Journal of the Mechanical Behavior of Materials (May 2015)

Analysis of serrations and shear bands fractality in UFGs

  • Iliopoulos Aggelos C.,
  • Nikolaidis Nikolaos S.,
  • Aifantis Elias C.

DOI
https://doi.org/10.1515/jmbm-2015-0001
Journal volume & issue
Vol. 24, no. 1-2
pp. 1 – 9

Abstract

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Tsallis nonextensive statistics is employed to characterize serrated flow, as well as multiple shear band formation in ultrafine grain (UFG) size materials. Two such UFG materials, a bi-modal Al-Mg alloy and a Fe-Cu alloy, were chosen. In the first case, at low strain rates serrated flow emerges as recorded in the stress-strain graphs, whereas at high strain rates, extensive shear banding occurs. In the second case, multiple shear banding is the only mechanism for plastic deformation, but serrations in the stress-strain graph are not recorded. The analysis aims at the estimation of Tsallis entropic index qstat (stat denotes stationary state), as well as the estimation of fractal dimension. The results reveal that the distributions of serrations and shear bands do not follow Gaussian statistics as implied by Boltzmann-Gibbs extensive thermodynamics, but are approximated instead by Tsallis q-Gaussian distributions, as suggested by nonextensive thermodynamics. In addition, fractal analysis of multiple shear band images reveals a (multi)fractal and hierarchical profile of the spatial arrangement of shear bands.

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