Contours for planar cracks growing in three dimensions

A three-dimensional dynamic steady state analysis for extension of a semi-infinite plane crack is considered. Fracture is brittle and driven by loads applied to the crack surfaces. An analytical solution is obtained, and examined in light of two criteria: energy release (rate) and strain energy density. Introduction of a quasipolar coordinate system allows, for each criterion, generation of a nonlinear first-order differential equation for the distance from the origin to any point on the crack edge. These in turn give insight into the crack contour generated by the crack edge. In particular, for loading by compressive point forces, the equation generated by the energy release (rate) criterion is solved exactly. Calculations depict a crack edge contour that tends to the rectilinear, but deviates markedly from that near the point forces.