PSI - Issue 33

D.D. Okulova et al. / Procedia Structural Integrity 33 (2021) 1055–1064 Author name / Structural Integrity Procedia 00 (2019) 000–000

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n are considered. The problem is considered within the framework of linearly elastic and bilinear elastic-plastic models.

It is required to analyse stress distribution in the vicinity of notches depending on the geometric parameters of the problem in the frame-work of bilinear plasticity hardening model and to investigate the effect of the distance between neighbouring defects on the growth of stresses in the vessel for a different number of defects in the framework of linearly elastic model. 3. Method of numerical analysis A numerical approach is the most practical way to calculate stress-strain state in the vicinity of inhomogeneities of different shapes (Vakaeva et al., 2018, Vakaeva et al., 2020, Ahmed et al., 2019, Wang et al., 2020). To perform a finite element analysis, we built an array of 3D CAD models of geometries of notched spheres. The inner and outer radii of the shell are r = 340 mm and R = 350 mm, respectively. The curvature radius of all the notches is δ = 6 mm, and their depth is h = 3 mm. Various numbers of defects were considered: n ∈ [16, 260]. The notches are randomly distributed on the equator of the sphere. Iron-Python scripts were created to automate the modelling of random defects patterns. A half of the sphere was considered due to the symmetry of the model. The generation of random numbers was implemented using the Python-function «random()», which generates random floating-point numbers uniformly distributed in the range [0.0, 1.0), using a pseudo-random number generator Mersenne twister. Since the probability of occurring a defect at every point on the equator is supposed to be the same for all the points, the uniform distribution was used. A series of finite element simulations were carried out by ANSYS Workbench package. A ten-node element SOLID187 was selected from the element library. Frictionless support was chosen as the boundary conditions on the surface of symmetry. The finite element mesh was refined in the vicinity of the defects using sizing options (Fig. 2).

Fig. 2. Finite element mesh in the vicinity of the defect

3.1. Elastic-plastic model Stainless Steel 304 with Young’s modulus E = 185 GPa and Poisson’s ratio ν = 0.27, yield strength T  = 210 MPa, Tangent modulus T = 1.16 GPa was used in the model. The sphere is subjected to internal pressure p = 6 MPa, which causes the plastic behaviour of the material. A bilinear hardening model was used in Ansys Mechanical to calculate stresses above the yield point. Bilinear hardening rule assumes a linear strain hardening portion and is defined using a tangent stiffness. To ensure the convergence of the solution, multiple calculations with different sizes of elements were carried out for each CAD-model. It took about 30 iterations to reach the convergence of the solution.