**1. Introduction**

With the rapid development of lightweight fabrication in ship industry, thick plate with high tensile strength steel was increasingly employed for marine and offshore structure fabrication [1]. Welding technology with high efficiency is an indispensable process used for ship and offshore fabrication. However, it is inevitable that the residual stress of the welded joint and/or structure was induced by welding. Welding residual stresses can be defined as self-equilibrating stresses in a welded component with the absence of external load [2, 3]. It is known to us all that they can interact with imposed stresses and affect the service performance and structural integrity of welded components. Reliable knowledge of welding residual stress is essential to investigate the root cause of degradation mechanism, carry out

structural integrity assessment for safety critical components, optimize the design of manufacturing routes, and validate residual stress predictions [4, 5].

welded joint FE model is established firstly using the solid element model according to the dimension of welded joint. The heat source model is considered to be an important aspect, and the double-ellipsoidal volumetric model is employed to simulate the welding transient temperature [18]. The heat flux is determined by the welding current, welding voltage, and welding speed. Besides considering the moving heat source, heat loss due to convection and radiation should also be taken into account in the thermal analysis. And the temperature-dependent thermal properties

The mechanical analysis is conducted using the welding temperature histories by thermal analysis as the input load. The same FE model used in thermal analysis is employed here. For mechanical analysis, temperature-dependent mechanical properties such as Poisson's ratio, yield strength, Young's modulus, and linear expansion coefficient are mainly considered. Moreover, the total strain was a summation of the elastic strain, thermal strain, plastic strain, creep strain, and strain induced by phase transformation during welding process, as was shown by Eq. (1). The thermal strain is considered using thermal expansion coefficient, and solid-state phase transformation has insignificant influence on the residual stress and deformation in the mild steel [19], so phase change was neglected in the present study. In addition, because the period with high temperature during the entire thermal cycle was very short (only a few seconds), the creep behavior was also ignored. In addition, the working hardening is neglected in this study since its effect on welding residual stress is not significant for mild steel. The total strain increment at a material point can be expressed as the summation of elastic, plastic, and thermal strains, as was

<sup>ε</sup>*total* <sup>¼</sup> *<sup>ε</sup>elastic* <sup>þ</sup> *<sup>ε</sup>thermal* <sup>þ</sup> *<sup>ε</sup>phase* <sup>þ</sup> *<sup>ε</sup>plastic* <sup>þ</sup> *<sup>ε</sup>creep* (1)

To ensure the weld fully penetrated, carbon arc gouging process is usually used to remove root metal. In principle, the root metal was melted by carbon arc and blown away by high pressured gas, increasing the original weld area and changing cross-section weld appearance. In this paper, it assumes that the welding arc plays the same role like carbon arc. Therefore, to investigate the effect of back-gouging on residual stresses in butt welded joint, the root weld bead of main weld was

In this section, the experimental procedure was introduced: the first step was to obtain the butt welded joint, and then the out-of-plane welding displacement was measured; the next step was to measure the welding residual stress through CM.

In this study, the butt welded joint was obtained by SMAW. In detail, the low carbon steel Q235 with the thickness of 30 mm was used as base metal, and the filler metal was J507 welding rod with the diameter of 4 mm. The welding groove was symmetric with the angle of 60°. The detailed dimensions and weld groove are

<sup>ε</sup>*total* <sup>¼</sup> *<sup>ε</sup>elastic* <sup>þ</sup> *<sup>ε</sup>thermal* <sup>þ</sup> *<sup>ε</sup>plastic* (2)

such as thermal conductivity, specific heat, and density are used.

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

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

shown by Eq. (2):

heated again when heating back weld.

Finally, the weld profile of cross-section was obtained.

**3. Experimental procedure**

**3.1 Welding work**

presented in **Figure 1**.

**109**

Up to now, several qualitative and quantitative techniques have been developed to measure residual stress, which are determined by using the specific elastic constants of material based on the measured strain rather than measured stress. All of them are divided into two categories: destructive techniques and nondestructive techniques [6]. For destructive techniques such as sectioning method, hole drilling method, and CM, the residual stress is measured by its relaxation due to the destruction of the state of the equilibrium of residual stress in a mechanical component. While for nondestructive techniques such as X-ray diffraction method and neutron diffraction method, residual stress is determined based on the relationship between residual stress crystallographic parameters of the material. Among the techniques above, according to the Bueckner's superposition principle, CM can provide a 2D cross-sectional map of residual stress normal to a plane of interest which combines the stress relaxation technology and finite element method [7]. The standard procedure of CM is implemented by the following steps [8]: (1) sample cutting on a plane of interest, (2) contour measurement of the cutting plane or surface, (3) data processing of the measurement results, and (4) residual stress back-calculation by using finite element analysis. CM has found a lot of literatures: Xie [9] estimated the residual stress in thick Ti-6Al-4V alloy welded joint by electron beam welding through finite element method and contour method. Murugan and Narayanan [10] employed both the finite element method and contour method to reveal the residual stress distribution induced by welding in tee joint and found that the experimental results agree well with the predicted stress. What's more, Turski and Edwards [11] efficiently measured the residual stress of 316L stainless steel by utilizing the contour method. Braga et al. [12] studied the welding residual stress profile of butt joints of S355 structural steel through contour method and neutron diffraction. Kainuma [13] investigated the welding residual stress in orthotropic steel decks which had a considerable effect on crack initiation and propagation by using cutting method and magnetostriction method. Woo [14] obtained the two-dimensional maps of the longitudinal residual stress through the thickness of 70-mm thick ferritic steel by using the CM. After that, Woo [15] determined the residual stress in an 80-mm thick ferritic steel by combining the neutron diffraction and CM. In addition to butt welded joint, Liu [16] measured the internal residual stress on inertia friction welding of nickel-based superalloy.

From the reviews above, the CM has obtained a lot of achievements. However, the accuracy of novel embedded cutting contour configuration for thick plate welded joint has not been evaluated. In this paper, the welding residual stress of 30-mm thick plate butt welded joint was investigated combining TEP FEM and CM. What's more, the effect of back-gouging on the residual stress distribution of butt welded joint was discussed.

### **2. Prediction of welding residual stress by TEP FEM**

In this study, the welding residual stress in the butt welded joint through shielded metal arc welding (SMAW) was predicted by TEP FEM, an uncoupled thermal/mechanical formulation procedure, which is mainly composed of two sections: (a) the thermal analysis process and (b) the stress analysis process. Because the former has decisive effect on the latter while the latter has only a small influence on the former, thermal-mechanical behavior during welding is analyzed by using uncoupled thermal/mechanical formulation [17]. During thermal analysis, the 3D

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

welded joint FE model is established firstly using the solid element model according to the dimension of welded joint. The heat source model is considered to be an important aspect, and the double-ellipsoidal volumetric model is employed to simulate the welding transient temperature [18]. The heat flux is determined by the welding current, welding voltage, and welding speed. Besides considering the moving heat source, heat loss due to convection and radiation should also be taken into account in the thermal analysis. And the temperature-dependent thermal properties such as thermal conductivity, specific heat, and density are used.

The mechanical analysis is conducted using the welding temperature histories by thermal analysis as the input load. The same FE model used in thermal analysis is employed here. For mechanical analysis, temperature-dependent mechanical properties such as Poisson's ratio, yield strength, Young's modulus, and linear expansion coefficient are mainly considered. Moreover, the total strain was a summation of the elastic strain, thermal strain, plastic strain, creep strain, and strain induced by phase transformation during welding process, as was shown by Eq. (1). The thermal strain is considered using thermal expansion coefficient, and solid-state phase transformation has insignificant influence on the residual stress and deformation in the mild steel [19], so phase change was neglected in the present study. In addition, because the period with high temperature during the entire thermal cycle was very short (only a few seconds), the creep behavior was also ignored. In addition, the working hardening is neglected in this study since its effect on welding residual stress is not significant for mild steel. The total strain increment at a material point can be expressed as the summation of elastic, plastic, and thermal strains, as was shown by Eq. (2):

$$e^{\text{total}} = e^{\text{elastic}} + e^{\text{thermal}} + e^{\text{phase}} + e^{\text{plastic}} + e^{\text{crep}} \tag{1}$$

$$
\varepsilon^{\text{total}} = \varepsilon^{\text{elastic}} + \varepsilon^{\text{thermal}} + \varepsilon^{\text{plastic}} \tag{2}
$$

To ensure the weld fully penetrated, carbon arc gouging process is usually used to remove root metal. In principle, the root metal was melted by carbon arc and blown away by high pressured gas, increasing the original weld area and changing cross-section weld appearance. In this paper, it assumes that the welding arc plays the same role like carbon arc. Therefore, to investigate the effect of back-gouging on residual stresses in butt welded joint, the root weld bead of main weld was heated again when heating back weld.
