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

TL;DR

This paper develops a statistical model for flow stress in polycrystalline materials, incorporating temperature and grain size effects, and extends it to include grain boundary phases, providing insights into the Hall-Petch law and temperature-dimension effects.

Contribution

It introduces a novel statistical energy spectrum model for flow stress that accounts for temperature, grain size, and phase dispersion, extending the classical Hall-Petch law.

Findings

Flow stress reaches a maximum at a specific grain size around 10^{-8} m.

Temperature decreases the maximum flow stress and shifts the extremal grain size.

The model's predictions align with experimental data for various crystal structures.

Abstract

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