Fracture modes in a triangular lattice crystal: Numerical and phenomenological studies.

Abstract

By numerical simulations we study the stationary or terminal crack propagation in the triangular lattice system with a truncated harmonic potential under several static external stresses. For the external stress called mode I we found three typical crack propagation modes for the strong external stress, and one more mode for the weak external stress. These crack propagation modes are classified by the potential depth scaled by the external stress. Two of the modes are related to two sound modes: The regions by the transverse and the longitudinal sound modes are separated from each other. There is a supersonic mode by which the crack propagation velocity exceeds the sound velocity. Only in the weak stress case does a zigzag crack pattern appear. By this mode the crack propagation velocity is about half of the transverse sound velocity. We examined the zigzag crack surface and found that its roughness exponent is about 0.75, which is near to those observed experimentally. A system size dependence of the critical potential depth for the crack propagation is also found. Different external stresses (so-called mode II, mode III, and spherical stresses) are also examined. Sometimes different aspects for the fracture were seen, but they are explained by the ame basic ideas that have been developed for mode I stress.