Elastically induced pattern formation in the initial and frustrated growth regime of bainitic subunits

Na Ta; Kai Wang; Xiaoyan Yin; Michael Fleck; Claas Hüter; Na Ta; Kai Wang; Xiaoyan Yin; Michael Fleck; Claas Hüter

doi:10.3934/matersci.2019.1.52

AIMS Materials Science

2019, Volume 6, Issue 1: 52-62. doi: 10.3934/matersci.2019.1.52

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Research article

Elastically induced pattern formation in the initial and frustrated growth regime of bainitic subunits

1.
Institut für Energie- und Klimaforschung IEK-2, Forschungszentrum Jülich, D-52425 Jülich, Germany
2.
Metals and Alloys, University Bayreuth, Ludwig-Thoma-Strae 36b, 95447 Bayreuth, Germany
3.
Jülich Aachen Reseach Alliance Energy, RWTH Aachen University, D-52056 Aachen, Germany

Received: 26 October 2018 Accepted: 16 January 2019 Published: 22 January 2019

We present analytical and numerical results for the dominant mechanisms of pattern selection in two growth regimes which are crucial in elastically influenced solid-solid transformations like the bainitic one. The first growth regime comprises the very early regime, when in a nucleation scenario the size of the nucleus is so small that the bulk crystal structure is typically not yet fully developed and the phase is elastically softened. Here we see a dominant effect of curvature effects in analogy to the theory on growth of lenticular melt inclusions. The second growth regime is of specific interest to bainitic steels. During the bainitic reaction subunits form, grow up to a point where the thermodynamic driving force is kinetically overcome by a deformation-induced growth barrier, stop growth and then nucleate new subunits. Thus, the regime prior to the new subunit nucleation corresponds to the limiting case of vanishing growth velocity. For both, analytical and numerical approach, we use sharp interface descriptions of the problem, for the numerical approach we invoke a representation of the problem in terms of boundary integral equations.
- bainite,
- sub-unit growth,
- Boundary Integral Method,
- bainitic transformation,
- carbon diffusion in bainitic transformations
Citation: Na Ta, Kai Wang, Xiaoyan Yin, Michael Fleck, Claas Hüter. Elastically induced pattern formation in the initial and frustrated growth regime of bainitic subunits[J]. AIMS Materials Science, 2019, 6(1): 52-62. doi: 10.3934/matersci.2019.1.52

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Abstract

We present analytical and numerical results for the dominant mechanisms of pattern selection in two growth regimes which are crucial in elastically influenced solid-solid transformations like the bainitic one. The first growth regime comprises the very early regime, when in a nucleation scenario the size of the nucleus is so small that the bulk crystal structure is typically not yet fully developed and the phase is elastically softened. Here we see a dominant effect of curvature effects in analogy to the theory on growth of lenticular melt inclusions. The second growth regime is of specific interest to bainitic steels. During the bainitic reaction subunits form, grow up to a point where the thermodynamic driving force is kinetically overcome by a deformation-induced growth barrier, stop growth and then nucleate new subunits. Thus, the regime prior to the new subunit nucleation corresponds to the limiting case of vanishing growth velocity. For both, analytical and numerical approach, we use sharp interface descriptions of the problem, for the numerical approach we invoke a representation of the problem in terms of boundary integral equations.

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