Three-dimensional analysis of scale dependence of sub-micron polycrystals due to configuration entropy

Abstract

The authors proposed a plausible explanation for the deviation of experimental data for sub-micron polycrystals from the Hall-Petch relation by introducing the configuration entropy. The present paper extends the previous twodimensional analysis to the three-dimensional case. The statistical distribution of dislocation lengths within a spherical grain and the bow-out of dislocations axe considered. According to Ashby's model, analyses are pursued for the statistically stored dislocations and geometrically necessary dislocations, respectively. It is confirmed that the configuration entropy model can predict the abnormal Hall-Petch dependence for grain sizes in the sub-micron range.

Generalized Variational Principles of Quasi-Static Electro-Magneto-Thermo-Elasticity

“…In Refs. [1][2][3][4][5][6] the variational principles of thermo-elasticity, variational principles of electro-magnetic, variational principles of piezoelectric materials and variational principles of magneto-elasticity were established respectively. And variational principles of electro-thermo-elasticity, variational principles of electro-magnetic-elasticity, variational principles of thermal-magneto-elasticity were established respectively in Refs.…”