Mechanics modeling for deformation of nano-grained metals

The electro-deposition technique is capable of producing nano-grained bulk copper specimens that exhibit superplastic extensibility at room temperature. Metals of such small grain sizes deform by grains squeezing past each other, with little distortion occurring in the grain cores. Accommodation mechanisms such as grain boundary diffusion and grain rotation control the kinetics of the process. A model of a 9-grain cluster is proposed that incorporates both the Ashby-Verrall mechanism and the 30° rotation of closely linked grain pairs. A constitutive relation is derived that relates the creep strain rate linearly to the difference between the applied stress and a threshold stress. The creep rate and the threshold stress predicted by the model are in quantitative agreement with the experimental data.