Intersonic Crack Propagation—Part II: Suddenly Stopping Crack

In Part I of this series, we have obtained the fundamental solution for a mode II intersonic crack which involves a crack moving uniformly at a velocity between the shear and longitudinal wave speeds while subjected to a pair of concentrated forces suddenly appearing at the crack tip and subsequently acting on the crack faces. The fundamental solution can be used to generate solutions for intersonic crack propagation under arbitrary initial equilibrium fields. In this paper, Part II of this series, we study a mode II crack suddenly stopping after propagating intersonically for a short time. The solution is obtained by superposing the fundamental solution and the auxiliary problem of a static crack emitting dynamic dislocations such that the relative crack face displacement in the fundamental solution is negated ahead of where the crack tip has stopped. We find that, after the crack stops moving, the stress intensity factor rapidly rises to a finite value and then starts to change gradually toward the equilibrium value for a static crack. A most interesting feature is that the static value of stress intensity is reached neither instantaneously like a suddenly stopping subsonic crack nor asymptotically like a suddenly stopping edge dislocation. Rather, the dynamic stress intensity factor changes continuously as the shear and Rayleigh waves catch up with the stopped crack tip from behind, approaches negative infinity when the Rayleigh wave arrives, and then suddenly assumes the equilibrium static value when all the waves have passed by. This study is an important step toward the study of intersonic crack propagation with arbitrary, nonuniform velocities.