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

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.

arXiv commentPublished in Europhysics Letters

References in corpus (6)

• Multifractal burst in the spatio-temporal dynamics of jerky flow
• Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect
• Critical Dynamics of Burst Instabilities in the Portevin-Le Chatelier Effect
• Incomplete approach to homoclinicity in a model with bent-slow manifold geometry
• Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality
• High order amplitude equation for steps on creep curve

Cited by in corpus (8)

• On the critical nature of plastic flow: one and two dimensional models
• General framework for acoustic emission during plastic deformation
• Dynamics of Crossover from a Chaotic to a Power Law State in Jerky Flow
• Recurrence analysis of the Portevin-Le Chatelier effect
• Modeling the complexity of acoustic emission spectra during intermittent plastic deformation: Power laws and multifractal spectra
• Projecting Low Dimensional Chaos from Spatio-temporal Dynamics in a Model for Plastic Instability
• Influence of Visco-elastic Nature on the Intermittent Peel Front Dynamics of the Adhesive Tape
• Effective dimensionality of the Portevin - Le Chatelier effect