A generalized interaction integral method for the evaluation of the T-stress in orthotropic functionally graded materials under thermal loading

The interaction integral method that is equipped with the nonequilibrium formulation is generalized to evaluate the nonsingular T-stress as well as mixed-mode stress intensity factors in orthotropic functionally graded materials under thermomechanical loads. This paper addresses both Mode-I and mixed-mode fracture problems and considers various types of orthotropic material gradation. The orthotropic thermomechanical material properties are graded spatially and integrated into the element stiffness matrix using the direct Gaussian formulation. The types of orthotropic material gradation considered include exponential, power-law, and hyperbolic-tangent functions, and the numerical formulation is generalized for any type of smooth material gradation. The T-stress and mixed-mode stress intensity factors are evaluated by means of the interaction integral method developed in conjunction with the finite element method. The accuracy of numerical results is assessed by means of thermomechanically equivalent problems.