NUCLEATION OF DISLOCATIONS FROM CRACK TIPS UNDER MIXED-MODES OF LOADING - IMPLICATIONS FOR BRITTLE AGAINST DUCTILE BEHAVIOR OF CRYSTALS

The variational boundary integral method of Xu and Ortiz is taken as a basis for studying dislocation nucleation from atomically sharp crack s under combined mode I-mode II loading. The tension-shear potential o f Rice et al. is extended to allow for skewness in the shear resistanc e curve and to account for the surface production resistance which acc ompanies ledge formation. The calculated unstable equilibrium configur ations of the incipient dislocations and the dependence of the associa ted activation energies on crack tip energy release rate are found to differ from the Rice-Beltz perturbation solution and the Schock-Puschl more approximate solution. Simulations of dislocation nucleation on i nclined slip planes reveal that, while tension softening facilitates n ucleation, surface production resistance impedes it. The extent to whi ch these two effects influence critical conditions for dislocation nuc leation is quantified. The calculations suggest that homogeneous dislo cation nucleation on inclined planes is not favoured for materials wit h all but the lowest of unstable stacking-energy-to-surface-energy rat ios. This emphasizes the importance of heterogeneous dislocation nucle ation and nucleation on oblique slip planes on which free surface prod uction should play a much weaker role. The implications of these findi ngs on the nucleation-controlled brittle-ductile transition in cleavag e fracture are discussed.