Numerical estimation of ultrasonic phase velocity and attenuation for longitudinal and shear waves in polycrystalline materials

Finite element computations offer ways to study the behavior of ultrasonic waves in polycrystals. In particular, the simulation of plane waves propagation through small representative elementary volumes of a microstructure allows estimating velocities and scattering-induced attenuation for an effective homogeneous material. Existing works on this topic have focused mainly on longitudinal waves. The approach presented here relies on generating periodic samples of microstructures in order to accommodate both longitudinal and shear waves. After some discussion on the parametrization of the simulations and the numerical errors, results are shown for several materials. These results are compared to an established theoretical attenuation model that has been adapted to use a fully analytical expression of the two-point correlation function for the polycrystals of interest, and to use velocities corresponding to different reference media. Promising comparisons are obtained for both longitudinal and shear waves when using more representative media, obtained through Hill averaging or a self-consistent approach. This illustrates how the numerical method can assist in developing and validating analytical models for elastic wave propagation in heterogeneous media.