An Einstein Model of Brittle Crack Propagation

TL;DR

This paper introduces a minimal nonlinear model for brittle crack propagation focusing on the crack-tip atom, accurately capturing steady-state velocities and lattice-trapping effects, and explaining low limiting velocities due to anharmonicity.

Contribution

It presents a novel minimal nonlinear model that explains key features of brittle crack propagation, including lattice-trapping and velocity limits, aligning well with dynamical simulations.

Findings

Model captures steady-state crack velocity features

Reveals low limiting velocity due to anharmonicity

Shows lattice-trapping effects in crack propagation

Abstract

We propose a minimal nonlinear model of brittle crack propagation by considering only the motion of the crack-tip atom. The model captures many essential features of steady-state crack velocity and is in excellent quantitative agreement with many-body dynamical simulations. The model exhibits lattice-trapping. For loads just above this, the crack velocity rises sharply, reaching a limiting value well below that predicted by elastic continuum theory. We trace the origin of the low limiting velocity to the anharmonicity of the potential well experienced by the crack-tip atom.