Scaling relations for crack-tip plasticity

The fracture toughness of semibrittle materials such as bee transition metals or semiconductor crystals strongly depends on loading rate and temperature. If crack-tip plasticity is considered to be thermally activated, a strong correlation between these quantities is expected. An Arrhenius-like scaling relation between the loading rate and the brittle-to-ductile transition temperature has already been reported. In the present work, two-dimensional discrete dislocation dynamics simulations of crack-tip plasticity are employed to show that the different combinations of loading rates and temperatures which yield the same fracture toughness are indeed correlated by a scaling relation. This scaling relation is closely related to the law used to describe dislocation motion. A strong correlation between loading rate and temperature is found in the entire temperature regime in which crack-tip plasticity is controlled by dislocation mobility. This shows the importance of dislocation mobility for fracture toughness below the brittle-to-ductile transition and for the transition itself. The findings of our simulations are consistent with experimental data gathered on tungsten single crystals and suggest that non-screw dislocations are dominating crack-tip plasticity in the semibrittle regime of this material.