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

TL;DR

This paper models the Portevin-Le Chatelier effect, demonstrating a transition from chaotic to power law behavior with increasing strain rate, aligning well with experimental observations.

Contribution

It introduces a dynamical model that reproduces the experimentally observed crossover from chaos to power law regimes in the Portevin-Le Chatelier effect.

Findings

Chaotic behavior at low and medium strain rates.

Power law statistics at high strain rates.

Largest Lyapunov exponent approaches zero at high strain rates.

Abstract

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