Effects of surface roughness on diffuse ultrasonic backscatter in the solids

Abstract

In the diffuse ultrasonic backscatter describing the scattering of elastic waves from polycrystalline metal material, the spatial variance of the signal is used as a primary measure of microstructure.Previously,theoretical singly-scattered response models have been developed for the diffuse backscatters of elastic waves within polycrystalline materials,which take into consideration both transducer beams and microstructural scattering information.However,the surface roughness of the liquid-solid interface induces a noticeable change of spatial variance amplitude,and its effect on the diffuse ultrasonic backscatter that can severely degrade the accuracy and practicability of the microstructure parameter evaluation was neglected in previous models.Therefore,a new singly-scattered response model for the rough surface polycrystalline samples is developed by following the forms similar to previous models for longitudinal-to-longitudinal scattering at normal incidence.In particular, we assume that the surface is slightly rough,specifically,the surface roughness value should not be larger than the magnitude of the wavelength.Hence,the modified expressions of ultrasonic reflection and transmission coefficients for the randomly rough interface can be applied to the singly-scattered response model.Then,with the modified transmission coefficient,a Gaussian beam is adopted to model the transducer beam pattern at normal incidence for longitudinal wave propagation through a rough liquid-solid interface to the polycrystal.Next,the Wigner transform of the displacement field is derived with a parameter of the surface roughness root mean square value.After that,a new expression of the calibration parameter including the modified reflection coefficient is given to provide a conversion between the displacement field and the experimental transducer voltage.Finally,the rough surface singly-scattered response model is built and the surface roughness correction coefficient is presented here to quantify the effect of the surface roughness on diffuse ultrasonic backscatter.The numerical results show that the Wigner distribution amplitude decreases and the acoustic energy coverage shrinks with the increase of the surface roughness.The theoretical spatial variance amplitude decreases by about 79.2% when the root mean square roughness value is set to be 40 m.The surface roughness correction coefficient is usually smaller than 1 when the reference calibration sample is smooth,but it can be bigger than 1 when the reference sample is rough.The results from the developed theory are then compared with the experimental measurements associated with a pulse echo transducer configuration for 304 stainless steel by using the smooth and rough surface samples.From these measurements,the mean grain size of the stainless steel can be determined.The experimental results show that although the corrected and uncorrected models both fit the experimental spatial variance curve from the smooth surface sample well,the uncorrected model fails to extract the grain size of the rough surface sample.The relative error of the grain size between optical microscopy and the uncorrected model can reach -21.35%.In contrast,good agreement with optical microscopy is observed by using the surface roughness corrected model,and the relative error is only 1.35%.In conclusion,the ultrasonic waves transmit though the rough interface twice,and the diffuse scattering which happens in these processes reduces the number of backscatter waves that can return to the transducer,so the spatial variance amplitudes drop dramatically.The correction coefficient presented here can describe the effect of surface roughness on diffuse ultrasonic backscatter.Moreover,it can improve the accuracy of grain size evaluation effectively.Thus,the surface roughness corrected ultrasonic backscatter model may be applicable for quality control of roughwrought castings or forgings during the manufacturing.