Ultrasonic Studies of the Fundamental Mechanisms of Recrystallization and Sintering of Metals

Abstract

ObjectivesThe purpose of this project was to develop a fundamental understanding of the interaction of an ultrasonic wave with complex media, with specific emphases on recrystallization and sintering of metals. A combined analytical, numerical, and experimental research program was implemented. Theoretical models of elastic wave propagation through these complex materials were developed using stochastic wave field techniques. The numerical simulations focused on finite element wave propagation solutions through complex media. The experimental efforts were focused on corroboration of the models developed and on the development of new experimental techniques. The analytical and numerical research allows the experimental results to be interpreted quantitatively. Alteration in Collaborative ArrangementIn fall 2002, the Ames Lab partner, Dr. James C. Foley, announced that he was leaving for another position at Los Alamos National Laboratory. Dr. R. Bruce Thompson has served as the primary contact for this collaboration since Dr. Foley departed. Accomplishments (Recrystallization)Analytical Modeling. Expressions for the ultrasonic attenuation in media with arbitrary texture have been developed using stochastic wave propagation theory. Initial attempts at deriving simple expressions for the attenuation were unsuccessful. Therefore, a modified technique was developed that relies slightly more on numerical calculations. The method is based on a generalized function of a single scalar variable σ that characterizes the state of texture. In this case the weighting function for the individual grains is given by ( ) with θ as the grain orientation angle. Thus, when σ → 0 all grains are aligned and the material is transversely isotropic at the macroscale. As σ → ∞, all grains are randomly oriented and the material is isotropic at the macroscale.In terms of attenuation, the covariance of the microstructure is the primary quantity needed for the calculation of attenuation. It is defined by in which both Eqs. (2) and (3) include the grain orientation distribution function F such that <C> and <CC> are dependent on σ. Example results using Eq. (2) are shown in Fig. 1 for both the average elastic properties as well as quasilongitudinal slowness surfaces in terms of σ. The transition from transversely isotropy to complete isotropy is captured well using the grain orientation distribution function. Example results for attenuation are shown in Fig. 2. Again, the transition from transverse isotropy to complete isotropy is shown. Of particular note is the peak observed in the SH attenuation when σ is about 0.5. Such information may be useful for process monitoring. (a) (b)Progress was also made in the study of multiple scattering in slab geometries. These results have applications associated with heterogeneous bonding and interface layers. Two example results are shown in Fig. 3. The layer is insonified by a plane longitudinal wave. One question in the multiple scattering regime is associated with the applicability of the diffusion li...