This paper proposes an algorithm to generate a statistically equivalent microstructure of alloys for polygonal mesh-based finite element modeling. Morphological and crystallographic characteristics obtained from scanning electron microscopy images of 2D surface slices are employed to generate the mesh. Titanium alloy microstructures are considered as an example to demonstrate the proposed method. The mean and standard deviation of the grain area distribution obtained from the images are employed as the statistical parameters. The algorithm uses the image data and applies perturbation using a distortion factor and Voronoi tessellation to generate the statistically equivalent polygonal microstructure that captures the randomness of grain shape and size iteratively. The grain area distribution of the simulated microstructure closely matches with the actual distribution. Lower-order elements (quadrilateral) on the domain boundary get introduced that may create artifacts when analyzed with the finite element method. A method to eliminate these artifacts is presented with an analysis of stress concentrations occurring due to grain orientation mismatch. Effective mechanical properties, deformation, and fracture behavior as a function of various microstructural parameters like grain area and crystallographic orientations can be analyzed using the polygonal finite element mesh.

本文提出了一种算法，可以为基于多边形网格的有限元建模生成合金的统计等效微观结构。从二维表面切片的扫描电子显微镜图像中获得的形态学和晶体学特征用于生成网格。以钛合金微观结构为例来说明所提出的方法。从图像中获得的颗粒面积分布的平均值和标准偏差被用作统计参数。该算法使用图像数据并使用畸变因子和 Voronoi 细分来应用扰动以生成统计等效的多边形微观结构，该微观结构迭代地捕获晶粒形状和尺寸的随机性。模拟微观结构的晶粒面积分布与实际分布紧密匹配。域边界上的低阶元素（四边形）被引入，当使用有限元方法进行分析时，这些元素可能会产生伪影。通过对由于晶粒取向不匹配而发生的应力集中的分析，提出了一种消除这些伪影的方法。可以使用多边形有限元网格分析作为各种微观结构参数（如晶粒面积和晶体取向）的函数的有效机械性能、变形和断裂行为。通过对由于晶粒取向不匹配而发生的应力集中的分析，提出了一种消除这些伪影的方法。可以使用多边形有限元网格分析作为各种微观结构参数（如晶粒面积和晶体取向）的函数的有效机械性能、变形和断裂行为。通过对由于晶粒取向不匹配而发生的应力集中的分析，提出了一种消除这些伪影的方法。可以使用多边形有限元网格分析作为各种微观结构参数（如晶粒面积和晶体取向）的函数的有效机械性能、变形和断裂行为。