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Bounds and an isotropically self‐consistent singular approximation of the linear elastic properties of cubic crystal aggregates for application in materials design
Author(s) -
Lobos Mauricio,
Böhlke Thomas
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410254
Subject(s) - anisotropy , isotropy , texture (cosmology) , linear approximation , orientation (vector space) , condensed matter physics , mathematical analysis , crystal (programming language) , transverse isotropy , physics , materials science , statistical physics , geometry , mathematics , optics , nonlinear system , quantum mechanics , image (mathematics) , artificial intelligence , computer science , programming language
For crystal aggregates, the orientation distribution of single crystals affects the anisotropic linear elastic properties. In the singular approximation for cubic materials, this influence is reflected by a fourth‐order texture coefficient. From this approximation, the statistical bounds of Voigt, Reuss and Hashin‐Shtrikman, and an isotropically self‐consistent singular approximation can be obtained. Here, an approximation is called isotropically self‐consistent, if, for a vanishing texture, it results in the isotropic self‐consistent approximation. The isotropically self‐consistent singular approximation has the following advantages: i) it lies between the bounds of Voigt, Reuss and Hashin‐Shtrikman, ii) it offers a useful approximation of the effective material behavior of textured anisotropic polycrystals, and iii) it can be used for material design purposes tailoring anisotropic properties mainly depending on the crystallographic texture. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)