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In this chapter, extended finite element method (XFEM) has been used to simulate the fatigue crack growth problems in functionally graded material (FGM) in the presence of hole, inclusion and minor crack under elastic and plastic conditions. The fatigue crack growth analysis of alloy/ceramic FGMs, alloy and equivalent composite is done by XFEM in the presence of multiple discontinuities under mode-I mechanical load. The validity of linear elastic fracture mechanics (LEFM) theory is limited to the brittle materials. Therefore, the elastic plastic fracture mechanics (EPFM) theory needs to be utilized to characterize the plastic behavior of the material. A generalized Ramberg-Osgood material model has been used to model the stress-strain behavior of the material. Plasticity has been checked by Von Mises Yield criteria. J-integral has been used to calculate the SIF. Crack growth direction is determined by maximum principal stress criteria.

Fatigue Fracture of Functionally Graded Materials Under Elastic-Plastic Loading Conditions Using Extended Finite Element Method