Chaotic and power law states in the Portevin-Le Chatelier effect

Abstract

Recent studies on the Portevin-Le Chatelier effect report an intriguingcrossover phenomenon from a low-dimensional chaotic to an infinite-dimensional scale-invariant power law regime in experiments on CuAl singlecrystals and AlMg polycrystals, as a function of strain rate. We devise afully dynamical model which reproduces these results. At low and mediumstrain rates, the model is chaotic with the structure of the attractor resembling thereconstructed experimental attractor. At high strain rates, power lawstatistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero.