A new approach to compute T-stress in functionally graded materials by means of the interaction integral method

A “non-equilibrium” formulation is developed for evaluating T-stress in functionally graded materials with mixed-mode cracks. The T-stress is evaluated by means of the interaction integral (conservation integral) method in conjunction with the finite element method. The gradation of material properties is integrated into the element stiffness matrix using the so-called “generalized isoparametric formulation”. The types of material gradation considered include exponential, linear, and radially graded exponential functions; however, the present formulation is not limited to specific functions and can be readily extended to micromechanics models. This paper investigates several fracture problems (including both homogeneous and functionally graded materials) to verify the proposed formulation, and also provides numerical solutions to various benchmark problems. The accuracy of numerical results is discussed by comparison with available analytical, semi-analytical, or numerical solutions. The revisited interaction integral method is shown to be an accurate and robust scheme for evaluating T-stress in functionally graded materials.