The question of whether a crack cleaved, or instead emitted a dislocation, was considered with respect to the ductile-brittle nature of fracture. It was recalled that a single-plane Peierls approach had recently been used to identify a critical energy release rate, for dislocation emission from a crack tip, in terms of the maximum unit area energy that was required for the uniform shear of a candidate slip plane. A Schmid-type factor was also used to resolve the mode-I crack loading on the candidate slip plane. A comparison with another cleavage analysis, that was based upon the surface energy, yielded an approximate single-plane condition for distinguishing between emission and cleavage. This equated the ratio (of the maximum unit area for shear to the surface energy) to twice the square of the Schmid factor. An attempt was made to assess this result by treating dislocation emission and cleavage as interacting, rather than isolated, processes. In particular, 2 non-linear Peierls-type planes were considered, such that the interactive competition between cleavage and dislocation emission on different planes could be studied. The results for one combination of Peierls plane orientations showed that the above critical ratio for the transition could deviate from the approximate single-plane value, by -25 to 35%, as the coupling which occurred between opening and shearing modes on a Peierls-type plane was increased. Profiles of the shear and opening distributions on the competing cleavage and slip planes revealed extensive interaction; especially when near to instability. Ledge effects were expected to enhance the interaction between competing cleavage and dislocation emission processes on different planes.

V.Shastry, P.M.Anderson: Philosophical Magazine A, 1997, 75[3], 771-89