Crack problems for bonded nonhomogeneous materials under antiplane shear loading

The singular nature of the crack tip stress field in a nonhomogeneous medium with a shear modulus with a discontinuous derivative was investigated. The simplest possible loading and geometry, the antiplane shear loading of two bonded half spaces in which the crack is perpendicular to the interface is considered. It is shown that the square root singularity of the crack tip stress field is unaffected by the discontinuity in the derivative of the shear modulus. The problem is solved for a finite crack and results for the stress intensity factors are presented.