The singular stress field of a crack terminating at a frictional interface between two materials

The problem of a crack terminating at an interface between two materials which is governed by Coulomb’s law of friction is studied using Mellin integral transforms. Depending on the relative slip directions of the two wedges that are created by the crack, both the case of the two wedges moving in opposite directions and that of the two wedges moving in the same direction are treated. The characteristic equations which yield the order of the crack-tip singularity are obtained in terms of the Dundurs constants, the inclination of the crack and the coefficient of firction. For the special case when the crack is perpendicular to the interface and the two wedges slip in opposite directions, it is shown that the problem decouples into mode I (symmetric) and mode H (antisymmetric) cracks, and numerical results are presented for this case.