Brittle fracture dynamics with arbitrary paths. II. Dynamic crack branching under general antiplane loading

The dynamic propagation of a bifurcated crack under antiplane loading is considered. The 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. Similar to the single crack case, a growth criterion for a branched crack is applied. It is based on the equality between the energy flux into each propagating tip and the surface energy which is added as a result of this propagation. It is shown that the minimum speed of the initial single crack which 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°.