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

Abstract

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.

Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media

“…We then use this relation and its derivatives recursively in the computation of the projection of ∇ x · ∇ k Γ. Secondly, we consider the projection of the Poisson's brackets in Eq. (33). It is derived from the following identity:…”

“…Different models of the phase functions q → R ij (q), which are the three-dimensional Fourier transforms of these normalized correlation functions (NCF), may be invoked as discussed in e.g. [33] and references therein. We will adopt here a Markov (exponential) model, by which:…”

Ultrasonic Scattering Attenuation in Nodular Cast Iron: Experimental and Simulation Studies

“…Later, Hirsekorn [28] and [29], Stanke and Kino [30], and Weaver [31] developed general solutions valid for all grain size to wavelength ratios and for cubic symmetry polycrystalline materials. However, other researchers demonstrated that those general solutions failed in more complex microstructures, such as the commercial aluminium alloys [32] and two-phase sintered powders [33]. More recent works deal with advances related to the interaction of ultrasound waves with polycrystalline materials.…”

Influence of the spatial correlation structure of an elastic random medium on its scattering properties

“…In the case of design of meta-materials, which comes down to an optimization problem, it is again crucial to have a good parameterization of the material to limit the complexity of the problem. Previous authors have tried to tackle this problem by considering simplifying assumptions [32] or one specific correlation model [33,3], but we concentrate here on comparison between several very classical correlation structures.…”