Continuum and atomistic studies of intersonic crack propagation

Mechanisms of intersonic crack propagation along a weak interface under she ar dominated loading are studied by both molecular dynamics and continuum e lastodynamics methods. Part of the objective is to test if continuum theory can accurately predict the critical time and length scales observed in mol ecular dynamics simulations. To facilitate the continuum-atomistic linkage, the problem is selected such that a block of linearly isotropic, plane-str ess elastic solid consisting of a two-dimensional triangular atomic lattice with pair interatomic potential is loaded by constant shear velocities alo ng 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 be gins. We observe that the crack quickly accelerates to the Rayleigh wave sp eed and, after propagating at this speed for a short time period, nucleates an intersonic daughter crack which jumps to the longitudinal wave speed. T he daughter crack emerges at a distance ahead of the mother crack. The chal lenge here is to test if a continuum elastodynamics analysis of the same pr oblem can correctly predict the length and time scales observed in the mole cular dynamics simulations. We make two assumptions in the continuum analys is. First, the crack initiation is assumed to be governed by the Griffith c riterion. Second, the nucleation of the daughter crack is assumed to be gov erned by the Burridge-Andrew mechanism of a peak of shear stress ahead of t he crack tip reaching the cohesive strength of the interface. Material prop erties such as elastic constants, fracture surface energy and cohesive stre ngth are determined from the interatomic potential. Under these assumptions , it is shown that the predictions based on the continuum analysis agree re markably well with the simulation results. (C) 2001 Elsevier Science Ltd. A ll rights reserved.