The equivalent elastic compliances of an elastic solid with interface cracks

Abstract

A periodic array of interface cracks was considered earlier as a simple model to study the effect of crack interaction on the elastic fields of a solid composed of two dissimilar isotropic elastic materials. This paper focuses on the perturbation of the elastic compliances of the solid due to the interacting interface cracks. The problem is formulated using Betti's reciprocal theorem. The analysis provides the equivalent elastic compliances in terms of the geometric parameters of the interface cracks for various levels of loadings and material combinations. The results show that the interaction between cracks is significant only when the crack spacing is less than four times the crack length. Also, contact between crack faces introduces coupling between applied shear stress and normal displacement, but it is significant only when the ratio of the magnitudes of the shear and normal stresses exceeds two.