Influence of spatial correlation function on attenuation of ultrasonic waves in two-phase materials

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. 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 article, expressions for the ultrasonic attenuations are developed based on the spatial statistics of the density and Lamé parameters of the material constituents under assumptions of statistical homogeneity and statistical isotropy. The formulation is based on the solution of the elastodynamic Dyson equation within the limits of the first-order smoothing approximation. Since the geometric two-point correlation function plays a central role in the model, numerical models are developed using Voronoi polycrystals surrounded by a matrix of different material properties. The spatial statistics of the medium are extracted from these models. The results presented suggest new ultrasonic techniques may be developed to extract multiple correlation lengths for such two-phase microstructures.