Evolution of dislocation densities and the critical conditions for the Portevin-Le Châtelier effect

Abstract

A model is proposed for the critical strains associated with the Portevin-Le Châtelier effect (PLC) in terms of the strain dependence of the densities of mobile and forest dislocations. The classical critical condition for the onset of the PLC effect, viz. that of vanishing of the strain rate sensitivity of flow stress under the influence of dynamic strain aging is reexamined. The analysis takes into account the strain dependence of a key quantity: the elementary strain produced when all mobile dislocations perform a successful thermally activated step through the forest obstacles. This elementary strain is estimated by studying a system of coupled differential equations for the evolution of the two densities. Results are obtained in semi-quantitative form and compared with available data. It is shown that the following effects are consistently explained: the occurrence of critical strains for the onset and termination of jerky flow, occasional observation of two PLC regimes within the same deformation curve, the behaviour of the critical strains at high strain rates and low temperatures and, possibly, the particular behaviour exhibited by some alloys at low strain rates and high temperatures. Consequences for the “friction” and “forest” models of dynamic strain aging are discussed.