Growth of nuclei in a cellular automaton simulation of recrystallisation

Abstract

Cellular automata (CA) have been extensively used to simulate solidification processes, but have received limited attention in the simulation of solid-state transformations. The attractiveness of CA simulation is that it captures the elegance of Monte Carlo simulations, but combined this with the practicality of models based on empirical measurements. The simulation of recrystallization by the CA method is demonstrated by Hesselbarth and Gobel, and Pezzee and Dunand. The limiting features of these works are that grain structure is not tied to any real microstructure (i.e., no scale is ascribed to the microstructures), and, more importantly, the recrystallization kinetics is not calibrated to real time. Such deficiencies necessarily prevent the use of the technique for quantitative simulation which can be applied to industrial processes. The primary aim of this paper is to address the second of the two deficiencies. The kinetics of a three dimensional CA simulation is related to real time using two growth models. Current growth algorithms used in non-CA models are derived directly from experimental data: Juul Jensen notes that before applying such a model, exhaustive experimental investigations are required. Whilst not disputing the capabilities of such an approach, in this paper this recursive method is compared tomore » an a priori calculation of a growth velocity. The results of the simulations are compared to each other, and to the experimental data and analytical solution of Vandermeer and Rath. The relative merits of the two growth models are discussed.« less