Path prediction of kinked and branched cracks in plane situations

Using the asymptotic expansion of the stress field ahead a curved extension of a straight crack, some general results on the paths selected by kinked and branched cracks are derived. When dealing with the dynamic branching instability of a single propagation crack, the experimentally observed shape of the branches is recovered without introducing any adjustable parameter. It is shown that the length scale introduced by the curved extension of the branches is given by the geometrical length scale of the experiment. The theoretical results agree quantitatively with the experimental findings.