A new correlation model for ultrasonic attenuation in polycrystals with broad grain size distributions

Ultrasonic characterization of polycrystalline materials is traditionally based on a single-exponential two-point correlation function (TPCF). However, industrial metallic polycrystals often exhibit a wide grain size distribution, for which the classical analytical scattering-induced attenuation frameworks fail to reproduce the experimental measurements. In this paper, we introduce a new closed-form TPCF that embeds the full volumetric grain size distribution through an analytic convolution of spherical grain statistics. The resulting expression naturally reduces to the classical spherical TPCF when the distribution width tends to zero. Coupling this TPCF with Weaver's framework for elastic wave attenuation produces frequency-dependent attenuation formulas that depend on the first two moments of the grain size distribution. To evaluate the robustness of the proposed model, we generated synthetic aluminum microstructures that span a wide range of coefficients of variation of grain sizes. TPCFs measured from Laguerre-Voronoi tessellation-based microstructures closely match our predictions across a wide range of coefficients of variations (CVs) from moderate to large, whereas other models systematically misestimate the correlation for large CVs. By conducting a series of comparisons with semi-analytical, numerical, and experimental attenuation coefficients reported in the literature, we show the robustness of our model. The proposed formulation, therefore, extends ultrasonic scattering theory to polycrystals with realistically broad grain size distributions, supplying a physically interpretable bridge between measurable grain statistics and macroscopic wave attenuation. This advance opens the door to nondestructive, distribution-aware inversion of microstructural parameters in polycrystalline materials.