Comparison of ultrasonic attenuation within two- and three-dimensional polycrystalline media

An analytical approach to develop explicit formulas of attenuation coefficient in both 2D and 3D cases is proposed. It results in a better understanding of the grain scattering mechanisms within a polycrystalline material and the grain size effects on the attenuation of an ultrasonic wave. It is based on the Stanke and Kino's model and uses the Born approximation. An explicit formula is deduced for untextured polycrystals with equiaxed grains of cubic symmetry and allows a rigorous comparison of the attenuation coefficient between both 2D and 3D cases. It confirms that the attenuation in the Rayleigh region is higher in 2D simulation than in 3D one, while very similar coefficients are obtained in the stochastic region for both cases. The study of the explicit formula allows the decomposition of the attenuation coefficient into various scattering-induced components, which leads to a better understanding of different grain scattering mechanisms. The reflection/transmission at grain boundaries between wave modes of a same type mainly explains a same attenuation coefficient in the stochastic region for both 2D and 3D modelings. The conversion at grain boundaries between different types of wave modes provides some explanations for a higher attenuation value given by the 2D modeling in the Rayleigh region. The effect of the grain size on the attenuation coefficient is then predicted by the 2D analytical calculation and by the FE simulation. The analytical-numerical comparison validates the numerical calculations and the approach suggests a way of using the 2D FE calculations to predict the evolution of the attenuation coefficient with the wave frequency in 3D.