Theoretical analysis of the dimensionality of ultrasonic attenuation in polycrystalline materials with elongated grains

In the present work, the grain scattering-induced attenuation coefficient is obtained for longitudinal bulk waves in untextured cubic polycrystalline materials with elongated grains using proposed 2D and 3D theoretical models. These models are obtained based on previously developed 2D and 3D models for equiaxed grains. Comparison of the 2D and 3D models allows an analysis of the dimensionality of grain scattering-induced attenuation, which involves more complex mechanisms with elongated grains. In the higher stochastic scattering regime, both 3D and 2D longitudinal attenuations are found to be dependent on the grain size parallel to the wave propagation. In the Rayleigh scattering regime the 3D attenuation is volume dependent and in contrast, the 2D longitudinal attenuation is found to be cross-section dependent and is therefore helpful for identifying the 3D grain shape/rotation.