Abstract

Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for detecting flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Quantitative ultrasonic scattering models include components of transducer beam patterns as well as microstructural scattering information. In this dissertation, the Wigner distribution is used in conjunction with the stochastic wave equation to model this scattering problem. The Wigner distribution represents a distribution in space and time of spectral energy density as a function of wave vector and frequency. The scattered response is derived within the context of the Wigner distribution of the beam pattern of a Gaussian transducer. The source and receiver distributions are included in the analysis in a rigorous fashion. The resulting scattered response is then simplified in the single-scattering limit—the singly-scattered response (SSR)—typical of many diffuse backscatter experiments.

Diffuse ultrasonic scattering experiments are usually done using a modified pulse-echo technique and utilize the variance of the signals in space as the primary measure to assess microstructure. Thus the SSR model is modified to account for normal and oblique incidence ultrasonic experiments where the wave propagates through planar or curved liquid-solid interfaces. The theoretical model is then compared with experimental results from polycrystalline materials with known microstructure.

The research in this dissertation provides a fundamental approach for the multiple scattering within the material which can be exploited in the future for design of new experiments and extraction of other microstructure properties. These results are anticipated to be relevant to ultrasonic nondestructive evaluation of polycrystalline and other heterogeneous solids.