Higher-order scattering of high-frequency ultrasound in strongly heterogeneous microstructures

Abstract

Ultrasonic waves get scattered from grain boundaries while propagating through polycrystals, thereby experiencing attenuation and a change in wavespeed. These grain boundaries act as the sole scattering sites for untextured aggregates of randomly oriented crystallites. In addition, porosity, texture, defects, precipitates, or inclusions also serve as scatterers when present in a microstructure. Existing analytical models rely on the first-order smoothing approximation (FOSA)-based homogenization to the mass operator series in the governing Dyson equation. They can accurately predict ultrasonic dispersion in some weakly inhomogeneous metals like Aluminum. However, while comparing against more realistic Finite Element (FE) predictions, serious discrepancies, as high as 70%, are found in the attenuation estimates for metals, like Lithium, that possess strong elastic fluctuations in their microstructures. Thus, the current model analytically investigates higher-order scattering effects corresponding to the third-order smoothing approximation (TOSA) for the first time. Current results reveal no higher-order scattering effects for Aluminum at any frequencies. However, the longitudinal attenuation estimates for Lithium are found to improve by 1.27% and 0.37% in the “stochastic” (high-frequency) and “Rayleigh” (low-frequency) regimes, respectively. The presentation will highlight the effects of including TOSA on analytical estimates of high-frequencyultrasonic dispersion in different strongly heterogeneous microstructures.