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Study on 3D von Neumann equation with anisotropy for convex grains

Wang Hao Liu Guo-Quan Luan Jun-Hua

Study on 3D von Neumann equation with anisotropy for convex grains

Wang Hao, Liu Guo-Quan, Luan Jun-Hua
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Publishing process
  • Received Date:  20 March 2011
  • Accepted Date:  09 June 2011
  • Published Online:  05 February 2012

Study on 3D von Neumann equation with anisotropy for convex grains

  • 1. School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China;
  • 2. State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 50901008, 50871017), the China Postdoctoral Science Foundation (Grant Nos. 20090460209, 201003050), the Doctoral Program Foundation of Institute of Higher Education of China (Grant No. 200800080003), and the Fundamental Research Funds for the Central Universities.

Abstract: Understanding the laws of grain growth in three dimensions is one of the classic problems of materials science. By considering the anisotropy in real polycrystalline structure and the relationship between the integral of surface mean curvature and the mean caliper diameter of a convex individual grain, three-dimensional von Neumann equation for accurate grain growth rate is studied. The result shows that accurate grain growth rate of a convex grain is related to the grain mean caliper diameter, the sum of the length of grain edges and the corresponding dihedral exterior angles. This result is verified by Kelvin tetrakaidecahedron and the only five convex regular polyhedra.

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