On Branched, Interface Cracks

Abstract

The problem of branched, external cracks in the interface between two elastic materials is considered under the plane strain condition. A small interface contact region is introduced in the vicinity of each crack tip in order to remove oscillatory singularities. The branches are replaced by continuous distribution of edge dislocations, and, with the aid of Muskhelishvili’s potential method, the problem is reduced to a system of singular integral equations which are defined on the branches and the perfectly bonded region of the interface. The unknown functions of these integral equations are the shear stress acting on the bonded region, and the density functions of the edge dislocations. Stress-intensity factors of the interface cracks and branches are obtained numerically for several branch angles and branch lengths. Finally, the question of kinking from a tip of an interface crack is discussed with the aid of the results.