Multiscale simulations of the lattice trapping barrier to
brittle fracture in silicon
Noam Bernstein
Center
for Computational Materials Science
Naval
Research Laboratory,
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.