A hybrid atomistic finite-element model was compared with the continuum-based Peierls-Nabarro model for several crack orientations in a crystal. Both methods incorporated the same embedded-atom potential in order to make the comparison as valid as possible. The agreement (expressed in terms of a stability diagram which showed the envelopes in loading space where fracture or dislocation nucleation were likely to occur) was excellent in the case of a crack lying on a {111} plane, with a crack front running along a <211> direction, subjected to mixed-mode I/II loading. That orientation involved dislocation nucleation on the prolongation of the crack plane, and hence no ledge was formed upon dislocation nucleation. In other geometries which were considered (involving a crack on a {100} plane), the agreement seemed to deteriorate with increasing size of the ledge that was created when a dislocation nucleated. For all of the geometries, the atomistic model showed that incipient dislocation-like features were present before dislocation nucleation took place. This again validated the continuum Peierls-Nabarro model.

On the Continuum versus Atomistic Descriptions of Dislocation Nucleation and Cleavage. P.Gumbsch, G.E.Beltz: Modelling and Simulation in Materials Science and Engineering, 1995, 3[5], 597-613