Elastic wave scattering in random anisotropic solids

Abstract

Abstract A general ultrasonic scattering model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is developed allowing the texture and grain orientation frames to be independent and the wave propagation direction arbitrary in those frames. Numerical examples are given for an approximate texture model exhibiting triclinic macroscopic symmetry for triclinic crystallites. The scattering coefficients are obtained from integrands of the attenuation coefficients recently derived elsewhere in the Born approximation for the same problem. The results obtained are reducible to the known scattering/backscattering coefficients for a macroscopically isotropic medium in the limit of negligible macroscopic anisotropy. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and ellipsoidal shaped grains. As in the macroscopically isotropic case, the scattering coefficients are factorized into an elastic factor dependent on the preferred crystallographic orientation of the grains and a frequency dependent geometric factor affected by grain size and shape. A general reciprocity relationship for the scattering coefficients is obtained and discussed. Simulation results are presented to shed light on the effect of texture, grain shape and nondimensional frequency on ultrasonic scattering. An approximation of the quasilongitudinal wave polarization, that neglects the deviation of the polarization vector from the propagation direction, on the backscattering coefficient is investigated and the error of the approximation is estimated.