Efficient grain size evaluation based on single direction measurement of ultrasonic backscattering coefficient

Abstract

<sec>GH4742 nickel-based superalloy exhibits excellent mechanical properties, and grain size is a key factor affecting its performance. A physical model-based ultrasonic backscattering method makes grain size measurement accurate and efficient. Nevertheless, it is constrained by complex models or multiple measurements taken from various beam angles. As a result, a backscattering coefficient method that requires only a single measurement for grain size evaluation is proposed. In contrast to the existing methods, the proposed method solely focuses on the backscattering coefficient component of the backscattering signal. It effectively eliminates the influence of unrelated factors, such as the measurement system and the acoustic field, through the utilization of reference signals.</sec><sec>The independent scattering model is employed to derive the backscattering coefficient, which solely pertains to the material itself. The relationship between grain size and backscattering coefficient is described by using a spatial correlation function. To consider the irrelevant factors, an experimental measurement method is developed by using the reference signals. Through numerical calculation and analysis, it has been observed that the backscattering coefficient is closely related to the frequency. When the product of the wavenumber and the grain size is significantly greater than 1 (<inline-formula><tex-math id="M1">\begin{document}$ ka\gg 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.png"/></alternatives></inline-formula>), a Stochastic scattering limit is reached. Conversely, when <inline-formula><tex-math id="M2">\begin{document}$ ka\ll 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.png"/></alternatives></inline-formula>, a Rayleigh scattering limit is observed. Furthermore, the backscattering coefficient is directly proportional to the grain size. As a general trend, larger grain sizes result in higher backscattering coefficient.</sec><sec>Three sets of GH4742 specimens with different grain sizes are prepared for phased array ultrasound experiments. It can be observed that the experimental backscattering coefficients, root mean square (RMS) values, and the amplitude trend of time domain signal are consistent. To perform grain size inversion, the backscattering coefficients in the effective bandwidth range of the probe are selected. By utilizing the least-square method, the theoretical backscattering coefficient is employed to fit the curves of the experimental backscattering coefficients. The evaluation results are compared with those obtained by metallographic analysis. The results show that the grain sizes obtained by the proposed method have a maximum relative error of –22.7% and a minimum relative error of –3.7%.</sec>