Mode III and mixed mode I–II crack kinking under stress-wave loading

Abstract

A stress jump is incident on a line crack in an elastic solid. At the instant that the crack tip is struck, the crack starts to propagate with a constant velocity cf in the forward direction, but under an angle ππ with the plane of the original crack. In the time interval before signals from the other crack tip arrive, approximate expressions have been obtained for the elastodynamic stress intensity factors of the kinked crack. The approximation is based on the assumption that the near-tip field for a kinked crack can be approximated by the field for a crack propagating in its own plane, provided that the new crack faces are subjected to appropriate surface tractions. For the Mode-III case the approximation of the elasto-dynamic stress intensity factor for the kinked crack can be checked by comparisons with exact results. The range of kinking angles and crack-tip speeds for which the approximation gives good results turns out to be surprisingly large. For the Mixed Mode I–II case comparisons with numerical results have been carried out, and satisfactory agreement has been obtained. The elastodynamic stress intensity factors have been used to compute the corresponding fluxes of energy into the propagating crack tip. For a specified angle of incidence the energy flux into the crack tip shows a distinct maximum at a specified combination of crack-kinking angle and crack-tip speed.