Non-planar deviation of an initially straight moving crack

The problem of dynamic crack curving in a brittle solid is investigated as a first step towards determining the velocity dependence of the stability of a running crack. By using a perturbation technique and the complex potential method, a solution for the slightly curved deviation of a running crack under mixed-mode loading conditions is presented. To the first order the angular distribution of the singular stress near the curved crack tip for a smooth running crack is found to depend only on the instantaneous crack-tip velocity and is independent of the crack-tip acceleration and the curvature. For steel the analysis indicates that cracks propagating more slowly than the critical branching velocity will exhibit nearly the same characteristics as those for quasi-static crack deviation and stability. The calculations also show that the critical branching velocity may increase with increasing Poisson's ratio of the material. The estimates of the crack path dependence on velocity presented here are consistent with the quasi-static crack growth solution of Sumi et al. [Int. J. Fracture 21, 67-79 (1983)].