Propagation and scattering of ultrasonic waves in macroscopically anisotropic polycrystalline materials with fiber texture

This work investigates the scattering of ultrasonic elastic waves in polycrystalline materials with macroscopic transverse isotropy (TI). Using the Dyson equation with the First-order smoothing approximation (FOSA) for the mass operator, we obtain the complex wavenumber of the qL, T₁, and qT₂ waves in 3D and qL and qT₂ in 2D. The equations are properly modified by including the Green solution for the reference TI homogeneous medium. Additionally, 2D numerical finite element (FE) models are developed, allowing for a direct comparison with the 2D theoretical amplitude attenuation and phase velocities estimations. The numerical simulations are carried out with a set of periodic boundary conditions (PBC), leading to a proper plane wave propagation even in the case of macroscopic anisotropy. The influence of the orientation of the axis of symmetry on the attenuation and phase velocities is discussed. The role of the symmetry-axis orientation is analyzed, and scattering mechanisms are contrasted between 2D and 3D. Numerical and theoretical results show excellent agreement, confirming the increased wave dispersion when propagation occurs along the cross-fiber (or cross-symmetry-axis) direction.