PSI - Issue 79

Lazar Jeremić et al. / Procedia Structural Integrity 79 (2026) 117 – 123

120

4. Finite Element Method The finite element method (FEM) is used here for the elastic-plastic stress-strain analysis, including the effect of a crack. Due to certain issues with the approximations adopted in the previous similar FEM models, as described in [3], it was decided to make two finite element models with slightly different geometry and boundary conditions, to provide a more realistic representation of the behavior of a pressure vessel with a crack in the weld metal. Keeping in mind relatively simple geometry, the idea of using a full 3D model was abandoned in favor of simplified 3D model generated in ABAQUS, [12], as shown in Fig. 3. As one can see, this model represents a small segment of the pressure vessel wall, in the vicinity of the welded joint where defects were detected, so the curvature can be neglected since the ratio between the thickness and the radius was less than 0.05 (50/1075). Thus, the loading was represented as biaxial, simulating circumferential and axial forces. Two different versions of boundary conditions were applied to determine if there would be any effect on the results. In the first case, boundary conditions were only defined in the bottom surface, as can be seen in Fig. 4a, with constraints in all directions expect the circumferential (X). In the second case, an additional boundary condition was introduced on the top surface, preventing translation along the Z axis, which is perpendicular to the pressure vessel wall segment, as can be seen in Figure 4b.

Fig. 3. Geometry, finite element mesh and the location of the crack

Fig. 4. Loads and boundary conditions in the models: a) Boundary conditions without the Y-axis constraint, b) Boundary conditions with the Y axis constraint

This section presents the results for stresses and strains around the defect with dimensions 180x32 mm, located in the circular welded joint of pressure vessel 971. Results are shown for both cases of boundary conditions, defined in Fig. 4. Figure 5 shows the stress distribution for the first case, whereas Figure 6 shows the same for the second boundary condition case. In both cases, these values were slightly above the yield stress of the weld metal, exceeding it by 6.7 MPa and 15 MPa, respectively. These values represent the difference between numerically obtained maximum stresses and the yield stress of the weld metal, (560 MPa, Table 1). Therefore, certain levels of plastic strain