Abstract
A Griffith crack in a brittle elastic material is struck by a plane longitudinal stress wave whose wavefront is parallel to the crack. The paper investigates the conditions for crack propagation at an instantaneous velocity upon diffraction of the incident wave by the crack. The investigation consists of two parts. In the first part, the particle velocity and the normal stress are determined in the vicinity of the crack tip for diffraction of a transient wave of arbitrary shape by a crack which extends at a constant speed once the wavefront has impinged on the crack. In the second part of the investigation a balance of rate of energy is employed to determine that shape of the incident pulse which is compatible with instantaneous crack propagation. If energy is dissipated only as fracture energy, and if the specific fracture energy is a constant, crack propagation at an instantaneous velocity occurs only if the stress has a square-root singularity at the wavefront of the incident wave.
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