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Journal of Materials Science

, Volume 53, Issue 21, pp 15165–15180 | Cite as

Correlation between three-dimensional and cross-sectional characteristics of ideal grain growth: large-scale phase-field simulation study

  • Eisuke Miyoshi
  • Tomohiro Takaki
  • Munekazu Ohno
  • Yasushi Shibuta
  • Shinji Sakane
  • Takashi Shimokawabe
  • Takayuki Aoki
Computation

Abstract

Grain growth is one of the most fundamental phenomena affecting the microstructure of polycrystalline materials. In experimental studies, three-dimensional (3D) grain growth is usually investigated by examining two-dimensional (2D) cross sections. However, the extent to which the 3D microstructural characteristics can be obtained from cross-sectional observations remains unclear. Additionally, there is some disagreement as to whether a cross-sectional view of 3D grain growth can be fully approximated by 2D growth. In this study, by employing the multi-phase-field method and parallel graphics processing unit computing on a supercomputer, we perform large-scale simulations of 3D and 2D ideal grain growth with approximately three million initial grains. This computational scale supports the detailed comparison of 3D, cross-sectional, and 2D grain structures with good statistical reliability. Our simulations reveal that grain growth behavior in a cross section is very different from those in 3D and fully 2D spaces, in terms of the average and distribution of the grain sizes, as well as the growth kinetics of individual grains. On the other hand, we find that the average grain size in 3D can be estimated as being around 1.2 times that observed in a cross section, which is in good agreement with classical theory in the stereology. Furthermore, based on the Saltykov–Schwartz method, we propose a predictive model that can estimate the 3D grain size distribution from the cross-sectional size distribution.

Notes

Acknowledgements

This research was supported by Grant-in-Aid for Scientific Research (B) (No. 16H04490) and for JSPS Fellows (No. 17J06356) from the Japan Society for the Promotion of Science (JSPS), the Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures, and the High Performance Computing Infrastructure in Japan (Project ID: jh170018-NAH), and MEXT as a social and scientific priority issue (Creation of new functional devices and high-performance materials to support next-generation industries) to be tackled using the post-K computer.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10853_2018_2680_MOESM1_ESM.mp4 (7.3 mb)
Supplementary material 1 (MP4 7460 kb)
10853_2018_2680_MOESM2_ESM.mp4 (13.9 mb)
Supplementary material 2 (MP4 14274 kb)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Eisuke Miyoshi
    • 1
  • Tomohiro Takaki
    • 2
  • Munekazu Ohno
    • 3
  • Yasushi Shibuta
    • 4
  • Shinji Sakane
    • 1
  • Takashi Shimokawabe
    • 5
  • Takayuki Aoki
    • 6
  1. 1.Graduate School of Science and TechnologyKyoto Institute of TechnologyKyotoJapan
  2. 2.Faculty of Mechanical EngineeringKyoto Institute of TechnologyKyotoJapan
  3. 3.Division of Materials Science and Engineering, Faculty of EngineeringHokkaido UniversitySapporoJapan
  4. 4.Department of Materials EngineeringThe University of TokyoTokyoJapan
  5. 5.The Supercomputing Division, Information Technology CenterThe University of TokyoTokyoJapan
  6. 6.Global Scientific Information and Computing CenterTokyo Institute of TechnologyTokyoJapan

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