Microbranching in mode-I fracture in a randomly perturbed lattice

Abstract

We study mode-I fracture in lattices using atomistic simulations with randomly distributed bond lengths. By using a small parameter that measures the variation of the bond length between the atoms in perfect lattices and using a three-body force law, simulations reproduce the qualitative behavior of the beyond-steady-state cracks in the high-velocity regime, including reasonable microbranching. In particular, the effect of the lattice structure on the crack appears minimal, even though in terms of the physical properties such as the structure factor g(r) and the radial or angular distributions, these lattices share the physical properties of perfect lattices rather than those of an amorphous material (e.g., the continuous random network model). A clear transition can be seen between steady-state cracks, where a single crack propagates in the midline of the sample, and the regime of unstable cracks, where microbranches start to appear near the main crack, in line with previous experimental results. This is seen in both a honeycomb lattice and a fully hexagonal lattice. This model reproduces the main physical features of propagating cracks in brittle materials, including the total length of microbranches as a function of driving displacement and the increasing amplitude of oscillations of the electrical resistance. In addition, preliminary indications of power-law behavior of the microbranch shapes can be seen, potentially reproducing one of the most intriguing experimental results of brittle fracture. There was found to exist a critical degree of disorder, i.e., a sharp threshold between the cleaving behavior characterizing perfect lattices and the microbranching behavior that characterizes amorphous materials.