Numerical Model of Longitudinal Wave Scattering in Polycrystals

The scattering of elastic waves in polycrystalline materials is relevant for ultrasonic materials characterization and nondestructive evaluation (NDE). Ultrasonic attenuation is used widely to extract microstructural parameters such as grain size. Accurate interpretation of experimental data requires robust scattering models. Such models typically assume constant density, uniform grain size, and ergodicity hypotheses. The accuracy and limits of applicability of these models cannot be fully tested with experiments due to practical limits of real materials processing. Here, this problem is examined in terms of numerical simulations using Voronoi polycrystals that are discretized using finite elements. Wave propagation is studied by integrating the system directly in time using a plane-strain formulation. Voronoi polycrystals with cubic symmetry and random orientations are used making the bulk material statistically isotropic. Example numerical results for materials with various degrees of scattering that are of common interest are presented. The numerical results are presented and compared with scattering theory for a wide range of frequencies. The numerical results show good agreement with the theory for the examples examined with evidence that the correlation function is frequency dependent. These results are anticipated to impact ultrasonic NDE of polycrystalline media.