On the Separation of Stress-Induced and Texture-Induced Birefringence in Acoustoelasticity

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 de ned; here the word \texture" always refers to the texture of the aggregate at the given prestressed con guration, not to that of a perhaps ctitious 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 e ects of the orthotropic texture on the acoustoelastic coe cients. From this formula we observe that, generally speaking, we cannot separate the total birefringence into two distinct parts, one re ecting purely the in uence of stress on the birefringence, and the other encompassing all the e ects of texture. The same formula, on the other hand, provides for each material speci c quantitative criteria under which the \separation of stress-induced and texture-induced birefringence" would become meaningful in an approximate sense.