Transient nature of dislocation emission from a crack tip gives a new twist to the study of brittle-to-ductile transition. In a class of materials, only the dislocations traveling at high speed may escape from the crack tip. The nucleation of a fast moving dislocation, however, requires a higher level of activation energy, as supported by many experimental data. The present paper explores this scenario under the restriction that the dislocation moves along the crack extension plane. Fundamental solutions of moving dislocations are derived, and which provide the drag forces on the dislocations and the shielding to the crack tip. Nucleation of a fast moving dislocation is examined under the Peierls–Nabarro theory. Incremental dislocation flux is created continuously from the crack tip, and moves away at a constant speed. At a judgmental time of dislocation emission, the displacement jump relates to the holding force along the crack extension plane by a periodic inter-planar potential, and the singular stress induced by the transient and rate-dependent displacement jump negates the original crack tip singularity. A dynamic overshoot calculation under quasi-steady assumption provides an escape velocity of dislocations. To achieve it, extra activation energy is required for the transient dislocation nucleation and that reduces the dislocation nucleation rate along the crack front. When compared with the rate-insensitive process of cleavage, the transient dislocation emission process allows us to predict the rate dependency of the brittle versus ductile behavior of materials.
Journal of the Mechanics and Physics of Solids 49(10), pp.2431-2453