 8% of CO2, is used as

The heat transfer model as well as the mechanical model used for the simulation of the welding process of the selected case study is implemented in the simulation software ABAQUS™.

A critical activation length per second of 6.12 mm is calculated to ensure temporal discretisation of 1 s for the third pass, which is conducted with the lower welding speed. Consequently, a 5 mm length discretization size, which ensures a temporal discretization <1 s for the three passes, is selected for the presented work. Furthermore, it allows fitting exactly with 40 dis-

**Table 1** shows the standard mechanical properties of S275JR structural steel used for the welded plated and the PRAXAIR M-86 filler material at room temperature. As it can be observed, both materials show similar ultimate strain and ultimate strength, but the yield

**3. Methodology implementation and experimental validation**

to obtain final RS pattern.

shielding gas.

**3.1. Numerical procedure**

*3.1.1. Geometric model*

*3.1.2. Material*

cretization volumes the 200 mm length of each pass.

stress of the filler material is 45% higher.

**Figure 9.** Welding configuration of the analysed case study.

**Figure 8.** (a) Example of a full geometric model of a multipass butt weld, (b) principle of the addition the weld bead and (c) multipass welding modelling of a three-pass weld case.

#### *2.2.2. Material*

Temperature-dependent thermal and thermomechanical properties of both plate material and filler material have to be defined to feed de thermal model and mechanical model, respectively:


Regarding phase transformation effects, the aim of the present modelling methodology is to reach to an agreement between the model simplicity and accuracy level. Therefore, even effect of phase transformation in the temperature-dependent properties such as density, thermal expansion or specific heat is considered, the mechanism of phase transformation is not included in the model. Some studies in the literature as the work presented by Payares-Asprino et al. in 2008 [45] have shown that this phase transformation could be significant for low temperature transformation (LTT) filler materials. However, in the present study, a conventional filler material is used, where the expansion that material suffers by martensitic transformation is relatively small and occurs at relatively high transformation temperature range. Consequently, its effect in the generated residual stresses and distortions is not significant [46].

#### *2.2.3. Loads and boundary conditions*

• **Modelization of the thermal field:** Based on the previously exposed analytic procedure, heat source is implemented as uniform body heat flux over the elements activated at the rebirth speed corresponding to the welding speed. Natural convection of the free surfaces as well as radiation should be considered.

• **Modelization of mechanical field**: Clamping restraints have to be considered as boundary conditions. In addition, temperature pattern is fed from the previously calculated thermal model considering the rebirth speed corresponding to the welding speed. Once the welding process and cooling down process are completed, clamping restrains are deactivated to obtain final RS pattern.

## **3. Methodology implementation and experimental validation**

The proposed procedure is implemented and validated for a case study of three-pass spray transfer butt weld of 10 mm thick and 200 mm length of two S275JR steel plates (see **Figure 9**). The used filler material is a 1.2 mm wire diameter PRAXAIR M-86 according to the AWS/ASME SFA 5.18 ER70S-6 standard. Stargon 82, with 8% of CO2, is used as shielding gas.

#### **3.1. Numerical procedure**

The heat transfer model as well as the mechanical model used for the simulation of the welding process of the selected case study is implemented in the simulation software ABAQUS™.

#### *3.1.1. Geometric model*

*2.2.2. Material*

specific heat are required.

(c) multipass welding modelling of a three-pass weld case.

*2.2.3. Loads and boundary conditions*

as well as radiation should be considered.

Temperature-dependent thermal and thermomechanical properties of both plate material and filler material have to be defined to feed de thermal model and mechanical model, respectively:

**Figure 8.** (a) Example of a full geometric model of a multipass butt weld, (b) principle of the addition the weld bead and

• **Modelization of the thermal field:** Density, latent heat, thermal conductivity as well as

• **Modelization of mechanical field:** Density, Young modulus, Poisson ration, thermal ex-

Regarding phase transformation effects, the aim of the present modelling methodology is to reach to an agreement between the model simplicity and accuracy level. Therefore, even effect of phase transformation in the temperature-dependent properties such as density, thermal expansion or specific heat is considered, the mechanism of phase transformation is not included in the model. Some studies in the literature as the work presented by Payares-Asprino et al. in 2008 [45] have shown that this phase transformation could be significant for low temperature transformation (LTT) filler materials. However, in the present study, a conventional filler material is used, where the expansion that material suffers by martensitic transformation is relatively small and occurs at relatively high transformation temperature range. Consequently, its effect in the generated residual stresses and distortions is not significant [46].

• **Modelization of the thermal field:** Based on the previously exposed analytic procedure, heat source is implemented as uniform body heat flux over the elements activated at the rebirth speed corresponding to the welding speed. Natural convection of the free surfaces

pansion coefficient as well flow stress curves are required.

100 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

A critical activation length per second of 6.12 mm is calculated to ensure temporal discretisation of 1 s for the third pass, which is conducted with the lower welding speed. Consequently, a 5 mm length discretization size, which ensures a temporal discretization <1 s for the three passes, is selected for the presented work. Furthermore, it allows fitting exactly with 40 discretization volumes the 200 mm length of each pass.

#### *3.1.2. Material*

**Table 1** shows the standard mechanical properties of S275JR structural steel used for the welded plated and the PRAXAIR M-86 filler material at room temperature. As it can be observed, both materials show similar ultimate strain and ultimate strength, but the yield stress of the filler material is 45% higher.

**Figure 9.** Welding configuration of the analysed case study.


**Table 1.** Standard mechanical properties of S275JR structural steel [47] and PRAXAIR M-86 filler material [48, 49].

Temperature-dependent flow stress curves at a quasi-static strain rate for the filler material are estimated based on S275JR data and considering a 45% higher temperature-dependent yield stress value. The rest of thermomechanical properties as well as thermal properties are considered the same as the base material. This simplification is considered acceptable according to the next statements:


#### *3.1.3. Thermal properties*

**Figure 10a** shows the utilised temperature-dependent density, thermal conductivity and specific heat data for both filler and plate materials. **Table 2** shows the considered latent heat and solidus-liquidus transition temperature.

facility, simulations for an efficiency range between 0.6 and 1 are conducted. **Table 3** shows

**Figure 10.** Temperature-dependant material properties. (a) Specific heat taken from [50], thermal conductivity taken from [22, 51] and density taken from [46]; (b) Young's modulus and thermal expansion taken from [52] and yield stress taken from [53, 54]; (c) plastic properties for the base material [22]; and (d) estimated plastic properties for the wire

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• **Transition welding intensity for spray transfer:** The use of a 1.2 mm wire diameter and

• **Wire properties:** The resistivity value of the used wire is *R*arc 0.0237 Ω [3]. The parameters *a*<sup>0</sup>

• **Welding torch configuration:** A 9 mm *L*arc (> *L*arc\_min of 4.5 mm [38]) and a 30 mm *L*CTW are

intensity of 245A to ensure proper spray transfer model. Therefore, for the present case

[55], determines a minimum welding

*<sup>m</sup>* resistivity of the stick-out material is set.

the heat source power for each pass calculated with the following parameters:

**Latent heat (kJ/kg) Solidus temperature (°C) Liquidus temperature (°C)**

study, an intensity value of 275 A, 12% higher than the transition limit, is used.

are set as 6.3 V and 1.55 V/mm respectively based on [4].

Stargon 82 as shielding gas, which contains 8% CO2

247 1500 1550

defined. For carbon steels [1], a 0.2821 \_\_<sup>Ω</sup>

and *a*<sup>1</sup>

material.

**Table 2.** Latent heat of fusion [36].

#### *3.1.4. Thermomechanical properties*

**Figure 10b**–**d** shows the temperature-dependent mechanical properties for both the base material and filler material.

#### **3.2. Loads and boundary conditions**

#### *3.2.1. Heat transfer model*

Heat source and welding speed for the specified case study are obtained with the new methodology exposed in Section 2. First, in order to determine the efficiency of the used welding

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**Figure 10.** Temperature-dependant material properties. (a) Specific heat taken from [50], thermal conductivity taken from [22, 51] and density taken from [46]; (b) Young's modulus and thermal expansion taken from [52] and yield stress taken from [53, 54]; (c) plastic properties for the base material [22]; and (d) estimated plastic properties for the wire material.


**Table 2.** Latent heat of fusion [36].

Temperature-dependent flow stress curves at a quasi-static strain rate for the filler material are estimated based on S275JR data and considering a 45% higher temperature-dependent yield stress value. The rest of thermomechanical properties as well as thermal properties are considered the same as the base material. This simplification is considered acceptable accord-

**Table 1.** Standard mechanical properties of S275JR structural steel [47] and PRAXAIR M-86 filler material [48, 49].

 **(MPa) A (%) E (GPa)**

• Considering same thermal properties as will have minor influence in the estimated temperature distribution and thermal expansion as both steels present similar, conductivity,

• Same temperature-dependent density and elastic modulus can be considered for both the base material and filler material, as low variations in the content of alloying elements of

• The temperature-dependent yield stress of the filler material is assumed to be 45% higher than the base material. As the plastic deformation level found in the welding process is low, near the yield stress values, considering the same temperature-dependent tangent modu-

• The cross section of the weld bead is small in comparison with both plates' cross section. For this reason, considering same thermal expansion value as for the base material will generate an insignificant deviation in comparison with the total thermal expansion. Consequently, it is considered that possible error gene rated from the previous assumptions in

**Figure 10a** shows the utilised temperature-dependent density, thermal conductivity and specific heat data for both filler and plate materials. **Table 2** shows the considered latent heat and

**Figure 10b**–**d** shows the temperature-dependent mechanical properties for both the base

Heat source and welding speed for the specified case study are obtained with the new methodology exposed in Section 2. First, in order to determine the efficiency of the used welding

structural steels have insignificant influence in these parameters [49].

lus will not have significant effect in the predicted RS pattern.

the computed transversal residual stress will be negligible.

ing to the next statements:

*3.1.3. Thermal properties*

solidus-liquidus transition temperature.

*3.1.4. Thermomechanical properties*

**3.2. Loads and boundary conditions**

material and filler material.

*3.2.1. Heat transfer model*

specific heat, latent heat and thermal expansion.

*σy*

 **(MPa)** *σ<sup>u</sup>*

102 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

S275JR 275 430–580 23 190–210 Filler M-86 >400 >480 >22 200

> facility, simulations for an efficiency range between 0.6 and 1 are conducted. **Table 3** shows the heat source power for each pass calculated with the following parameters:



process parameters such as the arc voltage, the arc length, the contact to workpiece length, the wire feed speed and the welding speed along the whole process. In addition, current intensity and voltage during the whole process are monitored by means of a TPS2024B Tektronix oscil-

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In order to conduct the validation of the proposed modelling methodology, temperature patter evolution during the welding process and the RS pattern of the welded samples are also

S275JR plates of 10 mm thick and 200 mm length are butt welded in three passes (**Figure 9**) with a 1.2 mm diameter PRAXAIR M-86 filler material. Stargon 82, with 8% of CO2 [54], is

Welding process parameters for each pass are previously determined with the proposed ana-

Temperature pattern history is acquired along the whole process to determine the welding facility's efficiency and to validate the numerically obtained temperature pattern. For this purpose two methods are used in parallel: (i) 10 N-type thermocouples (up to 1200°C) are positions parallel and perpendicular to the weld bead (**Figure 12a**) and (ii) a Titanium DC01 9 U-E

To ensure proper temperature pattern measurement with the thermographic camera, plates are painted with a black colour high temperature-resistant paint in which temperature-dependent emissivity is already determined [56]. However, for better accuracy, the temperature acquisition data of the thermocouples is used to calibrate the acquired temperature pattern.

In order to validate the numerically obtained RS pattern and, consequently, the proposed modelling methodology, RS measurements are conducted by using the hole-drilling method. To conduct the measurements, Vishay EA-06-062RE-120 rosette-type gauges are placed parallel to the welding bead, at a 52.5 mm distance from the weld toe at both sides of the weld bead as shown in **Figure 12**b. Then, hole-drilling tests are carried out in a CNC milling machine

**Pass V (V) I (A) Vw (m/min) P (W) Larc (mm) Lctw (mm) Vs (mm/min)** 28.2 275 9.2 7755 9 30 545.33 28.2 275 9.2 7755 9 30 482.83 28.2 275 9.2 7755 9 30 367.796

thermographic camera to record the surface temperature pattern evolution.

loscope, a PR HAMEG HZ115 voltmeter and a LEM PR 200 ammeter.

lytical procedure for spray transfer mode (**Table 4**).

*3.4.1. Temperature pattern measurement*

*3.4.2. Residual stress measurement*

according to ASTM E837 standard.

**Table 4.** Welding process parameters.

measured.

**3.4. Welding procedure**

used as shielding gas.

**Table 3.** Values of the heat power for different efficiencies.

Welding speed to be implemented as element rebirth rate has been calculated for each pass by using the parabolic model constants *α* ≈ 0.3 mmA-1 s-1 and *β* ≈ 5 ⋅ 1 0<sup>−</sup><sup>5</sup> A-2 s-1 for a 1.2 mm plain carbon steel wire [37]. Thus, the calculated welding speeds for each pass of the case study in the present work are 545.33, 482.53 and 367.79 mm/min.

Finally, a natural convection boundary condition has been assumed in all surfaces exposed to air of both plates and the rebirthed weld bead elements.

#### *3.2.2. Uncoupled thermomechanical model*

Temperature pattern at every iteration is fed from the previously run heat transfer simulation results. As a boundary condition, one of the plate end surfaces is assumed to be fully constrained.

#### **3.3. Experimental procedure**

**Figure 11** shows the CNC milling machined adapted with a Praxair Phoenix 421 welding machine in order to perform the welding process automatically. This enables to control all the

**Figure 11.** a) Set-up to automatically perform the welding process and b) Detail of the welding configuration.

process parameters such as the arc voltage, the arc length, the contact to workpiece length, the wire feed speed and the welding speed along the whole process. In addition, current intensity and voltage during the whole process are monitored by means of a TPS2024B Tektronix oscilloscope, a PR HAMEG HZ115 voltmeter and a LEM PR 200 ammeter.

In order to conduct the validation of the proposed modelling methodology, temperature patter evolution during the welding process and the RS pattern of the welded samples are also measured.

### **3.4. Welding procedure**

Welding speed to be implemented as element rebirth rate has been calculated for each pass by

**First pass Second pass Third pass**

carbon steel wire [37]. Thus, the calculated welding speeds for each pass of the case study in

Finally, a natural convection boundary condition has been assumed in all surfaces exposed to

Temperature pattern at every iteration is fed from the previously run heat transfer simulation results. As a boundary condition, one of the plate end surfaces is assumed to be fully

**Figure 11** shows the CNC milling machined adapted with a Praxair Phoenix 421 welding machine in order to perform the welding process automatically. This enables to control all the

**Figure 11.** a) Set-up to automatically perform the welding process and b) Detail of the welding configuration.

A-2 s-1 for a 1.2 mm plain

using the parabolic model constants *α* ≈ 0.3 mmA-1 s-1 and *β* ≈ 5 ⋅ 1 0<sup>−</sup><sup>5</sup>

1 7755 7755 7755 0.9 6980 6980 6980 0.85 6592 6592 6592 0.8 6204 6204 6204 0.75 5816 5816 5816 0.7 5429 5429 5429 0.6 4653 4653 4653

104 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

the present work are 545.33, 482.53 and 367.79 mm/min.

**Table 3.** Values of the heat power for different efficiencies.

air of both plates and the rebirthed weld bead elements.

*3.2.2. Uncoupled thermomechanical model*

**Efficiency (%) Power (W)**

**3.3. Experimental procedure**

constrained.

S275JR plates of 10 mm thick and 200 mm length are butt welded in three passes (**Figure 9**) with a 1.2 mm diameter PRAXAIR M-86 filler material. Stargon 82, with 8% of CO2 [54], is used as shielding gas.

Welding process parameters for each pass are previously determined with the proposed analytical procedure for spray transfer mode (**Table 4**).

#### *3.4.1. Temperature pattern measurement*

Temperature pattern history is acquired along the whole process to determine the welding facility's efficiency and to validate the numerically obtained temperature pattern. For this purpose two methods are used in parallel: (i) 10 N-type thermocouples (up to 1200°C) are positions parallel and perpendicular to the weld bead (**Figure 12a**) and (ii) a Titanium DC01 9 U-E thermographic camera to record the surface temperature pattern evolution.

To ensure proper temperature pattern measurement with the thermographic camera, plates are painted with a black colour high temperature-resistant paint in which temperature-dependent emissivity is already determined [56]. However, for better accuracy, the temperature acquisition data of the thermocouples is used to calibrate the acquired temperature pattern.

#### *3.4.2. Residual stress measurement*

In order to validate the numerically obtained RS pattern and, consequently, the proposed modelling methodology, RS measurements are conducted by using the hole-drilling method.

To conduct the measurements, Vishay EA-06-062RE-120 rosette-type gauges are placed parallel to the welding bead, at a 52.5 mm distance from the weld toe at both sides of the weld bead as shown in **Figure 12**b. Then, hole-drilling tests are carried out in a CNC milling machine according to ASTM E837 standard.


**Table 4.** Welding process parameters.

the peak temperature value for each pass also increases. From a quantitative point of view, as expected, a theoretical efficiency value of 1 provides higher temperature values than experi-

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For this reason, the efficiency of the used welding facility is determined comparing the temperature deviation of all thermocouples at each pass for the simulations conducted in an efficiency range between 0.6 and 1 (**Table 5**). The results show that the highest accuracy is obtained for an efficiency value of 0.8 with an average deviation of 9.16%. Therefore, it is assumed that the efficiency of the facility is 0.8, which is in accordance with the efficiency

**Figure 14** shows the comparison of the theoretical and experimental temperature evolution for thermocouple 1 for an efficiency of 0.8. An uncertainty attributed to a +/−0.5 mm thermocouple positioning error has been considered in the temperature validation. It can be observed that the temperature evolution present presents a positive quantitative correspondence along

In addition, **Figure 15** shows the comparison between the experimental temperature pattern acquired with the thermographic camera and the numerically predicted pattern at the end of each pass for an efficiency value of 0.8. Both temperature patterns show good correspondence in the shape of temperature contours from the high temperature zone over 700°C down to the

Considering the low deviation (9.16%) in the temperature evolution prediction together with the positive correspondence found in the temperature pattern contours at each pass, it is concluded that the numerical procedure to predict temperature pattern evolution of multipass

Once the performance of the proposed methodology in the thermal field prediction is vali-

1 21.94 20.02 21.77 21.24 0.9 12.8 10.46 16.7 13.33 0.85 8.47 5.82 16.68 10.32 0.8 3.9 5.31 18.26 9.16 0.75 3.45 6.57 19.82 9.95 0.7 6.61 9.97 21.44 12.67 0.6 17.44 20.24 31.17 22.95

**Table 5.** Calculated error for the peak temperatures at each pass for an efficiency range of 0.6–1.

**First pass Second pass Third pass Average**

dated, the RS field is verified to conclude with the model validation.

lower temperature areas at 300°C (limit of the filter use in the thermographic camera).

mentally acquired curves as no power losses are considered.

reference values found in the literature (0.66–0.85) [1].

the three passes.

spray transfer welding is valid.

**3.7. Residual stress validation**

**Efficiency Error (%)**

**Figure 12.** Position of the thermocouples (a) and (b) position of the hole-drilling gauges in the butt weld.

#### **3.5. Results and discussion**

In this section, theoretical results and experimental results are compared in order to validate the proposed modelling methodology. For that purpose, first the temperature pattern prediction, which determines the material's thermal expansion, is compared. Then, RS pattern generated by the thermal expansion is validated.

#### **3.6. Temperature pattern validation**

**Figure 13** shows the comparison of the experimental temperature evolution along the three passes and the theoretically estimated values for an efficiency value of 1. It can be observed that both curves present same process dynamic, where the temperature peaks when the welding torch is near to the reference thermocouple can be clearly identified, followed by a progressive cooling down related to the heat evacuation. In addition, it can be observed that as the cross section of each pass increases, the heat supply for each pass raises and, consequently,

**Figure 13.** Calculated and measured thermal cycles for thermocouple 1 with an efficiency factor of 1.

the peak temperature value for each pass also increases. From a quantitative point of view, as expected, a theoretical efficiency value of 1 provides higher temperature values than experimentally acquired curves as no power losses are considered.

For this reason, the efficiency of the used welding facility is determined comparing the temperature deviation of all thermocouples at each pass for the simulations conducted in an efficiency range between 0.6 and 1 (**Table 5**). The results show that the highest accuracy is obtained for an efficiency value of 0.8 with an average deviation of 9.16%. Therefore, it is assumed that the efficiency of the facility is 0.8, which is in accordance with the efficiency reference values found in the literature (0.66–0.85) [1].

**Figure 14** shows the comparison of the theoretical and experimental temperature evolution for thermocouple 1 for an efficiency of 0.8. An uncertainty attributed to a +/−0.5 mm thermocouple positioning error has been considered in the temperature validation. It can be observed that the temperature evolution present presents a positive quantitative correspondence along the three passes.

In addition, **Figure 15** shows the comparison between the experimental temperature pattern acquired with the thermographic camera and the numerically predicted pattern at the end of each pass for an efficiency value of 0.8. Both temperature patterns show good correspondence in the shape of temperature contours from the high temperature zone over 700°C down to the lower temperature areas at 300°C (limit of the filter use in the thermographic camera).

Considering the low deviation (9.16%) in the temperature evolution prediction together with the positive correspondence found in the temperature pattern contours at each pass, it is concluded that the numerical procedure to predict temperature pattern evolution of multipass spray transfer welding is valid.

#### **3.7. Residual stress validation**

**3.5. Results and discussion**

generated by the thermal expansion is validated.

**3.6. Temperature pattern validation**

In this section, theoretical results and experimental results are compared in order to validate the proposed modelling methodology. For that purpose, first the temperature pattern prediction, which determines the material's thermal expansion, is compared. Then, RS pattern

**Figure 12.** Position of the thermocouples (a) and (b) position of the hole-drilling gauges in the butt weld.

106 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 13** shows the comparison of the experimental temperature evolution along the three passes and the theoretically estimated values for an efficiency value of 1. It can be observed that both curves present same process dynamic, where the temperature peaks when the welding torch is near to the reference thermocouple can be clearly identified, followed by a progressive cooling down related to the heat evacuation. In addition, it can be observed that as the cross section of each pass increases, the heat supply for each pass raises and, consequently,

**Figure 13.** Calculated and measured thermal cycles for thermocouple 1 with an efficiency factor of 1.

Once the performance of the proposed methodology in the thermal field prediction is validated, the RS field is verified to conclude with the model validation.


**Table 5.** Calculated error for the peak temperatures at each pass for an efficiency range of 0.6–1.

**Figure 14.** Comparative of experimental versus FEM thermal results for a butt weld with an efficiency factor of 0.8.

stress pattern at both sides of the weld seam. Consequently, stress paths at both sides, path 1 and path 2 located in the maximum stress are at each side, are considered for validation purpose.

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**Figure 17** shows hole-drilling measurements of the transversal residual stress along half of the length (0–100 mm) for both, path 1 and path 2. The results show three differentiated zones: (i) compression zone (0–30 mm), (ii) transition zone (30–60 mm) and (iii) tensile zone (60– 100 mm). Additional measurements are conducted in the full length (at 160 mm and 175 mm)

High scatter among the measurement repetitions, inherent to the measuring technique, is observed, which is in accordance with stress deviations up to ±50 MPa reported by some authors [57]. Therefore, average hole-drilling results at each position are considered for both paths to perform the RS validation. **Figure 18a** and **b** shows the comparison between the average hole-drilling results with their standard deviation and simulation results for path 1

to ensure that the RS path shows quasi-symmetric behaviour.

**Figure 17.** Results of hole-drilling measurements for different plates and for both paths.

**Figure 16.** Transversal residual stresses pattern for a butt weld.

**Figure 15.** Comparative of experimental versus FEM thermal pattern for a butt weld with an efficiency factor of 0.8 (the points in the upper images are the position of the thermocouples).

**Figure 16** shows transverse residual stresses pattern obtained with the FEM uncoupled thermomechanical simulation. A high stress concentration in the clamping area where 6 degrees of freedom are fixed is observed (in accordance with the experimental set-up). However, the stress concentration located in the clamping is far enough from the area of interest, and they do not have any effect in the residual stress validation process. Analysing the area of interest, it is observed that even the stress concentration in the clamping area does not affect the area of interest near the weld bead, the asymmetry in the boundary restriction generates a mild asymmetric Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical… http://dx.doi.org/10.5772/intechopen.72134 109

**Figure 16.** Transversal residual stresses pattern for a butt weld.

stress pattern at both sides of the weld seam. Consequently, stress paths at both sides, path 1 and path 2 located in the maximum stress are at each side, are considered for validation purpose.

**Figure 17** shows hole-drilling measurements of the transversal residual stress along half of the length (0–100 mm) for both, path 1 and path 2. The results show three differentiated zones: (i) compression zone (0–30 mm), (ii) transition zone (30–60 mm) and (iii) tensile zone (60– 100 mm). Additional measurements are conducted in the full length (at 160 mm and 175 mm) to ensure that the RS path shows quasi-symmetric behaviour.

High scatter among the measurement repetitions, inherent to the measuring technique, is observed, which is in accordance with stress deviations up to ±50 MPa reported by some authors [57]. Therefore, average hole-drilling results at each position are considered for both paths to perform the RS validation. **Figure 18a** and **b** shows the comparison between the average hole-drilling results with their standard deviation and simulation results for path 1

**Figure 17.** Results of hole-drilling measurements for different plates and for both paths.

**Figure 16** shows transverse residual stresses pattern obtained with the FEM uncoupled thermomechanical simulation. A high stress concentration in the clamping area where 6 degrees of freedom are fixed is observed (in accordance with the experimental set-up). However, the stress concentration located in the clamping is far enough from the area of interest, and they do not have any effect in the residual stress validation process. Analysing the area of interest, it is observed that even the stress concentration in the clamping area does not affect the area of interest near the weld bead, the asymmetry in the boundary restriction generates a mild asymmetric

**Figure 15.** Comparative of experimental versus FEM thermal pattern for a butt weld with an efficiency factor of 0.8 (the

points in the upper images are the position of the thermocouples).

**Figure 14.** Comparative of experimental versus FEM thermal results for a butt weld with an efficiency factor of 0.8.

108 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 18.** Comparison of the FEM and experimental results for the results of hole.

and path 2, respectively. A positive correspondence is observed between the averaged measurements and the numerical results for both paths where the three zones, compression zone, transition zone and tensile zone, show similar trends. Considering both paths, an average error of 34 MPa, 35 MPa and 57 MPa for each zone, respectively, is calculated with an average total error of 42 MPa. As observed, numerically predicted residual stress values are mostly inside the measurement scatter band (±50 MPa [57]). Thus, it can be concluded that, considering the inherent error of the RS measuring technique, the proposed methodology to predict RS pattern can be considered valid with an average error of 42 MPa.

**4.1. Numerical procedure**

tion software ABAQUS™.

case study with 14 passes (T-joint\_40).

**Table 6.** Case studies configuration data. Numerical procedure.

**4.2. Geometric model**

In this section, the modelling procedure presented in Section 2 and validated in Section 3 is used. As in Section 3, the heat transfer model as well as the mechanical model used for the simulation of the welding process of the selected case studies is implemented in the simula-

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111

**Figure 19.** (a) 20 mm-, (b) 30 mm-, (c) 40 mm-, (d) 50 mm- and (e) 60 mm-thick T-joint case studies.

In this Section, 10 mm length discretization size is used, which ensures a temporal discretization lower than 2 s in all the passes. **Figure 20** shows the numerical model of a 40-mm thick

**Case study Dimensions Number of passes Thickness (mm) Wide (mm) Length (mm)**

T-joint\_20 20 120 150 4 T-joint\_30 30 160 250 8 T-joint\_40 40 200 350 14 T-joint\_50 50 240 450 22 T-joint\_60 60 280 550 31

## **4. Theoretical analysis of RS pattern on thick T-joint samples**

T-joint welding configurations are one of the most widely used in a wide range of structural applications. Particularly, when building large structures, T-joint of thick plates requires high amount of weld passes, and consequently, the RS pattern varies considerably depending on the plate thickness and the number passes, hence affecting to mechanical performance such as fatigue endurance.

Nowadays, most approaches to dimension-welded structures do not consider RS real value due to the difficulty of estimating them; hence, they tend to be conservative. However, recent works [gure erreferentziak] have demonstrated that considering RS, the error for example in fatigue life prediction can be reduced down to 15%.

In this section, the RS pattern of multipass T-joints at 70% penetration of S275JR plates for a thickness range from 20 to 60 mm is evaluated (see **Figure 19**). Same filler material, 1.2 mm diameter PRAXAIR M-86 filler wire, according to the AWS/ASME SFA 5.18 ER70S-6 standard, and a quasi-constant weld pass section are considered for all cases. **Table 6** shows the studied case configuration data where dimensions (wide and length) have been previously specified to avoid the influence of the edge boundary effects in the RS pattern.

Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical… http://dx.doi.org/10.5772/intechopen.72134 111

**Figure 19.** (a) 20 mm-, (b) 30 mm-, (c) 40 mm-, (d) 50 mm- and (e) 60 mm-thick T-joint case studies.

#### **4.1. Numerical procedure**

and path 2, respectively. A positive correspondence is observed between the averaged measurements and the numerical results for both paths where the three zones, compression zone, transition zone and tensile zone, show similar trends. Considering both paths, an average error of 34 MPa, 35 MPa and 57 MPa for each zone, respectively, is calculated with an average total error of 42 MPa. As observed, numerically predicted residual stress values are mostly inside the measurement scatter band (±50 MPa [57]). Thus, it can be concluded that, considering the inherent error of the RS measuring technique, the proposed methodology to predict

T-joint welding configurations are one of the most widely used in a wide range of structural applications. Particularly, when building large structures, T-joint of thick plates requires high amount of weld passes, and consequently, the RS pattern varies considerably depending on the plate thickness and the number passes, hence affecting to mechanical performance such

Nowadays, most approaches to dimension-welded structures do not consider RS real value due to the difficulty of estimating them; hence, they tend to be conservative. However, recent works [gure erreferentziak] have demonstrated that considering RS, the error for example in

In this section, the RS pattern of multipass T-joints at 70% penetration of S275JR plates for a thickness range from 20 to 60 mm is evaluated (see **Figure 19**). Same filler material, 1.2 mm diameter PRAXAIR M-86 filler wire, according to the AWS/ASME SFA 5.18 ER70S-6 standard, and a quasi-constant weld pass section are considered for all cases. **Table 6** shows the studied case configuration data where dimensions (wide and length) have been previously specified to avoid the influence of the edge boundary effects in the

RS pattern can be considered valid with an average error of 42 MPa.

**Figure 18.** Comparison of the FEM and experimental results for the results of hole.

110 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

fatigue life prediction can be reduced down to 15%.

as fatigue endurance.

RS pattern.

**4. Theoretical analysis of RS pattern on thick T-joint samples**

In this section, the modelling procedure presented in Section 2 and validated in Section 3 is used. As in Section 3, the heat transfer model as well as the mechanical model used for the simulation of the welding process of the selected case studies is implemented in the simulation software ABAQUS™.

#### **4.2. Geometric model**

In this Section, 10 mm length discretization size is used, which ensures a temporal discretization lower than 2 s in all the passes. **Figure 20** shows the numerical model of a 40-mm thick case study with 14 passes (T-joint\_40).


**Table 6.** Case studies configuration data. Numerical procedure.

**4.5. Results and discussion**

thickness plates.

increase of the total volume).

*Q*in and the welding time *t* (8):

length *L*seam (10):

*t* = *Lw*⁄

Thus, Eq. (8) can be rewritten as follows (11):

each weld pass cross section *A*<sup>s</sup>

*Ein* = *Qin*

*n* = *Aw*⁄

(12):

ness. Two different trends clearly are observed:

to 66% of yield stress (182 MPa) for 60-mm thick plates.

seam.

**Figure 21** shows the RS pattern in the normal direction to the weld seam for the case of 40-mm thick T-joint as example. It can be observed that maximum stress is generated next to the weld

Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical…

**Figure 22** shows the evolution of maximum equivalent uniaxial RS in the critical plane, which is especially interesting to conduct fatigue assessment [58], for different welded plate thick-

• For low thickness, maximum uniaxial RS value increases from 85% of the yield stress (235 MPa) for 20 mm thickness plates up to 95% of the yield stress (261 MPa) for 40 mm

• In contrast, for thickness higher than 40 mm, it is observed that RS value decreases down

As temperature gradients are the main responsible for RS generation, these opposite trends are attributed to the fact that when plate thickness is increased, two different phenomena occur: (i) the increase of provided total heat (directly related with the number of passes) and (ii) the increase of the heat absorption capacitance of the welded plates (directly related to the

The total supplied heat energy *E*in can be described as de product of the heat power supplied

*Ein* = *Qin*

The total welding length *L*w is the product of the total number of passes *n* and the weld pass

*Lw* = *nLseam* (10)

The number of weld passes *n* can be calculated based on the total cross section to weld *A*w and

*nL*\_\_\_\_\_ *seam vs*

The welding time *t* is dependent on the total welding length *L*w and the welding speed *v*<sup>s</sup>

*t* (8)

http://dx.doi.org/10.5772/intechopen.72134

113

*vs* (9)

*As* (12)

(9):

(11)

**Figure 20.** Numerical model of case study T-joint\_40.


**Table 7.** Theoretical welding process parameters and FEM input parameters.

#### **4.3. Material**

In this section, same material properties that are used in Section 3 are considered for S275JR plates and the 1.2 mm diameter PRAXAIR M-86 filler wire.

#### **4.4. Loads and boundary conditions**

The main input parameters to be implemented in the FEM model, i.e. heat source power and welding speed, have been defined according to the analytical procedure proposed in Section 2. Thus, welding speed to be implemented as element rebirth rate has been calculated for each pass by using the parabolic model constants *α* ≈ 0.3 mmA−1 s−1 and *β* ≈ 5 ⋅ 1 0<sup>−</sup><sup>5</sup> A−2 s−1 for a 1.2 mm plain carbon steel wire as previously specified. **Table 7** shows the calculated process parameters and input parameters for the FEM model.

Finally, a natural convection boundary condition has been assumed in all surfaces exposed to air (in both plates and rebirthed weld bead elements).

#### **4.5. Results and discussion**

**Figure 21** shows the RS pattern in the normal direction to the weld seam for the case of 40-mm thick T-joint as example. It can be observed that maximum stress is generated next to the weld seam.

**Figure 22** shows the evolution of maximum equivalent uniaxial RS in the critical plane, which is especially interesting to conduct fatigue assessment [58], for different welded plate thickness. Two different trends clearly are observed:


As temperature gradients are the main responsible for RS generation, these opposite trends are attributed to the fact that when plate thickness is increased, two different phenomena occur: (i) the increase of provided total heat (directly related with the number of passes) and (ii) the increase of the heat absorption capacitance of the welded plates (directly related to the increase of the total volume).

The total supplied heat energy *E*in can be described as de product of the heat power supplied *Q*in and the welding time *t* (8):

$$E\_{\rm in} = \mathbb{Q}\_{\rm in} t \tag{8}$$

The welding time *t* is dependent on the total welding length *L*w and the welding speed *v*<sup>s</sup> (9):

$$t = \, ^{L}\!\!\!\!\!\!\/ , \tag{9}$$

The total welding length *L*w is the product of the total number of passes *n* and the weld pass length *L*seam (10):

$$L\_w = nL\_{snow} \tag{10}$$

Thus, Eq. (8) can be rewritten as follows (11):

**4.3. Material**

**Case study Pass cross** 

In this section, same material properties that are used in Section 3 are considered for S275JR

**Process parameters FEM input parameters**

**Body heat flux**  *(W/mm***<sup>3</sup>** *)*

**Discret. length** *(mm)* **Kill-rebirth rate** *(s***−1***)*

**Welding speed (***mm/min)*

T-joint\_20 26.78 7201 388 23.37 10 0.65 T-joint\_30 29.20 7310 356 21.82 10 0.59 T-joint\_40 29.23 7311 356 21.82 10 0.59 T-joint\_50 30.63 7471 345 21.82 10 0.58 T-joint\_60 30.15 7567 345 21.93 10 0.58

The main input parameters to be implemented in the FEM model, i.e. heat source power and welding speed, have been defined according to the analytical procedure proposed in Section 2. Thus, welding speed to be implemented as element rebirth rate has been calculated for

1.2 mm plain carbon steel wire as previously specified. **Table 7** shows the calculated process

Finally, a natural convection boundary condition has been assumed in all surfaces exposed to

A−2 s−1 for a

each pass by using the parabolic model constants *α* ≈ 0.3 mmA−1 s−1 and *β* ≈ 5 ⋅ 1 0<sup>−</sup><sup>5</sup>

plates and the 1.2 mm diameter PRAXAIR M-86 filler wire.

**Table 7.** Theoretical welding process parameters and FEM input parameters.

parameters and input parameters for the FEM model.

air (in both plates and rebirthed weld bead elements).

**4.4. Loads and boundary conditions**

**Figure 20.** Numerical model of case study T-joint\_40.

**)**

**Welding power** *(W)*

112 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**section (***mm***<sup>2</sup>**

$$E\_{in} = Q\_{in} \frac{nL\_{nom}}{\upsilon\_s} \tag{11}$$

The number of weld passes *n* can be calculated based on the total cross section to weld *A*w and each weld pass cross section *A*<sup>s</sup> (12):

$$
\hbar \mathbf{u} = \mathbf{v}^{\lambda} \mathbf{v} \tag{12}
$$

**Figure 21.** RS pattern of case study T-joint\_40.

**Figure 22.** Maximum equivalent uniaxial stress vs. thickness.

**Figure 23** shows that number of passes *n* increases quadratic with the plate thickness *th*. Consequently, it can be concluded that the total heat energy supplied to the welded plates, which is proportional to the number of passes, also presents a quadratic behaviour.

On the other hand, Eq. (13) describes the heat capacitance *C*plate of the welded plates:

$$\mathbf{C}\_{\text{plate}} = \rho \, V\_{\text{plate}} \mathbf{c}\_p \tag{13}$$

where *ρ* is the plate material density, *V*plate is the volume of the welded plates and *c*p is the

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115

**Figure 24** shows the evolution of the supplied total heat energy *E*in and the heat power supply to plate heat capacitance ratio *Q*in/*C*plate with the plate thickness increase, which represents the plate average temperature increase rate without considering heat losses through convection. It can be observed that, even the total heat increase presents a quadratic increase, the *Q*in/*C*plate ratio decreases abruptly with thickness due to plate volume and, consequently, heat

**Figure 24.** Evolution of total heat supply and heat power supply to plate heat capacitance ration with the plate thickness

specific heat of the plate material.

increase.

**Figure 23.** Number of weld passes according to plate thickness.

Residual Stress Pattern Prediction in Spray Transfer Multipass Welding by Means of Numerical… http://dx.doi.org/10.5772/intechopen.72134 115

**Figure 23.** Number of weld passes according to plate thickness.

**Figure 23** shows that number of passes *n* increases quadratic with the plate thickness *th*. Consequently, it can be concluded that the total heat energy supplied to the welded plates,

*Cplate* = *ρ Vplate cp* (13)

which is proportional to the number of passes, also presents a quadratic behaviour.

**Figure 21.** RS pattern of case study T-joint\_40.

114 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 22.** Maximum equivalent uniaxial stress vs. thickness.

On the other hand, Eq. (13) describes the heat capacitance *C*plate of the welded plates:

where *ρ* is the plate material density, *V*plate is the volume of the welded plates and *c*p is the specific heat of the plate material.

**Figure 24** shows the evolution of the supplied total heat energy *E*in and the heat power supply to plate heat capacitance ratio *Q*in/*C*plate with the plate thickness increase, which represents the plate average temperature increase rate without considering heat losses through convection. It can be observed that, even the total heat increase presents a quadratic increase, the *Q*in/*C*plate ratio decreases abruptly with thickness due to plate volume and, consequently, heat

**Figure 24.** Evolution of total heat supply and heat power supply to plate heat capacitance ration with the plate thickness increase.

capacitance cubic increase. Thus, for plate thickness over 38 mm, the average plate temperature increase ratio is below 1°C/s. Therefore, it is observed that for low plate thickness, the provided total heat is predominant over the heat absorption capacity. In contrast, for high thickness, the heat absorption capacity increase overtakes the provided total heat effect.

[5] Maddox SJ. Fatigue strength of welded structures. Woodhead publishing. 1991

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## **5. Conclusions**

In the present chapter, a procedure to predict RS pattern in spray transfer multipass welding where the heat source is defined based on the welding physics is described and validated. The procedure does not require any welding experimental characterisation to define FEM input parameters, which enables its use as a predictive tool. Results showed good correlation, with an average deviation of 9.15% in the thermal field and 42 MPa in the RS field.

Following, the influence of plate thickness and number of passes in the RS pattern of thick T-joint welds is conducted. Results have shown that, in the studied range, the assumption of considering RS value as the yield stress (YS) [18,-20] is reasonable for low thickness plates, where RS around 85–95% of YS is observed. However, RS value can decrease down to 66% of the YS for high thickness plate welds.

## **Author details**

Jon Ander Esnaola\*, Ibai Ulacia, Arkaitz Lopez-Jauregi and Done Ugarte

\*Address all correspondence to: jaesnaola@mondragon.edu

Structural Mechanics and Design, Engineering Faculty, Mondragon Unibertsitatea, Mondragón, Spain

## **References**


[5] Maddox SJ. Fatigue strength of welded structures. Woodhead publishing. 1991

capacitance cubic increase. Thus, for plate thickness over 38 mm, the average plate temperature increase ratio is below 1°C/s. Therefore, it is observed that for low plate thickness, the provided total heat is predominant over the heat absorption capacity. In contrast, for high thickness, the heat absorption capacity increase overtakes the provided total heat effect.

In the present chapter, a procedure to predict RS pattern in spray transfer multipass welding where the heat source is defined based on the welding physics is described and validated. The procedure does not require any welding experimental characterisation to define FEM input parameters, which enables its use as a predictive tool. Results showed good correlation, with

Following, the influence of plate thickness and number of passes in the RS pattern of thick T-joint welds is conducted. Results have shown that, in the studied range, the assumption of considering RS value as the yield stress (YS) [18,-20] is reasonable for low thickness plates, where RS around 85–95% of YS is observed. However, RS value can decrease down to 66% of

an average deviation of 9.15% in the thermal field and 42 MPa in the RS field.

116 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Jon Ander Esnaola\*, Ibai Ulacia, Arkaitz Lopez-Jauregi and Done Ugarte

Structural Mechanics and Design, Engineering Faculty, Mondragon Unibertsitatea,

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**Chapter 6**

**Provisional chapter**

**Numerical Simulation of Residual Stresses in Welding**

Welding technology is considered as a reliable and efficient joining method, which has been widely used in almost all the industry departments. Detrimental factors induced by welding such as micro-cracks/flaws, tensile residual stresses, high stress concentration may degrade the mechanical and fatigue properties of weld joints. Ultrasonic impact treatment (UIT) is considered one of the most efficient post-weld treatment which could improve the fatigue performance of weld joints. In this study, the effect of the UIT on residual stress distribution of 304L weld joints was particularly investigated. FE analysis simulation and the XRD experiment were performed to predict and measure residual stresses of both as-welded and the UIT-treated joints. Compared results show that simulated stresses are in good agreement with the experimental results along various paths, confirming the validity of welding model. The UIT introduces a compressive residual stress layer with depth between 2 and 3 mm near the impacting surface of weld joint.

**Keywords:** ultrasonic impact treatment (UIT), finite element modeling (FEM),

weld residual stress, stress and strain, weld simulation

**Numerical Simulation of Residual Stresses in Welding** 

DOI: 10.5772/intechopen.72394

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Welding technology has been widely applied in the fields of automobile, aviation, nuclear, vessel manufacturing and other industrial sectors due to its low cost, geometrical flexibility and desirable mechanical properties [1]. On the other hand, welding comes with the expense of some detrimental effects on welded structures such as micro-cracks/flaws, high stress concentration and tensile residual stresses. Hence, from the point view of fatigue design, welded areas are deemed as weak structural joints where cracks and tensile residual stresses are easily to be found [2]. A number of numerical techniques have been developed to model the

**and Ultrasonic Impact Treatment Process**

**and Ultrasonic Impact Treatment Process**

Lanqing Tang, Ayhan Ince and Jing Zheng

Lanqing Tang, Ayhan Ince and Jing Zheng

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72394

**Abstract**

**1. Introduction**


**Provisional chapter**

## **Numerical Simulation of Residual Stresses in Welding and Ultrasonic Impact Treatment Process and Ultrasonic Impact Treatment Process**

**Numerical Simulation of Residual Stresses in Welding** 

DOI: 10.5772/intechopen.72394

Lanqing Tang, Ayhan Ince and Jing Zheng Lanqing Tang, Ayhan Ince and Jing Zheng Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72394

#### **Abstract**

[51] Thermal conductivity for carbon steel AISI 1010 [Internet]. Available from: http://www. egunda.com/materials/alloys/carbon\_steels/show\_carbon.cfm?ID=AISI\_1010&show\_

[52] Pitz M. Merklein M. FE simulation laser assisted bending. Proceedings of the 11th

[53] Tensile properties at high temperature for S275 steel [Internet]. Available from: http:// www.thyssenfrance.com/fich\_tech\_en.asp?product\_id=17930 [Accessed: 11-06-2014] [54] EN 1993-1-2: Eurocode 3: Design of Steel Structures-Part 1-2: General Rules-Structural

[55] Safety data sheet for Stargon 82 [Internet]. Available from: http://www.cialgas.com/wp-

[56] Larrañaga J. Geometrical accuracy improvement in flexible roll forming process by

[57] Withers PJ, Bhadeshia HKDH. Residual stress. Part 1-measurement techniques. Materials

[58] Lopez-Jauregi A, Esnaola JA, Ulacia I, Urrutibeaskoa I, Madariaga A. Fatigue analysis of multipass welded joints considering residual stresses. International Journal of Fatigue.

content/uplads/2012/09/STARGON-82.pdf [Accessed: 11-06-2014]

means of local heating. PhD thesis, Mondragon Unibertsitatea. 2011

prop=tc&Page\_Title=Carbon%20Steel%20AISI%201010 [Accessed: 11-06-2014]

International Conference: Sheet Metal. 745-752

120 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Science and Technology. 2001;**17**(4):355-365

Fire Design. 2005

2015;**79**:75-85

Welding technology is considered as a reliable and efficient joining method, which has been widely used in almost all the industry departments. Detrimental factors induced by welding such as micro-cracks/flaws, tensile residual stresses, high stress concentration may degrade the mechanical and fatigue properties of weld joints. Ultrasonic impact treatment (UIT) is considered one of the most efficient post-weld treatment which could improve the fatigue performance of weld joints. In this study, the effect of the UIT on residual stress distribution of 304L weld joints was particularly investigated. FE analysis simulation and the XRD experiment were performed to predict and measure residual stresses of both as-welded and the UIT-treated joints. Compared results show that simulated stresses are in good agreement with the experimental results along various paths, confirming the validity of welding model. The UIT introduces a compressive residual stress layer with depth between 2 and 3 mm near the impacting surface of weld joint.

**Keywords:** ultrasonic impact treatment (UIT), finite element modeling (FEM), weld residual stress, stress and strain, weld simulation

#### **1. Introduction**

Welding technology has been widely applied in the fields of automobile, aviation, nuclear, vessel manufacturing and other industrial sectors due to its low cost, geometrical flexibility and desirable mechanical properties [1]. On the other hand, welding comes with the expense of some detrimental effects on welded structures such as micro-cracks/flaws, high stress concentration and tensile residual stresses. Hence, from the point view of fatigue design, welded areas are deemed as weak structural joints where cracks and tensile residual stresses are easily to be found [2]. A number of numerical techniques have been developed to model the

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

influence of tensile residual stresses on fatigue strength of welded joints [3–6]. Over the past several decades, numerous post-weld treatment techniques, including grinding, TIG dressing, hammer peening and shot peening, have been developed to address this vexing issue and improve fatigue performance of weld joints [7]. These treatments are generally classified into two different categories: geometry improvement and residual stress modification techniques. Geometry improvement techniques such as TIG dressing and grinding focus on eliminating flaws and reducing stress concentration of welded components. While residual stress modification techniques like hammer peening and shot peening lay emphasis on introducing beneficial compressive residual stresses and improving residual stress distributions of welded joints [8].

[13, 15, 16]. It was well known that the isotropic hardening model is valid for monotonic loading [9]. However, due to the Bauschinger effect, isotropic hardening model is not suitable for cyclic loadings experienced under of the UIT process [17]. On the other hand, linear kinematic hardening model could be adopted to describe material deformation behavior under cyclic loading conditions, but it could provide reasonable results under small strains loading conditions [18]. Therefore, the combined isotropic-kinematic hardening model, or Chaboche model was applied to the UIT simulation [19, 20]. In addition, in the modeling of the UIT process, regardless the complex components and ultrasonic transducer of the UIT device, the pin impact can be simplified as the movement of the impact pin tool given proper controlling parameters. These parameters consist of impact velocity, the contact force and the pin displacement. Hence, modeling strategies of the UIT can be classified into three categories: velocity-controlled simulation (VCS), force-controlled-simulation (FCS) and displacementcontrolled-simulation (DCS) [21–23]. In the VSC strategy, the velocity of the impact pin can be obtained through the approximated motion using a sinusoidal harmonic function, where the first derivative represents the velocity [17]. The FCS strategy defines the pin impact with a given load force while the DCS utilizes the permanent indentation obtained by the UIT to

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This paper focuses on effects of the UIT on residual stresses of 304L weld joints. FE analysis was carried out to simulate residual stress distributions of as-welded and the UIT-treated joints. The UIT process was simulated with the pre-existing validated stress field of residual stresses, which considered the effects of the UIT in transverse, longitudinal and throughthickness directions. In addition, the DCS and Chaboche model was introduced to improve

FE simulation of both butt and T weld joints have been performed using the Coupled Temperature-Displacement analysis provided by ABAQUS software package. The 3-D finite element models of butt joint and T-joint are depicted in **Figure 1**. As shown in **Figure 2**, to reduce the computation time, the FE models of welded joints were reduced by one-half and one-quarter using the overall symmetry and both models were simplified as the single pass welding. Geometries of both butt and T weld joints were modeled with the C3D8T element. In order to improve computed results, the refined meshes with the minimum element size of 1 × 1 × 1 mm were created in the heat affected zone (HAZ) and the weld area of FE models. The butt joint had 251,585 nodes while the T-joint had 240,692 nodes. Outer surfaces of weld joints were under both radiation and convection condition with emissivity of 0.85

symmetry plane Y-Z, line H-I/G-J and line G-H were constrained in X-direction, Y-direction and Z-direction, respectively. For the T-joint, similarly, nodes on symmetry plane Y-Z, line F-I/G-H and line F-G were restricted in X axis, Y axis and Z axis, respectively. As seen in

°C). As shown in **Figure 2(a)**, for the butt joint, nodes on

define the displacement of the pin [22, 23].

**2. Finite element (FE) modeling**

**2.1. FE modeling of weld joints**

and filming coefficient of 10 W/(m2

both the time efficiency and the preciseness of prediction.

Ultrasonic impact treatment (UIT) is a recently introduced treatment technique developed by Statnikov et al. in former Soviet Union [9]. This technique has become increasingly popular for several reasons such as reducing manpower requirements, eliminating the weld induced distortions. The UIT uses needles or hammer-like rods to impact the welding surface/toe at a high ultrasonic frequency of 18,000–27,000 Hz. The UIT, not only reduces the local stress concentration by modifying the weld toe geometry but also introduces compressive residual stresses by eliminating tensile residual stresses and introducing beneficial compressive stresses [10].

In recent years, numerous studies have been carried out to investigate effects of the UIT on the weld residual stresses and fatigue performance of weld joints [11–14]. A number of numerical models have been developed to predict the residual stress distribution and fatigue performance of UIT-treated weld joints [13, 15]. Meanwhile, experimental studies of the UIT have been also conducted [11, 12, 14]. Various measurement techniques such as X-ray diffraction and neutron diffraction were used to obtain experimental data for the validation of simulated residual stresses. In most of the cases, it has been found that the UIT introduces compressive residual stresses along varying depths and improves fatigue performances of weld joints in various extent. Turski et al. [11] found that the UIT produced compressive residual stress fields of about 2 mm in depth for 304 stainless steel. Liu et al. [12] measured residual stresses of UIT-treated high strength steel weld joints. The results indicated that the UIT had the same effect on both longitudinal and transverse stresses and introduced a compressive residual stress layer up to 4 mm in depth. Foehrenbach et al. [13] developed a computationally efficient approach to predict residual stresses induced by the UIT process using a commercial finite element software package. It was found that compressive residual stresses up to a base material yield strength occurred after the UIT treatment. Dekhtyar et al. [14] studied the effect of the UIT on fatigue behavior of Ti–6Al–4V specimens. Based on experimental data, it was reported that the UIT introduced compressive stresses of −570 MPa, achieving two thirds of yield limit of the material. Fatigue strength of as-welded joints increased by 60% at 10<sup>7</sup> cycles and fatigue life was extended 102 times at stress amplitude of 300 MPa.

To assess fatigue life improvement by the UIT treatment, it is necessary to accurately estimate residual stress distribution through finite element analysis (FEA). Recent numerical studies emphasized on the influence of mesh type, material properties, boundary conditions, pin tool size, modeling strategy and material hardening rules on computed numerical results [13, 15, 16]. It was well known that the isotropic hardening model is valid for monotonic loading [9]. However, due to the Bauschinger effect, isotropic hardening model is not suitable for cyclic loadings experienced under of the UIT process [17]. On the other hand, linear kinematic hardening model could be adopted to describe material deformation behavior under cyclic loading conditions, but it could provide reasonable results under small strains loading conditions [18]. Therefore, the combined isotropic-kinematic hardening model, or Chaboche model was applied to the UIT simulation [19, 20]. In addition, in the modeling of the UIT process, regardless the complex components and ultrasonic transducer of the UIT device, the pin impact can be simplified as the movement of the impact pin tool given proper controlling parameters. These parameters consist of impact velocity, the contact force and the pin displacement. Hence, modeling strategies of the UIT can be classified into three categories: velocity-controlled simulation (VCS), force-controlled-simulation (FCS) and displacementcontrolled-simulation (DCS) [21–23]. In the VSC strategy, the velocity of the impact pin can be obtained through the approximated motion using a sinusoidal harmonic function, where the first derivative represents the velocity [17]. The FCS strategy defines the pin impact with a given load force while the DCS utilizes the permanent indentation obtained by the UIT to define the displacement of the pin [22, 23].

This paper focuses on effects of the UIT on residual stresses of 304L weld joints. FE analysis was carried out to simulate residual stress distributions of as-welded and the UIT-treated joints. The UIT process was simulated with the pre-existing validated stress field of residual stresses, which considered the effects of the UIT in transverse, longitudinal and throughthickness directions. In addition, the DCS and Chaboche model was introduced to improve both the time efficiency and the preciseness of prediction.

## **2. Finite element (FE) modeling**

#### **2.1. FE modeling of weld joints**

influence of tensile residual stresses on fatigue strength of welded joints [3–6]. Over the past several decades, numerous post-weld treatment techniques, including grinding, TIG dressing, hammer peening and shot peening, have been developed to address this vexing issue and improve fatigue performance of weld joints [7]. These treatments are generally classified into two different categories: geometry improvement and residual stress modification techniques. Geometry improvement techniques such as TIG dressing and grinding focus on eliminating flaws and reducing stress concentration of welded components. While residual stress modification techniques like hammer peening and shot peening lay emphasis on introducing beneficial compressive residual stresses and improving residual stress distributions

122 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Ultrasonic impact treatment (UIT) is a recently introduced treatment technique developed by Statnikov et al. in former Soviet Union [9]. This technique has become increasingly popular for several reasons such as reducing manpower requirements, eliminating the weld induced distortions. The UIT uses needles or hammer-like rods to impact the welding surface/toe at a high ultrasonic frequency of 18,000–27,000 Hz. The UIT, not only reduces the local stress concentration by modifying the weld toe geometry but also introduces compressive residual stresses by eliminating tensile residual stresses and introducing beneficial compressive

In recent years, numerous studies have been carried out to investigate effects of the UIT on the weld residual stresses and fatigue performance of weld joints [11–14]. A number of numerical models have been developed to predict the residual stress distribution and fatigue performance of UIT-treated weld joints [13, 15]. Meanwhile, experimental studies of the UIT have been also conducted [11, 12, 14]. Various measurement techniques such as X-ray diffraction and neutron diffraction were used to obtain experimental data for the validation of simulated residual stresses. In most of the cases, it has been found that the UIT introduces compressive residual stresses along varying depths and improves fatigue performances of weld joints in various extent. Turski et al. [11] found that the UIT produced compressive residual stress fields of about 2 mm in depth for 304 stainless steel. Liu et al. [12] measured residual stresses of UIT-treated high strength steel weld joints. The results indicated that the UIT had the same effect on both longitudinal and transverse stresses and introduced a compressive residual stress layer up to 4 mm in depth. Foehrenbach et al. [13] developed a computationally efficient approach to predict residual stresses induced by the UIT process using a commercial finite element software package. It was found that compressive residual stresses up to a base material yield strength occurred after the UIT treatment. Dekhtyar et al. [14] studied the effect of the UIT on fatigue behavior of Ti–6Al–4V specimens. Based on experimental data, it was reported that the UIT introduced compressive stresses of −570 MPa, achieving two thirds of yield limit of the material. Fatigue strength of as-welded joints increased by 60% at 10<sup>7</sup> cycles

times at stress amplitude of 300 MPa.

To assess fatigue life improvement by the UIT treatment, it is necessary to accurately estimate residual stress distribution through finite element analysis (FEA). Recent numerical studies emphasized on the influence of mesh type, material properties, boundary conditions, pin tool size, modeling strategy and material hardening rules on computed numerical results

of welded joints [8].

stresses [10].

and fatigue life was extended 102

FE simulation of both butt and T weld joints have been performed using the Coupled Temperature-Displacement analysis provided by ABAQUS software package. The 3-D finite element models of butt joint and T-joint are depicted in **Figure 1**. As shown in **Figure 2**, to reduce the computation time, the FE models of welded joints were reduced by one-half and one-quarter using the overall symmetry and both models were simplified as the single pass welding. Geometries of both butt and T weld joints were modeled with the C3D8T element. In order to improve computed results, the refined meshes with the minimum element size of 1 × 1 × 1 mm were created in the heat affected zone (HAZ) and the weld area of FE models. The butt joint had 251,585 nodes while the T-joint had 240,692 nodes. Outer surfaces of weld joints were under both radiation and convection condition with emissivity of 0.85 and filming coefficient of 10 W/(m2 °C). As shown in **Figure 2(a)**, for the butt joint, nodes on symmetry plane Y-Z, line H-I/G-J and line G-H were constrained in X-direction, Y-direction and Z-direction, respectively. For the T-joint, similarly, nodes on symmetry plane Y-Z, line F-I/G-H and line F-G were restricted in X axis, Y axis and Z axis, respectively. As seen in

**Figure 3**, temperature dependent properties of 304L were obtained from the literature [24]. A double-ellipsoid heat source model was adopted in numerical simulation of welding process. The actual welding experimental data for welding process and parameters was listed

**Material C Si Mn Cr Ni S P Fe** Base metal (06Cr19Ni10) 0.045 0.45 1.10 17.1 8.00 0.001 0.028 Rest Electrode (ER308L) 0.03 0.60 1.80 20.0 10.0 0.008 0.015 Rest

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In the FE modeling of the UIT process, residual stress results obtained from the welding process were taken as the initial model state. As shown in **Figure 4**, in the middle of the weld zone, an impact area with the minimum element size of 0.1 × 0.1 × 0.5 mm were created in the weld simulation to achieve refined mesh area for the impact simulation so that a re-meshing routine could be avoided to reduce computational time during the UIT simulation. For the material hardening rule, the combined isotropic and kinematic model was used to characterize the material deformation behavior in the FE model of the UIT simulation. The DCS strategy was adopted to control the displacement motion of the pin tool. The pin was set to hit the weld toe at the speed of 2 m/s until it reached the design depth, which was considered as one complete impact. **Figure 5** shows the position and indentation of pin tool for both the butt and T joints. The diameter and the permanent indentation of the pin were 3 and 0.1 mm respectively. The angles of pins in butt joint and T-joint were determined as 75 and 67.5°, respectively. The pin model was modeled as a discrete rigid body and, the pin was traveling along the welding direction and hitting the weld joint every 0.3 mm to ensure a sufficient overlap during the UIT treatment. It was worth noting that in the DCS strategy, the speed of

in **Tables 1** and **2**.

**2.2. FE modeling of UIT process**

the UIT treatment was considered to be non-essential.

**Parameter name Value** Welding voltage (volts) 24.5 Welding current (amperes) 217 Welding speed (cm/min) 40 Electrode type ER308L Welding electrode diameter (mm) 1.2

Shielding gas type Argon (97%), O2

Shielding gas flow rate (L/min) 20

**Table 2.** Welding parameters of MIG welding technology.

(3%)

**Table 1.** Chemical composition of base metal and welding electrode (wt%).

**Figure 1.** 3-D finite element model: (a) butt joint and (b) T-joint.

**Figure 2.** A schematic representation of weld geometry: (a) butt joint and (b) T-joint.

**Figure 3.** Thermal properties and mechanical properties.


**Table 1.** Chemical composition of base metal and welding electrode (wt%).

**Figure 3**, temperature dependent properties of 304L were obtained from the literature [24]. A double-ellipsoid heat source model was adopted in numerical simulation of welding process. The actual welding experimental data for welding process and parameters was listed in **Tables 1** and **2**.

#### **2.2. FE modeling of UIT process**

In the FE modeling of the UIT process, residual stress results obtained from the welding process were taken as the initial model state. As shown in **Figure 4**, in the middle of the weld zone, an impact area with the minimum element size of 0.1 × 0.1 × 0.5 mm were created in the weld simulation to achieve refined mesh area for the impact simulation so that a re-meshing routine could be avoided to reduce computational time during the UIT simulation. For the material hardening rule, the combined isotropic and kinematic model was used to characterize the material deformation behavior in the FE model of the UIT simulation. The DCS strategy was adopted to control the displacement motion of the pin tool. The pin was set to hit the weld toe at the speed of 2 m/s until it reached the design depth, which was considered as one complete impact. **Figure 5** shows the position and indentation of pin tool for both the butt and T joints. The diameter and the permanent indentation of the pin were 3 and 0.1 mm respectively. The angles of pins in butt joint and T-joint were determined as 75 and 67.5°, respectively. The pin model was modeled as a discrete rigid body and, the pin was traveling along the welding direction and hitting the weld joint every 0.3 mm to ensure a sufficient overlap during the UIT treatment. It was worth noting that in the DCS strategy, the speed of the UIT treatment was considered to be non-essential.


**Table 2.** Welding parameters of MIG welding technology.

**Figure 3.** Thermal properties and mechanical properties.

**Figure 1.** 3-D finite element model: (a) butt joint and (b) T-joint.

124 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 2.** A schematic representation of weld geometry: (a) butt joint and (b) T-joint.

**Figure 4.** Impact zone of UIT simulation: (a) butt joint and (b) T-joint.

**3.1. Residual stress predictions in weld butt joint**

For validating the FE model of welding process, experimental data obtained from previous works [25, 26] were compared with the predicted residual stress results. As shown in **Figures 6** and **7**, predicted and experimental residual stresses of butt joint along paths A-B and A-C are compared, respectively. In particular, the blue lines and the red dots marked in figures demonstrate the predicted residual stresses by FEA and the experimental data obtained by the XRD method, respectively. As depicted in **Figure 6**, both σ\_xx and σ\_zz reached their maximum values near the weld zone, then dropped as distance from the point A increased and finally stabilized around the zero value. Additionally, it was found that the simulation results are in good agreement with the experimental results along the A-B path, confirming the prediction capability of welding model.

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**Figure 6.** Transverse (a) and longitudinal (b) residual stress distributions along A-B path in butt welded joints.

**Figure 7** shows the predicted and measured transverse residual stresses along the A-C path. Obviously, at the point A, the point C and in their vicinity, the residual stresses are compressive stresses. In the middle of the A-C path, the transverse residual stresses converted into tensile stresses with peak value of 275 MPa. It was also indicated that there existed some

**Figure 5.** Pin tool position and indentation: (a) butt joint and (b) T-joint.

#### **3. Discussions and results**

As shown in **Figures 6**–**11**, paths A-B, A-C and A-D were selected to evaluate residual stress distributions for the both butt and T joints. Meanwhile, in order to describe residual stresses in directions of X, Y and Z axes, three specific words "transverse," "through-thickness" and "longitudinal" were introduced. The transverse residual stress, the through-thickness residual stress and the longitudinal residual stress indicated σ\_xx, σ\_yy and σ\_zz, respectively.

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**Figure 6.** Transverse (a) and longitudinal (b) residual stress distributions along A-B path in butt welded joints.

#### **3.1. Residual stress predictions in weld butt joint**

**3. Discussions and results**

**Figure 4.** Impact zone of UIT simulation: (a) butt joint and (b) T-joint.

126 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 5.** Pin tool position and indentation: (a) butt joint and (b) T-joint.

As shown in **Figures 6**–**11**, paths A-B, A-C and A-D were selected to evaluate residual stress distributions for the both butt and T joints. Meanwhile, in order to describe residual stresses in directions of X, Y and Z axes, three specific words "transverse," "through-thickness" and "longitudinal" were introduced. The transverse residual stress, the through-thickness residual stress and the longitudinal residual stress indicated σ\_xx, σ\_yy and σ\_zz, respectively.

For validating the FE model of welding process, experimental data obtained from previous works [25, 26] were compared with the predicted residual stress results. As shown in **Figures 6** and **7**, predicted and experimental residual stresses of butt joint along paths A-B and A-C are compared, respectively. In particular, the blue lines and the red dots marked in figures demonstrate the predicted residual stresses by FEA and the experimental data obtained by the XRD method, respectively. As depicted in **Figure 6**, both σ\_xx and σ\_zz reached their maximum values near the weld zone, then dropped as distance from the point A increased and finally stabilized around the zero value. Additionally, it was found that the simulation results are in good agreement with the experimental results along the A-B path, confirming the prediction capability of welding model.

**Figure 7** shows the predicted and measured transverse residual stresses along the A-C path. Obviously, at the point A, the point C and in their vicinity, the residual stresses are compressive stresses. In the middle of the A-C path, the transverse residual stresses converted into tensile stresses with peak value of 275 MPa. It was also indicated that there existed some

**Figure 7.** Transverse residual stress distributions along A-C path in butt welded joints.

errors between the calculated results and the measured ones. The measured residual stresses were higher in the middle of the A-C path but lower at each end of the A-C path. Those errors may be attributed to the measurement error of the XRD method, which was sensitive to the

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**Figure 9.** Transverse (a) and longitudinal (b) residual stress distributions along A-C path in T-joints.

**Figures 8** and **9** depict residual stresses of T-joint along the path A-B and path A-C, respectively. As shown in **Figure 8**, along the path A-B, both the transverse residual stress σ\_xx and the longitudinal residual stress σ\_zz achieved their peaks in the vicinity of weld area. Nevertheless, with the distance from the point A, transverse residual stresses showed a relatively different trend with the longitudinal residual stresses. Transverse residual stresses decreased as the distance from the point A increased and dropped to the zero value at the point B, shown in **Figure 8(a)**. Unlike the transverse residual stresses, longitudinal residual

microstructure evolution of welding zone [10].

**3.2. Residual stress predictions in weld T-joint**

**Figure 8.** Transverse (a) and longitudinal (b) residual stress distributions along A-B path in T-joints.

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**Figure 9.** Transverse (a) and longitudinal (b) residual stress distributions along A-C path in T-joints.

errors between the calculated results and the measured ones. The measured residual stresses were higher in the middle of the A-C path but lower at each end of the A-C path. Those errors may be attributed to the measurement error of the XRD method, which was sensitive to the microstructure evolution of welding zone [10].

#### **3.2. Residual stress predictions in weld T-joint**

**Figure 7.** Transverse residual stress distributions along A-C path in butt welded joints.

128 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

**Figure 8.** Transverse (a) and longitudinal (b) residual stress distributions along A-B path in T-joints.

**Figures 8** and **9** depict residual stresses of T-joint along the path A-B and path A-C, respectively. As shown in **Figure 8**, along the path A-B, both the transverse residual stress σ\_xx and the longitudinal residual stress σ\_zz achieved their peaks in the vicinity of weld area. Nevertheless, with the distance from the point A, transverse residual stresses showed a relatively different trend with the longitudinal residual stresses. Transverse residual stresses decreased as the distance from the point A increased and dropped to the zero value at the point B, shown in **Figure 8(a)**. Unlike the transverse residual stresses, longitudinal residual stresses first dropped dramatically with the increasing distance from the point A and reached the compressive peak value of −75 MPa at the distance of approximately 5 mm from the point A. Then longitudinal residual stresses increase significantly to zero at the distance of 25 mm from the point and remained stable. Notably, both transverse and longitudinal residual stresses changed into negligible values in the relatively far distant from the weld zone, which was consistent with the results of previous studies [27, 29–31, 34, 35].

**Figure 9(a)** and **(b)** demonstrate transverse and longitudinal residual stresses along the A-C path of the T-joint, respectively. Obviously, the distribution trend of the transverse residual stresses was in line with that of the longitudinal residual stresses. Both the transverse and longitudinal residual stresses obtained their peak values of 345 and 205 MPa in the middle of the welding line (near point A). With the increasing distance from the point A, transverse and longitudinal stresses dropped, changing from the tensile values into the compressive ones. The maximum compressive value of transverse residual stresses (−285 MPa) were considerably higher than that of longitudinal residual stresses (−70 MPa).

#### **3.3. Effects of UIT on weld residual stresses**

In order to evaluate the effects of the UIT on residual stresses along the A-D path (the depth direction), FE simulation residual stresses for the UIT-treated model were analyzed and compared with those for the as-welded model. **Figures 10** and **11** depict residual stresses of butt joint and T-joint, respectively. As shown in **Figure 10**, before the UIT, the transverse, longitudinal and through-thickness residual stresses of butt weld joint remained stable along the A-D path, with the average values of 189, 267 and 9 MPa. After the UIT, near the upper impacting surface of butt weld joint, the transverse, longitudinal and through-thickness residual stresses changed into compressive stresses with peak values of −150, −355 and −75 MPa. As for the T-joint, before the UIT, high tensile stresses which were close to the yield strength of the base metal appeared near the upper surface of the as-welded joint. The maximum values of the transverse, longitudinal and through-thickness residual stresses were 364, 372 and 151 MPa. Like the butt joint, after the UIT, the transverse, longitudinal and through-thickness residual stresses of T-joint also transformed into the compressive stresses. The peak values of compressive stresses in the transverse direction, the longitudinal direction and the through-thickness direction were −255, −320 and −70 MPa, respectively. It was noteworthy that the maximum compressive stresses in the longitudinal direction for both butt joint and T-joint were relatively higher than the compressive limit of 304L steel, which implied cold working by the UIT induced plastic deformation of the weld joint. The similar level of compressive residual stresses higher than the material's yield limit was also obtained and reported by previous studies [11, 28, 32].

It was also found that the influence of the UIT decreased with depth. For the butt joint, the depth of compressive stresses in three directions was around 2 mm. Similarly, as for the T-joint, the effective depth of compressive layer in the transverse, longitudinal and through thickness directions introduced by the UIT were 2.5, 2.3 and 3.1 mm, respectively. The depths of compressive residual stresses by UIT were similar with the results of previous studies [33].

**Figure 10.** Transverse (a), longitudinal (b) and through-thickness (c) residual stress distributions along A-D path in

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as-welded and UIT-treated butt joints.

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stresses first dropped dramatically with the increasing distance from the point A and reached the compressive peak value of −75 MPa at the distance of approximately 5 mm from the point A. Then longitudinal residual stresses increase significantly to zero at the distance of 25 mm from the point and remained stable. Notably, both transverse and longitudinal residual stresses changed into negligible values in the relatively far distant from the weld zone, which

**Figure 9(a)** and **(b)** demonstrate transverse and longitudinal residual stresses along the A-C path of the T-joint, respectively. Obviously, the distribution trend of the transverse residual stresses was in line with that of the longitudinal residual stresses. Both the transverse and longitudinal residual stresses obtained their peak values of 345 and 205 MPa in the middle of the welding line (near point A). With the increasing distance from the point A, transverse and longitudinal stresses dropped, changing from the tensile values into the compressive ones. The maximum compressive value of transverse residual stresses (−285 MPa) were consider-

In order to evaluate the effects of the UIT on residual stresses along the A-D path (the depth direction), FE simulation residual stresses for the UIT-treated model were analyzed and compared with those for the as-welded model. **Figures 10** and **11** depict residual stresses of butt joint and T-joint, respectively. As shown in **Figure 10**, before the UIT, the transverse, longitudinal and through-thickness residual stresses of butt weld joint remained stable along the A-D path, with the average values of 189, 267 and 9 MPa. After the UIT, near the upper impacting surface of butt weld joint, the transverse, longitudinal and through-thickness residual stresses changed into compressive stresses with peak values of −150, −355 and −75 MPa. As for the T-joint, before the UIT, high tensile stresses which were close to the yield strength of the base metal appeared near the upper surface of the as-welded joint. The maximum values of the transverse, longitudinal and through-thickness residual stresses were 364, 372 and 151 MPa. Like the butt joint, after the UIT, the transverse, longitudinal and through-thickness residual stresses of T-joint also transformed into the compressive stresses. The peak values of compressive stresses in the transverse direction, the longitudinal direction and the through-thickness direction were −255, −320 and −70 MPa, respectively. It was noteworthy that the maximum compressive stresses in the longitudinal direction for both butt joint and T-joint were relatively higher than the compressive limit of 304L steel, which implied cold working by the UIT induced plastic deformation of the weld joint. The similar level of compressive residual stresses higher than the material's yield limit was also obtained and reported by previous studies [11, 28, 32]. It was also found that the influence of the UIT decreased with depth. For the butt joint, the depth of compressive stresses in three directions was around 2 mm. Similarly, as for the T-joint, the effective depth of compressive layer in the transverse, longitudinal and through thickness directions introduced by the UIT were 2.5, 2.3 and 3.1 mm, respectively. The depths of compressive residual stresses by UIT were similar with the results of previous studies [33].

was consistent with the results of previous studies [27, 29–31, 34, 35].

130 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

ably higher than that of longitudinal residual stresses (−70 MPa).

**3.3. Effects of UIT on weld residual stresses**

**Figure 10.** Transverse (a), longitudinal (b) and through-thickness (c) residual stress distributions along A-D path in as-welded and UIT-treated butt joints.

The FE residual stress results in UIT-treated weld joint demonstrated that the UIT introduced compressive residual stress layer with various depth, which brought beneficial effect on

Numerical Simulation of Residual Stresses in Welding and Ultrasonic Impact Treatment Process

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133

This study focuses on evaluating effects of the UIT on the residual stresses of 304L butt and T-joints. FEA method was used to simulate both the welding and the UIT processes. To validate the prediction accuracy of the welding model, experimental data were compared with

**1.** Both the simulation and the experimental results indicated that residual stresses reached their maximum values near the weld zone, then dropped with the increasing distance from

**2.** The simulation results are in good agreement with the experimental results along the A-B

**3.** The UIT introduces a compressive residual stress layer with depth between 2 and 3 mm near the impacting surface of weld joint. The effect of the UIT decreased with depth.

2 Department of Mechanical, Industrial and Aerospace Engineering, Concordia University,

[1] Teng TL, Fung CP, Chang PH, Yang WC. Analysis of residual stresses and distortions in T-joint fillet welds. International Journal of Pressure Vessels and Piping. 2001;**78**:523-538.

[2] Weich I, Thomas U, Thomas N, Dilger K, Chalandar HE. Fatigue behavior of welded high-strength steels after high frequency mechanical post-weld treatments. Weld World.

the simulated ones. Based on the results, the following conclusions can be drawn:

fatigue strength of the material [7, 33–38].

the weld zone and finally stabilized the zero value.

, Ayhan Ince1,2\* and Jing Zheng<sup>1</sup>

1 Purdue Polytechnic Institute, Purdue University, West Lafayette, IN, USA

\*Address all correspondence to: aince@purdue.edu

DOI: 10.1016/S0308-0161(01)00074-6

2009;**53**:R322-R332. DOI: 10.1007/BF03263475

path, confirming the welding model accuracy

**4. Conclusions**

**Author details**

Montreal, Quebec, Canada

Lanqing Tang<sup>1</sup>

**References**

**Figure 11.** Transverse (a), longitudinal (b) and through-thickness (c) residual stress distributions along A-D path in as-welded and UIT-treated T-joints.

The FE residual stress results in UIT-treated weld joint demonstrated that the UIT introduced compressive residual stress layer with various depth, which brought beneficial effect on fatigue strength of the material [7, 33–38].

## **4. Conclusions**

This study focuses on evaluating effects of the UIT on the residual stresses of 304L butt and T-joints. FEA method was used to simulate both the welding and the UIT processes. To validate the prediction accuracy of the welding model, experimental data were compared with the simulated ones. Based on the results, the following conclusions can be drawn:


## **Author details**

Lanqing Tang<sup>1</sup> , Ayhan Ince1,2\* and Jing Zheng<sup>1</sup>


2 Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, Canada

## **References**

**Figure 11.** Transverse (a), longitudinal (b) and through-thickness (c) residual stress distributions along A-D path in

132 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

as-welded and UIT-treated T-joints.


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**Chapter 7**

Provisional chapter

**Rapid Calculation of Residual Notch Stress Intensity**

Rapid Calculation of Residual Notch Stress Intensity

Marco Colussi, Paolo Ferro, Filippo Berto and

Marco Colussi, Paolo Ferro, Filippo Berto and

Additional information is available at the end of the chapter

the zone very close to the notch tip is negligible.

finite element analysis, coarse mesh

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73514

Giovanni Meneghetti

Giovanni Meneghetti

Abstract

**Factors (R-NSIFs) by Means of the Peak Stress Method**

DOI: 10.5772/intechopen.73514

The intensity of the residual singular stress distribution can be quantified by the residual notch stress intensity factor (R-NSIF), which might be a useful stress parameter to include in local approaches for fatigue strength assessments of welded joints. In order to calculate the residual stress fields by means of welding process simulations, the mesh adopted in numerical models has necessarily to be very fine. Unfortunately, the nonlinear and transient behavior of the welding simulation makes numerical analyses extremely demanding in terms of computational time, particularly, if large welded structures and/or multipass welds have to be simulated. In this scenario, the use of methods aimed at reducing the computational effort to estimate local stresses and strains in welded structures can be effective. Among these, the peak stress method has been proposed to estimate the notch stress intensity factors (NSIFs) at sharp V-notches, using coarse finite element patterns. In this work, the peak stress method (PSM) has been used to calculate the R-NSIF of a full penetration welded T-joint. It has been shown that the PSM can successfully be used to estimate R-NSIFs values, provided that the stress redistribution induced by plasticity in

Keywords: residual notch stress intensity factor, residual stress, peak stress method,

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Factors (R-NSIFs) by Means of the Peak Stress Method


#### **Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method** Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method

DOI: 10.5772/intechopen.73514

Marco Colussi, Paolo Ferro, Filippo Berto and Giovanni Meneghetti Marco Colussi, Paolo Ferro, Filippo Berto and Giovanni Meneghetti

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73514

#### Abstract

[27] Liang W, Murakawa H, Deng D. Investigation of welding residual stress distribution in a thick-plate joint with an emphasis on the features near weld end-start. Materials &

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[34] Liu Y, Wang DP, Deng CY, Xia LQ, Huo LH, Wang LJ, Gong BM. Influence of re-ultrasonic impact treatment on fatigue behaviors of S690QL welded joints. International Journal of

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[38] Ince A, Bang A. Deviatoric Neuber method for stress and strain analysis at notches under multiaxial loadings. International Journal of Fatigue. 2017;**102**:229-240. DOI: 10.1016/j.

Vessels and Piping. 1992;**51**:241-256. DOI: 10.1016/0308-0161(92)90083-R

Design. 2015;**67**:303-312. DOI: 10.1016/j.matdes.2014.11.037

136 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

190. DOI: 10.1016/j.jmatprotec.2015.09.007

2006;**22**:232-237. DOI: 10.1179/174328406X83897

2005;**13**:553-566. DOI: 10.1088/0965-0393/13/4/006

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Fatigue. 2014;**66**:155-160. DOI: 10.1016/j.ijfatigue.2014.03.024

10.1016/S0142-1123(03)00151-8

IJVD.2015.069486

10.4271/2017-01-0329

ijfatigue.2017.05.007

The intensity of the residual singular stress distribution can be quantified by the residual notch stress intensity factor (R-NSIF), which might be a useful stress parameter to include in local approaches for fatigue strength assessments of welded joints. In order to calculate the residual stress fields by means of welding process simulations, the mesh adopted in numerical models has necessarily to be very fine. Unfortunately, the nonlinear and transient behavior of the welding simulation makes numerical analyses extremely demanding in terms of computational time, particularly, if large welded structures and/or multipass welds have to be simulated. In this scenario, the use of methods aimed at reducing the computational effort to estimate local stresses and strains in welded structures can be effective. Among these, the peak stress method has been proposed to estimate the notch stress intensity factors (NSIFs) at sharp V-notches, using coarse finite element patterns. In this work, the peak stress method (PSM) has been used to calculate the R-NSIF of a full penetration welded T-joint. It has been shown that the PSM can successfully be used to estimate R-NSIFs values, provided that the stress redistribution induced by plasticity in the zone very close to the notch tip is negligible.

Keywords: residual notch stress intensity factor, residual stress, peak stress method, finite element analysis, coarse mesh

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 1. Introduction

Residual stresses are induced on fusion-welded joints as a consequence of thermal gradients and nonuniform plastic deformations during the cooling phase. According to clamping conditions, process parameters and kind of alloys to be welded, they can be negative or positive. Positive, or tensile residual stresses, are known to be detrimental for the high cycle fatigue strength joints [1, 2], whereas their effect on low cycle fatigue resistance is found negligible or null, as well. This is because the higher the stress amplitude, the higher the extension of plastic deformation in the fatigue crack initiation sites (weld toe or weld root) that cancels the preexisting residual stress state. On the other hand, negative residual stresses induced by fusion welding have been found to increase the fatigue strength of joints [3] and thus are considered beneficial for the joint itself. Residual stress effect on fatigue strength of welded components is implicitly taken into account by design fatigue curves obtained from experimental data generated by testing welded joints prepared with different process parameters. Despite this current methodology, new design approaches that take into account residual stress explicitly were published in recent literature [4–8]. Hensel et al. proposed a method that replaces the nominal stress ratio with the effective stress ratio to describe the combined effect of mean and residual stresses. Ferro [4], on the other hand, suggested the use of the strain energy density (SED) approach [9] to quantify the residual stress effect on fatigue strength of welded joints through the assessment of residual notch stress intensity factors (R-NSIFs). The analysis of residual stress distribution has been a challenging task since many years. The a posteriori assessment of residual stress can be performed by experimental techniques, though they are time-consuming and expensive and provide data at single points (in most cases at the surface) of the joint. A priori residual stress determination can be obtained by numerical models, yet they need to be validated. Welding simulations are very complex because fluid dynamics, metallurgical, thermal and mechanical phenomena interact with each other [10]. When residual stress and strain are the major goals of the simulation, fluid dynamics of welding pool is almost always not taken into account. In these cases, the fusion zone is modeled by power density distribution functions whose shape and dimensions depend on welding technology (laser welding, arc welding and so on) and process parameters, respectively. Furthermore, the analysis is transient and nonlinear [11]. Numerical models require high mesh densities in order to capture the severe thermal gradient induced by the welding source. Moreover, in real components, multipass welding is often adopted. Promising approaches are already present in literature, but not yet extensively validated. In the 'macroweld deposit approach', the heat is applied in a welding instantaneously, without using a power source. The macrosteps number is chosen a priori based on the experience and real welding speed. The higher the welding speed, the longer is the single macrostep. The heat transferred into the structure is the same as in the real process, but it occurs in another time frame. In contrast to the macroweld deposit methodology, with the local-global method, the welding simulation is carried out on a refined local model (LM), whose geometry is extracted from the global structure (GS). The nodal displacements coming from LM solution are applied to the GS and a linear elastic computation is finally performed to assess the global distortion. The mesh can be locally refined and the refined zone follows the welding source by saving computational time. Models with coupled 3D and shell elements are also used to simplify the analysis. The bead is modeled with 3D elements, while the plates are modeled with shell elements. Finally, a 2D model can also be used to simplify the simulation. In this case, the welding source is thought to pass across the modeled cross section and melting the alloy. Stress and stain are computed under generalized plain strain condition. In previous works, it has been demonstrated that if the weld toe is modeled as a sharp, zero radius, V-shaped notch, residual stress field near that zone is singular [12–14] and its sign depends on both clamping conditions and metallurgical characteristics of the alloy to be welded [13, 14]. This outcome of numerical simulations allows to treat the asymptotic residual stress field like the load-induced singular stress field by means of the R-NSIF (residual-notch stress intensity factor), i.e., a stress field parameter able to quantify the intensity of the residual stresses near the weld toe. Because, direct R-NSIF calculation from asymptotic local stress fields requires very fine meshes, new strategies are needed to speed up numerical analysis. In this context, the peak stress method (PSM) has been proved to be suitable for the notch stress intensity factors (NSIFs) calculation by means of coarse meshes [15]. Therefore, in the present work, the use of

Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method

http://dx.doi.org/10.5772/intechopen.73514

139

The peak stress method (PSM) is an engineering, FE-based method to estimate the notch stress intensity factors (NSIFs) at the weld toe and at the weld root of welded joints. The basic idea is to use very coarse meshes, if compared with those required to evaluate directly the asymptotic stress distributions required to apply the NSIFs definitions. The second peculiarity of the method is that the sole linear elastic peak stress evaluated at the sharp V-notch tip is necessary and sufficient to estimate the NSIF: therefore, the singular stress fields do not need to be postprocessed according to the NSIFs definitions (Eqs. (1) and (2)). Both these features of the

In plane problems, the local linear elastic stress fields close to the tip of sharp V-notches, like those shown in the welded joint of Figure 1, can be expressed as functions of the relevant NSIFs, which quantify the magnitude of the asymptotic singular stress distributions. The asymptotic, singular stress distributions ahead of sharp V-notches under mode I (opening) and mode II (sliding) loadings have been determined by Williams [16]. The mode I and mode II NSIFs can be defined according to Gross and Mendelson [17] by means of Eqs. (1) and (2), respectively.

<sup>r</sup>!<sup>0</sup> ð Þ σθθ <sup>θ</sup>¼<sup>θ</sup> � <sup>r</sup>

<sup>r</sup>!<sup>0</sup> ð Þ <sup>τ</sup><sup>r</sup><sup>θ</sup> <sup>θ</sup>¼<sup>θ</sup> � <sup>r</sup>

The stress singularity exponents λ<sup>1</sup> and λ<sup>2</sup> depend on the notch opening angle 2α [16] and are reported in Table 1. The stress components σθθ and τr<sup>θ</sup> are calculated along the direction θ = 0,

1�λ<sup>2</sup>

<sup>1</sup>�λ<sup>1</sup> � � (1)

� � (2)

the PSM is validated also for the R-NSIFs assessment.

method make it useful in practical applications.

i.e., the notch bisector (see Figure 1).

2. Analytical background of the peak stress method

<sup>K</sup><sup>1</sup> <sup>¼</sup> ffiffiffiffiffiffi

<sup>K</sup><sup>2</sup> <sup>¼</sup> ffiffiffiffiffiffi

<sup>2</sup><sup>π</sup> <sup>p</sup> � lim

<sup>2</sup><sup>π</sup> <sup>p</sup> � lim

computational time. Models with coupled 3D and shell elements are also used to simplify the analysis. The bead is modeled with 3D elements, while the plates are modeled with shell elements. Finally, a 2D model can also be used to simplify the simulation. In this case, the welding source is thought to pass across the modeled cross section and melting the alloy. Stress and stain are computed under generalized plain strain condition. In previous works, it has been demonstrated that if the weld toe is modeled as a sharp, zero radius, V-shaped notch, residual stress field near that zone is singular [12–14] and its sign depends on both clamping conditions and metallurgical characteristics of the alloy to be welded [13, 14]. This outcome of numerical simulations allows to treat the asymptotic residual stress field like the load-induced singular stress field by means of the R-NSIF (residual-notch stress intensity factor), i.e., a stress field parameter able to quantify the intensity of the residual stresses near the weld toe. Because, direct R-NSIF calculation from asymptotic local stress fields requires very fine meshes, new strategies are needed to speed up numerical analysis. In this context, the peak stress method (PSM) has been proved to be suitable for the notch stress intensity factors (NSIFs) calculation by means of coarse meshes [15]. Therefore, in the present work, the use of the PSM is validated also for the R-NSIFs assessment.

### 2. Analytical background of the peak stress method

1. Introduction

Residual stresses are induced on fusion-welded joints as a consequence of thermal gradients and nonuniform plastic deformations during the cooling phase. According to clamping conditions, process parameters and kind of alloys to be welded, they can be negative or positive. Positive, or tensile residual stresses, are known to be detrimental for the high cycle fatigue strength joints [1, 2], whereas their effect on low cycle fatigue resistance is found negligible or null, as well. This is because the higher the stress amplitude, the higher the extension of plastic deformation in the fatigue crack initiation sites (weld toe or weld root) that cancels the preexisting residual stress state. On the other hand, negative residual stresses induced by fusion welding have been found to increase the fatigue strength of joints [3] and thus are considered beneficial for the joint itself. Residual stress effect on fatigue strength of welded components is implicitly taken into account by design fatigue curves obtained from experimental data generated by testing welded joints prepared with different process parameters. Despite this current methodology, new design approaches that take into account residual stress explicitly were published in recent literature [4–8]. Hensel et al. proposed a method that replaces the nominal stress ratio with the effective stress ratio to describe the combined effect of mean and residual stresses. Ferro [4], on the other hand, suggested the use of the strain energy density (SED) approach [9] to quantify the residual stress effect on fatigue strength of welded joints through the assessment of residual notch stress intensity factors (R-NSIFs). The analysis of residual stress distribution has been a challenging task since many years. The a posteriori assessment of residual stress can be performed by experimental techniques, though they are time-consuming and expensive and provide data at single points (in most cases at the surface) of the joint. A priori residual stress determination can be obtained by numerical models, yet they need to be validated. Welding simulations are very complex because fluid dynamics, metallurgical, thermal and mechanical phenomena interact with each other [10]. When residual stress and strain are the major goals of the simulation, fluid dynamics of welding pool is almost always not taken into account. In these cases, the fusion zone is modeled by power density distribution functions whose shape and dimensions depend on welding technology (laser welding, arc welding and so on) and process parameters, respectively. Furthermore, the analysis is transient and nonlinear [11]. Numerical models require high mesh densities in order to capture the severe thermal gradient induced by the welding source. Moreover, in real components, multipass welding is often adopted. Promising approaches are already present in literature, but not yet extensively validated. In the 'macroweld deposit approach', the heat is applied in a welding instantaneously, without using a power source. The macrosteps number is chosen a priori based on the experience and real welding speed. The higher the welding speed, the longer is the single macrostep. The heat transferred into the structure is the same as in the real process, but it occurs in another time frame. In contrast to the macroweld deposit methodology, with the local-global method, the welding simulation is carried out on a refined local model (LM), whose geometry is extracted from the global structure (GS). The nodal displacements coming from LM solution are applied to the GS and a linear elastic computation is finally performed to assess the global distortion. The mesh can be locally refined and the refined zone follows the welding source by saving

138 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

The peak stress method (PSM) is an engineering, FE-based method to estimate the notch stress intensity factors (NSIFs) at the weld toe and at the weld root of welded joints. The basic idea is to use very coarse meshes, if compared with those required to evaluate directly the asymptotic stress distributions required to apply the NSIFs definitions. The second peculiarity of the method is that the sole linear elastic peak stress evaluated at the sharp V-notch tip is necessary and sufficient to estimate the NSIF: therefore, the singular stress fields do not need to be postprocessed according to the NSIFs definitions (Eqs. (1) and (2)). Both these features of the method make it useful in practical applications.

In plane problems, the local linear elastic stress fields close to the tip of sharp V-notches, like those shown in the welded joint of Figure 1, can be expressed as functions of the relevant NSIFs, which quantify the magnitude of the asymptotic singular stress distributions. The asymptotic, singular stress distributions ahead of sharp V-notches under mode I (opening) and mode II (sliding) loadings have been determined by Williams [16]. The mode I and mode II NSIFs can be defined according to Gross and Mendelson [17] by means of Eqs. (1) and (2), respectively.

$$K\_1 = \sqrt{2\pi} \cdot \lim\_{r \to 0} \left[ (\sigma\_{\theta\theta})\_{\theta=\theta} \cdot r^{1-\lambda\_1} \right] \tag{1}$$

$$K\_2 = \sqrt{2\pi} \cdot \lim\_{r \to 0} \left[ (\tau\_{r\theta})\_{\theta = \theta} \cdot r^{1-\lambda\_2} \right] \tag{2}$$

The stress singularity exponents λ<sup>1</sup> and λ<sup>2</sup> depend on the notch opening angle 2α [16] and are reported in Table 1. The stress components σθθ and τr<sup>θ</sup> are calculated along the direction θ = 0, i.e., the notch bisector (see Figure 1).

• the FE mesh pattern;

• the criteria for stress extrapolation at FE nodes.

algorithm available in the numerical code, while K\*

• Element types (element library of Ansys code):

strain' formulation activated).

a Fourier series expansion (PLANE 25).

parameters mentioned previously.

• Adopted FE code: Ansys

(1 � λ2) = 0.5).

3.38. To apply expressions (3) and (4) with K\*

conditions:

In more detail, the expressions of the PSM are the following [34, 36]:

<sup>K</sup><sup>1</sup> ffi <sup>K</sup><sup>∗</sup>

<sup>K</sup><sup>2</sup> ffi <sup>K</sup><sup>∗</sup>

In previous expressions, d is the so-called global element size parameter to input in the FE software, i.e., the mean size of the finite elements adopted by the free mesh generation

With reference to plane models, the PSM has been calibrated [34, 36] under the following

• Two-dimensional, 4-node quadrilateral finite elements with linear shape functions (PLANE 42 or alternatively PLANE 182 with K-option 1 set to 3, i.e., 'simple enhanced

• Three-dimensional, eight-node brick elements (SOLID 45 or equivalently SOLID 185

• Two-dimensional, harmonic, 4-node linear quadrilateral elements, to analyze axissymmetric components subjected to external loads that can be expressed according to

• There is a standard mesh pattern close to the V-notch or crack tip that is reported in Figure 2 [34, 36], where it is seen that four elements share the node located at the notch tip if the notch opening angle 2α is equal to or lower than 90�; conversely, if the notch opening angle is 2α > 90�, then two elements share the node at notch tip. Figure 2 shows examples of such mesh patterns in case of symmetric FE models. It should be noted that the mesh patterns according to the PSM are automatically generated by the free-mesh generation algorithm of Ansys code, after having input the average FE size d by means of the command 'global element size' available in the software. There are not additional

• Eq. (3) can be applied to sharp V-notches with an opening angle 2α between 0� and 135�; while calibration for mode II loading, Eq. (4), is restricted to the crack case (2α = 0,

d can be chosen arbitrarily, but within a range of applicability defined in the relevant literature

FE = 1.38 and K\*\*

with K-option 2 set to 3, i.e., 'simple enhanced strain' option activated).

parameters or special settings to input in order to generate the mesh.

Under these conditions, the following values have been calibrated: K\*

FE and K\*\*

Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method

FE � <sup>σ</sup>I,peak � <sup>d</sup><sup>1</sup>�λ<sup>1</sup> (3)

FE � <sup>τ</sup>II, peak � <sup>d</sup><sup>0</sup>:<sup>5</sup> (4)

FE take into account all calibration

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141

FE ffi 1.38 and <sup>K</sup>\*\*

FE = 3.38, the average element size

FE ffi

Figure 1. Sharp V-shaped notches in a welded joint (a) at the toe (2α typically equal to 135) (b) and at the root (2α = 0) (c) sides. Definition of peak stresses σI,peak and τII,peak evaluated at the weld toe and the weld root by means of a linear elastic finite element analysis.


Table 1. Values of the stress singularity exponents λ<sup>1</sup> and λ2.

Notch stress intensity factors (NSIFs) proved to correlate the static strength of components made of brittle or quasi-brittle materials and weakened by sharp V-notches [18–23], as well as the medium and high-cycle fatigue strength of notched components made of structural materials [24, 25]. Concerning welded joints, NSIFs have been used to analyze the fatigue strength both under uniaxial [26–30] and multiaxial cyclic loadings [31]. However, to apply the NSIF approach by means of finite element (FE) analyses in engineering problems, a major drawback arises, because of the very refined FE meshes needed to evaluate the NSIFs on the basis of the definitions reported in Eqs. (1) and (2). In the case of three-dimensional components, the numerical analyses are even more time-consuming.

Recently, a simplified and rapid technique, the so-called peak stress method (PSM), has been proposed in order to speed up the numerical evaluation of the NSIFs by adopting FE models with coarse meshes. Inspired by previous contributions by Nisitani and Teranishi [32, 33] to rapidly estimate the mode I SIF of cracks, the PSM has been theoretically justified and extended to estimate also the mode I NSIF of pointed V-notches [34, 35]; subsequently, it has been formulated for the mode II SIF of cracks [36] and the mode III NSIF of pointed V-notches [37].

Essentially, the PSM allows to rapidly estimate the NSIFs K<sup>1</sup> and K<sup>2</sup> (Eqs. (1) and (2)) from the singular, linear elastic, opening (mode I) and sliding (mode II) FE peak stresses σI,peak and τII,peak, respectively, which are calculated at the node located at the V-notch tip (see Figure 1) by means of an FE analysis in which the following parameters are calibrated:


In more detail, the expressions of the PSM are the following [34, 36]:

$$K\_1 \cong K\_{FE}^\* \cdot \sigma\_{I,peak} \cdot d^{1-\lambda\_1} \tag{3}$$

$$K\_2 \cong K\_{FE}^\* \cdot \pi\_{II, \text{peak}} \cdot d^{0.5} \tag{4}$$

In previous expressions, d is the so-called global element size parameter to input in the FE software, i.e., the mean size of the finite elements adopted by the free mesh generation algorithm available in the numerical code, while K\* FE and K\*\* FE take into account all calibration parameters mentioned previously.

With reference to plane models, the PSM has been calibrated [34, 36] under the following conditions:

• Adopted FE code: Ansys

Notch stress intensity factors (NSIFs) proved to correlate the static strength of components made of brittle or quasi-brittle materials and weakened by sharp V-notches [18–23], as well as the medium and high-cycle fatigue strength of notched components made of structural materials [24, 25]. Concerning welded joints, NSIFs have been used to analyze the fatigue strength both under uniaxial [26–30] and multiaxial cyclic loadings [31]. However, to apply the NSIF approach by means of finite element (FE) analyses in engineering problems, a major drawback arises, because of the very refined FE meshes needed to evaluate the NSIFs on the basis of the definitions reported in Eqs. (1) and (2). In the case of three-dimensional components, the

Figure 1. Sharp V-shaped notches in a welded joint (a) at the toe (2α typically equal to 135) (b) and at the root (2α = 0) (c) sides. Definition of peak stresses σI,peak and τII,peak evaluated at the weld toe and the weld root by means of a linear elastic

2α (deg) λ<sup>1</sup> λ<sup>2</sup> 0 0.500 0.500 90 0.544 0.909

140 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Recently, a simplified and rapid technique, the so-called peak stress method (PSM), has been proposed in order to speed up the numerical evaluation of the NSIFs by adopting FE models with coarse meshes. Inspired by previous contributions by Nisitani and Teranishi [32, 33] to rapidly estimate the mode I SIF of cracks, the PSM has been theoretically justified and extended to estimate also the mode I NSIF of pointed V-notches [34, 35]; subsequently, it has been formulated for the mode II SIF of cracks [36] and the mode III NSIF of pointed V-notches [37].

Essentially, the PSM allows to rapidly estimate the NSIFs K<sup>1</sup> and K<sup>2</sup> (Eqs. (1) and (2)) from the singular, linear elastic, opening (mode I) and sliding (mode II) FE peak stresses σI,peak and τII,peak, respectively, which are calculated at the node located at the V-notch tip (see Figure 1) by means

numerical analyses are even more time-consuming.

135 0.674

Table 1. Values of the stress singularity exponents λ<sup>1</sup> and λ2.

• the adopted FE code;

finite element analysis.

• the element type and formulation;

of an FE analysis in which the following parameters are calibrated:

	- Two-dimensional, 4-node quadrilateral finite elements with linear shape functions (PLANE 42 or alternatively PLANE 182 with K-option 1 set to 3, i.e., 'simple enhanced strain' formulation activated).
	- Three-dimensional, eight-node brick elements (SOLID 45 or equivalently SOLID 185 with K-option 2 set to 3, i.e., 'simple enhanced strain' option activated).
	- Two-dimensional, harmonic, 4-node linear quadrilateral elements, to analyze axissymmetric components subjected to external loads that can be expressed according to a Fourier series expansion (PLANE 25).

Under these conditions, the following values have been calibrated: K\* FE ffi 1.38 and <sup>K</sup>\*\* FE ffi 3.38. To apply expressions (3) and (4) with K\* FE = 1.38 and K\*\* FE = 3.38, the average element size d can be chosen arbitrarily, but within a range of applicability defined in the relevant literature

The aim of this section is to show the procedure of R-NSIFs evaluation through the PSM with a practical application. With this purpose, a full penetration welded T-joint has been analyzed using the finite element code Sysweld®. Generalized plane strain condition has been assumed, this choice being appropriate to describe the out-of-plane stress values in 2D cross section model of welding process [44]. The welded joint geometry and the assumed dimensions are

Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method

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143

According to the PSM hypothesis, the weld toe has been modeled as a sharp, zero radius, Vshaped notch. The notch opening angle 2α has been chosen equal to 135. It has been assumed carbon steel with chemical composition according to the Standard ASTM SA 516 (Grade 65 resp. 70) and the corresponding thermomechanical properties have been taken from Sysweld® database. Thermometallurgical and mechanical properties as a function of phase and temperature have been taken into account (Sysweld Toolbox 2011). In the metallurgical analysis, the following phases have been included: martensite, bainite, and ferrite-pearlite. The metallurgical transformations mainly depend on thermal history, according to the continuous cooling transformation (CCT) diagrams, which plot the start and the end transformation temperatures as a function of cooling rate or cooling time. In the present work, the diffusion-controlled phase transformations and the displacive martensitic transformation have been modeled according to Leblond and Devaux [45] and to Koistinen and Marburger [46] kinetic law, respectively. Radiative and convective heat losses have been applied at the boundary (external surfaces) of the plates to be joined—the former by using the Stefan-Boltzman law and the latter by using a convective heat transfer coefficient equal to 25 W/m2 K. The thermal gradient in the out-of-plane direction cannot be taken into account in a 2D cross section model because of its intrinsic formulation. However, it is supposed that the higher the welding speed, the lower the out-of-plane thermal gradient. The thermal history at nodes of the numerical model is the only load applied in welding simulation. Such thermal load is simulated by means of a power density distribution function whose shape depends on welding technology. In this work, the heat source has been modeled using a double ellipsoid power density distribution function [47] described by Eq. (5), which has been widely

shown in Figure 3.

used in literature for arc welding simulation [10].

Figure 3. Schematic representation of the T-joint. Dimensions are in mm.

Figure 2. Mesh patterns according to the PSM [34, 36]. Symmetry boundary conditions are applied to the FE model.

[34, 36]: for mode I loading (Eq. (3)), the mesh density ratio a/d that can be adopted in FE analyses must exceed 3 to obtain K<sup>∗</sup> FE ¼ 1:38 � 3%; in case of mode II loading (Eq. (4)), more refined meshes are needed, the mesh density ratio a/d having to be greater than 14 to obtain K∗∗ FE ¼ 3:38 � 3%. In previous expressions, a is the characteristic size of the analyzed sharp Vnotch, i.e., the notch depth in Figure 2. In case of welded T-joints analyzed at the weld toe side, a is the main plate thickness (a = 6 mm in next Figure 3).

Any structural strength assessment criterion, which is based on NSIF parameters, could be reformulated by using the PSM by means of Eqs. (3) and (4). In the recent literature, the PSM has been coupled to the averaged strain energy density (SED) criterion to assess the fatigue strength of welded joints subjected to axial [15, 36, 38, 39], torsion [37, 40] and multiaxial [41, 42] loading conditions.

#### 3. R-NSIFs evaluation by using the peak stress method

The PSM has been recently calibrated in Sysweld® finite element environment, to rapidly evaluate the linear elastic notch stress intensity factor (NSIF) under mode I loading [43]. According to such calibration, the mode I NSIF is proportional to a constant K\*FE, which is equal to 1.64 in case of V-notches with opening angle ranging from 90� to 135� and equal to 1.90 in case of cracks (0� opening angle). Provided that the mesh density ratio is equal to or greater than 4, all FE results fall within a scatter band of �5%, regardless of the V-notch depth. The aim of this section is to show the procedure of R-NSIFs evaluation through the PSM with a practical application. With this purpose, a full penetration welded T-joint has been analyzed using the finite element code Sysweld®. Generalized plane strain condition has been assumed, this choice being appropriate to describe the out-of-plane stress values in 2D cross section model of welding process [44]. The welded joint geometry and the assumed dimensions are shown in Figure 3.

According to the PSM hypothesis, the weld toe has been modeled as a sharp, zero radius, Vshaped notch. The notch opening angle 2α has been chosen equal to 135. It has been assumed carbon steel with chemical composition according to the Standard ASTM SA 516 (Grade 65 resp. 70) and the corresponding thermomechanical properties have been taken from Sysweld® database. Thermometallurgical and mechanical properties as a function of phase and temperature have been taken into account (Sysweld Toolbox 2011). In the metallurgical analysis, the following phases have been included: martensite, bainite, and ferrite-pearlite. The metallurgical transformations mainly depend on thermal history, according to the continuous cooling transformation (CCT) diagrams, which plot the start and the end transformation temperatures as a function of cooling rate or cooling time. In the present work, the diffusion-controlled phase transformations and the displacive martensitic transformation have been modeled according to Leblond and Devaux [45] and to Koistinen and Marburger [46] kinetic law, respectively. Radiative and convective heat losses have been applied at the boundary (external surfaces) of the plates to be joined—the former by using the Stefan-Boltzman law and the latter by using a convective heat transfer coefficient equal to 25 W/m2 K. The thermal gradient in the out-of-plane direction cannot be taken into account in a 2D cross section model because of its intrinsic formulation. However, it is supposed that the higher the welding speed, the lower the out-of-plane thermal gradient. The thermal history at nodes of the numerical model is the only load applied in welding simulation. Such thermal load is simulated by means of a power density distribution function whose shape depends on welding technology. In this work, the heat source has been modeled using a double ellipsoid power density distribution function [47] described by Eq. (5), which has been widely used in literature for arc welding simulation [10].

Figure 3. Schematic representation of the T-joint. Dimensions are in mm.

[34, 36]: for mode I loading (Eq. (3)), the mesh density ratio a/d that can be adopted in FE

Figure 2. Mesh patterns according to the PSM [34, 36]. Symmetry boundary conditions are applied to the FE model.

refined meshes are needed, the mesh density ratio a/d having to be greater than 14 to obtain

Any structural strength assessment criterion, which is based on NSIF parameters, could be reformulated by using the PSM by means of Eqs. (3) and (4). In the recent literature, the PSM has been coupled to the averaged strain energy density (SED) criterion to assess the fatigue strength of welded joints subjected to axial [15, 36, 38, 39], torsion [37, 40] and multiaxial

The PSM has been recently calibrated in Sysweld® finite element environment, to rapidly evaluate the linear elastic notch stress intensity factor (NSIF) under mode I loading [43]. According to such calibration, the mode I NSIF is proportional to a constant K\*FE, which is equal to 1.64 in case of V-notches with opening angle ranging from 90� to 135� and equal to 1.90 in case of cracks (0� opening angle). Provided that the mesh density ratio is equal to or greater than 4, all FE results fall within a scatter band of �5%, regardless of the V-notch depth.

FE ¼ 3:38 � 3%. In previous expressions, a is the characteristic size of the analyzed sharp Vnotch, i.e., the notch depth in Figure 2. In case of welded T-joints analyzed at the weld toe side,

FE ¼ 1:38 � 3%; in case of mode II loading (Eq. (4)), more

analyses must exceed 3 to obtain K<sup>∗</sup>

[41, 42] loading conditions.

a is the main plate thickness (a = 6 mm in next Figure 3).

3. R-NSIFs evaluation by using the peak stress method

142 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

K∗∗

$$q(\mathbf{x}, y, t) = \frac{6\sqrt{3} \begin{array}{cc} f\_{1,2} & Q \\ \hline \pi\sqrt{\pi} \ a\_0 & b\_0 \ c\_{1,2} \end{array} e^{-\frac{y\_0^2}{a\_0^2}} e^{-\frac{y\_0^2}{b\_{1,2}^2}} e^{-\frac{3|\mathbf{r}(\mathbf{r} - t)|^2}{\frac{2}{\mathbf{r}\_{1,2}}}} \tag{5}$$

typical free-generated mesh pattern according to the PSM evaluation are compared. The FE model used to compute R-NSIFs from local stress fields had a minimum element size at the

Table 3. Finite element meshes used to directly compute the R-NSIF from local stress and to estimate it by using the

PSM 52.9 1350 0.9

Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method

The FE models used to estimate the R-NSIFs by means of the PSM were generated by using a mesh pattern as similar as possible to the standard PSM shown in Figure 2, according to the PSM calibration rules for Sysweld® finite element code listed in the previous section. The mesh generation algorithm provided by visual mesh has been adopted. Four-node 2004 quadrilateral elements from Sysweld library have been used and the numerical integration scheme was set to 2 2 Gauss points. The average finite element size d imposed to the mesh generation algorithm is 0.29 mm, which translates into a mesh density ratio a/d equal to 10. Such FE size was necessary to obtain a temperature field in agreement with that obtained with the very refined mesh pattern. More precisely, to establish the appropriate d value, a difference in nodal temperatures of few percentage points was allowed between the very refined and the PSM coarse meshes. Uncoupled thermomechanical analyses were carried out, where the molten effect was simulated by using a specific function implemented in Sysweld code that cancels the history of an element if its temperature exceeds the melting temperature. Welded plates

have been supposed free of restraints, except for the symmetry boundary condition.

The asymptotic nature of the residual stress distribution near a sharp V-notch has been numerically investigated by using Sysweld®. Figure 5 shows the temperature distribution when the melted zone has reached its maximum extension. It has been found that the stress

4. Results and discussion

notch tip equal to about 5 <sup>10</sup><sup>5</sup> mm, according to the literature [27].

Method Global FEM model Detail of mesh refinement near

Local stress filed calculation

PSM.

the weld toe

R-NSIF value [MPa mm0.326]

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N of FE in model

52.4 2500 —

Δ % 145

The double ellipsoid heat source and the meaning of the symbols used in Eq. (5) are shown in Figure 4, whereas the adopted numerical values are summarized in Table 2. The power density provided by Eq. (5) has the unit W/m<sup>3</sup> .

By taking advantage on the symmetry, one-half of the joint has been modeled. In Table 3, the very refined mesh pattern used in the calculation of R-NSIF from the local stress field and the

Figure 4. Schematic of Goldak's heat source with symbols taken from the original paper [45].


Table 2. Goldak's source parameters adopted in the present analysis.

Table 3. Finite element meshes used to directly compute the R-NSIF from local stress and to estimate it by using the PSM.

typical free-generated mesh pattern according to the PSM evaluation are compared. The FE model used to compute R-NSIFs from local stress fields had a minimum element size at the notch tip equal to about 5 <sup>10</sup><sup>5</sup> mm, according to the literature [27].

The FE models used to estimate the R-NSIFs by means of the PSM were generated by using a mesh pattern as similar as possible to the standard PSM shown in Figure 2, according to the PSM calibration rules for Sysweld® finite element code listed in the previous section. The mesh generation algorithm provided by visual mesh has been adopted. Four-node 2004 quadrilateral elements from Sysweld library have been used and the numerical integration scheme was set to 2 2 Gauss points. The average finite element size d imposed to the mesh generation algorithm is 0.29 mm, which translates into a mesh density ratio a/d equal to 10. Such FE size was necessary to obtain a temperature field in agreement with that obtained with the very refined mesh pattern. More precisely, to establish the appropriate d value, a difference in nodal temperatures of few percentage points was allowed between the very refined and the PSM coarse meshes. Uncoupled thermomechanical analyses were carried out, where the molten effect was simulated by using a specific function implemented in Sysweld code that cancels the history of an element if its temperature exceeds the melting temperature. Welded plates have been supposed free of restraints, except for the symmetry boundary condition.

#### 4. Results and discussion

q xð Þ¼ ; y; t

density provided by Eq. (5) has the unit W/m<sup>3</sup>

6 ffiffiffi 3 <sup>p</sup> <sup>f</sup> <sup>1</sup>,<sup>2</sup> <sup>Q</sup>

<sup>π</sup> <sup>p</sup> <sup>a</sup><sup>0</sup> <sup>b</sup><sup>0</sup> <sup>c</sup>1,<sup>2</sup>

The double ellipsoid heat source and the meaning of the symbols used in Eq. (5) are shown in Figure 4, whereas the adopted numerical values are summarized in Table 2. The power

. By taking advantage on the symmetry, one-half of the joint has been modeled. In Table 3, the very refined mesh pattern used in the calculation of R-NSIF from the local stress field and the

e �3x<sup>2</sup> a0 2 e �3y2 b0 2 e �3½ � <sup>v</sup>ð Þ <sup>τ</sup>�<sup>t</sup> <sup>2</sup> c2

<sup>1</sup>,<sup>2</sup> (5)

π ffiffiffi

144 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Figure 4. Schematic of Goldak's heat source with symbols taken from the original paper [45].

Table 2. Goldak's source parameters adopted in the present analysis.

Q\* Power input [W] 11,500 η Efficiency 0.64 Q Absorbed power [W] η∙Q\* a<sup>0</sup> Molten pool dimensions [mm] 3.5 b<sup>0</sup> 11 c<sup>1</sup> 2.3 c<sup>2</sup> 7.9 f<sup>1</sup> Fractions of heat deposit in the front and rear quadrants, with f<sup>1</sup> + f<sup>2</sup> = 2 0.6 f<sup>2</sup> (subscript 1 for ξ > 0; subscript 2 for ξ < 0) 1.4 v Welding speed [mm/s] 11 τ Total time before the welding torch is over the transverse cross section [s] 3

The asymptotic nature of the residual stress distribution near a sharp V-notch has been numerically investigated by using Sysweld®. Figure 5 shows the temperature distribution when the melted zone has reached its maximum extension. It has been found that the stress distribution near the weld toe is linear in a log-log plot (Figure 6) and its slope is equal to 0.326, which corresponds to the analytical solution for open V-notches with zero radius. The intensity of such residual stress field can therefore be given in terms of R-NSIFs.

This investigation confirms that the PSM can be used for a rapid, engineering R-NSIF evaluation. To illustrate the advantage of the PSM, the solution time associated to the very refined meshes was about 1 min for thermal analyses and 4 min for mechanical analyses, whereas the PSM required few seconds for thermal analyses and a minute for mechanical analyses. Moreover, the following main advantages can be exploited if the R-NSIFs are estimated by means of the PSM rather than directly computed from local stress fields: (a) only one nodal stress value calculated at the point of singularity is sufficient to compute the R-NSIF, the whole stress distribution along the notch bisector being no longer required; (b) four orders of magnitude coarser meshes could be employed by using the PSM, as compared to the very refined meshes required to evaluate the local stress field directly. In the authors' opinion, both reasons make the PSM of easy and fast applicability in industrial and research applications. Finally, the PSM appears also suitable, with further developments and investigation, for the R-NSIF value calculation by using three-dimensional FE models

Rapid Calculation of Residual Notch Stress Intensity Factors (R-NSIFs) by Means of the Peak Stress Method

In the present contribution, a practical application of the PSM in the residual notch stress intensity factor (R-NSIF) estimation on a full penetration welded T-joint has been given. It has been found that, provided that the stress redistribution induced by plasticity in the zone very close to the notch tip is negligible, the PSM allows the rapid, coarse mesh-based, estimation of the R-NSIF. This result is promising because, in principle, R-NSIFs may be useful parameters

, Filippo Berto<sup>2</sup> and Giovanni Meneghetti<sup>3</sup>

\*

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147

to include the residual stress effect in fatigue strength assessments of welded joints.

1 Department of Engineering and Management, University of Padova, Vicenza, Italy

3 Department of Industrial Engineering, University of Padova, Padova, Italy

2 Department of Industrial and Mechanical Engineering, Norwegian University of Science

[1] Livieri P, Lazzarin P. Fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values. International Journal of

of welding process.

5. Conclusions

Author details

, Paolo Ferro<sup>1</sup>

and Technology, Trondheim, Norway

Fracture. 2005;133:247-278

\*Address all correspondence to: giovanni.meneghetti@unipd.it

Marco Colussi<sup>1</sup>

References

Concerning the PSM, a peak stress value equal to 48.3 MPa was calculated at the node located at the weld toe. A mesh pattern having element size equal to 0.29 mm was adopted near the weld toe, which corresponds to a mesh density ratio a/d = 10 ≥ 4, according to the PSM calibration in Sysweld® [43]. Results are summarized in Table 3, where it is possible to notice a good agreement between the K<sup>1</sup> value obtained from the local stress field computed with a very fine mesh and the one estimated by means of the coarse PSM mesh. In the latter case, the PSM calibration constant for K\*FE = 1.64, valid for Sysweld®, has been used.

Figure 5. Temperature distribution at the instant of maximum width of the fusion zone (in red).

Figure 6. Asymptotic σθθ component of the residual stress field near the notch tip along the notch bisector, i.e., θ = 0.

This investigation confirms that the PSM can be used for a rapid, engineering R-NSIF evaluation. To illustrate the advantage of the PSM, the solution time associated to the very refined meshes was about 1 min for thermal analyses and 4 min for mechanical analyses, whereas the PSM required few seconds for thermal analyses and a minute for mechanical analyses. Moreover, the following main advantages can be exploited if the R-NSIFs are estimated by means of the PSM rather than directly computed from local stress fields: (a) only one nodal stress value calculated at the point of singularity is sufficient to compute the R-NSIF, the whole stress distribution along the notch bisector being no longer required; (b) four orders of magnitude coarser meshes could be employed by using the PSM, as compared to the very refined meshes required to evaluate the local stress field directly. In the authors' opinion, both reasons make the PSM of easy and fast applicability in industrial and research applications. Finally, the PSM appears also suitable, with further developments and investigation, for the R-NSIF value calculation by using three-dimensional FE models of welding process.

## 5. Conclusions

distribution near the weld toe is linear in a log-log plot (Figure 6) and its slope is equal to 0.326, which corresponds to the analytical solution for open V-notches with zero radius. The intensity

Concerning the PSM, a peak stress value equal to 48.3 MPa was calculated at the node located at the weld toe. A mesh pattern having element size equal to 0.29 mm was adopted near the weld toe, which corresponds to a mesh density ratio a/d = 10 ≥ 4, according to the PSM calibration in Sysweld® [43]. Results are summarized in Table 3, where it is possible to notice a good agreement between the K<sup>1</sup> value obtained from the local stress field computed with a very fine mesh and the one estimated by means of the coarse PSM mesh. In the latter case, the

Figure 6. Asymptotic σθθ component of the residual stress field near the notch tip along the notch bisector, i.e., θ = 0.

of such residual stress field can therefore be given in terms of R-NSIFs.

146 Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

PSM calibration constant for K\*FE = 1.64, valid for Sysweld®, has been used.

Figure 5. Temperature distribution at the instant of maximum width of the fusion zone (in red).

In the present contribution, a practical application of the PSM in the residual notch stress intensity factor (R-NSIF) estimation on a full penetration welded T-joint has been given. It has been found that, provided that the stress redistribution induced by plasticity in the zone very close to the notch tip is negligible, the PSM allows the rapid, coarse mesh-based, estimation of the R-NSIF. This result is promising because, in principle, R-NSIFs may be useful parameters to include the residual stress effect in fatigue strength assessments of welded joints.

## Author details

Marco Colussi<sup>1</sup> , Paolo Ferro<sup>1</sup> , Filippo Berto<sup>2</sup> and Giovanni Meneghetti<sup>3</sup> \*

\*Address all correspondence to: giovanni.meneghetti@unipd.it

1 Department of Engineering and Management, University of Padova, Vicenza, Italy

2 Department of Industrial and Mechanical Engineering, Norwegian University of Science and Technology, Trondheim, Norway

3 Department of Industrial Engineering, University of Padova, Padova, Italy

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## *Edited by Paolo Ferro and Filippo Berto*

The ability to quantify residual stresses induced by welding processes through experimentation or numerical simulation has become, today more than ever, of strategic importance in the context of their application to advanced design. This is an ongoing challenge that commenced many years ago. Recent design criteria endeavour to quantify the effect of residual stresses on fatigue strength of welded joints to allow a more efficient use of materials and a greater reliability of welded structures. The aim of the present book is contributing to these aspects of design through a collection of case-studies that illustrate both standard and advanced experimental and numerical methodologies used to assess the residual stress field in welded joints. The work is intended to be of assistance to designers, industrial engineers and academics who want to deepen their knowledge of this challenging topic.

Published in London, UK © 2018 IntechOpen © Tanantornanutra / iStock

Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments

Residual Stress Analysis

on Welded Joints by Means

of Numerical Simulation

and Experiments

*Edited by Paolo Ferro and Filippo Berto*