**5. Results and discussion**

The experimental results and simulation results were discussed in section. Based on the reliable welding temperature simulation, the longitudinal residual stress through TEP FEM and CM was analyzed. After that the transverse welding residual stress through TEP FEM was obtained. The comparison analysis of welding displacement was conducted to further validate the efficiency and accuracy of the proposed TEP FEM.

#### **5.1 Maximum welding temperature distribution**

**Figure 8** displays two FEM models of the butt welded joint, which contain 13,702 nodes, 12,300 elements and 22,072 nodes, 20,400 elements, respectively, and the mechanical boundary constraint conditions are displayed in **Figure 8** by the arrows. It can be evidently seen from the picture that there are a large amount of nodes in the vicinity of weld and mesh toward the plate edge gradually reduced. The way of mesh arrangement is useful for improving computation efficiency and

*Residual Stress Evaluation with Contour Method for Thick Butt Welded Joint DOI: http://dx.doi.org/10.5772/intechopen.90409*

**Figure 8.**

data is applied as the nodal displacement condition of the finite element model which is often created according to the half of the whole welded specimen by using ABAQUS or ANSYS code. **Figure 7** displayed the finite element model of half welded joint, and red arrows representing boundary condition prevented the movement of rigid body. The inverse of the measured contour has been applied to the cut surface (deformation in this figure has been magnified �185). A fine element size (1 mm) is that faces the cutting surface in addition to a fine mesh density

According to the concept of CM, the residual stress existing in welded specimens

*∂*2 2*∂x∂y*

*∂*2 *∂x*<sup>2</sup> þ *∂*2 *∂z*<sup>2</sup> � � ð Þ <sup>1</sup> � <sup>2</sup>*<sup>υ</sup>*

*∂*2 2*∂y∂z*

½ � *K* ½ �¼ *u* ½ � *F* (4)

*∂*2 ð Þ 1 � *υ ∂z*<sup>2</sup> þ

2

*∂*2 2*∂x∂z*

*∂*2 2*∂y∂z*

*∂*2 *∂x*<sup>2</sup> þ *∂*2 *∂y*<sup>2</sup> � � ð Þ <sup>1</sup> � <sup>2</sup>*<sup>υ</sup>*

2

can be calculated through the measured out-of-plane displacement normal to a plane of interest. Several assumptions are made in the linear elastic finite element analysis: (1) small displacements or deformations of the welded components or structures, (2) linear elastic behavior during the material removal, and (3) unchanged boundary conditions during loading process. Therefore, it can be defined as an inverse finite element method (IFEM). In general, a set of linear equation below describes the welded components or structures in the linear elastic

around the cutting plane are used in the present FE model.

*New Challenges in Residual Stress Measurements and Evaluation*

**4. IFEM**

finite element:

*∂*2 ð Þ 1 � *υ ∂x*<sup>2</sup> þ

**5. Results and discussion**

proposed TEP FEM.

**114**

*∂*2 *∂y*<sup>2</sup> þ *∂*2 *∂z*<sup>2</sup> � � ð Þ <sup>1</sup> � <sup>2</sup>*<sup>υ</sup>*

*∂*2 2*∂x∂y*

*∂*2 2*∂x∂z* 2

displacements, and ½ � *F* is the matrix of external nodal force.

**5.1 Maximum welding temperature distribution**

*∂*2 ð Þ 1 � *υ ∂y*<sup>2</sup> þ

where *E* is the Young's modulus, 210 GPa, *υ* is Poisson's ratio, 0.3, ½ � *K* is the stiffness matrix of the welded component or structure, ½ � *u* is the matrix of nodal

The experimental results and simulation results were discussed in section. Based

on the reliable welding temperature simulation, the longitudinal residual stress through TEP FEM and CM was analyzed. After that the transverse welding residual stress through TEP FEM was obtained. The comparison analysis of welding displacement was conducted to further validate the efficiency and accuracy of the

**Figure 8** displays two FEM models of the butt welded joint, which contain 13,702 nodes, 12,300 elements and 22,072 nodes, 20,400 elements, respectively, and the mechanical boundary constraint conditions are displayed in **Figure 8** by the arrows. It can be evidently seen from the picture that there are a large amount of nodes in the vicinity of weld and mesh toward the plate edge gradually reduced. The way of mesh arrangement is useful for improving computation efficiency and

½ �¼ *K*

*E* ð Þ 1 � 2*υ* ð Þ 1 þ *υ* *Simulation model and weld sequence of butt welded joint: (a) without considering back-gouging; (b) with considering back-gouging.*

ensuring computation accuracy when carrying out transient welding temperature nonlinear heat transfer computation.

#### *5.1.1 Root weld*

In principle, plastic strain is the generation source of welding residual stress, which is mainly determined by the maximum welding temperature and restraint condition. Here, the restraint condition is not considered, and the maximum welding temperature distribution is used to describe the features of welding temperature field of the butt welded joint. During the thermal analysis of the butt welded joint, the initial temperature is assumed to be 20°C. To simulate the heat input of moving welding arc during welding, the volumetric heat source with uniform density distribution is employed. For this heat source, the welding arc energy is dependent on the welding current, voltage, speed, and arc efficiency. When the welding process is SMAW, the arc heat efficiency is 0.6 and the welding arc length is 30 mm. And the heat source volume denoted the considered weld pool volume and can be obtained by calculating the volume fraction of the elements in currently being welded zone. The nonlinear isotropic Fourier heat flux was also employed for heat conduction. The temperature-dependent thermal properties such as thermal conductivity, specific heat, and density are considered. **Figure 9** presents the fusion zone in middle cross-section of the butt welded joint with or without considering back-gouging. The simulated fusion zone is slightly greater than the Xgroove area, while the maximum temperature is approximately 2300°C. Comparing to the macrostructure of the butt welded joint, the fusion zone with considering back-gouging agrees better than that without considering back-gouging. Therefore,

**Figure 9.** *Fusion zone of butt welded joint: (a) without considering back-gouging; (b) with considering back-gouging.*

the tensile stress area of main weld. In addition, **Figure 10c** shows some irregularities at the edges of the cut surfaces; these irregularities may be produced due to

*2D mapping of longitudinal welding residual stress distribution of middle cross-section: (a) without considering*

*Residual Stress Evaluation with Contour Method for Thick Butt Welded Joint*

*DOI: http://dx.doi.org/10.5772/intechopen.90409*

**Figure 11a–c** quantitatively compares the longitudinal welding residual stress distributions in the middle cross-section along L1, L2, and L3 computed by TEP FE

**Figure 12a, b** displays the features of transverse residual stresses in butt welded joint with or without considering back-gouging, respectively. It can be seen from the picture that the tensile stress is almost constant, while the compressive stress considering back-gouging is greater than that without considering back-gouging. And the middle cross-section mappings show that the signal of transverse residual stresses of local root weld and its distribution are changed obviously. Finally, the

and the corresponding measurements, respectively. It can be seen from the **Figure 11a, b** that the computed longitudinal residual stress distributions along L1 and L2 agree well with the measured stress distribution. It can be seen from **Figure 11c** that the through-thickness longitudinal stresses distribution in center weld was obviously smaller than that in cap welds, which can be increased by backgouging process. Therefore, it can be found that the peak longitudinal stresses were in cap welds and the longitudinal stresses in center weld can be increased by back-

wire entrance and exit during the specimen cutting.

*back-gouging; (b) with considering back-gouging; (c) IFEM.*

gouging process.

**117**

**Figure 10.**

it can be concluded that the fusion area predicted by FEM with considering back-gouging is reasonable.
