Generalized balanced power diagrams for 3D representations of polycrystals

Alpers, Andreas ORCID: 0000-0003-0663-6037, Brieden, Andreas, Gritzmann, Peter, Lyckegaard, Allan and Poulsen, Henning Friis (2015) Generalized balanced power diagrams for 3D representations of polycrystals. PHILOSOPHICAL MAGAZINE, 95 (9). pp. 1016-1028.

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Official URL: http://dx.doi.org/10.1080/14786435.2015.1015469

Abstract

Characterizing the grain structure of polycrystalline material is an important task in material science. The present paper introduces the concept of generalized balanced power diagrams as a concise alternative to voxelated mappings. Here, each grain is represented by (measured approximations of) its center-of-mass position, its volume and, if available, by its second-order moments (in the non-equiaxed case). Such parameters may be obtained from 3D x-ray diffraction. As the exact global optimum of our model results from the solution of a suitable linear program it can be computed quite efficiently. Based on verified real-world measurements we show that from the few parameters per grain (3, respectively 6 in 2D and 4, respectively 10 in 3D) we obtain excellent representations of both equiaxed and non-equiaxed structures. Hence our approach seems to capture the physical principles governing the forming of such polycrystals in the underlying process quite well.

Item Type:	Article
Uncontrolled Keywords:	linear programming, tessellations, grains, polycrystals, power diagrams, generalized balanced power diagrams
Depositing User:	Symplectic Admin
Date Deposited:	05 May 2020 10:23
Last Modified:	18 Jan 2023 23:53
DOI:	10.1080/14786435.2015.1015469
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3085596