Grain growth and collective migration of grain boundaries during plastic deformation of nanocrystalline materials

A theoretical model is proposed for the collective migration of two neighboring grain boundaries (GBs) in a nanocrystalline material under applied elastic stress. By analyzing the change in the energy of the system, it is shown that GBs can remain immobile or migrate toward each other depending on the values of the applied shear stress and misorientation angles. The process of GB migration can proceed either in a stable regime, wherein the GBs occupy equilibrium positions corresponding to a minimum of the energy of the system under relatively small applied stress, or in an unstable regime, wherein the motion of GBs under relatively high stress is accompanied by a continuous decrease in the system energy and becomes uncontrollable. The stable migration of GBs leads to a decrease of the grain bounded by them at the cost of growth of the neighbor grains and can result in complete or partial annihilation of the GBs and the collapse of this grain. Unstable migration leads either to annihilation of GBs or to passage of them through each other, which can be considered as the disappearance of the grain and nucleation and growth of a new grain.