Interfacial crack in a two-dimensional hexagonal lattice

In this paper we compare a set of atomic calculations of interfacial crack structure and properties with the predictions of an augmented elastic theory. Our intent is to critique the elastic predictions, especially the mode conversion and displacement closure oscillation features of the elastic theory. A simple physical picture is developed based on a crack stability diagram, using two sets of stress intensity axes. The first set is the normal applied stress intensity K and the second is a local stress intensity factor k, defined to describe the physics of the core region. The Griffith condition and dislocation emission criterion are defined in terms of the local k, and its associated effective core size parameter. Unfortunately, the physical core size is not a unique parameter in the problem, but varies directly with the amount of shear in the core. Thus, the effective core size for the Griffith condition is different from that for dislocation emission. In each case, the effective core size is much smaller than the physical core size, which means that the mode shift at the crack tip is considerably larger than would be expected on the basis of linear elasticity. However, with appropriately defined effective core size parameters, the Griffith condition is well satisfied, and the emission criterion based on the Rice unstable-stacking-fault condition is also surprisingly well satisfied in the mode-II emission configuration. The crack is found never to exhibit displacement oscillations, in part, because of the necessary condition that the Griffith condition be satisfied at the crack tip, and in part because the amount of shear in the core is limited by dislocation emission.