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

Area of Science:

• Materials Science
• Solid Mechanics
• Acoustics

Background:

• Understanding wave propagation in polycrystalline materials is crucial for non-destructive evaluation.
• Rayleigh wave scattering attenuation in such media is complex, involving mode conversions to bulk waves.
• Existing models have limitations in fully capturing these scattering phenomena.

Purpose of the Study:

• To develop a theoretical model for Rayleigh wave scattering attenuation in 3D polycrystalline materials.
• To separately calculate Rayleigh-to-Rayleigh (R-R), Rayleigh-to-Shear (R-S), and Rayleigh-to-Longitudinal (R-L) wave attenuation.
• To investigate the influence of frequency, grain size, and crystalline symmetry on scattering attenuation.

Main Methods:

• Development of a theoretical model based on the zero-order Born approximation.
• Calculation of scattering attenuation for R-R, R-S, and R-L wave conversions.
• Numerical simulations to analyze frequency and grain size dependence, and the role of crystalline symmetry.

Main Results:

• The model accurately predicts R-R, R-S, and R-L attenuation, showing similar frequency and grain size dependence as bulk wave scattering.
• R-L attenuation is found to be negligible; R-R and R-S contributions remain constant relative to each other.
• Crystalline symmetry significantly impacts scattering attenuation, more so than the anisotropy index.

Conclusions:

• The proposed theoretical model provides a robust framework for analyzing Rayleigh wave scattering attenuation in polycrystalline media.
• Crystalline symmetry is a dominant factor in scattering attenuation, offering insights for material characterization.
• The findings lay the groundwork for advancing more sophisticated models, like the second-order Born approximation, for stochastic regimes.