Computer Modeling of Cracks

Abstract

The theoretical techniques used in modeling cracks in crystalline lattices are reviewed. It is shown that there is generally a trade-off between sample size and realistic interatomic potentials. Infinite discrete one and two-dimensional lattices can be handled by the methods of lattice statics, but only with simple unrealistic potentials. In the hybrid lattice statics models a very small crystalline region, where the calculations are done with realistic potentials, is imbedded in an infinite elastic continuum. In this approach the boundary matching between the two regions is the difficulty. At the other end of the scale, molecular dynamic techniques can be used on an unconstrained system of a “large” number of atoms interacting with a reasonably realistic interatomic potential (this is the only way dynamic simulations have been done so far). Here, of course, the question is how “large” is large enough to simulate the behavior of the corresponding infinite system.

This work was supported in part by U.S. Army Research Office, and in part by the U.S. Department of Energy under Contract N0. DE-AC02-76CH00016.