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/R_m ≈ 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.

中文翻译：

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基于三维元胞自动机的AZ31镁合金晶粒长大

基于热力学转换机理和能量转移原理，从晶粒取向，晶粒尺寸分布，晶粒长大动力学和晶粒拓扑学三个方面建立了晶粒长大的三维元胞自动机模型。另外，分析了温度对AZ31镁合金三维晶粒生长过程的影响。结果表明，三维晶粒的正常生长满足Aboav-weaire方程，在420°C和2000 CAS时，平均晶面数在12和14之间，最大晶面数超过40。不同大小的晶粒在不同的时间呈正态分布，其中大多数是晶粒直径与平均晶粒直径之比R / R _m的晶粒 ≈1.0，符合晶粒演化的最低能量标准。AZ31镁合金的晶粒尺寸随温度的升高而增大，晶粒数量随时间的增加而减小。三维晶粒的二维切片之间的角度约为120°，这与传统的二维细胞自动机的角度一致。晶粒尺寸的前和后保温的相对误差是在0.1-0.6的范围内 μ米，这表明所述3D细胞自动机能够准确地模拟AZ31镁合金的保温过程。