Tsallis 𝑞-triplet, Intermittent Turbulence and Portevin–Le Chatelier Effect

Document Type

Article

Publication Date

5-15-2018

Department

Department of Mechanical Engineering-Engineering Mechanics

Abstract

In this paper, we extend a previous study concerning Portevin–LeChatelier (PLC) effect and Tsallis statistics (Iliopoulos et al., 2015). In particular, we estimate Tsallis’ q-triplet, namely {𝑞stat, 𝑞sens, 𝑞rel} for two sets of stress serration time series concerning the deformation of Cu-15%Al alloy corresponding to different deformation temperatures and thus types (A and B) of PLC bands. The results concerning the stress serrations analysis reveal that Tsallis q- triplet attains values different from unity ({qstat, qsens, qrel} ≠ {1,1,1}). In particular, PLC type A bands’ serrations were found to follow Tsallis super-𝑞-Gaussian, non-extensive, sub-additive, multifractal statistics indicating that the underlying dynamics are at the edge of chaos, characterized by global long range correlations and power law scaling. For PLC type B bands’ serrations, the results revealed a Tsallis sub-𝑞-Gaussian, non-extensive, super-additive, multifractal statistical profile. In addition, our results reveal also significant differences in statistical and dynamical features, indicating important variations of the stress field dynamics in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states. We also estimate parameters commonly used for characterizing fully developed turbulence, such as structure functions and flatness coefficient (𝐹), in order to provide further information about jerky flow underlying dynamics. Finally, we use two multifractal models developed to describe turbulence, namely Arimitsu and Arimitsu (A&A) [2000, 2001] theoretical model which is based on Tsallis statistics and p-model to estimate theoretical multifractal spectrums𝒇(a). Furthermore, we estimate flatness coefficient (𝐹) using a theoretical formula based on Tsallis statistics. The theoretical results are compared with the experimental ones showing a remarkable agreement between modeling and experiment. Finally, the results of this study verify, as well as, extend previous studies which stated that type B and type A PLC bands underlying dynamics are connected with distinct dynamical behavior, namely chaotic behavior for the first and self-organized critical (SOC) behavior for the latter, while they shed new light concerning the turbulent character of the PLC jerky flow.

Publisher's Statement

© 2018 Elsevier B.V. All rights reserved.

Publication Title

Physica A: Statistical Mechanics and its Applications

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