PSI - Issue 60

Prakash Bharadwaj et al. / Procedia Structural Integrity 60 (2024) 655–664 Prakash Bharadwaj / StructuralIntegrity Procedia 00 (2019) 000 – 000

656

2

1. Introduction Working loads on structural components can be static or dynamic in nature. Cyclic loading is one type of dynamic loading. During service conditions, most of the structural components are subjected to cyclic loadings. Due to the cyclic loading, damage occurs inside the material in every cycle, which progressively grows and leads to nucleation and initiation of fatigue cracks in the structural component (Dowling et al. 1999). Localized plastic deformation is the important responsible factor for the Fatigue Crack Growth (FCG) in each cycle. In ductile materials fatigue crack propagates through the region which undergoes local plastic deformation due to cyclic loading. As the crack propagates, the plastically deformed region moves with the crack tip. Fatigue damage is more severe inside the cyclically plastic-deformed region, which is related to local strain ranges (Gao et al. 2022). The local plastically deformed region ahead of the crack tip under cyclic loading is divided into two regions namely monotonic plastic zone and cyclic plastic zone. The monotonic plastic zone depends on the load maxima of the cycle while the cyclic plastic zone depends on the load maxima as well as the load range. The monotonic plastic zone is the plastically deformed region ahead of the crack tip under the monotonic loading where equivalent plastic strain ≥ 0.0005% (Hosseini et al. 2020). The cyclic plastic zone is defined as the region where a hysteresis loop of stress and strain forms due to cyclic plastic deformation. The cyclic plastic zone is also called the reverse plastic zone because the material in this region sees plastic deformation from tensile to compressive yielding during unloading to the minimum load. The size of the cyclic plastic zone is smaller compared to the size of the monotonic plastic zone. For fatigue damage, two deformation mechanisms are responsible. The monotonic deformation is controlled by the maximum stress intensity factor (K max ) and cyclic deformation occurs due to the tensile part of a range of stress intensity factor (ΔK). Thus, ΔK determines the size of the cyclic plastic zone (Gonzales et al. 2023). Analytical expressions consisting material’s yield strength and ΔK for the calculation of the size of a cyclic plastic zone are available (Nicholls et al. 1990, Bathis et al. 1973, Pineau et al. 1974 and Chapetti et al. 2005). Most of these expressions are material-specific and do not consider the cyclic hardening effect of the material. In a few cases crack closure effect was also considered. Besides analytical expressions an application of a strain energy density-based approach is used to get the strain fields under cyclic loading and an estimation of the size of the plastic zone is carried out by Glinka et al. (1985). Zhao et al. (2004) performed finite element analyses for the calculation of the size and shape of the cyclic plastic zone and reported the phenomenon of ratcheting for load ratio < 0.5. With the help of finite element analysis, the response of the cyclic plastic deformation has been studied for different load ratios. Progressive accumulation of strain inside the cyclic plastic zone is shown and the butterfly-type shape of the cyclic plastic zone is reported by Paul et al. (2013). By using a technique of back stress variation inside the finite element analysis, the calculation of the size of the cyclic plastic zone has been carried out. Irwin’s analytical model was modified by considering the kinematic hardening response of the material by Hosseini et al. (2020). Experimental investigation with the help of EBSD and SEM was carried out to characterize the cyclic plastic zone at the microstructural level (Gao et al. 2019). In recent times optical microscopy has evolved as a strong tool to estimate the strain fields under FCG loading. To verify the small-scale formulation of fatigue crack growth, the full strain field surrounding the crack tip is measured by Zhang et al. (2011), with the help of a digital image correlation system. In-situ measurement of continuous strain field at the surface of the specimen and around the crack tip is carried out for the growing crack. With the help of the strain field, the size of the cyclic plastic zone is calculated by Zhao el al. (2020) and its shape is found to be of butterfly type. Gonzales et al. (2023) conducted an investigation to explore the reverse plastic zone as a potential parameter of fatigue crack growth (FCG). The researchers employed the digital image correlation approach to measure the cyclic plastic zone at the crack tip. Cyclic plastic zone size influences fatigue crack propagation. In fact, if the size of the CPZ is large, significant energy will dissipate during FCG. Fatigue crack growth rate is directly related to the size of the CPZ (Hosseini et al. 2020, Chikh et al. 2008). Thus, the size and shape of the cyclic plastic zone is one of the important aspects of the study of fatigue crack growth. A limited study has been reported in the literature to calculate the size of CPZ using a digital image correlation system. In view of the above, systematic investigations of the size, and shape of the CPZ have been carried out in this paper. The FCGR tests has been carried out on nuclear piping material steel SA333Gr6 under constant load range