A weak scattering attenuation model for Rayleigh waves in three-dimensional polycrystals with arbitrary symmetry

This paper presents a theoretical model for the scattering attenuation of Rayleigh waves propagating along the stress-free planar surface of a three-dimensional (3D) semi-infinite polycrystalline medium with single-phase, untextured, equiaxed grains and arbitrary symmetry. The model can explain the behavior of the Rayleigh wave scattering into Rayleigh and bulk waves, i.e., it can provide a detailed calculation of Rayleigh-to-Rayleigh (R-R), Rayleigh-to-Shear (R-S), and Rayleigh-to-Longitudinal (R-L) attenuation separately. Numerical results reveal that the attenuation of R-R, R-S, and R-L exhibits the same frequency and grain size dependence as observed in the scattering of bulk waves in the Rayleigh regime. The R-L attenuation is negligible compared to the other two types of attenuation. Meanwhile, for a given material, the relative contributions from R-R and R-S attenuation to total scattering attenuation of Rayleigh waves remain unchanged, regardless of changes in frequency or grain size. Crystalline symmetry affects the relative contributions of the three types of wave mode conversions to the total scattering attenuation. Moreover, it plays a more critical role in determining scattering attenuation than the anisotropy index. Quantitative agreement is observed between the theoretical model and the existing attenuation model proposed by Ryzy et al. [AIP Adv. 8, 125019 (2010)] with only a relative error of 3.9% and 5.4% for aluminum (cubic symmetry) and copper sulfate pentahydrate (triclinic symmetry), respectively, within the applicable range of the theoretical model. However, the theoretical model is limited in applicability within stochastic and geometric regimes due to the constraints of the zero-order Born approximation. The proposed method and the obtained findings contribute to the understanding of Rayleigh wave propagation along the 3D polycrystalline surface and provide a basis for advancing the second-order Born approximation toward application in the stochastic regime.