Evaluation of stress intensity factors and T-stress in functionally graded materials using the interaction integral method

The interaction integral method is revisited to evaluate both the mixed-mode stress intensity factors and the T-stress in functionally graded materials under mechanical loading. In particular, a non-equilibrium formulation is developed in an equivalent domain integral form of the interaction integral, which is naturally suitable to the finite element method. The material gradation is integrated into the element stiffness matrix using the generalized isoparametric formulation. The types of material gradation include continuum functions such as an exponential function, but the present formulation can be readily extended to micromechanical models. This paper presents a fracture problem with an inclined crack and assesses the accuracy of the present method compared with available semi-analytical solutions. The revisited interaction integral method is shown to be an accurate scheme for evaluating such parameters in functionally graded materials.