Interaction and multiscale mechanics

  • 제1권3호
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  • Pages.369-379
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  • 2008
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
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DOI QR Code

A combined stochastic diffusion and mean-field model for grain growth

  • Zheng, Y.G. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology) ;
  • Zhang, H.W. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology) ;
  • Chen, Z. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology)
  • 투고 : 2008.01.30
  • 심사 : 2008.07.08
  • 발행 : 2008.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J $m^{-2}$ in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

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참고문헌

  1. Atkinson, H.V. (1988), "Theories of normal grain growth in pure single phase systems", Acta Metall., 36, 469-491. https://doi.org/10.1016/0001-6160(88)90079-X
  2. Gusak, A.M. and Tu, K.N. (2003), "Theory of normal grain growth in normalized size space", Acta Mater., 51, 3895-3904. https://doi.org/10.1016/S1359-6454(03)00214-3
  3. Helfen, L., Wu, D.T., Birringer, R. and Krill, C.E. (2003), "The impact of stochastic atomic jumps on the kinetics of curvature-driven grain growth", Acta Mater., 51, 2743-2754. https://doi.org/10.1016/S1359-6454(03)00010-7
  4. Lifshitz, I.M. and Slyozov, V.V. (1961), "The kinetics of precipitation from supersaturated solid solutions", J. Phys. Chem. Solids, 19, 35-50. https://doi.org/10.1016/0022-3697(61)90054-3
  5. Mulheran, P.A. and Harding, J.H. (1992), "A statistical theory of normal grain growth", Mater. Sci. Forum, 94-96, 367-372. https://doi.org/10.4028/www.scientific.net/MSF.94-96.367
  6. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery B.P. (1992), Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 2nd ed., Cambridge.
  7. Tjong, S.C. and Chen, H. (2004), "Nanocrystalline materials and coatings", Mater. Sci. Eng. R, 45, 1-88. https://doi.org/10.1016/j.mser.2004.07.001
  8. Zhang, C., Suzuki, A., Ishimaru, T. and Enomoto, M. (2004), "Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning", Metall. Mater. Trans., 35, 1927-1933. https://doi.org/10.1007/s11661-004-0141-5
  9. Zheng, Y.G., Lu, C., Mai, Y-W., Gu, Y.X., Zhang, H.W. and Chen, Z. (2006a), "Monte Carlo simulation of grain growth in two-phase nanocrystalline materials", Appl. Phys. Lett., 88, 144103(1-3). https://doi.org/10.1063/1.2192151
  10. Zheng, Y.G., Lu, C., Mai, Y-W., Zhang, H.W. and Chen, Z. (2006b), "Grain growth as a stochastic and curvature-driven process", Phil. Mag. Lett., 86, 787-794. https://doi.org/10.1080/09500830601042357