Ultrasonic scattering in polycrystalline materials with elongated grains: A comparative 3D and 2D theoretical and numerical analysis

Abstract

In this paper, a previously developed theoretical model for the ultrasonic elastic wave scattering, based on the Stanke and Kino model and applicable to both 2D and 3D single-phase untextured polycrystals, is extended to microstructures with elongated grains. The effect of elongated grains on wave attenuation and phase velocity induced by scattering is investigated, highlighting similarities and discrepancies between the 2D and 3D cases. Additionally, 2D and 3D finite element (FE) models are developed to compare and validate the theoretical predictions under fixed assumptions. The morphology of the numerical polycrystalline samples is characterized using a multi-exponential two-point correlation (TPC) function which, when incorporated with the theoretical model, enables a more direct and accurate comparison. The FE models demonstrate excellent quantitative agreement with the theoretical predictions and, moreover, support the wave propagation’s directional dependency in the stochastic scattering region and the 2D-3D dimensionality dissimilarities in the Rayleigh region. It is shown that 2D attenuation can predict 3D behavior in the stochastic limit and provide insights into the estimation of 3D grain morphology in the Rayleigh limit.