Computer simulation of recrystallization in non-uniformly deformed metals

Abstract

The classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [F = 1 - exp(- kt)n] for nucleation and growth transformations works very well for most solid state transformations but fails regularly when applied to recrystallization of plastically deformed metals. Under conditions of near constant growth rate, a high exponent (n [ges] 3) is predicted but low exponents (n [les] 2) are typically measured. Another common observation is that the slope of a JMAK plot, from which the exponent is inferred, decreases as recrystallization proceeds. Analysis of the published data suggested the hypothesis that the failure of the JMAK theory as applied to recrystallization is because of the lack of uniformity of the stored energy of plastic deformation on the grain size scale. This hypothesis was tested by use of Monte Carlo simulations of the type previously used successfully to model grain growth and recrystallization. The earlier simulations of recrystallization used uniform stored energies whereas the simulations presented here varied the stored energy from grain to grain. The kinetics were plotted on JMAK plots which exhibited low and varying exponents closely resembling experimental data. Specific simulations were performed to test the basic JMAK assumption that makes a correction for the effect of impingement under conditions of random nucleation, namely dF/dFe = (1 - F), where F is the actual volume fraction and Fe is the extended volume fraction--that which would obtain in the absence of impingement and overlap between new grains. It was found the assumption is accurate under conditions of uniform stored energy. With non-uniform stored energy, however, the correction underestimated the effect of impingement by a factor that rapidly increased (to over two orders of magnitude) during recrystallization.