Fig. 4.
Schematic illustration of the micromechanics model of a polycrystalline aggregate. a Polycrystal consisting of different {hkl} grain families oriented along the uniaxial loading direction. For example, the {111} grain family refers to a set of grains with the unit normal vector n of {111} planes along the loading direction. X-rays reflected by the {hkl} planes are collected to track the average interplanar spacing of these {hkl} planes with deformation due to applied stress σ a. b In the self-consistent polycrystal model, each single-crystal grain is approximated as a spherical inclusion with the anisotropic elastic stiffness tensor L(r) embedded in a homogeneous matrix with the effective stiffness tensor