Global bifurcation criterion for oscillatory crack path instability

Abstract

A bifurcation criterion for the transition from straight to oscillatory quasistatic crack propagation in an isotropic material is derived from the requirement of pure mode I stress fields at the crack tip (K_{II}=0) on the entire crack path, henceforth called global bifurcation criterion. For a small-amplitude sine-shaped crack path which is observed in experiments at the transition, it is shown to be sufficient to postulate K_{II}=0 only for two phases of the crack path instead, which simplifies calculations. By using the measured temperature fields to solve the thermoelastic problem of dipping a hot thin glass slab into cold water, critical wavelengths of the oscillating crack growth obtained with the derived global bifurcation criterion agree remarkably well with those observed in experiments by Ronsin and Perrin. It is also shown that local bifurcation criteria, which do not take into account K_{II}=0 on the entire crack path, lead to incorrect results for the oscillatory crack path instability.