期刊
JOURNAL OF STATISTICAL PHYSICS
卷 154, 期 4, 页码 913-928出版社
SPRINGER
DOI: 10.1007/s10955-013-0893-7
关键词
Polycrystalline microstructure; Laguerre tessellation; Orthogonal regression; Convex cells
资金
- Deutsche Forschungsgemeinschaft through NSF/DFG Materials World Network Project [KR 1658/4-1]
As a straightforward generalization of the well-known Voronoi construction, Laguerre tessellations have long found application in the modelling, analysis and simulation of polycrystalline microstructures. The application of Laguerre tessellations to real (as opposed to computed) microstructures-such as those obtained by modern 3D characterization techniques like X-ray microtomography or focused-ion-beam serial sectioning-is hindered by the mathematical difficulty of determining the correct seed location and weighting factor for each of the grains in the measured volume. In this paper, we propose an alternative to the Laguerre approach, representing grain ensembles with convex cells parametrized by orthogonal regression with respect to 3D image data. Applying our algorithm to artificial microstructures and to microtomographic data sets of an Al-5 wt% Cu alloy, we demonstrate that the new approach represents statistical features of the underlying data-like distributions of grain sizes and coordination numbers-as well as or better than a recently introduced approximation method based on the Laguerre tessellation; furthermore, our method reproduces the local arrangement of grains (i.e., grain shapes and connectivities) much more accurately. The additional computational cost associated with orthogonal regression is marginal.
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