On the Use of Laguerre Tessellations for Representations of 3D Grain Structures
On the Use of Laguerre Tessellations for Representations of 3D Grain Structures
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关于使用 Laguerre Tessellation 表示 3D 颗粒结构
DOI：
10.1002/adem.201000258
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发表时间：
2011
影响因子：
3.6
通讯作者：
H. Poulsen
中科院分区：
文献类型：
--
作者：
A. Lyckegaard;E. Lauridsen;W. Ludwig;Rich Fonda;H. Poulsen
多晶材料中的3D晶粒结构的准确描述是关键的兴趣，因为晶粒结构与材料的宏观性质密切相关。在本研究中，我们调查的准确性，使用拉盖尔镶嵌表示三维晶粒结构，从只有空间质心位置和体积的晶粒。通过与通过相衬显微断层扫描获得的未变形Meta稳β钛合金的3D重建进行直接比较，揭示了拉盖尔镶嵌法描述真实的3D晶粒结构的精确晶粒形状和拓扑结构的能力。这项研究表明，（体积加权）Laguerre镶嵌是上级经典Voronoi镶嵌，当谈到提供准确的表示真实的三维晶粒结构。此外，虽然拉盖尔镶嵌法只能正确描述晶粒的局部排列（即，晶粒近邻和晶粒刻面数）的31.8%的研究晶粒，拉盖尔镶嵌能够准确地描述统计晶粒特征，如晶粒尺寸分布和晶粒近邻分布。
Accurate descriptions of 3D grain structures in polycrystalline materials are of key interest as the grain structure is closely correlated to the macroscopic properties of the material. In the present study, we investigate the accuracy of using Laguerre tessellations to represent 3D grain structures from only the spatial center of mass location and the volume of the grains. The ability of Laguerre tessellations to describe accurate grain shapes and topologies of real 3D grain structures are revealed by direct comparison to 3D reconstructions of an un‐deformed meta‐stable β ‐titanium alloy obtained by phase‐contrast micro‐tomography. This study reveals that (volume weighted) Laguerre tessellations are superior to classical Voronoi tessellations when it comes to providing accurate representations of real 3D grain structures. Furthermore, although the Laguerre tessellations were only able to correctly describe the local arrangements of grains (i.e., the grain neighbors and number of grain facets) for 31.8% of the investigated grains, the Laguerre tessellations were able to accurately describe statistical grain characteristics such as grain size distributions and grain neighbor distributions.