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Author: Sakamoto, Kenichi × DDC: 510 ×

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    A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hömberg, Dietmar; Patacchini, Francesco Saverio; Sakamoto, Kenichi; Zimmer, Johannes
    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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    Parameter identification in non-isothermal nucleation and growth processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hömberg, Dietmar; Lu, Shuai; Sakamoto, Kenichi; Yamamoto, Masahiro
    We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.