Representation of Hashin–Shtrikman Bounds in Terms of Texture Coefficients for Arbitrarily Anisotropic Polycrystalline Materials

Representation of Hashin–Shtrikman Bounds in Terms of Texture Coefficients for Arbitrarily... JElast https://doi.org/10.1007/s10659-018-9679-0 Representation of Hashin–Shtrikman Bounds in Terms of Texture Coefficients for Arbitrarily Anisotropic Polycrystalline Materials 1 2 Mauricio Lobos Fernández · Thomas Böhlke Received: 23 May 2017 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract The present work generalizes the results of Böhlke and Lobos (Acta Mater. 67:324–334, 2014) by giving an explicit representation of the Hashin–Shtrikman (HS) bounds of linear elastic properties in terms of tensorial Fourier texture coefficients not only for cubic materials but for arbitrarily anisotropic linear elastic polycrystalline materials. Based on the HS bounds as given by Walpole (J. Mech. Phys. Solids 14(3):151–162, 1966) and tensor functions for the representation of the crystallite orientation distribution func- tion, it is shown that the HS bounds are represented in terms of the exact same second- and fourth-order texture coefficients which appear in the consideration of the Voigt and Reuss bounds. The derived representations in terms of tensorial texture coefficients are valid for all symmetry classes in elasticity and present expressions highly attractive for the descrip- tion of physical quantities in terms of tensorial variables. In order to make these results also accessible for the community of quantitative texture analysis, transformation relations be- tween http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Elasticity Springer Journals

Representation of Hashin–Shtrikman Bounds in Terms of Texture Coefficients for Arbitrarily Anisotropic Polycrystalline Materials

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Physics; Classical Mechanics; Automotive Engineering
ISSN
0374-3535
eISSN
1573-2681
D.O.I.
10.1007/s10659-018-9679-0
Publisher site
See Article on Publisher Site

Abstract

JElast https://doi.org/10.1007/s10659-018-9679-0 Representation of Hashin–Shtrikman Bounds in Terms of Texture Coefficients for Arbitrarily Anisotropic Polycrystalline Materials 1 2 Mauricio Lobos Fernández · Thomas Böhlke Received: 23 May 2017 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract The present work generalizes the results of Böhlke and Lobos (Acta Mater. 67:324–334, 2014) by giving an explicit representation of the Hashin–Shtrikman (HS) bounds of linear elastic properties in terms of tensorial Fourier texture coefficients not only for cubic materials but for arbitrarily anisotropic linear elastic polycrystalline materials. Based on the HS bounds as given by Walpole (J. Mech. Phys. Solids 14(3):151–162, 1966) and tensor functions for the representation of the crystallite orientation distribution func- tion, it is shown that the HS bounds are represented in terms of the exact same second- and fourth-order texture coefficients which appear in the consideration of the Voigt and Reuss bounds. The derived representations in terms of tensorial texture coefficients are valid for all symmetry classes in elasticity and present expressions highly attractive for the descrip- tion of physical quantities in terms of tensorial variables. In order to make these results also accessible for the community of quantitative texture analysis, transformation relations be- tween

Journal

Journal of ElasticitySpringer Journals

Published: May 29, 2018

References

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