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This paper presents theoretical and numerical models for the backscatteringof 2D Rayleigh waves in single-phase, untextured polycrystalline materials withstatistically equiaxed grains. The theoretical model, based on our priorinclusion-induced Rayleigh wave scattering model and the independent scatteringapproximation, considers single scattering of Rayleigh-to-Rayleigh (R-R) waves.The numerical finite element model is established to accurately simulate thescattering problem and evaluate the theoretical model. Good quantitativeagreement is observed between the theoretical model and the finite elementresults, especially for weakly scattering materials. The agreement decreaseswith the increase of the anisotropy index, owing to the reduced applicabilityof the Born approximation. However, the agreement remains generally good whenweak multiple scattering is involved. In addition, the R-R backscatteringbehaviour of 2D Rayleigh waves is similar to the longitudinal-to-longitudinaland transverse-to-transverse backscattering of bulk waves, with the formerexhibiting stronger scattering. These findings establish a foundation for usingRayleigh waves in quantitative characterisation of polycrystalline materials.

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