Abstract
Based on the thermodynamic conversion mechanism and energy transition principle, a three-dimensional cellular automata model of grain growth is established from the aspects of grain orientation, grain size distribution, grain growth kinetics, and grain topology. Also, the effect of temperature on the three-dimensional grain growth process of AZ31 magnesium alloy is analyzed. The results show that the normal growth of three-dimensional grains satisfies the Aboav-weaire equation, the average number of grain planes is between 12 and 14 at 420°C and 2000 CAS, and the maximum number of grain planes is more than 40. Grains of different sizes are distributed normally at different times, most of which are grains with the ratio of grain diameter to average grain diameter R/Rm ≈ 1.0, which meets the minimum energy criterion of grain evolution. The grain of AZ31 magnesium alloy increases in size with the increase of temperature, and the number of grains decreases with the increase in time. The angle between the two-dimensional slices of three-dimensional grains is approximately 120°, which is consistent with that of the traditional two-dimensional cellular automata. The relative error of grain size before and after heat preservation is in the range of 0.1–0.6 μm, which indicates that the 3D cellular automata can accurately simulate the heat preservation process of AZ31 magnesium alloy.
Highlights
Since grain growth is closely related to the mechanical properties of polycrystalline materials, such as plasticity, strength, and rigidity, it is important to study the grain growth for controlling and improving the mechanical properties of material [1]
With the development and progress of computer technology, a large number of simulation methods have been used in the research of the microstructure evolution process, such as the phase field method, Monte Carlo method, and cellular automata method, which have been recognized by the majority of researchers [3]
Three-Dimensional Cellular Automata Model ree-dimensional cellular automata (3D-CA) is an important model to obtain the information of grain size, morphology, grain boundary, and orientation through three-dimensional characterization technology. e model can simulate the process of grain growth by establishing the model parameters of a three-dimensional cell and using the cell transformation rules, which plays an irreplaceable role in promoting the development of microstructure evolution theory
Summary
Since grain growth is closely related to the mechanical properties of polycrystalline materials, such as plasticity, strength, and rigidity, it is important to study the grain growth for controlling and improving the mechanical properties of material [1]. Geiger et al [5], based on the principle of grain boundary transition, simulated the growth of twodimensional grains by improving the transformation rule of cellular automata. The grain growth process of AZ31 magnesium alloy is simulated by using a three-dimensional cellular automata model based on the thermodynamic conversion mechanism and energy conversion principle. E model can simulate the process of grain growth by establishing the model parameters of a three-dimensional cell and using the cell transformation rules, which plays an irreplaceable role in promoting the development of microstructure evolution theory. In equation (5), P3 exp(−ΔE/RT).In every step of the transformation process of cellular automata, each cell is transformed according to the probability P. erefore, the final transformation rule of a cell can be expressed as follows: 1, ΔE ≤ 0,. We go to the step and judge all cells. is process needs to be repeated again and again to make the grains grow gradually
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