Interface cracks in anisotropic dissimilar materials : An analytic solution

Abstract

Based on linear elastic fracture mechanics, analytic solutions are given for displacement and stress fields of in-plane deformation of two anisotropic half-planes, forming a composite bimaterial, with an interface crack, assuming strictly two-dimensional problems; this requires suitable orientation of the material symmetry axes to ensure decoupling of the anti-plane fracture mode from the in-plane ones. It is shown that the field equations are fully characterized in terms of four dimensionless parameters, and these parameters are expressed in terms of the twelve involved elastic constants, six for each half-plane. Analytic solutions are given for two models: (1) the fully open-crack model, involving oscillatory square-root singularities at crack tips ; and (2) the Comninou model which allows possible small contact zones close to the crack tips. Analytic expressions are obtained for the crack opening displacement, the size of the contact zone, the total force transmitted across the contact zone, and the stress field. The results are discussed and related to those for isotropic bimaterials, given by Gautesen and Dundurs.