Phase field modeling for fatigue fracture in functional graded materials

A phase field modeling framework for fatigue fracture was proposed in functionally graded materials (FGMs). This framework is constructed based on homogenization theory and takes into consideration the spatial variation of effective properties, critical energy release rate, and fatigue degradation function. Several exemplary cases are shown according to the model to prove the capabilities of the presented framework. These cases present fatigue crack propagation and crack length variation, and the influences of cyclic load, the nonhomogeneous and geometric parameters on crack propagation and crack length. The framework enables capture fatigue crack propagation in FGMs under cyclic loading and considering the spatial variation of effective properties, critical energy release rate, and fatigue degradation function. Furthermore, a monolithic scheme applying the quasi-Newton method to address the issue of fatigue fracture in FGMs is proposes.