Initiation, Propagation, and Kinking of an Antiplane Crack

An infinite linear elastic body containing a semi-infinite crack is loaded by a planar antiplane stress pulse parallel to the crack. The stress wave strikes the crack at time t=0 and at some arbitrary later time t_f, the crack begins to extend straight ahead with constant speed v_o. After some later t_b, the crack suddenly stops, then kinks and propagates with constant speed v_c, making an angle δ with the original crack. A superposition scheme is used to construct the exact full-field solution of the propagating crack. The full-field solution for stresses for the constant speed propagating crack with a delay time t_f is found to be the Mode III analog of Baker’s problem in Mode I plus the stress pulse, and the displacement on the crack faces behind the moving crack tip is just the solution of Baker’s problem when expressed in crack tip coordinates and is independent of the delay time t_f. When the crack suddenly stops, the stress field, which is radiated out from the stopped crack tip, corresponds to the stationary crack stress field of a crack whose crack tip has been at the stopped crack position for all time. The dynamic stress intensity factor at the kinked crack tip is then obtained by using a perturbation method. The region of the stress intensity factor controlled field is investigated for both stationary and propagating cracks. It is found that this region depends on the loading conditions and which stress components are considered. The region also depends on the crack tip speed and will contract as the crack tip speed increases.