Portevin-Le Chatelier Effect and Tsallis Nonextensive Statistics
Document Type
Article
Publication Date
7-31-2015
Department
Department of Mechanical Engineering-Engineering Mechanics
Abstract
In this paper, we estimate Tsallis' entropic index πβ‘πstat (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 π-Gaussian), nonextensive, sub-additive, character of the underlying dynamics of the PLC type-A bands (π> 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 π < 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 π-index for the spatial data of PLC type C bands was found above unity (π> 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.
Publication Title
Physica A: Statistical Mechanics and its Applications
Recommended Citation
Iliopoulos, A.,
Nikolaidis, N.,
&
Aifantis, E.
(2015).
Portevin-Le Chatelier Effect and Tsallis Nonextensive Statistics.
Physica A: Statistical Mechanics and its Applications,
438, 509-518.
http://doi.org/10.1016/j.physa.2015.07.007
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6983
Publisher's Statement
Β© 2015 Elsevier B.V.