Multiscale simulations of the lattice trapping barrier to

brittle fracture in silicon


Noam Bernstein

Center for Computational Materials Science

Naval Research Laboratory,

Washington, DC, USA


Simulations of fracture in silicon, a prototype brittle material, have the potential to give insight into fundamental properties that control the behavior of the material at the crack tip.  By direct calculations of the energy path of the propagation of an atomically sharp crack, I show that in many empirical potentials there is a large energy barrier to brittle fracture.  This lattice trapping barrier is caused by the discrete nature of the atomic lattice.  In some cases the barrier is large enough to completely suppress brittle fracture, explaining the ductile behavior seen in many simulations.  In contrast, a method that dynamically couples a quantum-mechanical tight-binding description of bonding at the crack tip to a larger empirical potential simulation shows brittle fracture with only minimal lattice trapping, in agreement with experiment.  A simple model for the interplay between the energy to break the crack tip bond and elastic energy relaxation correctly predicts the barrier for both the empirical-potential and coupled simulations.  The success of the model indicates that the bond breaking process is highly local, and that deviations from linear elasticity at the crack tip are essential for determining the extent of lattice trapping.  Two length scales emerge from the model: one for bond breaking, and another for elastic relaxation.  Finally, I present ongoing work on dynamically coupled simulations for the fracture process in silicon at high temperatures, and fracture in other materials.