Portevin–Le Chatelier effect and Tsallis nonextensive statistics

Abstract

In this paper, we estimate Tsallis’ entropic index q≡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.