Fatigue crack growth simulations of plastically graded materials using XFEM and J-integral decomposition approach

In this work, fatigue crack growth in functionally graded materials (FGM)/plastically graded materials (PGM) is simulated using the J-integral decomposition approach and extended finite element method (XFEM). The fatigue crack growth rate is estimated by the stress intensity factor based Paris law. The stress intensity factor is computed by the J-integral decomposition approach. In this approach, state variables such as stress, strain and displacement derivatives are decomposed into their symmetric and anti-symmetric parts across the crack surface. The numerical issues faced in J-integral computation such as the evaluation of stress at spatial mirror point and strain energy density derivative are properly addressed. A novel data transfer scheme is proposed to evaluate the stresses at the spatial mirror point. In this scheme, the derivative of strain energy density is calculated by surface approximation of the strain energy density. Various fatigue crack growth problems are simulated by the proposed methodology under mode-I and mixed mode loading. A component level problem i.e. fatigue crack growth in an aero-engine turbine disc made of plastically graded material is solved to demonstrate the versatility of the presented methodology.