Limiting velocity of crack propagation in dynamically fractured materials

A model of a fractal crack is considered. It is found that the limiting velocity of crack propagation is determined by the fractal dimension of the crack contour. It is shown that for commercial steels, the limiting crack velocity is in the range $V_{\operatorname{lim}}=(0.155-0.537)c_1$ ($c_1$ is the speed of sound).