Dislocation nucleation and crack stability: Lattice Green’s-function treatment of cracks in a model hexagonal lattice

A series of atomistic calculations is performed in order to evaluate the effects of several physical factors on dislocation emission in a model hexagonal lattice. The method of calculation is the lattice Green's-function method, together with several pair potentials with variable parameters. The physical factors of interest are the dislocation width (or, more precisely, maximum strain) and ``unstable stacking energy'' suggested by several continuum-based calculations, as well as the mode-I loading. We find that the continuum theories are surprisingly accurate, provided that some modifications are made. Typical discrepancies are of order 10% in the emission stress intensity. However, the atomistic calculations indicate that several of the assumptions underlying the continuum theories are inaccurate. In addition, we find strong mode-I--mode-II interactions, which are summarized in the form of a crack-stability diagram.