A mesoscale cellular automaton model for curvature-driven grain growth
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I. INTRODUCTION
CURVATURE-DRIVEN grain growth is an important phenomenon during materials processing such as hot rolling and annealing. The grain shape, the grain size, and the distribution of grain shapes and sizes during grain growth determine the characteristics of the microstructure, which, in turn, have a significant influence on the property of materials. In addition, the austenite grain size remarkably influences the dynamics of the microstructural evolution during austenite decomposition in steels. Finer austenite grains transform more rapidly and decompose into finer final microstructures. To obtain the quantitative relationship that links the grain size to the process parameters, numerous studies of grain growth were performed and a variety of grain-growth models were proposed during past decades. These grain-growth models can be classified into empirical models,[1–4] Potts models,[5–9] vertex models,[10–17] probabilistic cellular automaton techniques,[18] phase-field models,[19] and gradient-weighted moving finite-element models.[20,21] Although empirical models are simple and convenient for engineering applications, the extrapolation of these models is questionable when industry processes are different from the conditions employed in developing these models. Potts models and probabilistic cellular automaton algorithms have an advantage in the simplicity of switch rules. However, it is still very difficult to scale the Monte Carlo time or probabilistic cellular automaton time to the physical time, although Raabe[22] scaled the real-time-step elapsing during one Monte Carlo step by the maximum occurring grain-boundary mobility, the maximum occurring driving force, and the lattice parameter of the simulation grid, using a rate theory. The vertex approach can accurately handle the relation between the local curvature and the local mobility, but the extension from two to three dimensions is much more difficult and computationally costly, because of the complexity of the topological transformation, although Y.J. LAN, Postdoctoral Student, D.Z. LI, Professor, and Y.Y. LI, Professor and Academician of the Chinese Academy of Sciences (CAS), are with the Laboratory for Special Environment Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China. Contact e-mail: [email protected] or [email protected] Manuscript submitted November 11, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
Weygand et al.[23] have established a three-dimensional vertex model for grain growth. Field variables are employed in phase-field models to represent the microstructures, thus giving detailed information about the microstructural evolution. One drawback of phase-field models is that a very fine grid must be used across grain boundaries. This requires very significant and costly computational resources. The objective of this work is to develop an alternative cellular automaton approach for simulating the curvaturedriven grain growth on mesoscale, in two dimensions. A deterministic swi
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