The brittle-to-ductile transition - II: Dislocation dynamics and the strain-rate dependence of the transition temperature

In this paper, the author describes how effects related to dislocation mobility can be incorporated in the instability criterion in a straightforward manner and used to analyze the strain-rate dependence of (Tc). He begins with a simple example and studies the dynamics of a group of dislocations in the vicinity of a crack subjected to Mode 3 loading. If an empirical velocity-stress power-law is assumed for the thermallly activated dislocation motion, the dislocation dynamics in the vicinity of the crack tip can be described in terms of similarity'' solutions. The correlation between the strain-rate dependence of Tc and the temperature dependence of the dislocation mobility is then deduced by incorporating the analytical dynamical solutions in the static criterion for the cooperative instability obtained in 1. The analysis shows that the strain-rate dependence of Tc is due to a combination of the scale-invariant thermal dislocation screening which causes the BDT and the self-similar stress-induced dynamics of dislocation dipoles (or loops) in the vicinity of the crack tip.