Transient analyses of dislocation emission in the three modes of fracture

Exact transient solutions for a micromechanical process of dislocation emission from stationary cracks in each of the three Modes of fracture are assembled. Each process involves a possible slip mechanism for the Mode, and the loading in each case is due to plane wave diffraction.

The solutions are examined in view of an emissions criterion similar to one developed for quasi-static studies on the basis of standard dislocation force concepts. Among the results are formulas for three parameters: emission time, distance traveled by an emitted dislocation prior to arrest, and the time of arrest. The formulas involve material properties such as yield stress and surface energy, as well as a dimensionless variable parameter governing the size of a zone of dislocation attraction at the crack edge.

The parameters themselves exhibit dislocation speed-dependent dynamic effects, but, on the other hand, the Mode I and Mode III cases achieve minimum emission times for the zero-speed limit. The effect of crack blunting serves to raise the emission time required. Order-of-magnitude estimates of the parameters indicate that they are definitely on a micromechanical scale, suggesting that emission may depend only on the region very near the crack edge.