It was pointed out that only dislocations which travelled at high speeds could escape from a crack tip. The nucleation of a fast-moving dislocation required a higher level of activation energy. This situation was explored under the condition that the dislocation moved along the crack extension plane. Fundamental solutions were derived, for moving dislocations, which included drag forces and crack-tip shielding. The nucleation of a fast-moving dislocation was treated within the framework of the Peierls-Nabarro model. An incremental dislocation flux was continuously created at the crack tip, and moved away at a constant speed. At a given moment of dislocation emission the displacement jump was related to the holding force, along the crack extension plane, by a periodic interplanar potential. The singular stress which was caused by the transient and rate-dependent displacement jump negated the original crack-tip singularity. A dynamic overshoot calculation, for quasi-steady conditions, yielded an escape velocity for the dislocations. In order to permit this, an additional activation energy was required for the transient dislocation nucleation, and this reduced the dislocation nucleation rate along the crack front. Overall, the results permitted the rate-dependence of the ductile-brittle transition to be predicted.

Transient Dislocation Emission from a Crack Tip. W.Yang, J.C.Tang, Y.S.Ing, C.C.Ma: Journal of the Mechanics and Physics of Solids, 2001, 49[10], 2431-53