Graduate Studies


First Advisor

Joseph Turner

Date of this Version

Spring 4-2017

Document Type



A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science, Major: Mechanical Engineering and Applied Mechanics, Under the Supervision of Professor Joseph A. Turner. Lincoln, Nebraska: April, 2017

Copyright (c) 2017 Nathanial Matz


Diffuse ultrasonic backscatter, the result of the interaction of elastic waves with material heterogeneity, can be used to characterize microstructural information. The scattering that occurs within the material can be complex and requires accurate modeling in order to interpret measurements quantitatively. This effect is particularly important for higher-scattering materials with large single crystal anisotropy. Recently, a double-scattering model was derived for which the wave was assumed to scatter twice prior to detection. This model was an improvement upon an earlier model that assumed only single scattering. The significance of this addition to the model has not been thoroughly explored with experiments. The first portion of this thesis is devoted to theoretical results for both the single-scattering and double-scattering models. The contribution of the second scattering within the detected response is quantified with respect to numerous measurement parameters including the transducer size, frequency and focal length as well as the material properties and focal depth of the experiment. The results show that single-scattering models are appropriate for weakly scattered materials, such as aluminum, for a wide range of experiments and correlation lengths. However, stronger scattering materials are predicted to have significant components beyond single-scattering for certain measurement parameters. Next, experimental results for two highly-scattering materials, one steel and one nickel alloy, are presented for a range of frequencies from 5-15 MHz, and several inspection depths. The experimental work shows the domain for which the doubly-scattered response becomes significant as well as the limitations at which the model is no longer applicable. The results can be used to predict the frequency range that applies for each model given a material, its grain size and experimental details.

Adviser: Joseph A. Turner