Power-law relationships between the dependence of ultrasonic attenuation on wavelength and the grain size distribution

Abstract

Grain size is one of the factors that influence mechanical properties of metals like strength and fracture toughness. Ultrasonic waves propagating in polycrystalline materials are subject to attenuation dominated by grain boundary scattering. The importance of grain size estimation for industrial applications warrants the investigation of alternative methods of nondestructive grain size determination. Analysis of the power-law behavior of ultrasonic attenuation experimental data is used to link the wavelength dependence of the attenuation coefficient directly to the grain size distribution. The outcome is a simple relationship between the power law that describes the grain size distribution and the power-law dependence of attenuation on wavelength. Careful attention is given to the limitations in terms of a practical grain size distribution with finite limits. Two types of measurements are presented to verify the theoretical development: grain size distribution and ultrasonic attenuation. Nickel samples were prepared using three different annealing durations. The attenuation exponent is experimentally shown to be an appropriate nondestructive measurement of the grain size distribution exponent.