Numerical Simulations of Elastic Wave Scattering in Polycrystalline Materials

Goutam Ghoshal - M.S. Thesis Defense
Advisor:  Dr. Joseph Turner

Date:  Thursday, December 4, 2003
Time:  3:30 p.m.
Place:  105 Othmer Hall

The scattering of elastic waves in polycrystalline materials is relevant for ultrasonic materials characterization and nondestructive evaluation (NDE). Heterogeneity in the material ensures that ultrasonic scattering will take place, with the scattering dependent on frequency. Ultrasonic backscatter and attenuation are used widely to extract the microstructural parameters such as grain size. Accurate interpretation of experimental data requires robust ultrasonic scattering models. Such models typically assume constant density, uniform grain size and randomness hypotheses. The accuracy and limits of applicability of these models cannot be fully tested with to experiments due to practical limits of real materials processing. Here, this problem is examined in terms of numerical simulations using Voronoi polycrystals.

The Voronoi diagram is used to model microstructures of polycrystalline materials. It is a method of geometric subdivision of space that is widely used in numerous science and engineering applications. The “Method of Virtual Nuclei” is presented to create Voronoi polycrystals in finite domains within any arbitrary convex geometry. Algorithms are developed to construct elongated Voronoi polycrystals with a specified aspect ratio and angle of orientation. Microstructures are presented of various processed materials such as rolled materials and functionally graded materials. The polycrystals are created for various distributions of grain size.

The Voronoi cells are discretized using finite elements. Wave propagation is studied by integrating the system directly in time. Six-noded prism elements are used for the discretization. ABAQUS/Explicit is used as the finite element software package. Voronoi polycrystals with cubic symmetry are used and given random orientations. Therefore, the bulk material is statistically isotropic. Example numerical results for materials with various degrees of scattering that are of common interest are presented. Simulations from ABAQUS/CAE are also presented for these materials. The simulations provide insight into the attenuation models relevant for polycrystalline materials. The numerical results are presented and compared with scattering theory. The theory for elastic wave attenuation is derived for a two-dimensional domain using elastodynamics and stochastic wave theory. The dependence of attenuation on the frequency of the input wave and the mean grain diameter are examined using the numerical results.

The numerical scattering results suggest that the two-dimensional theory is better for weakly scattering media, while the three-dimensional is better for strongly scattering media. These results are anticipated to impact ultrasonic NDE of polycrystalline media.