Electro-deposition technique is capable of producing nano-gralned bulk copper specimens that exhibit superplastic extensibility at room temperature. Metals of such small grain sizes deform by grains sliding, with little distortion occurring in the grain cores. Accommodation mechanisms such as grain boundary diffusion, sliding and grain rotation control the kinetics of the process. Actual deformation minimizes the plastic dissipation and stored strain energy for representative steps of grain neighbor switching. Numerical simulations based on these principles are discussed in this paper.

In this paper the Euler equation of the deflection of elastic thin plate is reduced to the equation with Schrodinger form by the principle of quantum electro-dynanlics.Then we can obtain the general solution of deflection of elastic thin bending plato by the joint action of dynamical lateral pressure, force in central surface and external field on the elastic base.

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.

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