Direction-dependent elastic grain-interaction models -: a comparative study

Mechanical and diffraction (X-ray) elastic constants (diffraction (X-ray) stress factors for macroscopically elastically anisotropic specimens) can be calculated for polycrystalline specimens from single-crystal elastic data by employing elastic grain-interaction models. Traditionally, only so-called isotropic grain-interaction models are considered: all directions in the polycrystal are taken equivalent with respect to the grain interaction. Only recently, so-called direction-dependent, i.e. anisotropic grain-interaction models, have been proposed. These models can express the effects of the reduced dimensionality of thin films, of the surface anisotropy of bulk polycrystals and of a grain-shape (morphological) texture on the elastic properties of polycrystals. In this work, the available, recently proposed direction-dependent grain-interaction models will be compared, in particular on the basis of numerical calculations of diffraction and mechanical elastic constants, of variances of certain orientation-dependent stress and strain tensor components and of the distributions of strains in the Euler (orientation) space. It will be demonstrated that the so-called Vook-Witt and inverse Vook-Witt models become (but only approximate) equivalent to the Eshelby-Kroner model for certain grain- shape textures.