A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel
File(s)grain_distribution.pdf (4.61 MB)
Accepted version
Author(s)
Homberg, D
Patacchini, F
Sakamoto, K
Zimmer, J
Type
Journal Article
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 mul-
tiphase 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 dis-
tributions with area distributions experimentally gained from polished micrograph sections.
models of diffusive phase transitions is revisited and applied to model the growth of ferrite in mul-
tiphase 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 dis-
tributions with area distributions experimentally gained from polished micrograph sections.
Date Issued
2017-05-18
Date Acceptance
2017-04-20
Citation
IMA Journal of Applied Mathematics, 2017, 82 (4), pp.763-780
ISSN
0272-4960
Publisher
Oxford University Press (OUP)
Start Page
763
End Page
780
Journal / Book Title
IMA Journal of Applied Mathematics
Volume
82
Issue
4
Copyright Statement
© The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copy-editing, author-produced version of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version is available online at: https://academic.oup.com/imamat/article/3832242
Subjects
0102 Applied Mathematics
Applied Mathematics
Publication Status
Published