Crack propagation generated by a horizontally polarized shear wave

A plane horizontally-polarized shear wave propagates into an undisturbed brittle elastic material containing a void. This paper inquires into the conditions for initiation of crack propagation at an instantaneous velocity upon diffraction of the wave by the void. The investigation consists of two parts. In the first, the particle velocity and the shear stresses are determined for diffraction of a transient wave of arbitrary shape by a wedge-shaped void which produces a running crack at the instant the wave front strikes the tip of the wedge. In the second, the balance of rate-of-energy is employed to determine that shape of the incident pulse which is consistent with crack propagation at an instantaneous velocity. It is shown that near the wave front the incident displacement wave must be of the form of a square root of the general argument t-ax-by. For this particular type of incident wave, the instantaneous velocity of crack propagation is computed as a function of the angle of incidence, the "amplitude" of the incident wave, and of the material parameters.