Behaviors of the quasi-steady state grain size distribution and the corresponding topological relationship were investigated using the Ports Monte Carlo method to simulate the normal grain growth process. The observed quasi-steady state grain size distribution can be well fit by the Weibull function rather than the Hillert distribution. It is also found that the grain size and average number of grain sides are not linearly related. The reason that the quasi-steady state grain size distribution deviates from the Hillert distribution may contribute to the nonlinearity of the relation of the average number of grain sides with the grain size. The results also exhibit the reasonability of the relationship deduced by Mullins between the grain size distribution and the average number of grain sides.
采用Potts Monte Carlo方法对正常晶粒长大过程进行了仿真,并实现了晶粒的准稳态长大。仿真结果显示,准稳态晶粒长大阶段的尺寸分布不是经典Hillert理论预测的Hillert(v=4)分布,却可以用Weibull函数来描述或由v<4的解析函数来表征。其中v为晶粒尺寸分布因子。本研究的Monte Carlo仿真结果证实了v<4的准稳态晶粒尺寸分布的存在。
为改善三维晶粒组织可视化模型的统计性,采用Monte Carlo Potts方法建立了材料多晶体组织的一种大尺度三维数字化模型,并实现了其定量表征和三维可视化.逾万晶粒的统计结果表明,该模型的平均晶粒面数为13.8±0.1,晶粒尺寸分布和晶粒面数分布均可用Log-normal函数近似拟合,与实际材料晶粒组织情况相近.
A Hillert-type three-dimensional grain growth rate model was derived through the grain topology-size correlation model,combined with a topology-dependent grain growth rate equation in three dimensions. It shows clearly that the Hillert-type 3D grain growth rate model may also be described with topology considerations of microstructure. The size parameter bearing in the model is further discussed both according to the derived model and in another approach with the aid of quantitative relationship between the grain size and the integral mean curvature over grain surface. Both approaches successfully demonstrate that, if the concerned grains can be well approximated by a space-filling convex polyhedra in shape, the grain size parameter bearing in the Hillert-type 3D grain growth model should be a parameter proportional to the mean grain tangent radius.
Based on Hillert's 3D grain growth rate equation, the grain growth continuity equation was solved. The results show that there are an infinite number of 3D quasi-stationary grain size distributions. This conclusion has gained strong supports from results of different computer simulations reported in the literature.
