Debonding of rigid curvilinear inclusions in longitudinal shear deformation

Abstract

The problem of two symmetrically placed interface cracks at rigid curvilinear inclusions under longitudinal shear deformation is considered. A solution valid for arbitrary inclusion shapes is found. It depends on a parameter β describing the cracks. For β = e iα where α is an angle, the cracks lie in the interface. For β real and greater than unity, we have two radial cracks emanating from a curvilinear cavity. The solution for β = 1 corresponds to a completely debonded inclusion. Examples of elliptic, square with rounded corners, and rectangular inclusions are worked out in detail. It is shown that the crack tip stress intensity factor becomes infinite for interface cracks terminating at cusps and corners. This phenomenon is attributed to the change in the nature of the singularity as the crack tip approaches a cusp or corner. The singularity is three-quarter power at a cusp and two-thirds power at a corner of a rectangular inclusion. Finally, the application of the results to composite materials is indicated.