A Correction Method for the Measurement of Frequency-Dependent Attenuation Coefficient With Curved Surface Specimens Using Normal Contact Transducer

The ultrasonic pulse-echo technique has been widely employed for the measurement of the frequency-dependent attenuation coefficient in polycrystalline metals. The nonuniform thickness of the coupling layer between the transducer piston and the curved surface is, however, inevitable for curved specimens, resulting in a significant overestimation. In addition, the curved surface also affects the diffraction loss caused by the divergence and convergence of ultrasonic beams during the propagation path. In this study, a correction method is proposed for the experimental calculation of the frequency-dependent attenuation with the curved surface components using a contact transducer. First, with the analysis of the nonuniform coupling layer created by the curved surface and transducer piston, the integral over the effective cross-sectional area is introduced to determine the reflection coefficient. Second, an equivalent rectangular transducer sound field model is proposed to calculate the diffraction loss for different curvatures and propagation distances based on the multi-Gaussian beam (MGB) theory. Then, a correction model is established to compensate for the deviation caused by the curved surfaces. To verify the feasibility of the proposed method, two cylindrical bars and five blanks with different curvatures were designed. The experimental results show that the proposed correction method can effectively eliminate the deviation caused by the curved surface and improve the stability of measurement. With the correction, the variation of the attenuation spectrum for the curved specimens is reduced by approximately 5%. This facilitates researchers to better develop and use frequency-dependent attenuation coefficients of materials for further applications.