This work is a natural extension of the authors previous work, Multiple
scattering theory for heterogeneous elastic continua with strong property
fluctuation, theoretical fundamentals and applications, which established the
foundation for developing multiple scattering model for strongly scattering
heterogeneous elastic continua. In this work, the corresponding multiple
scattering theory for polycrystalline materials with randomly oriented
anisotropic crystallites is developed. As applications in ultrasonic
nondestructive evaluation, we calculated the dispersion and attenuation
coefficient of one of the most important polycrystalline materials in
aeronautics engineering, high temperature titanium alloys. The effects of grain
symmetry, grain size, and alloying elements on the dispersion and attenuation
behaviors are examined. Key information is obtained which has significant
implications for quantitatively evaluating the average grain size, monitoring
the phase transition, and even estimating gradual change in chemical
composition of titanium components in gas turbine engines. For applications in
seismology, the velocities and Q-factors for both hexagonal and cubic
polycrystalline iron models for the Earth uppermost inner core are obtained in
the whole frequency range. This work provides a universal, quantitative model
for characterization of a large variety of polycrystalline materials. It also
can be extended to incorporate more complicated microstructures, including
ellipsoidal grains with or without textures, and even multiphase
polycrystalline materials. The new model demonstrates great potential of
applications in ultrasonic nondestructive evaluation and inspection of
aerospace and aeronautic structures. It also provides a theoretical framework
for quantitative seismic data explanation and inversion for the material
composition and structural formations of the Earth inner core.Comment: 37 pages, 16 figure