Peculiarities of temperature dependence for generalized Hall-Petch law and two-phase model for deformable polycrystalline materials

In the framework of the suggested in [arxiv:1803.08247 [cond-mat.mtrl-sci]] statistical theory of the equilibrium flow stress, including yield strength, ${\sigma}_y$, of polycrystalline materials under quasi-static (in case of tensile strain) plastic deformation in dependence on average size, d, of the crystallites (grains) in the range, $10^{-8}$ m - $10^{-2}$ m. it is found the coincidences of the theoretical and experimental data of ${\sigma}_y$ for the materials with BCC (${\alpha}$- Fe), FCC (Cu, Al, Ni) and HCP (${\alpha}$-Ti, Zr) crystal lattice at T=300K. The temperature dependence of the strength characteristics is studied. It is shown on the example of Al, that the yield strength grows with decreasing of the temperature for all grains with d greater than $3*d_0$ (with $d_0$ being extremal size of the grain for maximal ${\sigma}_y$) and then ${\sigma}_y$ decreases in the nano-crystalline region, thus determining a temperature-dimension effect. Stress-strain curves, ${\sigma}={\sigma}({\epsilon})$, are constructed for the pure crystalline phase of ${\alpha}$-Fe with Backofen-Consid\'ere fracture criterion validity. The single-phase model of polycrystalline material is augmented by means of inclusion of a softening grain boundary phase.