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Layman, Christopher N.

Materials Science Program

2007

Ph. D.

This thesis investigates both theoretically and experimentally the ballistic propagation of ultrasonic waves through random particulate composites as a function of the volume concentration of the scatterers. The scattering behavior of the materials is governed by different regimes, which are determined by examining the nature of the scattering mean free path (MFP). When the MFP is large, compared to the size of the scatterer, the scattering process can be described by single independent scattering theory. As the MFP decreases, a regime is reached in which the propagating waves scatter multiple times between sites. If the MFP is not too small this regime can be modeled as a multiple scattering effective medium. Initially, a review is given for well known single scattering formalisms. The failure of these methods in the multiple scattering regime is illuminated by employing a self-consistent solution to the coherent potential approximation (CPA). It has been known that the best single-site mean field theory for substitutional and topologically disordered systems is the CPA. This method has been used extensively in the fields of disordered electronic systems; here it is being used to examine elastic wave propagation. Essentially, the CPA allows for the self-consistent determination of the effective Green's function for a random medium, based on the critical assumption that the comprehensive scattering matrix (T-matrix) can be written as simply a sum of the single site scattering matrices. The CPA condition is that, relative to the effective medium, the scattering off any impurities vanishes. Simulations are produced for the concerned theoretical models. When applicable, the simulations are compared to data obtained from ultrasonically testing composites manufactured in our lab. These materials consist of glass micro-spheres imbedded in an epoxy matrix, at various inclusion concentrations.