Attenuation and velocity of elastic waves in polycrystals with generally anisotropic grains: Analytic and numerical modeling.

Better understanding of elastic wave propagation in polycrystals has interest for applications in seismology and nondestructive material characterization. In this study, a second-order wave propagation (SOA) model that considers forward multiple scattering events is developed for macroscopically isotropic polycrystals with equiaxed grains of arbitrary anisotropy (triclinic). It predicts scattering-induced wave attenuation and dispersion of phase velocity. The SOA model implements the generalized two-point correlation (TPC) function, which relates to the actual numeric TPC of simulated microstructure. The analytical Rayleigh and stochastic asymptotes for both attenuation and phase velocity are derived for triclinic symmetry grains, which elucidate the effects of the elastic scattering factors and the generalized TPC in different frequency regimes. Also, the computationally efficient far field approximation attenuation model is obtained for this case; it shows good agreement with the SOA model in all frequency ranges. To assess the analytical models, a three-dimensional (3D) finite element (FE) model for triclinic polycrystals is developed and implemented on simulated 3D triclinic polycrystalline aggregates. Quantitative agreement is observed between the analytical and the FE simulations for both the attenuation and phase velocity. Also, the quasi-static velocities obtained from the SOA and FE models are in excellent agreement with the static self-consistent velocity.