Modeling the recrystallization process using inverse cellular automata and genetic algorithms: Studies using differential evolution

Abstract

An inverse modeling approach was taken up in this work to model the process of recrystallization using cellular automata (CA). Using this method after formulating a CA model of recrystallization, differential evaluation (DE), a real-coded variant of genetic algorithms, was used to search for the value of nucleation rate, providing an acceptable matching between the theoretical and experimentally observed values of fraction-recrystallized (X). Initially, the inverse modeling was attempted with a simple CA strategy, in which each of the CA cells had an equal probability of becoming nucleated. DE searched for the value of the nucleation rate yielding the best results for single-crystal iron at 550 °C. A good match could not be simultaneously achieved this way for the early stages of recrystallization as well as for the later stages. To overcome this difficulty, the CA grid was divided into two zones, having lower and higher probabilities of nucleation. This resulted in good correspondence between the predicted and experimental values of X for the entire duration of recrystallization. The introduction of a distribution in the probability of nucleation made the model even closer to the actual process, in which the probability of nucleation is often nonuniform due to nonuniformity in dislocation density as well as the presence of grain/interface boundaries.