Many engineering components fail in the presence of service loads like thermal residual stresses and thermomechanical loading. An accurate evaluation of the fracture parameter (J-integral) at the crack tip is essential for the safe design of structures.

In this work, a novel computational method called the Extended Finite Element Method (XFEM) has been implemented to analyze the plastically graded material (PGM) subjected to thermal and thermo-mechanical loading. For crack discontinuity modeling, a partition of unity enrichment concept can be employed with additional mathematical functions like Heaviside and branch enrichment for crack discontinuity and stress field gradient, respectively. The modeling of the stressstrain relationship of material has been done using the Ramberg-Osgood material model. The isotropic hardening and Von-Mises yield criteria have been considered to check the plasticity condition. The variation in plasticity properties for PGM has been modeled by exponential law. Further, the nonlinear discrete equation has been numerically solved using a Newton-Rhapson iterative scheme.

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