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Chaotic and power law states in the PortevinLe Chatelier effect (2002)
| Venue: | Europhysics Letters |
| Citations: | 6 - 1 self |
BibTeX
@ARTICLE{Bharathi02chaoticand,
author = {M. S. Bharathi and G. Ananthakrishna},
title = {Chaotic and power law states in the PortevinLe Chatelier effect},
journal = {Europhysics Letters},
year = {2002},
pages = {234--240}
}
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Abstract
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. The Portevin-Le Chatelier (PLC) effect, discovered at the turn of the last century [1], is a striking example where collective behaviour of defects leads to complex spatio-temporal patterns [2,3,4]. The PLC effect manifests itself as a series of serrations on the stress-strain curves when samples of dilute alloys are deformed under constant strain rate, ˙ǫa (actually constant pulling speed). The effect is observed only in a window of strain rates and temperatures. Each stress drop is associated with the formation and often the propagation of a dislocation band. In polycrystals, at low ˙ǫa, the randomly nucleated type C bands with large stress drop
Keyphrases
power law state portevinle chatelier effect strain rate portevin-le chatelier dynamical model almg polycrystals last century low dimensional chaotic dislocation band plc effect striking example high strain rate stress-strain curve lyapunov exponent intriguing crossover phenomenon constant strain rate medium strain rate reconstructed experimental attractor spatio-temporal pattern portevin le chatelier effect report cual single crystal large stress drop dilute alloy collective behaviour stress drop recent study power law statistic
