Portevin-Le Chatelier effect and Tsallis nonextensive statistics

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© 2015 Elsevier B.V. In this paper, we estimate Tsallis' entropic index q < sup> qstat (stat denotes stationary states) for various stress serration time series of Cu-15%Al alloys corresponding to different deformation temperatures and types (A, B, C) of Portevin-Le Chatelier (PLC) bands. Tsallis statistical analysis is also conducted on experimental data derived from correlation diagrams focusing on PLC type C bands' spatial organization at the surface of various specimens. The results concerning the stress serrations analysis reveal the non-Gaussian (Tsallis q-Gaussian), nonextensive, sub-additive, character of the underlying dynamics of the PLC type-A bands (q> 1) indicating dynamics at the edge of chaos, with global long range correlations and power law scaling. Similarly, for PLC type B bands, a Tsallis q-Gaussian, non-extensive, super-additive, statistical profile was found with q < 1, while for the PLC type C bands, a near Boltzmann-Gibbs (BG) statistical character was verified indicating Gaussian dynamics with short (weak) range correlations. Finally, Tsallis q-index for the spatial data of PLC type C bands was found above unity (q> 1) indicating that type C bands are not randomly nucleated in the specimen (e.g. yielding a Gaussian distribution) but there exist spatial coupling and long range deformation correlations in the PLC type C bands spatial localization.

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Physica A: Statistical Mechanics and its Applications