On lattice trapping of cracks

Abstract

A simple analytic theory to quantify the extent of “trapping” of cracks by a crystal lattice and its dependence on the range of the interatomic force law is presented. The theory requires a priori knowledge of only one or two lattice-dependent, but force law independent, parameters and can then reproduce nearly all previous (numerically demanding) theoretical results. Moreover, the extent of lattice trapping does not decrease monotonically with increasing range of the force law. For realistic interatomic potentials, however, lattice trapping is quite small. The analysis is then extended to the case of chemical corrosion by direct chemical attack of the crack tip bond. It is shown that similar slow crack growth thresholds can be predicted by the thermodynamic Griffith approach and a fracture criterion based on a local bond instability.