The effect of small plastic deformation and annealing on the properties of polycrystals: Part II. Theoretical model for the transformation of nonequilibrium grain boundaries

Abstract

The nonequilibrium grain boundary state which has a high energy state is the result of absorption of a certain density of extrinsic grain boundary dislocations (EGBD’s). The equilibrium of such a boundary occurs by annealing at higher temperatures. A model has been proposed in this paper which assumes that the equilibrium of a nonequilibrium grain boundary involves the annihilation of EGBD’s by climbvia lattice diffusion of vacancies at the triple points. Due to the stress field of the EGBD’s, there is a vacancy concentration gradient around the triple points. The profile of the vacancy concentration gradient is derived by assuming a steady state flux of vacancies. Using this vacancy concentration profile, the expressions for the rate of climb of EGBD’s are derived. The proposed model predicts that the time required for the equilibration of nonequilibrium grain boundaries is dependent not only on the annealing temperature but also on the initial density of EGBD’s and the boundary length (which is related to the grain size). It has also been shown that the equilibrium behavior predicted by our model is in good agreement with the experimental results obtained for 316L stainless steel.