Influence of grain size distribution type on statistical moments of ultrasonic attenuations and phase velocities in random polycrystals.

This study investigates the sensitivity of ultrasonic phase velocity and attenuation statistics to grain size distribution types, specifically monomodal and bimodal, in cubic finite-sized polycrystals with identical overall arithmetic or volumetric grain size statistics. A large ensemble of synthetic polycrystalline microstructures was generated, and their ultrasonic responses were computed using a modified spectral function method. The latter enables estimation of both effective phase velocities and attenuation coefficients while rigorously accounting for finite specimen dimensions and statistical variabilities across different samples. When samples share identical grain size statistics based on arithmetic averages, bimodal and monomodal specimens exhibit pronounced differences in the first-order statistical moments of ultrasonic attenuation, while their mean phase velocities remain virtually similar. In contrast, the second-order statistical moments of the phase velocities exhibit more pronounced differences, primarily influenced by the number of grains interacting with the waves. Typically, the bimodal sample shows intermediate standard deviations of the ultrasonic phase velocities, while monomodal samples with matching volumetric and arithmetic grain size statistics yield the highest and lowest variabilities, respectively. These findings suggest that the statistical analysis of ultrasonic responses offers a promising non-destructive methodology for identifying subtle microstructural variations, particularly higher-order characteristics beyond the average grain size, such as the shape of the grain size distribution.