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

Abstract

The 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 existing methods, the proposed method solely focuses on the backscattering coefficient component of the backscattering signals. It effectively eliminates the influence of unrelated factors, such as the measurement system and the acoustic field, through the utilization of reference signals.<br>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 using a spatial correlation function. To account for irrelevant factors, an experimental measurement method is developed by 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 (ka≫1), a Stochastic scattering limit is reached. Conversely, when ka≪1, 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 coefficients.<br>Three sets of GH4742 specimens with different grain sizes are prepared for phased array ultrasound experiments. The consistency of the experimental backscattering coefficients, root mean square (RMS) values, and time-domain signal amplitude trends can be observed. To perform grain size inversion, the backscattering coefficients within the effective bandwidth range of the probe are selected. By utilizing the least-squares 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%.