WIAS Preprint No. 2283, (2016)

A revisited Johnson--Mehl--Avrami--Kolmogorov model and the evolution of grain-size distributions in steel


  • Hömberg, Dietmar
  • Patacchini, Francesco Saverio
  • Sakamoto, Kenichi
  • Zimmer, Johannes

2010 Mathematics Subject Classification

  • 35Q84 35Q74 35K10 74H40


  • grain size distribution, Fokker-Planck equation, nucleation and growth, phase transitions


The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker-Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studies are given and confirm expected properties qualitatively. As a preparation for future work on parameter identification, a strategy is presented for the comparison of volume distributions with area distributions experimentally gained from polished micrograph sections.

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