Attenuation and dispersion of leaky Rayleigh wave in polycrystals

In this work, we use the characteristic equation of leaky Rayleigh waves (LRWs) and a unified approach of bulk waves proposed by Stanke and Kino [J. Acoust. Soc. Am. 75, 665–681 (1984)] to calculate the attenuation and velocity dispersion of LRWs in polycrystals. Numerical results demonstrate that the total attenuation including the leakage attenuation and scattering attenuation is proportional to frequency and independent of grain size in the Rayleigh scattering regime. Meanwhile, the variation of phase velocity in all scattering regimes remains at ∼0.7% according to the theoretical expectation; this means that the velocity dispersion of the LRWs can be ignored, consistent with the conventional viewpoint. Measurements are conducted on stainless steel at different ultrasonic frequencies (all in the Rayleigh scattering regime). The non-paraxial sound field model is used here to eliminate the diffraction loss and to obtain the total attenuation. Experimental results verify that LRWs have very little velocity dispersion. Meanwhile, experimental fitting data reveal that the modified theoretical model can be used to evaluate the total attenuation (only ∼2% discrepancies) of LRWs under the consideration of the diffraction effect. The relative errors between experimental scattering attenuation and theoretical value ranged from 11% to 18%, mainly owing to the effect of surface roughness and measurement inaccuracy.