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A theory of flow stress (FS), reviewing and developing our research,e.g.arxiv:1803.08247;1908.09338, is proposed,including yield strength (YS) of PCmaterials for quasi-static plastic loading for grain of average size d in range10^{-8}-10^{-2}m. It's based on statistical model of energy spectrumdistribution in each grain of 1-mode PC sample under plastic loading,withhighest level equal to maximal dislocation energy. Found distribution of scalardislocation density leads to FS due to Taylor strain hardening containing usualand anomalous HP laws for coarse and NC grains, respectively, and reachesmaximum for extreme grain size d_0 of order 10^{-8}m. Maximum undergoes shiftto region of larger grains for decreasing T and increasing strains. Coincidenceis established among theoretical and experimental data on YS forBCC(\alpha-Fe), FCC(Cu,Al,Ni),HCP(\alpha-Ti,Zr) PC materials at T=300K.TheT-dependence of strength quantities is studied. It is shown using Al that YSgrows with decrease in T for all grains with d>3d_0,and then YS decreases in NCregion,thus determining a temperature-dimension effect (TDE).1-phase model ofPC sample is extended by including softening GB phase into 2-phase model,andthen by dispersion (un)hardening. A quasi-particle interpretation ofcrystallite energy quantization is suggested.Analytic and graphic forms of HPlaws are obtained in above samples with different values of small-,large-angleGB and constant pores.The maximum of YS and respective extremal grain size ofthe samples are shifted by change of 2-nd phase.The T-dependence of YS in rangeof 150-350K for Al demonstrates the validity of TDE. An enlargement of 2-ndphase neutralizes TDE.Deformation curves for 1- and 2-mode 2-phase \alpha-Fe PCmodel are constructed with Backofen-Considere fracture criterion,as compared toexperimental,1-phase model data, and strongly depend on multimodality and GB

A quantized statistical model of flow stress and generalized Hall-Petch law for deformable polycrystalline materials. A temperature-dimension effect