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

Johannes Zimmer, Francesco Patacchini, Dietmar Hömberg, Kenichi Sakamoto

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Abstract

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.
Original languageEnglish
Pages (from-to)763-780
JournalIMA Journal of Applied Mathematics
Volume82
Issue number4
Early online date18 May 2017
DOIs
Publication statusPublished - 1 Aug 2017

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Grain Size
Ferrite
Steel
Crystal microstructure
Identification (control systems)
Nucleation
Fokker-Planck
Phase transitions
Parameter Identification
Growth Model
Mechanical properties
Mechanical Properties
Preparation
Phase Transition
Model
Prediction

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A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel. / Zimmer, Johannes; Patacchini, Francesco; Hömberg, Dietmar; Sakamoto, Kenichi.

In: IMA Journal of Applied Mathematics, Vol. 82, No. 4, 01.08.2017, p. 763-780.

Research output: Contribution to journalArticle

Zimmer, Johannes ; Patacchini, Francesco ; Hömberg, Dietmar ; Sakamoto, Kenichi. / A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel. In: IMA Journal of Applied Mathematics. 2017 ; Vol. 82, No. 4. pp. 763-780.
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