  Anisotropic core-shell model of a nano-grained polycrystal, proposed recently
for nanocrystalline copper, is applied to estimate elastic effective properties
for a set of crystals of cubic symmetry. Materials selected for analysis differ
in the lattice geometry (face-centered cubic vs. body-centered cubic) as well
as the value of a Zener factor: a ratio of two shear moduli defining elastic
anisotropy of a cubic crystal. The predictions are verified by means of the
atomistic simulations. The dependence of the overall bulk and shear moduli on
the average grain diameter is analysed. In the mean-field approach the
thickness of the shell is specified by the \emph{cutoff radius} of a
corresponding atomistic potential, while the grain shell is isotropic and its
properties are identified by molecular simulations performed for very small
grains with approximately all atoms belonging to the grain boundary zone. It is
shown that the core-shell model provides predictions of satisfactory
qualitative and quantitative agreement with atomistic simulations. Performed
study indicates that the variation of the bulk and shear moduli with the grain
size changes qualitatively when the Zener anisotropy factor is smaller or
greater than one.
