Abstract
Based on Hillert's 3D grain growth rate equation, the grain growth continuity equation was solved. The results show that there are an infinite number of 3D quasi-stationary grain size distributions. This conclusion has gained strong supports from results of different computer simulations reported in the literature.
Similar content being viewed by others
References
Feppon, J. M., Hutchinson, W. B., On the growth of grains, Acta Mater., 2002, 50: 3293–3300.
Liu Guoquan, Yu Haibo, Song Xiaoyan et al., A new model of three-dimensional grain growth: Theory and computer simulation of topology-dependency of individual grain growth rate, Materials and Design, 2001, 22:33–38.
Liu Guoquan, Yu Haibo, Qin Xiangge, Three-dimensional grain topology—size relationships in a real metallic polycrystal compared with theoretical models, Materials Science and Engineering A, 2002, 326 276–281.
Hillert, M., On the theory of normal and abnormal grain growth, Acta Metall., 1965, 13(3): 227–238.
Hillert, M., Analytical treatments of normal grain growth, Materials Science Forum, 1996, 202–206: 3–18.
Wagner, C., Thoerie der altering von neiderschlagen durch umlosen, Z. Elektrochem, 1961, 65: 581–591.
Brown, L. C., A new reexamination of classical coarsening theory, Acta Metall., 1989, 37(1): 71–77.
Coughlan, S. D., Fortes, M. A., Self-similar size distribution in particle coarsening, Scripta Metall. Mater., 1993, 28: 1471–1476.
Rios, P. R., Comparison between a computer simulated and an analytical grain size distribution, Scripta Mater., 1999, 40(6): 665–668.
Atkinson, H. V., Theories of normal grain growth in pure single phase system, Acta Metal., 1988, 36(3), 469–491.
Weygand, D., Brechet, Y., Three-dimensional grain growth A vertex dynamics simulation, Phil. Mag. B, 1999, 79(5): 703–716.
Wakai, F., Enomoto, N., Ogawa, H., Three-dimensional microstructural evolution in ideal grain growth—general statistics, Acta Mater., 2000, 48: 1297–1311.
Krill, III C. E., Chen, L. Q., Computer simulation of 3D grain growth using a phase-field model, Acta Mater., 2002, 50: 3057–3073.
Song Xiaoyan, Liu Guoquan, Gu Nanju, Re-analysis on grain size distribution during normal grain growth based on Monte Carlo simulation, Scripta Mater., 2000, 43: 355–359.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, C., Liu, G. Reanalysis of the 3D quasi-stationary grain size distribution based on Hillert's grain growth rate equation. Sci. China Ser. E-Technol. Sci. 47, 112–120 (2004). https://doi.org/10.1007/BF03037688
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03037688