The Effect of Texture on Acoustoelasticity

The theory for stress determination using acoustoelasticity is most frequently based on the evaluation of the motion of an infinitesimal plane wave propagating through an isotropic, elastic body which is subjected to a homogeneous deformation. The assumption of isotropy in this analysis allows the characterization of the acoustoelastic response to be carried out in terms of two second-order and three third-order elastic constants. Unfortunately, most structural materials do not behave isotropically, but instead have some degree of texture caused by the crystals aligning themselves in certain preferred orientations during the forming process. This paper examines the effect of texture on the acoustoelastic response of polycrystalline materials. In particular, the five second-order and nine third-order elastic constants of bodies exhibiting transverse isotropy are computed in terms of the elastic constants and orientation of the constituent crystals. Two methods of evaluating the constants are presented, the first being a Voigt type procedure in which the elastic stiffnesses are averaged for the chosen crystal orientation distribution, and the second being a Reuss type procedure in which the compliances are averaged. Acoustoelastic constants of the various waves in aluminum and copper are presented for the entire range of ideal textures in which all grains have the same direction cosines between the symmetry axis and the crystallographic axes