Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials

The interface crack between two nonhomogeneous materials is investigated and the stress singularity is obtained. A new interaction (energy) integral is derived for obtaining mixed-mode stress intensity factors (SIFs) of an interface crack between two nonhomogeneous materials with continuous or discontinuous properties. The basis of the interaction integral method is a conservation integral which relies on two admissible mechanical states (actual and auxiliary fields). By a suitable definition of the auxiliary fields, the domain formulation of the interaction integral which is not related to any derivatives of material properties can be obtained. Moreover, it is proved to be valid even when the integral domain contains other material interfaces. Therefore, the derived formulation can be applied to deal with interfacial fracture problems of complicated nonhomogeneous materials. The numerical implementation of the derived expression is combined with the extended finite element method (XFEM). The numerical results show that the present results agree well with the analytical solutions and the interaction integral is very reliable and domain-independent. Finally, in order to show the applicability of the present method, several representative examples on complicated interface crack problems between nonhomogeneous materials are considered.