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Combined Stochastic Diffusion and Mean-Field Model for Grain Growth

In: Computational Mechanics

Author

Listed:
  • Y. G. Zheng

    (Dalian University of Technology, State Key Laboratory of Structural Analysis of Industrial Equipment, Department of Engineering Mechanics)

  • H. W. Zhang

    (Dalian University of Technology, State Key Laboratory of Structural Analysis of Industrial Equipment, Department of Engineering Mechanics)

  • Z. Chen

    (Dalian University of Technology, State Key Laboratory of Structural Analysis of Industrial Equipment, Department of Engineering Mechanics
    University of Missouri-Columbia, Department of Civil and Environmental Engineering)

Abstract

A combined stochastic diffusion and mean-field model has been proposed to describe the grain growth in a single-phase material. A corresponding Fokker-Planck continuity equation was constructed and the interplay/competition of stochastic and curvature-driven mechanisms has also been investigated. Finite-difference results to the equation have shown that the dominative mechanism is stochastic diffusion of boundaries when the grains are smaller than several tens of nanometres. As the grains grow the influence of the deterministic curvature-driven mechanism increases and finally controls the process. The predicted grain size distribution accords to a log-normal function, which is in good agreement with experimental observations.

Suggested Citation

  • Y. G. Zheng & H. W. Zhang & Z. Chen, 2007. "Combined Stochastic Diffusion and Mean-Field Model for Grain Growth," Springer Books, in: Computational Mechanics, pages 234-234, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75999-7_34
    DOI: 10.1007/978-3-540-75999-7_34
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