Ultrasonic backscattering model for Rayleigh waves in polycrystals with Born and independent scattering approximations

TL;DR

This paper develops and validates theoretical and numerical models for Rayleigh wave backscattering in polycrystals, demonstrating good agreement and highlighting the effects of anisotropy and multiple scattering.

Contribution

It introduces a combined theoretical and numerical approach to model Rayleigh wave backscattering in polycrystals, considering Born and independent scattering approximations.

Findings

Good agreement between models for weak scattering

Agreement decreases with higher anisotropy

Backscattering behavior similar to bulk waves

Abstract

This paper presents theoretical and numerical models for the backscattering of 2D Rayleigh waves in single-phase, untextured polycrystalline materials with statistically equiaxed grains. The theoretical model, based on our prior inclusion-induced Rayleigh wave scattering model and the independent scattering approximation, considers single scattering of Rayleigh-to-Rayleigh (R-R) waves. The numerical finite element model is established to accurately simulate the scattering problem and evaluate the theoretical model. Good quantitative agreement is observed between the theoretical model and the finite element results, especially for weakly scattering materials. The agreement decreases with the increase of the anisotropy index, owing to the reduced applicability of the Born approximation. However, the agreement remains generally good when weak multiple scattering is involved. In addition, the R-R backscattering behaviour of 2D Rayleigh waves is similar to the longitudinal-to-longitudinal and transverse-to-transverse backscattering of bulk waves, with the former exhibiting stronger scattering. These findings establish a foundation for using Rayleigh waves in quantitative characterisation of polycrystalline materials.