Zheng Xingshuai, Sun Tengfei, Zhou Jixing, Zhang Rupeng, Ming Pingmei
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China.
Materials (Basel). 2022 Mar 8;15(6):1996. doi: 10.3390/ma15061996.
Voronoi tessellations are shown to be statistically representative of polycrystalline microstructures, which have been widely accepted for the modeling of microstructures of metallurgic and ceramic materials. In this paper, a new implementation of the Voronoi diagram in Laguerre geometry is presented for the generation of numerical models of polycrystalline microstructures, where the size and shape of the grains can be controlled, and the 3D grain boundaries can be modeled with a specified thickness. The distribution of grain sizes in the models is fitted to a lognormal distribution, compared with the normal distribution in the Voronoi tessellation methods. Finally, statistical analyses of grain face and grain size distribution are performed with the models, and the macroscopic elastic properties of polycrystalline ceramic materials are simulated to verify the capability of the presented method.
Voronoi镶嵌被证明在统计学上能够代表多晶微观结构，这已被广泛用于冶金和陶瓷材料微观结构的建模。本文提出了一种在拉盖尔几何中Voronoi图的新实现方法，用于生成多晶微观结构的数值模型，其中晶粒的尺寸和形状可以控制，并且三维晶界可以用指定的厚度进行建模。与Voronoi镶嵌方法中的正态分布相比，模型中晶粒尺寸的分布拟合为对数正态分布。最后，利用这些模型对晶粒面和晶粒尺寸分布进行了统计分析，并模拟了多晶陶瓷材料的宏观弹性性能，以验证所提出方法的能力。
