Nucleation of dislocations from crack tips under mixed modes of loading: Implications for brittle against ductile behaviour of crystals

The variational boundary integral method of Xu and Ortiz is taken as a basis for studying dislocation nucleation from atomically sharp cracks under combined mode I-mode II loading. The tension-shear potential of Rice et al. is extended to allow for skewness in the shear resistance curve and to account for the surface production resistance which accompanies ledge formation. The calculated unstable equilibrium configurations of the incipient dislocations and the dependence of the associated activation energies on crack tip energy release rate are found to differ from the Rice-Beltz perturbation solution and the Schöck-Püschl more approximate solution. Simulations of dislocation nucleation on inclined slip planes reveal that, while tension softening facilitates nucleation, surface production resistance impedes it. The extent to which these two effects influence critical conditions for dislocation nucleation is quantified. The calculations suggest that homogeneous dislocation nucleation on inclined planes is not favoured for materials with all but the lowest of unstable stacking-energy-to-surface-energy ratios. This emphasizes the importance of heterogeneous dislocation nucleation and nucleation on oblique slip planes on which free surface production should play a much weaker role. The implications of these findings on the nucleation-controlled brittle-ductile transition in cleavage fracture are discussed