The Scattering of Elastic Waves in Statistically Anisotropic Media
Liyong Yang - Ph.D. Dissertation Defense
Advisor: Dr. Joseph Turner
Date: Wednesday, December 3, 2003
Time: 2:30 p.m.
Place: W196 Nebraska Hall
The investigation of wave propagation and scattering of ultrasonic waves in heterogeneous, anisotropic media is of substantial interest to quantitative nondestructive evaluation and materials characterization, particularly for ultrasonic techniques. In this dissertation, models for wave propagation and scattering in statistically anisotropic media, such as cracked media and textured media are developed. These models provide insightful information about the wave propagation parameters and can also be used to guide experimental design for determining the microstructure properties for nondestructive evaluation techniques. Compact expressions are derived for attenuations and wave velocities of the quasilongitudinal and two quasishear waves using stochastic wave theory in a generalized dyadic approach. Those derivations are based upon the diagrammatic approach, in which the mean response is governed by the Dyson equation. The Dyson equation is then solved in the Fourier transform domain within the limits of the first-order smoothing approximation (FOSA).
In cracked media, the derivation of explicit expressions of wave attenuations and velocities in a medium with damage from randomly distributed penny-shaped microcracks is first discussed. Under the same framework, wave propagation and scattering in a solid medium permeated by uniaxially aligned and perfectly aligned penny-shaped cracks are then studied, respectively. The resulting attenuations are investigated in terms of the directional, frequency, and damage dependence.
In the case of polycrystalline media with texture, attenuations and wave velocities are developed in a general orthorhombic material made up of cubic crystallites. The attenuations of each wave type are calculated numerically as a function of dimensionless frequency and wave propagation direction, respectively, for given orientation distribution coefficients (ODCs). The ODCs are, in essence, the coefficients of an expansion of the orientation distribution function (ODF) of the crystallite in terms of a series of generalized spherical harmonics. The relationship between the phase velocity and recrystallization variables, such as annealing time, is also investigated for specific examples. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters. It is anticipated that these models will improve the understanding of the microstructure characterization for both statistically anisotropic media.
