Monte Carlo Simulations of Grain Growth in Metals

Abstract

The application of the Monte Carlo (MC) method to simulate the grain growth in metals originates from Potts’ model for magnetic domain evolution (Potts, 1952), which generalized the two-state spin up or spin down ferromagnetic Ising model to systems with arbitrary spin degeneracy. Subsequently, the so-called n-fold method for expediting simulations of the time evolution of systems was developed (Bortz et al., 1975). Anderson and his co-workers were the first to introduce the Potts model into grain growth simulations, applying this method to model the grain growth kinetics (Anderson et al., 1984), grain size distribution and topology (Srolovitz et al., 1984a), influence of particle dispersions (Srolovitz et al., 1984b), anisotropic grain boundary energies (Grest et al., 1985) as well as abnormal grain growth (Srolovitz et al., 1985; Rollett et al., 1989; Rollett & Mullins, 1996). By incorporating specific elements corresponding to various microstructural processes into the basic algorithm, the MC method has been adapted to model for instance grain growth in twophase materials (Holm et al., 1993) and composites (Miodownik et al., 2000), abnormal grain growth (Lee at al., 2000, Messina et al., 2001; Ivasishin et al., 2004), static recrystallization (Srolovitz et al., 1986; Srolovitz et al., 1988; Rollett et al., 1992a, Rollett & Raabe, 2001; Song & Rettenmayr, 2002)), dynamic recrystallization (Peczak, 1995; Rollett et al., 1992b) and sintering (Hassold, et al., 1990; Chen et al., 1990, Matsubara, 1999), and it has been demonstrated that such MC simulations are capable of reproducing the essential features of these microstructural phenomena. Nowadays, the MC method is often preferred to deterministic methods such as cellular automaton (Geiger et al., 2001) and phase-field models (Tikare et al., 1998) at the mesoscopic level, mainly due to its inherent simplicity and flexibility. More recently, the MC method has also been employed to predict the final microstructures in engineering applications (Yang et al., 2000; Yu & Esche, 2005). For quite some time, numerous efforts geared toward improving the accuracy and efficiency of the conventional MC method have been reported in the literature (Radhakrishnan & Zacharia, 1995; Song & Liu, 1998, Yu & Esche, 2003a), aiming at providing the foundation for the application of the MC method in engineering practice. Various modifications of the conventional Monte Carlo (CMC) algorithm have been reported. For instance, an increase in processing speed of up to two orders of magnitude compared with the CMC algorithm were achieved in grain growth simulations by employing a modified MC algorithm (Yu & Esche, 2003a). Furthermore, this modified algorithm also led to an improved accuracy of the predicted grain growth exponent in the kinetic equations, particularly in small grain size