It was recalled that many crystalline solids fail by cleavage at low temperatures and via plastic processes at high temperatures. In the transition region, cleavage failure occurred at stresses which increased with increasing temperature; thus reflecting a decrease in yield stress and a consequent increase in plasticity around the crack tip. The occurrence of crack-tip plasticity blunted the crack and shielded it due to compressive stresses in the plastic zone. This competition between cleavage and plastic flow could be modelled in terms of the generation, motion and interaction of dislocations moving on the slip plane which contained the crack tip. Assumptions had to be made concerning the criterion for cleavage fracture, and the density and strength of the dislocation sources. Whereas the temperature range and strain-rate sensitivity of the transition depended upon the velocity law, the form of the transition (sharp or gradual) depended upon the spacing of the dislocation sources and the transition was therefore structure-sensitive. Static equilibrium arrays of discrete dislocations were also modelled, and were compared with continuum plasticity models for the plastic zone.

Modelling Plastic Zones and the Brittle-Ductile Transition. P.B.Hirsch, S.G.Roberts: Philosophical Transactions of the Royal Society, 1997, 355, 1991-2002