A Class of Interface Crack Problems

The problem of an arc crack lying within the interface between a rigid curvilinear inclusion and an unbounded matrix is considered under the assumption of plane deformation, and a general solution method is presented. The particular examples of a single arc crack debonding one end of a rigid elliptic, a square with rounded corners, and a circular inclusion under uniaxial and equal biaxial loading at infinity are considered in detail. It is shown that there is an oscillating square root stress singularity at the crack tips unless the crack tips happen to lie at a geometrical discontinuity of the inclusion boundary. In that case, the singularity is different. In particular, the singularity is three-quarter power for a crack tip at an inclusion cusp.