  In this paper, we propose a generalized variant of Kr\"oner's self-consistent
scheme for evaluation of the effective standard and gradient elastic moduli of
polycrystalline materials within Mindlin-Toupin second-gradient elasticity
theory. Assuming random orientation of crystallites (grains) we use an extended
Eshelby's equivalent inclusion method and mapping conditions between the
prescribed linear distribution of macro-strain and corresponding micro-scale
field variables averaged over the volume and all possible orientations of
single grain. It is found that developed self-consistent scheme predicts the
absence of strong gradient effects at the macro-scale level for the model of
spherical grains. However, for the more general shape of the grains, considered
approach allows to obtain a set of non-linear relations for determination of
all effective standard and gradient elastic moduli of polycrystals.
