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تسجيل مستخدم جديدPeculiarities of temperature dependence for generalized Hall-Petch law and two-phase model for deformable polycrystalline materials
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Alexander A. Reshetnyak
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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-Considere fracture criterion validity. The single-phase model of polycrystalline material is augmented by means of inclusion of a softening grain boundary phase.
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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 PC materials for quasi-static plastic loading for grain of average size d in range 10^{-8}-10^{-2}m. It
s based on statistical model of energy spectrum distribution in each grain of 1-mode PC sample under plastic loading,with highest level equal to maximal dislocation energy. Found distribution of scalar dislocation density leads to FS due to Taylor strain hardening containing usual and anomalous HP laws for coarse and NC grains, respectively, and reaches maximum for extreme grain size d_0 of order 10^{-8}m. Maximum undergoes shift to region of larger grains for decreasing T and increasing strains. Coincidence is established among theoretical and experimental data on YS for BCC(alpha-Fe), FCC(Cu,Al,Ni),HCP(alpha-Ti,Zr) PC materials at T=300K.The T-dependence of strength quantities is studied. It is shown using Al that YS grows with decrease in T for all grains with d>3d_0,and then YS decreases in NC region,thus determining a temperature-dimension effect (TDE).1-phase model of PC sample is extended by including softening GB phase into 2-phase model,and then by dispersion (un)hardening. A quasi-particle interpretation of crystallite energy quantization is suggested.Analytic and graphic forms of HP laws are obtained in above samples with different values of small-,large-angle GB and constant pores.The maximum of YS and respective extremal grain size of the samples are shifted by change of 2-nd phase.The T-dependence of YS in range of 150-350K for Al demonstrates the validity of TDE. An enlargement of 2-nd phase neutralizes TDE.Deformation curves for 1- and 2-mode 2-phase alpha-Fe PC model are constructed with Backofen-Considere fracture criterion,as compared to experimental,1-phase model data, and strongly depend on multimodality and GB
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