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Modeling the recrystallization process using inverse cellular automata and genetic algorithms: Studies using differential evolution

  • Basic And Applied Research
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Abstract

An inverse modeling approach was taken up in this work to model the process of recrystallization using cellular automata (CA). Using this method after formulating a CA model of recrystallization, differential evaluation (DE), a real-coded variant of genetic algorithms, was used to search for the value of nucleation rate, providing an acceptable matching between the theoretical and experimentally observed values of fraction-recrystallized (X). Initially, the inverse modeling was attempted with a simple CA strategy, in which each of the CA cells had an equal probability of becoming nucleated. DE searched for the value of the nucleation rate yielding the best results for single-crystal iron at 550 °C. A good match could not be simultaneously achieved this way for the early stages of recrystallization as well as for the later stages. To overcome this difficulty, the CA grid was divided into two zones, having lower and higher probabilities of nucleation. This resulted in good correspondence between the predicted and experimental values of X for the entire duration of recrystallization. The introduction of a distribution in the probability of nucleation made the model even closer to the actual process, in which the probability of nucleation is often nonuniform due to nonuniformity in dislocation density as well as the presence of grain/interface boundaries.

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References

  1. K.W. Mahin, K. Hanson, and J.W. Morris, Comparative-Analysis of the Cellular and Johnson-Mehl Microstructures Through Computer-Simulation, Acta Metall., Vol 28, 1980, p 443–453

    Article  Google Scholar 

  2. D.J. Srolovitz, G.A. Grest, and M.P. Anderson, Computer-Simulation of Recrystallization: 1. Homogeneous Nucleation and Growth, Acta Metall., Vol 34, 1986, p 1833–1845

    Article  Google Scholar 

  3. D.J. Srolovitz, G.A. Grest, M.P. Anderson, and A.D. Rollett, Computer-Simulation of Recrystallization: 2. Heterogeneous Nucleation and Growth, Acta Metall., Vol 36, 1989, p 2115–2128

    Google Scholar 

  4. K. Marthinsen, O. Lohne, and E. Nes, The Development of Recrystallization Microstructures Studied Experimentally and by Computer-Simulation. Acta Metall., Vol 37, 1989, p 135–145

    Article  Google Scholar 

  5. R.A. Vandermeer and B.B. Rath, Modeling Recrystallization Kinetics in a Deformed Iron Single-Crystal, Metall. Trans., Vol 20A, 1989, p 391–401

    Google Scholar 

  6. H.E. Vatne, T. Furu, R. Orsund, and E. Nes, Modelling Recrystallization After Hot Deformation of Aluminum, Acta Mater., Vol 44 (No. 11), 1996, p 4463–4473

    Article  Google Scholar 

  7. D. Juul Jensen, Modeling of Microstructure Development During Recrystallization Scr. Metall. Mater., Vol 27, 1992, p 1551–1556

    Article  Google Scholar 

  8. E. Woldt, New Kinetic Model for Primary Recrystallization of Pure Metals, Metall. Mater. Trans. A, Vol 32, 2001, p 2465–2473

    Article  Google Scholar 

  9. A.T.W. Kempen, F. Sommer, and E.J. Mittemeijer, Determination and Interpretation of Isothermal and Non-Isothermal Transformation Kinetics: The Effective Activation Energies in Terms of Nucleation and Growth, J. Mater. Sci., Vol 37, 2002, p 1321–1322

    Article  Google Scholar 

  10. H.W. Hesselbarth and I.R. Gobel, Simulation of Recrystallization by Cellular Automata, Acta Metall., Vol 39, 1991, p 2135–2143

    Article  Google Scholar 

  11. C.F. Pezzee and D.C. Dunand, The Impingement Effect of an Inert, Immobile 2nd Phase on the Recrystallization of a Matrix, Acta Metall. Mater., Vol 42, 1994, p 1509–1524

    Article  Google Scholar 

  12. C.H.J. Davies, The Effect of Neighborhood on the Kinetics of a Cellular-Automaton Recrystallization Model, Scr. Mater., Vol 33, 1995, p 1139–1143

    Article  Google Scholar 

  13. C.H.J. Davies, Growth of Nuclei in a Cellular Automaton Simulation of Recrystallisation, Scripta Mater., Vol 36, 1997, p 35–40

    Article  Google Scholar 

  14. R.L. Goetz and V. Seetharaman, Static Recrystallization Kinetics With Homogeneous and Heterogeneous Nucleation Using a Cellular Automata Model, Metall. Mater. Trans., Vol 29, 1998, p 2307–2321

    Article  Google Scholar 

  15. R.L. Goetz and V. Seetharaman, Modeling Dynamic Recrystallization Using Cellular Automata, Scr. Mater., Vol 38, 1998, p 405–413

    Article  Google Scholar 

  16. C. H. J. Davies and L. Hong, The Cellular Automaton Simulation of Static Recrystallization in Cold-Rolled AA1050, Scr. Mater., Vol 40, 1999, p 1145–1150

    Article  Google Scholar 

  17. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1999

    Google Scholar 

  18. N. Chakraborti, Genetic Algorithms in Ferrous Production Metallurgy, Surveys Math. Indust., Vol 10, 2002, p 269–291

    MATH  MathSciNet  Google Scholar 

  19. K. Price and R. Storn, Differential Evolution, Dr. Dobbs J., Vol 22, 1997, p 18

    Google Scholar 

  20. N. Chakraborti and A. Kumar, The Optimal Scheduling of a Reversing Strip Mill: Studies Using Multipopulation Genetic Algorithms and Differential Evolution, Mater. Manufact. Proc., Vol 18, 2003, p 433–445

    Article  Google Scholar 

  21. M. Mitchell, J.P. Crutchfield, and R. Das, Evolving Cellular Automata to Perform Computations, Handbook of Evolutionary Computation, T. Back, D.B. Fogel, and Z. Michalewicz, Ed., Institute of Physics Publishing, Bristol, and Oxford University Press, Oxford, 1997

    Google Scholar 

  22. S. Wolfram, Theory and Applications of Cellular Automata, World Scientific, Singapore, 1986

    MATH  Google Scholar 

  23. A. Ilachinski, Cellular Automata: A Discrete Universe, World Scientific, Singapore, 2001.

    MATH  Google Scholar 

  24. T. Toffoli and N. Margolus, Cellular Automata Machines: A New Environment for Modeling, MIT Press, Cambridge, MA, 1987.

    Google Scholar 

  25. S. Wolfram, A New Kind of Science, Wolfram Media Inc, Champaign, IL, 2002

    MATH  Google Scholar 

  26. B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems, Cambridge University Press, Cambridge, UK, 1998

    MATH  Google Scholar 

  27. M. Rapapaz, and C.A. Gandin, Probabilistic Modeling of Microstructure Formation in Solidification Processes, Acta Metall. Mater., Vol 41, 1993, p 345–360

    Article  Google Scholar 

  28. J.A. Spittle and S.G.R. Brown, A 3d Cellular-Automaton Model of Coupled Growth in 2-Component Systems, Acta Metall. Mater., Vol 42, 1994, p 1811–1815

    Article  Google Scholar 

  29. N. Chakraborti, P. Mishra, and Ş. Erkoç, A Study of the Cu Clusters Using Gray-Coded Genetic Algorithms and Differential Evolution, J. Phase Equlib. Diffusion, Vol 25, 2003, p 16–21

    Google Scholar 

  30. N. Chakraborti, P. Mishra, and A. Banerjee, Optimization of Aluminum Oxynitride Compaction Process Using a Gray-Coded Genetic Algorithm, Mater. Lett., Vol 58, 2004, p 136–141

    Article  Google Scholar 

  31. J.W. Christian, The Theory of Transformations in Metals and Alloys (Part-I), Pergamon, Oxford, UK, 2002

    Google Scholar 

  32. K. Deb, A.R. Reddy and G. Singh, Optimal Scheduling of Casting Sequence Using Genetic Algorithms, Mater. Manufact. Proc., Vol 18, 2003, p 409–432

    Article  Google Scholar 

  33. N. Chakraborti, Genetic Algorithms in Materials Design and Processing, Int. Mater, Rev., Vol 49, 2004, p 246–260

    Article  Google Scholar 

  34. D.D. Wang, A.K. Tieu, and G. D’Alessio, Computational Intelligence Based Process Optimization for Tandem Cold Rolling, Mater. Manufact. Proc., Vol 20, 2005, p 479–496

    Article  Google Scholar 

  35. R. Nandan, R. Rai, R. Jayakanth, S. Moitra, N. Chakraborti, and A. Mukhopadhyay, Regulating Crown and Flatness During Hot Rolling: A Multi-Objective Optimization Study Using Genetic Algorithms, Mater. Manufact. Proc., Vol 20, 2005, p 459–478

    Article  Google Scholar 

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Authors and Affiliations

  1. the Department of Mechanical Engineering, Indian Institute of Technology Bombay, 400 076, Powai, Mumbai, India

    Tushar D. Rane

  2. the Department of Mathematics and Computing, Indian Institute of Technology, 721 302, Kharagpur, India

    Rinku Dewri

  3. the Department of Metallurgical and Materials Engineering, Indian Institute of Technology, 721 302, Kharagpur, India

    Sudipto Ghosh & N. Chakraborti

  4. Manufacturing Industrial Practice, Tata Consultancy Service, 54B Hadapsar Industrial Estate, 411 013, Pune, India

    Kishalay Mitra

Authors
  1. Tushar D. Rane
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  2. Rinku Dewri
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  3. Sudipto Ghosh
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  4. N. Chakraborti
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  5. Kishalay Mitra
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Rane, T.D., Dewri, R., Ghosh, S. et al. Modeling the recrystallization process using inverse cellular automata and genetic algorithms: Studies using differential evolution. J Phs Eqil and Diff 26, 311–321 (2005). https://doi.org/10.1007/s11669-005-0080-x

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  • DOI: https://doi.org/10.1007/s11669-005-0080-x

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