Quantifying the impact of grain size distribution models on ultrasonic attenuation in polycrystals

The volumetric grain size distribution (GSD) plays an important role in the mechanical response of polycrystalline materials and is often assumed to be lognormal in ultrasonic studies, although gamma- and Gaussian-type distributions have also been reported. However, the influence of GSD type on elastic-wave scattering in polycrystals remains insufficiently understood. In this work, we compare three commonly used GSD types, namely Gamma, lognormal, and truncated Gaussian, and quantify their effects on the two-point correlation function (TPCF) and ultrasonic attenuation. Synthetic polycrystals with identical mean grain size and coefficient of variation (CV) are generated for two representative materials, aluminum and α-iron. The TPCFs measured from the synthetic microstructures are accurately reproduced by a recent analytical model introduced by the authors. For identical low-order grain size statistics, the truncated Gaussian distribution yields the shortest correlation length, followed by the Gamma distribution, whereas the lognormal distribution gives the longest one. Analytical expressions for attenuation in the Rayleigh regime are also derived for different GSDs, and comparison with the semi-analytical Weaver's model confirms the robustness of the proposed framework. The results show that changing only the GSD type can produce significant differences in low-frequency attenuation, with maximum relative differences of about 28% and 58% for CVs of 0.35 and 0.5, between the truncated Gaussian and lognormal cases. An inversion study further shows that the relative errors for identified mean grain size can reach 90%. These findings highlight the importance of the GSD type in ultrasonic characterization.