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以MacPherson-Srolovitz提出的三维个体晶粒长大拓扑依赖速率方程以及三维晶粒组织的晶粒尺寸一晶粒面数间的抛物线型统计关系为基础,导出了相应的描述三维准稳态晶粒尺寸分布的函数族.采用纯Fe实验数据以及顶点法、基元演化法,相场模型和Monte Carlo法进行了验证,结果表明,函数族中峰值左偏的函数适合三维准稳态晶粒尺寸分布的定量表述.将该函数与Liu等提出的2种三维准稳态晶粒尺寸分布函数进行的对比表明:此3种函数的解析表达形式有所不同,但其曲线图在一定条件下相互吻合.此外,MacPherson-Srolovitz三维拓扑依赖速率方程、Hillert三维速率方程及Yu-Liu三维速率方程尽管表达形式不同均能较好地反映三维正常晶粒长大的动力学规律.
Based on the parabolic statistical relationship between the topological dependence velocity of three-dimensional individual grains grown by MacPherson-Srolovitz and the grain size-grain number of three-dimensional grain structure, corresponding three-dimensional quasi-steady state grains And the size distribution function family.The pure Fe experimental data and the vertex method, the primitive evolution method, the phase field model and the Monte Carlo method were used to verify the results. The results show that the function of the peak left-deviation function is fit for the three-dimensional quasi-steady-state grain size The comparison between the function and the two kinds of three-dimensional quasi-steady-state grain size distribution functions proposed by Liu et al shows that the analytical expressions of these three kinds of functions are different, but the graphs of them are mutually different under certain conditions In addition, MacPherson-Srolovitz’s three-dimensional topological dependency rate equation, Hillert three-dimensional velocity equation and Yu-Liu three-dimensional velocity equation can well reflect the dynamic laws of three-dimensional normal grain growth despite their different forms of expression.