Atomistic and continuum studies of a suddenly stopping supersonic crack

Abstract

Large-scale atomistic simulations are used to study a suddenly stopping crack under mode I and mode II loading conditions. For both cases, linear system solutions are established with harmonic interatomic potentials and it is shown that these reproduce the continuum mechanics solution. We find that the Griffith criterion gives predictions for the onset of fracture in good agreement with the atomistic simulation. The simulation results of the suddenly stopping crack agree well with continuum mechanics and experiments. At the atomic scale, we observe a thermalization effect where mechanical energy is dissipated as heat soon after crack stopping. This result does not affect the basic nature of crack tip fields as predicted by continuum mechanics. The harmonic models are further used as reference systems to probe crack dynamics in the nonlinear materials. We discuss cracks stopping from super-Rayleigh and supersonic velocities in hyperelastic solids. We demonstrate via ab initio crack dynamics that it is difficult to define a unique wave front in the nonlinear solid. This observation supports the idea that there is no unique wave speeds near the crack tip. There exists a train of “longitudinal” and “shear” waves associated with the rapidly changing stress state near the crack tip. For supersonic mode II cracks, the mother crack seems to transform from a singularity into a less localized stress concentration after the daughter crack is nucleated. In addition to this result, we observe an anisotropy of wave velocities close to the crack tip leading to elliptical instead of circular wave fronts. This study exemplifies joint atomistic and continuum modelling of nanoscale dynamic systems.