PSI - Issue 68

Saeid Hadidimoud et al. / Procedia Structural Integrity 68 (2025) 788–794 Saeid Hadidimoud et al./ Structural Integrity Procedia 00 (2025) 000–000

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Limit (or bursting) pressure of the cylinder Axial force

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Limit axial force Normalized pressure Normalized axial load

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2. The Finite Element Model All numerical simulation were conducted with ABAQUS standard. To reduce the model size, symmetry along the x, y and z axes was incorporated into the boundary conditions. To enhance computational efficiency, only one-eighth of the cylinder was modeled in the 3D simulations for both crack-free and circumferentially cracked cylinders. In the case of thick-walled cylinders with axial cracks, only one-quarter of the cylinder was modeled. For the 2D analysis, CAX4R elements were used for closed-end cylinders, whereas CPS4R elements were utilized for open-end cylinders, and CAX8R elements were considered in the analysis of 3D models. In the 3D simulation of the closed-end cylinder, the end of the cylinder was modeled as open end subjected to uniform axial stress due to the closed end ( ) applied as tensile stress. The combined loading involving internal pressure and axial tension was conducted by performing a two-step process: in the first step, internal pressure and the tensile stress (replacing ) were applied, and in the second step, an additional axial tension was applied until the entire thickness of the cylinder wall became plastic and local failure extended through the entire wall thickness (local collapse) occurred. This sequential loading approach enabled a comprehensive analysis of the cylinder's structural response under a range of combined loading conditions. The geometry and material used in the analyses is described n table 1. Figure 1 shows various crack configurations considered in the study. Normalization makes the outcome independent of the geometry and the material. ! ! ! !

Table 1. Geometric parameters and material properties for FE Analyses

Parameter

Value (Unit) 0.3 210 (GPa) 370 (MPa) 100 (mm) 500 (mm)

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Fig. 1. extended axial and hoop crack configurations in a cylindrical vessel: (a) internal hoop crack; (b) external hoop crack; (c) internal axial crack; (d) external axial crack; (e) Elastic and plastic deformation regions in a cylindrical vessel.

To induce residual stresses in both closed-end and open-end cylinders, autofrettage loading was applied. To evaluate the influence of residual stresses on the limit load of cracked cylinders for different types of cracks under combined loading, a numerical study was conducted in ABAQUS by following a 5-step process, as outlined: