Ultrasonic attenuation based on the Roney generalized theory and multiple power-law grain-size distributions

We investigate ultrasonic attenuation as a nondestructive determination of grain-size distributions. Previous work showed power-law relationships between the wavelength dependence of ultrasonic attenuation and a single power-law grain-size distribution, along with experimental verification. The work presented here further validates the previously reported relationship for single power-law grain-size distributions, and generalizes the relationships to cases where the grain-size distribution follows multiple power-laws. Roney's generalized approach to ultrasonic attenuation is used. Numerical results are presented for the single power-law and multiple power-law cases. The attenuation exponents computed from the numerical calculations correspond well with theoretical expectations. For wavelengths greater than all the grain sizes, Rayleigh scattering dominates and the attenuation exponent approaches 4. For single power-laws and wavelengths between the smallest and largest grain size, the attenuation exponent equals the grain-size distribution exponent. When multiple power-laws are used to describe the grain-size distribution, the attenuation exponent is a combination of the grain-size distribution exponent, and therefore cannot be directly measured from the attenuation curve.<
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