A simultaneous non-destructive characterisation method for grain size and single-crystal elastic constants of cubic polycrystals from ultrasonic measurements

Abstract

A systematic method was proposed to simultaneously determine both the grain size and elastic constants of a crystallite for cubic polycrystalline materials from ultrasonic velocities, backscattering and attenuation by model-based inversion. The direct model for backscattering was based on single scattering assumption while attenuation was under the frame of the far-field scattering model. At the beginning of the inversion, metal density and ultrasonic velocities, including longitudinal and shear velocities, were measured. Longitudinal backscattering and attenuation coefficients were extracted from the immersion scanning to implement model-based inversion. There were two independent steps to reconstruct grain size and single-crystal elastic constants. The grain sizes were obtained first from the attenuation-to-backscattering ratio, which was exclusively dependent on grain geometry. Furthermore, the anisotropy factor of a cubic crystal can be reconstructed from backscattering amplitude and attenuation coefficients. Since there are only three independent elastic constants for a cubic symmetry crystallite, all three can be determined from experiments. Finally, this method was validated using a pure copper sample. The determined grain size is reasonably close to that identified by optical microscopy and the reconstructed elastic constants are in close agreement with those offered in the literature. Thus, this study provides a practical non-destructive approach for microstructure characterisation.