MODELING THE SPATIOTEMPORAL ASPECTS OF THE PORTEVIN-LE-CHATELIER EFFECT

Based on a phenomenological treatment of dynamic strain ageing, the spatiotemporal dynamics of Portevin-Le Chatelier band propagation is modelled. To this end, the efficiencies of several potential propagation mechanisms, i.e. cross-slip, long-range dislocation interactions, and incompatibility stresses, are compared. For constant-stress-rate testing conditions, pulse-like solutions are constructed using a piecewise linear caricature of the stress-strain rate characteristic. Expressions for the propagation velocity and the strain-burst amplitude are derived. For constant-strain-rate testing, control parameters are given for (1) the occurrence of non-propagative type C bands and (2) the transition (Hopf bifurcation) from the continuous propagation of a type A band to the hopping motion of a type B band. The results are compared with experimental findings, and future experiments are proposed to check theoretical predictions.