A mode III crack at the interface between two nonlinear materials

The stress singularity at the tip of a crack at the interface between two different power-law materials under mode III loading (longitudinal shear) is considered. By considering expansions at the crack tip in each region, and matching across the interface ahead of the crack, it is found that the stress singularities are the same in each material, and correspond to that for a crack in a homogeneous material with hardening exponent equal to the maximum of the hardening exponents of the two materials. The displacements near the crack tip are found to be of different orders in the two materials, and it is shown that all the crack tip energy is concentrated in the material with the largest hardening exponent. The results are illustrated by means of an example involving a displacement loaded bimaterial strip.