On the separation of stress-induced and texture-induced birefringence in acoustoelasticity |
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Authors: | Chi-Sing Man Roberto Paroni |
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Institution: | (1) Department of Mathematics, University of Kentucky, 40506-0027 Lexington, KY, USA |
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Abstract: | In this paper we develop a simple micromechanical model of a prestressed polycrystalline aggregate, in which the texture-induced and stress-induced anisotropies of the aggregate are precisely defined; here the word texture always refers to the texture of the aggregate at the given prestressed configuration, not to that of a perhaps fictitious natural state of the aggregate. We use this model to derive, for a prestressed orthotropic aggregate of cubic crystallites, a birefringence formula which shows explicitly the effects of the orthotropic texture on the acoustoelastic coefficients. From this formula we observe that, generally speaking, we cannot separate the total birefringence into two distinct parts, one reflecting purely the influence of stress on the birefringence, and the other encompassing all the effects of texture. The same formula, on the other hand, provides for each material specific quantitative criteria under which the separation of stress-induced and texture-induced birefringence would become meaningful in an approximate sense. |
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Keywords: | 73B40 73C99 73S10 |
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