PSI - Issue 71

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

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and 0 R K

Chaboche’s material constants Equivalent incremental plastic strain Incremental plastic strain tensor

Saturated cyclic yield strength of the material

Deviatoric stress component

Load ratio (P min /P max ) Stress intensity factor

1. Introduction Structural integrity of a piping component with crack-like-flaw needs to be ensured for its long-term operations. Under fatigue loading conditions, crack tip blunting and re-sharpening occur. The blunting of the crack tip, it’s re -sharpening, and the dimensions of the Cyclic Plastic Zone (CPZ) significantly influence crack propagation under fatigue loading. Structural components subjected to elevated temperature and fatigue loading experiences the synergistic damage due to cyclic plastic deformation and material behaviour at high temperatures. The ferritic pearlitic low carbon-manganese steels are prone to Dynamic Strain Aging (DSA) at specific elevated temperatures and strain rate ranges [Moris Devotta et al. (2019)]. The DSA phenomenon occurs in metals due to the interaction of solutes (typically carbon and nitrogen atoms) with movable dislocations. The DSA behaviour results in inhomogeneous deformation, characterized by serrated flow on the stress-strain curve, known as the Portevin – Le Chatelier (PLC) effect [Lacombe et al. (1985)] . Multiple effects are noted on the mechanical characteristics of the material operating in DSA regime. This encompasses the elevation in flow stress, Ultimate Tensile Strength (UTS), strain/work hardening rate, along with the decrease in ductility for majority of the materials [Wagner et al. (2002)]. The fracture toughness behaviour also varies across different iron-based materials inside the DSA regime. The C-Mn steels exhibit a reduction in fracture toughness [Yoon et al. (1999)], whereas pure Armco irons exhibit an enhancement in fracture toughness under the DSA regime [Srinivas et al. (1991)]. The various mechanical tests conducted on the material, SA333Gr6 (used in this investigation), at strain rates ranging from 1 x 10 -5 s -1 to 1 x 10 -2 s -1 , demonstrate that the DSA regime of the material exists between 175 °C and 300 °C [Samuel et al. (2004), Singh et al. (1998), Kamat et al. (2011) and Kumar et al. (2021)]. \The reduction in fatigue life demonstrates the adverse effect of DSA on both crack initiation and propagation [Samuel et al. (2004)]. In addition to the DSA effect, the localized strain field at the cracked tip serves as a driving force for crack propagation under fatigue loading. A damage evolution model utilizing a CPZ for fatigue life prediction has been established at room temperature (RT), effectively estimating the notch tip stress [Taddesse et al. (2020)]. The literature reports the fatigue crack growth rate (FCGR) expression with regard to the CPZ as a crack driving parameter [Chikh et al. (2008)]. Multiple analytical expressions exist to determine the size of the CPZ. These are formulated by modifying Irwin's [Irwin et al. (196.)] expressions. Such expressions do not account the hardening response of the material. Researchers employed Scanning Electron Microscopy (SEM) and Electron Backscatter Diffraction (EBSD) to experimentally examine the CPZ at the microstructural level [Gao et al. (2019)]. The cyclic plastic deformation zone at the specimen's surface, in front of the crack tip, is assessed using digital image correlation techniques [Bharadwaj et al. (2024)] also. The size of the numerically calculated CPZ is determined using finite element analysis considering the theory of back stress variation. Irwin's analytical model is adjusted to incorporate the kinematic hardening behaviour of the material [Hosseini et al. (2020)]. In view of above, present study performs systematic finite element investigations on the size and shape of the CPZ for SA333Gr6 steel at RT and 300 °C. Parametric studies have been carried out using different crack sizes and different load ratios. The ratchetting response of the material is also studied at the maximum triaxiality point and at the midpoint of the CPZ for a given crack size. 2. Finite element analysis 1.1. FE geometry and boundary conditions Two-dimensional finite element model of 25 mm thick compact tension (CT) specimen is modelled using 8 node plain strain serendipity element as shown in Fig. 1(a). The reduced integration strategy is employed to minimize computing time and effort. A Mesh convergence study was conducted to determine the optimal element size near the