  We elaborate the recently introduced theory of flow stress, including yield
strength, in polycrystalline materials under quasi-static plastic deformations,
thereby extending the case of single-mode aggregates to multimodal ones in the
framework of a two-phase model which is characterized by the presence of
crystalline and grain-boundary phases. Both analytic and graphic forms of the
generalized Hall-Petch relations are obtained for multimodal samples with BCC
($\alpha$-phase Fe), FCC (Cu, Al, Ni) and HCP (Cu, Al, Ni) and HCP
($\alpha$-Ti, Zr) crystalline lattices at $T=300K$ with different values of the
grain-boundary (second) phase. The case of dispersion hardening due to a
natural incorporation into the model of a third phase including additional
particles of doping materials is considered. The maximum of yield strength and
the respective extremal grain size of samples are shifted by changing both the
input from different grain modes and the values at the second and third phases.
We study the influence of multimodality and dispersion hardening on the
temperature-dimensional effect for yield strength within the range of
$150-350K$.
