Multiple scattering theory for polycrystalline materials with strong grain anisotropy: theoretical fundamentals and applications

Abstract: 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.