Preface

**Section 2 Fracture Mechanics 141**

**VI** Contents

Chapter 8 **Fracture Toughness Determination with the Use of**

Jan Dzugan, Pavel Konopik and Martin Rund

Chapter 9 **Fatigue Fracture of Functionally Graded Materials Under**

**Elastic-Plastic Loading Conditions Using Extended Finite**

Somnath Bhattacharya, Kamal Sharma and Vaibhav Sonkar

Iñigo Llavori, Jon Ander Esnaola, Alaitz Zabala, Miren Larrañaga

Chapter 10 **Fretting: Review on the Numerical Simulation and Modeling of**

Chapter 11 **Determination of Fracture Toughness Characteristics of Small-**

Chapter 12 **Numerical Analysis Methods of Structural Fatigue and Fracture**

**Size Chevron-Notched Specimens 215**

Qiu Zhiping, Zhang Zesheng and Wang Lei

Chapter 13 **Accelerated Fatigue Test in Mechanical Components 253**

**Miniaturized Specimens 143**

**Wear, Fatigue and Fracture 195**

**Element Method 169**

and Xabier Gomez

Yevgeny Deryugin

**Problems 235**

Moises Jimenez

During recent years, the contact mechanics and fracture mechanics have found a considera‐ ble application in the solution of engineering problems to increase the life of the component. Contact mechanics studies the stress and strain states of bodies in contact; it is a contact that leads to friction interaction and wear. In recent years, computational contact mechanics has been a topic of intense research. The aim of this research is to devise robust solution schemes and new discretization techniques for the description of contact phenomena, which can then be applied to a much broader range of engineering analysis areas than is currently the case. The focus will be on a detailed treatment of the theoretical formulation of contact problems with regard to mechanics and mathematics. Fracture is understood to be the sepa‐ ration of a body of material into two or more pieces, whereby the load carrying is reduced to zero. The process of fracture can be considered to be made up of two components, crack initiation and crack propagation. Fracture mechanics has developed into a useful tool in the design of crack-tolerant structures and in fracture control; it also has a place in failure analy‐ sis. Fracture mechanics makes it possible to determine whether a crack of a given length in a material of known fracture toughness is dangerous because it will propagate to fracture at a given stress level. If the cause of crack extension may not be controlled, the only thing left to designer is to calculate the critical length in advance.

The different contributions of this book will cover the various advanced topics of research. It provides some needed background with respect to contact mechanics, fracture mechanics, and the use of finite element methods in both. All the covered chapters of this book are of a theoreti‐ cal and applied nature, suitable for the researchers of engineering, physics, applied mathemat‐ ics and mechanics with an interest in computer simulation of contact and fracture problems.

This book contains two sections as its name; Chapters 1–7 deal with contact mechanics, and Chapters 8–13 deal with fracture mechanics. Hermetic sealing studies are carried out in Chapter 1. Sealing capacity depends on the contact characteristics—the relative contact area and the gap density in the joint. In this chapter, the contact of a single asperity is considered taking into account the influence of the remaining contacting asperities. The response of a nanometer-scaled single asperity onto flat surfaces is experimentally accessible using atomic force microscopy, which is studied in Chapter 2. The author describes three experimental methods based on atomic force microscopy and corresponding methods for statistical data analysis. Chapter 3 presents an update of theories involving the differential hardness prob‐ lem, starting from the hypothesis made by Tabor for the contact between a sphere and a

plane. In this way, the reader interested in problems that directly affect these formulations, such as contact area and contact fatigue, can take part in a fundamental theoretical basis to perform investigations in this field. In Chapter 4, a new approach is presented by the au‐ thors, whose main purpose is to improve the efficiency of the semianalytical methods that are used to solve frictionless elastic contact problems. To do so, an adaptive refinement of the pressure element mesh is implemented. This strategy allows for a reduction of the com‐ putational cost of the method, while its accuracy remains unaffected. In Chapter 5, the con‐ tact load-bearing response and surface damage resistance of multilayered hierarchical structured (MHSed) Ti were evaluated by experimental indentation on the overall loading response in conjunction with detailed computational simulations of local stresses and strain distribution. The purpose of Chapter 6 is to illustrate the experimental/numerical tools and methods developed to fill this gap on a common family of friction dampers, called "under‐ platform dampers" with a curved-flat cross section. Both cylinder-on-flat and flat-on-flat in‐ terfaces are addressed. The study contained in Chapter 7 presents a comprehensive report on the dynamic response and shock resistance of singly curved sandwich panels, compris‐ ing two aluminium alloy face sheets and an aluminium foam core, subjected to air-blast loading, in terms of the experimental investigation and numerical simulation. The results are significant to guide the engineering applications of sandwich structures with metallic foam cores subjected to air-blast loading.

We feel amazing pleasure to edit this book. We are deeply gratified by the enthusiastic re‐ sponse given by all the authors and their outstanding research contribution in the form of book chapters. We take this opportunity to thank the IntechOpen editorial staff, in particu‐ lar, Ms. Maja Bozicevic and Mr. Slobodan Momcilovic, Publishing Process Manager, for obligatory technical assistance and continuous follow-up during book preparation and pub‐ lishing. And of course , my special thanks to our parents and family members for the sup‐

> **Prof. (Dr.) Pranav H. Darji** Professor and Principal

P. G. Studies and Research

Wadhwan City, Gujarat (India)

Wadhwan City, Gujarat (India)

Department of Mechanical Engineering

C. U. Shah College of Engineering and Technology

C. U. Shah University

**Prof. (Dr.) Veera P. Darji** Professor and Head

C. U. Shah University

Director

Preface IX

C. U. Shah College of Engineering and Technology

Research, Development and Innovation Centre

port they always gave to us.

Fracture toughness determination with the use of miniaturized specimens is discussed in Chapter 8. This chapter provides an overview of the reported values of the results obtained with the use of miniaturized specimens with hints of how can small-size-based results be re‐ lated to the standard-sized specimen results. In Chapter 9, extended finite element method (XFEM) has been used to simulate the fatigue crack growth problems in functionally graded material (FGM) in the presence of hole, inclusion and minor crack under elastic and plastic conditions. Chapter 10 has introduced the state of the art of the currently available modeling and simulation methods to analyse the fretting phenomenon. Finally, a numerical architecture of coupled wear, fatigue, and fracture methodology has been introduced, which allows to analyse the fretting phenomena as a whole. Chapter 11 presents a new method for determin‐ ing the fracture toughness of materials according to the test data of nonstandard small-size chevron-notched specimens. There are no empirical constants and phenomenological de‐ pendencies in the calculations. Chapter 12 reviews the most common empirical models and numerical methods of structural fatigue lifetime prediction. FEM (extended finite element method and fractal finite element method) is introduced as an important method to obtain the stress intensity factor or crack growth route. Chapter 13 deals with the review of accelerated fatigue tests, as it can be used to evaluate the component fatigue strength but is necessary to perform the statistical analysis during the test to monitor the test development, or this analy‐ sis is used to evaluate the test results, through the slope and its standard deviation.

Our intention for this book is to make current research on contact mechanics and fracture mechanics accessible to the researchers and scientists working in this field. It is also intend‐ ed to bring together solutions of special problems, which may be of practical importance, and to describe theoretical and experimental methods of the solution of associated fields' problems. The work presented in this book will be useful, effective, and beneficial to me‐ chanical engineers, automobile engineers, civil engineers, and material scientists from in‐ dustry, research, and education and will stimulate new research in these fields.

We feel amazing pleasure to edit this book. We are deeply gratified by the enthusiastic re‐ sponse given by all the authors and their outstanding research contribution in the form of book chapters. We take this opportunity to thank the IntechOpen editorial staff, in particu‐ lar, Ms. Maja Bozicevic and Mr. Slobodan Momcilovic, Publishing Process Manager, for obligatory technical assistance and continuous follow-up during book preparation and pub‐ lishing. And of course , my special thanks to our parents and family members for the sup‐ port they always gave to us.

plane. In this way, the reader interested in problems that directly affect these formulations, such as contact area and contact fatigue, can take part in a fundamental theoretical basis to perform investigations in this field. In Chapter 4, a new approach is presented by the au‐ thors, whose main purpose is to improve the efficiency of the semianalytical methods that are used to solve frictionless elastic contact problems. To do so, an adaptive refinement of the pressure element mesh is implemented. This strategy allows for a reduction of the com‐ putational cost of the method, while its accuracy remains unaffected. In Chapter 5, the con‐ tact load-bearing response and surface damage resistance of multilayered hierarchical structured (MHSed) Ti were evaluated by experimental indentation on the overall loading response in conjunction with detailed computational simulations of local stresses and strain distribution. The purpose of Chapter 6 is to illustrate the experimental/numerical tools and methods developed to fill this gap on a common family of friction dampers, called "under‐ platform dampers" with a curved-flat cross section. Both cylinder-on-flat and flat-on-flat in‐ terfaces are addressed. The study contained in Chapter 7 presents a comprehensive report on the dynamic response and shock resistance of singly curved sandwich panels, compris‐ ing two aluminium alloy face sheets and an aluminium foam core, subjected to air-blast loading, in terms of the experimental investigation and numerical simulation. The results are significant to guide the engineering applications of sandwich structures with metallic

Fracture toughness determination with the use of miniaturized specimens is discussed in Chapter 8. This chapter provides an overview of the reported values of the results obtained with the use of miniaturized specimens with hints of how can small-size-based results be re‐ lated to the standard-sized specimen results. In Chapter 9, extended finite element method (XFEM) has been used to simulate the fatigue crack growth problems in functionally graded material (FGM) in the presence of hole, inclusion and minor crack under elastic and plastic conditions. Chapter 10 has introduced the state of the art of the currently available modeling and simulation methods to analyse the fretting phenomenon. Finally, a numerical architecture of coupled wear, fatigue, and fracture methodology has been introduced, which allows to analyse the fretting phenomena as a whole. Chapter 11 presents a new method for determin‐ ing the fracture toughness of materials according to the test data of nonstandard small-size chevron-notched specimens. There are no empirical constants and phenomenological de‐ pendencies in the calculations. Chapter 12 reviews the most common empirical models and numerical methods of structural fatigue lifetime prediction. FEM (extended finite element method and fractal finite element method) is introduced as an important method to obtain the stress intensity factor or crack growth route. Chapter 13 deals with the review of accelerated fatigue tests, as it can be used to evaluate the component fatigue strength but is necessary to perform the statistical analysis during the test to monitor the test development, or this analy‐

sis is used to evaluate the test results, through the slope and its standard deviation.

dustry, research, and education and will stimulate new research in these fields.

Our intention for this book is to make current research on contact mechanics and fracture mechanics accessible to the researchers and scientists working in this field. It is also intend‐ ed to bring together solutions of special problems, which may be of practical importance, and to describe theoretical and experimental methods of the solution of associated fields' problems. The work presented in this book will be useful, effective, and beneficial to me‐ chanical engineers, automobile engineers, civil engineers, and material scientists from in‐

foam cores subjected to air-blast loading.

VIII Preface

#### **Prof. (Dr.) Pranav H. Darji**

Professor and Principal C. U. Shah College of Engineering and Technology Director P. G. Studies and Research Research, Development and Innovation Centre C. U. Shah University Wadhwan City, Gujarat (India)
