Wedging of an Elastic Half Plane Along a Semiinfinite Interface Crack

We consider the problem of equilibrium of an elastic half plane with a semiinfinite crack on its boundary. At a certain distance from the crack tip, the crack edge is in contact with a rigid semiinfinite wedge and, in the vicinity of the tip, the crack edge is in contact with the rigid base. Frictional forces are taken into account in the zone of contact between the crack edge and the rigid base. The analytic solution of the problem is obtained by the Wiener–Hopf method. The boundaries of the contact zones, the distributions of stresses in these zones and on the boundary of the half plane outside the crack are determined, as well as the mode II stress intensity factors.