A Three-Dimensional Cellular Automata Model Coupling Energy and Curvature-Driven Mechanisms for Austenitic Grain Growth
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A Three-Dimensional Cellular Automata Model Coupling Energy and Curvature-Driven Mechanisms for Austenitic Grain Growth MIN WANG, JIANXIN ZHOU, YAJUN YIN, HAI NAN, DONGQIAO ZHANG, and ZHIXIN TU A 3D cellular automata model is used to simulate normal austenitic grain growth in this study. The proposed model considers both the curvature- and thermodynamics-driven mechanisms of growth. The 3D grain growth kinetics shows good agreement with the Beck equation. Moreover, the growth exponent and grain size distribution calculated by the proposed model coincides well with experimental and simulation results from other researchers. A linear relationship is found between the average relative grain size and the grain face number. More specifically, for average relative grain sizes exceeding ~0.5, the number of faces increases linearly with relative grain size. For average relative grain sizes 0.5. However, the existing linear relationship changes for R/Ra < 0.5. This
phenomenon was also found by Kamachali, who explained that this behavior originated from the geometrical complexity of the system, which remains incompletely understood.
METALLURGICAL AND MATERIALS TRANSACTIONS B
D. Kinetics of Grain growth The relationship between the average grain size and grain-evolution time follows Beck’s law[46]; the grain growth kinetics described by Beck can be expressed as follows: Ra ¼ Btn ;
The grain growth exponent has been the most controversial point of Beck’s law in recent decades. Results from previous studies differ and are based on different experiments and simulation models.[47–49] In practical applications, many studies select the theoretical value of n = 0.5. The logarithmic form of Beck’s law is expressed as follows: ln Ra ¼ ln B þ n ln t
where Ra denotes the average grain size and n is the growth exponent. Austenitic grain growth is simulated at three different temperatures with results plotted in Figure 11. The simulation results are fitted using an exponential function with fitting lines depicted in the picture. The fitting lines are very close to the simulation results, allowing the conclusion that the relationship between grain size and CA simulation step basically meets Beck’s law.
The slope of the ln(Ra) ln(t) yields the value of n. Kinetic curves of grain growth in logarithmic form at different temperatures are plotted in Figure 12. The logarithmic forms for grain size approach straight lines. From the above, the average grain size increases with the increasing temperature, and the growth exponents calculated at three different temperatures are 0.4102, 0.4212, and 0.4321, respectively.
Fig. 9—Grain size distributions for four topological classes.
Fig. 11—Relation between average grain size and time during grain growth.
Fig. 10—Square root of grain faces number changing over their relative sizes: (a) at 2000; (b) at 3000 CAS.
METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 12—Relation between the log form of average relative grain size and log time during grain growth.
The grain growth exponents calculated by t
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