Mode-III crack kinking with delay time: An analytical approximation

Abstract

The singular part of the elastodynamic field in the vicinity of a propagating crack tip plays an important role in fracture mechanics considerations. The dynamic solution near a crack tip which branches or kinks is required to understand the observed bifurcation events in brittle materials. We consider a rather general time dependent stress wave loading incident at an arbitrary angle on a semi-infinite crack in a linear elastic solid. To model the kinking of a stationary crack under stress wave loading correctly, a delay time for initiation of the new crack must be included which means the problem loses the property of self-similarity and makes it significantly more difficult. A perturbation method is used to obtain the dynamic stress intensity factor for the kinking crack. The method relies on solving simple problems which can be used with linear superposition to solve the problem of a kinked crack. The solution is represented in a simple closed form as a function of the incident angle α of the stress wave, the kink angle δ, the kinking crack speed υc, and the finite delay time tf. This gives more information about the effect of parameters on the solution than the purely numerical results. Finally, the maximum of the energy flux into the propagating kinked crack tip is found as a function of kink angle and crack tip velocity, and some implications of this are discussed.