PSI - Issue 13

Rui Guo et al. / Procedia Structural Integrity 13 (2018) 2202–2209 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

2204

3

2. FEM Modeling 2.1 The geometric and material models

Figure 1 shows the schematic diagram of the welded joint in the pressure vessel safety end of the PWR. The thickness of the welded pipe wall is 74mm, which can be divided into 5 zones in terms of the materials differences. The four kinds of material parameters are shown in Table 1. The geometric model shown in Fig. 1 is reasonably simplified, the welded part is simplified to a two-dimensional plane strain model with a length of 160mm and a width of 74mm, the width direction according to the wall thickness of the welded structure, as shown in Fig. 1(b). According to the material area in Fig. 1(a), different material parameters are defined to establish a model of welded joints with uneven material and geometry, as shown in Fig. 1(c).

Table 1 Material properties of the welded joint specimens

Materials Young ’ s Modulus E /MPa

Poisson's Ratio v

Yield Stress σ 0 (MPa)

Hardening Exponent n

Offset Index α

alloy182 A533B

193000 193000 193000 193000

0.288 0.288 0.288 0.288

385 440 345 196

4.779 5.333 4.402 5.000

1.0 1.0 1.0 1.0

316L

304

2.2 Residual stress field There are various methods for numerical simulating residual stress. The most commonly used methods are force loading method, displacement loading method and predefined temperature field method. However, due to the growth of cracks and its length will change, the residual stress will be redistributed. The force loading method can not simulate the redistribution of the residual stress field because it directly applies the force load on the model boundary. On the other hand, according to the studies of former researchers, the residual stress field simulated by the force-load method and displacement-load method tends to be linear to the middle region, and the most widely used predefined temperature field method can get better results to simulated uniform residual stress field in the length direction. According to the studies of Hayashi et al. (2009), the residual stress field of the welded joints in the PWR safety end can usually be divided into two directions, axial and hoop. The distribution curve is shown in Fig. 2. The research object in this paper is cracks in hoop direction, which is mainly affected by the axial residual stress field. The hoop residual stress has little influence on the object of this study, therefore, the axial stress data in the figure is used as the residual stress distribution data.

Figure 2 Welding residual stress distribution curve The predefined temperature field method was firstly adopted in this study to simulate the welding residual stress. However, according to the result, it is found that the residual stress field simulated directly by the predefined temperature field method is due to the fact that the model consists of multiple materials, the residual stress value is higher than the yield limit of the material, and the middle region of the wall thickness is negative. The simulation result does not truly reflect the actual situation, as shown in Figure 3. For avoiding the change of the predefined residual stress field caused by the material mechanics heterogeneity, the stress import method was introduced to simulate the welding residual stress. Using predefined field in the finite element software ABAQUS, a simulated temperature field is applied to the two-dimensional model as shown in Fig. 1(c), and all the materials in the model are defined as the same linear elastic material. The expansion coefficient in