Reconciliation of continuum and atomistic models for the ductile versus brittle response of iron

We present a detailed analysis of the ductile versus brittle response of bcc iron containing a sharp crack and show that a continuum model based on the Peierls Nabarro model for dislocation formation is consistent with our atomistic results. Specifically, we compare continuum predictions for dislocation emission from a crack tip loaded in mode I under plane strain, tensile conditions with atomistic results for a ((1) over bar 1 0)[1 1 0] crack emitting full edge dislocations in the [1 1 1] {1 1 2} slip system. The simulations are based on an N-body potential of the Finnis - Sinclair type for iron at 0 K, and the continuum dislocation model incorporates recent improvements that account for tension - shear coupling on a prescribed slip plane, as well as the T-stress, in an anisotropic solid. We show that the critical load for dislocation nucleation is influenced by the T-stress ( modulated by the level of external stress applied parallel to the crack plane in a biaxially-loaded plate), which possesses a critical value associated with a change of mechanism between dislocation emission and crack extension. The results are consistent with recent preliminary analyses that address the effect of crack size and the role of the T-stress in the ductile versus brittle response of crystals.