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Experimental time series obtained from single and poly-crystals subjected toa constant strain rate tests report an intriguing dynamical crossover from alow dimensional chaotic state at medium strain rates to an infinite dimensionalpower law state of stress drops at high strain rates. We present results of anextensive study of all aspects of the PLC effect within the context a modelthat reproduces this crossover. A study of the distribution of the Lyapunovexponents as a function of strain rate shows that it changes from a small setof positive exponents in the chaotic regime to a dense set of null exponents inthe scaling regime. As the latter feature is similar to the GOY shell model forturbulence, we compare our results with the GOY model. Interestingly, the nullexponents in our model themselves obey a power law. The configuration ofdislocations is visualized through the slow manifold analysis. This shows thatwhile a large proportion of dislocations are in the pinned state in the chaoticregime, most of them are at the threshold of unpinning in the scaling regime.The model qualitatively reproduces the different types of deformation bandsseen in experiments. At high strain rates where propagating bands are seen, themodel equations are reduced to the Fisher-Kolmogorov equation for propagativefronts. This shows that the velocity of the bands varies linearly with thestrain rate and inversely with the dislocation density, consistent with theknown experimental results. Thus, this simple dynamical model captures thecomplex spatio-temporal features of the PLC effect.Comment: 17 pages, 18 figure

Dynamical approach to the spatiotemporal aspects of the Portevin–Le Chatelier effect: Chaos, turbulence, and band propagation