Numerical modeling of the ultrasonic determination of scatterer size distribution

Ultrasonic attenuation in metals is dependent upon the scatterer sizes and the wavelengths of the ultrasonic pulse. For grain-size distributions that follow a truncated single power-law, the wavelength dependence of attenuation follows power-laws with exponent equal to zero (wavelength≪smallest grain), four (wavelength≫largest grain), or equal to the grain-size distribution exponent (smallest grain≪wavelength≪largest grain). We discuss a numerical model that corroborates previous experimental and theoretical work. This model is explored to determine what ranges of grain-size distribution exponent allow for the power-law relationships, the effect of the width of the grain-size distribution on the exponent estimation and corner detection, the estimation of the largest grain size from the attenuation curve, and the inclusion of a scatterer larger than the grain sizes to model a flaw