An integrated model for ultrasonic wave propagation and scattering in a polycrystalline medium with elongated hexagonal grains

Abstract

Attenuation coefficients for longitudinal and transverse ultrasonic waves are obtained for polycrystals with elongated hexagonal grains using an integrated approach suitable in all frequency regions. Below the geometric limit the attenuation coefficients are obtained in a general form for ellipsoidal grains using the Born approximation while in the upper part of the stochastic frequency range and in the geometric regime the Karal and Keller [F.C. Karal, J.B. Keller, Elastic, electromagnetic, and other waves in a random medium, J. Math. Phys. 5 (1964) 537–547] scalar model is generalized and applied to obtain the dispersion equation and the attenuation coefficients for ellipsoidal grains. Both solutions are combined to describe attenuation behavior in the entire frequency range thus generalizing the Stanke and Kino unified model [F.E. Stanke, G.S. Kino, A unified theory for elastic wave propagation in polycrystalline materials, J. Acoust. Soc. Am. 75 (1984) 665–681] to a medium with elongated grains. The results show that in the Rayleigh region the attenuation is an isotropic function depending only on the effective grain volume; in the stochastic region it scales linearly with the grain dimension in the propagation direction but it is independent of the cross-section of the ellipsoidal grains, and in the Rayleigh-to-stochastic transition region it depends strongly on the ellipsoidal grain shape. In the geometric regime it is inversely proportional to the grain size in the direction of wave propagation.