PSI - Issue 71

Prakash Bharadwaj et al. / Procedia Structural Integrity 71 (2025) 26–33

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crack tip, ensuring precise recording of the strain field at that location. The smallest element size of 4  m is selected ahead of the crack tip. Contact element is applied between the crack flank to avoid the penetration during the unloading. Pin holes are modelled using rigid constraints. A fixed boundary condition is imposed in all directions at the centre of the bottom pin, whereas the upper pin experiences applied cyclic loading in the y-direction and a fixed boundary condition in the x-direction. Cyclic loading is applied using a triangle loading pattern as illustrated in Fig. 1(b). The finite element analysis matrix is shown in Table 1.

(a) (b) Fig. 1. (a) Two-dimensional CT specimen with applied boundary/loading condition and (b) cyclic loading pattern.

Table 1. Finite element analysis matrix

Crack Size (mm)

Temperature

R

10, 11.25, 12.5, 13.75, 15, 16.25, 17.5, 18.75, 20, 22.5, 25 10, 11.25, 12.5, 13.75, 15, 16.25, 17.5, 18.75, 20, 22.5, 25

RT

-1, -0.5, 0.1 ,0.5

300 °C

-1, -0.5, 0.1 ,0.5

1.2. Material Model The material SA333 Gr. 6 utilized in this study is a nuclear piping steel for the Indian Pressurized Heavy Water Reactor (IPHWR). This material was sourced from a seamless extruded pipe subjected to normalizing heat treatment. An adequate material constitutive model is necessary to simulate ratcheting and plastic cycling processes, ahead of the crack tip. Previous research by Paul et al. (2013) has indicated that the isotropic hardening behaviour of SA333Gr6 steel is negligible. The three-component decomposed Chaboche non-linear kinematic material hardening model [Chaboche et al. (1986)] accurately represents the behaviour at the crack tip. The Chaboche hardening equation, along with the corresponding flow rule and von-Mises yield function, are presented in equations (1) to (5). = [32 ( − ):( − )] 1 2 − 0 =0 (1) = ( ) (2) = 2 3 − (3)