BRANCHING INSTABILITY OF BRITTLE FRACTURE

A new method for determining the elastodynamic stress fields associated with the propagation of anti-plane branched cracks is presented. The exact dependence of the stress intensity factor just after branching is given as a function of the stress intensity factor just before branching, the branching angle and the instantaneous velocity of the crack tip. The jump in the dynamic energy release rate due to the branching process is also computed. Applying a growth criterion for a branched crack, it is shown that the minimum speed of the initial single crack that allows branching is equal to 0.39c, where c is the shear wave speed. At the branching threshold, the corresponding bifurcated cracks start their propagation at a vanishing speed with a branching angle of approximately 40 degrees. Using these exact results, the branching of a single propagating crack under mode I loading is also considered and the critical velocity for branching is computed. Moreover, using the asymptotic expansion of the stress field ahead a curved extension of a crack, the experimentally observed shape of the branches is recovered without introducing any additional parameter. It is shown that the length scale introduced by the curved extension of the branches is the geometrical length scale of the experiment. The quantitative comparison with the experimental results agrees with the theoretical findings. The present study confirms that the continuum theory of brittle fracture mechanics provides the minimal ingredients for predicting the branching instability threshold, the branching angle and the subsequent paths of the branches.