Ultrasonic scattering in two-phase media

The microstructure of sintered metals and ceramics is manipulated in many ways to create engineering materials with superior properties. Successful processing of materials by powder sintering relies on the creation of strong interparticle bonds. During certain critical stages of the sintering process, the medium may be modeled as two phases consisting of the particles and a surrounding matrix with different material properties. Ultrasonic methods have been proposed as a potential tool for monitoring such sintering processes. Thus, an understanding of the propagation and scattering of elastic waves in two-phase solids is of fundamental importance to these monitoring techniques. In this dissertation, wave propagation and scattering in two-phase media are studied theoretically and numerically. Explicit expressions of attenuation are developed using elastodynamic and stochastic wave theory, based on the spatial statistics of the density and Lame parameters of the materials constituents under assumptions of statistical homogeneity and statistical isotropy. The geometric two-point correlation function plays a central role in the theoretical model. The influence of correlation functions on the attenuation is investigated. The theoretical analysis provides insightful information for modeling the microstructure of complex materials and is also useful for the development of new ultrasonic monitoring techniques during sintering processes.;In addition, this problem is studied numerically based on Voronoi polycrystals that are used to model the two-phase microstructure. The numerical models with various combinations of geometric parameters are created as needed. Wave propagation is studied by integrating the system in time using a plane strain formulation. Numerical simulations are presented with various material and geometric parameters of the two-phase model. The commercial software package ABAQUS is used to discretize and formulate the plane strain model with infinite boundaries. Example results are presented and compared with the scattering theory for different input wave frequencies. The influence of the correlation function on the numerical attenuation is also examined. The variation of the correlation characteristic parameters with the frequency of the input wave is observed. Such model can be used to verify theoretical models efficiently and to design further experimental methods for characterization of microstructures. Finally, a singly-scattered response model is used to predict the grain noise in the two-phase model and compared with the experimental measurements of decorated particle boundaries. It is also anticipated that the theoretical and numerical models presented here will improve the understanding of the microstructure characterization for other two-phase composites such as cement, ceramic and concrete.