# Continuum and atomistic studies of intersonic crack propagation

## Abstract

Mechanisms of intersonic crack propagation along a weak interface under shear dominated loading are studied by both molecular dynamics and continuum elastodynamics methods. Part of the objective is to test if continuum theory can accurately predict the critical time and length scales observed in molecular dynamics simulations. To facilitate the continuum-atomistic linkage, the problem is selected such that a block of linearly isotropic, plane-stress elastic solid consisting of a two-dimensional triangular atomic lattice with pair interatomic potential is loaded by constant shear velocities along the boundary. A pre-existing notch is introduced to represent an initial crack which starts to grow at a critical time after the loading process begins. We observe that the crack quickly accelerates to the Rayleigh wave speed and, after propagating at this speed for a short time period, nucleates an intersonic daughter crack which jumps to the longitudinal wave speed. The daughter crack emerges at a distance ahea d of the mother crack. The challenge here is to test if a continuum elastodynamics analysis of the same problem can correctly predict the length and time scales observed in the molecular dynamics simulations. We make two assumptions in the continuum analysis. First, the crack initiation is assumed to be governed by the Griffith criterion. Second, the nucleation of the daughter crack is assumed to be governed by the Burridge - Andrew mechanism of a peak of shear stress ahead of the crack tip reaching the cohesive strength of the interface. Material properties such as elastic constants, fracture surface energy and cohesive strength are determined from the interatomic potential. Under these assumptions, it is shown that the predictions based on the continuum analysis agree remarkably well with the simulation results. © 2001 Elsevier Science Ltd. All rights reserved.