Three-dimensional multi-parameter correction method for oblique incidence ultrasonic backscattering measurement

Oblique incidence ultrasonic backscattering is an important method for characterising the internal microstructure of polycrystalline materials. However, in existing measurements, the coupling effects between oblique incidence angles and cylindrical bars significantly compromise the inversion accuracy. To address this issue, this paper proposes a three-dimensional multi-parameter correction (3D-MPC) method based on single scattering response theory. The ultrasonic field in the transducer’s single scattering response model was decomposed into three dimensions to establish the 3D-MPC model. Subsequently, numerical simulations were performed to analyse the variation of the correction parameters with the incident angle. On this basis, three-dimensional acoustic field simulations were conducted to further illustrate, through representative examples, that the correction model improves the single scattering response model by optimising the single Gaussian beam under oblique incidence. In addition, a series of controlled-variable experiments were conducted on the induction-hardened 40Cr bar, with EBSD measurements along the radial depth serving as the reference data. Compared to the results without correction, the introduction of the 3D-MPC model significantly improved the inversion accuracy of the grain size-depth distribution. The average absolute improvement in accuracy across the six experimental datasets was approximately 12% (ranging from 5.72% to 15.75%), demonstrating the overall effectiveness and reliability of the proposed correction method.