T-stress evaluations of an interface crack in the materials with complex interfaces

This paper develops an interaction integral method for extracting the T-stress of an interface crack in the materials with complex interfaces. In numerical computations, the interaction integral should be converted into an equivalent domain formulation to ensure numerical precision. It can be found that the present domain formulation does not contain any terms related to material interfaces, namely, the interaction integral is domain-independent for material interfaces. As a deduction, the present interaction integral can be used to solve the T-stress for a crack located on a curved interface effectively. Combined with the extended finite element method, the interaction integral method is employed to solve several interface crack problems. Good accuracy can be obtained for the interface fracture of a typical bimaterial strip. Meanwhile, it can be noted that the T-stress converges to a stable value only when the integral domain reaches up to an enough size. Since it is extremely difficult to select a large enough integral domain without any interfaces for the materials with complex interfaces, the domain-independence of the present interaction integral for interfaces is practical significant. Due to this point, the interaction integral method will become a quite reliable and convenient technique to solve the T-stress of an interface crack in the materials with complex interfaces. Finally, the interfacial fracture problem is investigated for several representative centrosymmetric structures formed by two constituent materials.