On accurate numerical evaluation of stress intensity factors and T-stress in functionally graded materials

This paper revisits the interaction integral method to evaluate both the mixed-mode stress intensity factors and the T-stress in functionally graded materials under mechanical loading. A non-equilibrium formulation is developed in an equivalent domain integral form, which is naturally suitable to the finite element method. Graded material properties are integrated into the element stiffness matrix using the generalized isoparametric formulation. The type of material gradation considered includes 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 center crack in a plate and assesses the accuracy of the present method compared with available semi-analytical solutions.