Elastic wave propagation and scattering in heterogeneous, anisotropic media: Textured polycrystalline materials

The propagation of elastic waves through heterogeneous, anisotropic media i s considered. Appropriate ensemble averaging of the elastic wave equation l eads to the Dyson equation which governs the mean response of the field. Th e Dyson equation is given here in terms of anisotropic elastic Green's dyad ics for the medium with and without heterogeneities. The solution of the Dy son equation for the mean response is given for heterogeneities that are we ak. The formalism is further specified for the case of equiaxed cubic polyc rystalline metals with a single aligned axis. The Green's dyadics in this c ase are those for a transversely isotropic medium. Simple expressions for t he attenuations of the shear horizontal, quasicompressional, and quasishear waves are given in terms of integrations on the unit circle. The derived e xpressions are limited to frequencies below the geometric optics limit, but give the attenuations in a direct manner. Comparisons with previous result s are also discussed. It is anticipated that a similar approach is necessar y for the study of wave propagation in complex anisotropic materials such a s! fiber-reinforced composites. In addition, the results are applicable to diffuse ultrasonic inspection: of textured polycrystalline media. (C) 1999 Acoustical Society of America. [S0001 -4966(99)04008-4].