Towards the distribution of a class of polycrystalline materials with an equilibrium defect structure by grain diameters: Temperature behavior of the yield strength

We modify a theory of flow stress introduced in [arXiv:1803.08247[cond-mat.mtrl-sci]], [arXiv:1809.03628[cond-mat.mes-hall]], [arXiv:1908.09338[cond-mat.mtrl-sci]] for a class of polycrystalline materials with equilibrium and quasy-equilibrium defect structure under quasi-static plastic deformations. We suggest, in addition to modified Bose-Einstein distribution, Maxwell-like distribution law for defects (within dislocation-disclination mechanism) in the grains of polycrystalline samples with respect to grain's diameter. Polycrystalline aggregates are considered within single- and two-phase models that correspond to the presence of crystalline and grain-boundary (porous) phases. The scalar dislocation density is derived. Analytic and graphic forms of the generalized Hall-Petch relations for yield strength are produced for single-mode samples with BCC ($\alpha$-Fe), FCC (Cu, Al, Ni) and HCP ($\alpha$-Ti, Zr) crystal lattices at T=300 K with different values of the grain-boundary phase. We derived new form of the temperature-dimensional effect. The values of extremal grain and maximum of yield strength are decreased with raising the temperature in accordance with experiments up to NC region.