Effects of grain size distributions on scattering attenuation of elastic waves in polycrystalline materials

The propagation characteristics of elastic waves in polycrystalline materials depend not only on grain size, but also on grain size distribution. In this paper, based on Weaver's polycrystalline scattering model, two grain size distribution models, namely the truncated lognormal distribution and the fractal distribution based on fractal dimension, are considered. At the same time, the ultrasonic attenuation of polycrystalline materials is studied by considering the existence of finite interval of grain size. The grain size of the classical lognormal distribution ranges from zero to infinity, which is inconsistent with the actual situation. The present work modifies Turner's study based on the lognormal distribution and compares the numerical results with Turner's. The numerical results obtained from the two kinds of distributions show that the scattering attenuation in the Rayleigh scattering region is affected by both the grain size distribution and the average grain size. In the transition scattering region, the attenuation of P -wave scattering is related to the average grain size and size distribution, while the attenuation of S -wave scattering is mainly affected by the average grain size. In the stochastic scattering region, the scattering attenuation is mainly affected by the average grain size and is not sensitive to the grain size distribution. Moreover, the numerical results also show that the difference of scattering attenuation due to the grain size distribution is most obvious in the Rayleigh scattering region.