Investigation of stress intensity factors for an interface crack in multi-interface materials using an interaction integral method

A new interaction integral formulation is derived for obtaining mixed-mode stress intensity factors (SIFs) of an interface crack with the tip close to complicated material interfaces. The method is a conservation integral that relies on two admissible mechanical states (actual and auxiliary fields). By a suitable selection of the auxiliary fields, the domain formulation does not contain any integral related to the material interfaces, which makes it quite convenient to deal with complicated interface problems. The numerical implementation of the derived expression is combined with the extended finite element method (XFEM). According to the numerical calculations, the interaction integral shows good accuracy for straight and curved interface crack problems and exhibits domain-independence for material interfaces. Finally, an interfacial fracture problem is investigated for the representative centrosymmetric structure formed by two constituent materials.