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A Quantitative Evaluation of Phase Field Microstructure by the Spectral Analysis

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Abstract

Two-phase microstructure calculated by Phase Field calculations is perturbed by Gaussian filtration processes to produce a series of deteriorated images. Fourier spectral analysis is, then, performed on the resultant images to derive information of spatial distribution of phases consisting of the microstructure. It is shown that Fourier spectrum is correlated with characteristic length involved in the microstructure. By inverting a particular spectrum peak, one can estimate the spatial distribution of a particular phase.

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References

  1. L.Q. Chen, Phase-Field Models for Microstructure Evolution, Annu. Rev. Mater. Res., 2002, 32, p 113-140

    Article  Google Scholar 

  2. Thermodynamics and Kinetics of Engineering Materials, papers presented at Hume Rothery Award Symposium, TMS 2014 Annual Meeting & Exhibition, Feb 17-19, 2014 (San Diego)

  3. N. Provatas and K. Elder, Phase-Field Methods in Materials Science and Engineering, Wiley-VCH, Weinheim, 2010

    Book  Google Scholar 

  4. I. Steinbach, Phase-field models in materials science, Model. Simul. Mater. Sci. Eng., 2009, 17, p 073001

    Article  ADS  MathSciNet  Google Scholar 

  5. H. Ramanarayan and T.A. Abinandanan, Phase Field Study of Grain Boundary Effects on Spinodal Decomposition, Acta Mater., 2003, 51, p 4761-4772

    Article  Google Scholar 

  6. S.Y. Hu and L.Q. Chen, A Phase-Field Model for Evolving Microstructures with Strong Elastic Inhomogeneity, Acta Mater., 2001, 49, p 1879-1890

    Article  Google Scholar 

  7. L. Proville and A. Finel, Kinetics of the Coherent Order-Disorder Transition in Al3Zr, Phys. Rev. B, 2001, 64, p 054104

    Article  ADS  Google Scholar 

  8. Y. Wang, D. Banerjee, C.C. Su, and A.G. Khachaturyan, Field Kinetic Model and Computer Simulation of Precipitation of L12 Ordered Intermetallics From f.c.c. Solid Solution, Acta Mater, 1998, 46, p 2983-3001

    Article  Google Scholar 

  9. T. Kitashima and H. Harada, A New Phase-Field Method for Simulating γ′ Precipitation in Multicomponent Nickel-Base Superalloys, Acta Mater., 2009, 57, p 2020-2028

    Article  Google Scholar 

  10. A. Yamanaka, T. Takaki, and Y. Tomita, Coupled Simulation of Microstructural Formation and Deformation Behavior of Ferrite-Pearlite Steel by Phase-Field Method and Homogenization Method, Mat. Sci. Eng. A, 2008, 480, p 244-252

    Article  Google Scholar 

  11. B.S. Fromm, K. Chang, D.L. McDowell, and L.-Q. Chen, Linking Phase-Field and Finite-Element Modeling for Process-Structure-Property Relations of a Ni-Base Superalloy, Acta Mater., 2012, 60, p 5984-5999

    Article  Google Scholar 

  12. A. Bruce and D. Wallace, Critical Point Phenomena: Universal Physics at Large Length Scales, The New Physics, P. Davies, Ed., Cambridge University Press, Cambridge, 1989, p 236-267

    Google Scholar 

  13. R. Kikuchi, A Theory of Cooperative Phenomena, Phys. Rev., 1951, 81, p 988-1003

    Article  ADS  MATH  MathSciNet  Google Scholar 

  14. T. Morita, Formal Structure of the Cluster Variation Method, Prog. Theor. Phys. Suppl., 1994, 115, p 27-39

    Article  ADS  Google Scholar 

  15. K. Tanaka and T. Morita, Cluster Variation Method and Image Restoration Problem, Phys. Lett. A, 1995, 203, p 122-128

    Article  ADS  Google Scholar 

  16. K. Tanaka and T. Morita, Application of the Cluster Variation Method to the Image Restoration Problem, Theory and Applications of the Cluster Variation and Path Probability Methods, J.L. Morán-López and J.M. Sanchez, Ed., Plenum, New York, 1996, p 353-373

    Chapter  Google Scholar 

  17. K. Iseya and T. Mohri, Quantitative Evaluation of Phase Field Microstructure Based on the Variational Principle, Mat. Trans., 2014, 55, p 489-492

    Google Scholar 

  18. T. Mohri and Y. Chen, Thermodynamics and Kinetics of Engineering Materials, presented at Hume Rothery Award Symposium, TMS 2014 Annual Meeting & Exhibition, Feb 17-19, 2014 (San Diego)

  19. G. Laschet, T. Kashko, S. Angel, J. Scheele, R. Nickel, W. Bleck, and K. Bobzin, Microstructure Based Model for Permeability Predictions of Open-Cell Metallic Foams Via Homogenization, Mater. Sci. Eng. A, 2008, 472, p 214-226

    Article  Google Scholar 

  20. H. Yao, T. Jifeng, and W. Zhongguang, Analysis of the Intergranular Fracture Surface by the Fourier Spectrum Method, Mat. Sci. Eng. A, 1991, 148, p 45-51

    Article  Google Scholar 

  21. Y. Wang and A.G. Khachaturyan, Shape Instability During Precipitate Growth in Coherent Solids, Acta Metal. Mater., 1995, 43, p 1837-1857

    Article  ADS  Google Scholar 

  22. M. Ohno, Ph.D dissertation, Grad. School of Engr., Hokkaido Univ., 2004

  23. J.W. Cahn and J.E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1958, 28, p 258

    Article  ADS  Google Scholar 

  24. S.M. Allen and J.W. Cahn, A Microscopic Theory for Antiphase Boundary Motion and its Application to Antiphase Domain Coarsening, Acta Metal., 1979, 27, p 1085-1095

    Article  Google Scholar 

  25. M.S. Nixon and A.S. Aguado, Feature Extraction & Image Processing, Academic Press, New York, 2008

    Google Scholar 

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Authors and Affiliations

  1. Division of Materials Science and Engineering, Graduate School of Engineering, Hokkaido University, Sapporo, 060-8628, Japan

    Kenji Iseya & Seiji Miura

  2. Center for Computational Materials Science, Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai, 980-8577, Japan

    Tetsuo Mohri

Authors
  1. Kenji Iseya
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  2. Seiji Miura
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  3. Tetsuo Mohri
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Corresponding author

Correspondence to Tetsuo Mohri.

Additional information

This article is an invited paper selected from presentations at the Hume-Rothery Award Symposium on “Thermodynamics and Kinetics of Engineering Materials,” during TMS 2014, held February 16-20, 2014, in San Diego, Calif., and has been expanded from the original presentation. This symposium was held in honor of the 2014 Hume-Rothery award recipient, Rainer Schmid-Fetzer, for his seminal contributions to alloy thermodynamics and phase diagrams, both computationally and experimentally.

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Iseya, K., Miura, S. & Mohri, T. A Quantitative Evaluation of Phase Field Microstructure by the Spectral Analysis. J. Phase Equilib. Diffus. 35, 788–793 (2014). https://doi.org/10.1007/s11669-014-0338-2

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  • DOI: https://doi.org/10.1007/s11669-014-0338-2

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