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A Three-Dimensional Cellular Automata Model Coupling Energy and Curvature-Driven Mechanisms for Austenitic Grain Growth

  • Topical Collection: Physical and Numerical Simulations of Materials Processing
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Abstract

A 3D cellular automata model is used to simulate normal austenitic grain growth in this study. The proposed model considers both the curvature- and thermodynamics-driven mechanisms of growth. The 3D grain growth kinetics shows good agreement with the Beck equation. Moreover, the growth exponent and grain size distribution calculated by the proposed model coincides well with experimental and simulation results from other researchers. A linear relationship is found between the average relative grain size and the grain face number. More specifically, for average relative grain sizes exceeding ~0.5, the number of faces increases linearly with relative grain size. For average relative grain sizes <0.5, this relationship is changed. Results simulated by the proposed model are translated to physical meaning by adjusting the actual temperature, space, and time for austenitic grain growth. The calibrated results are found to be in agreement with the simulation results from other research as well as the experimental results. By means of calibration of the proposed model, we can reliably predict the grain size in actual grain growth.

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References

  1. Anderson MP, Srolovitz DJ, Grest GS, Sahni PS. Acta metallurgica. 1984 vol. 32(5), pp. 783-91.

    Article  Google Scholar 

  2. Srolovitz DJ, Anderson MP, Sahni PS, Grest GS. Acta metallurgica. 1984 vol. 32(5), pp. 793-802.

    Article  Google Scholar 

  3. Srolovitz DJ, Anderson MP, Grest GS, Sahni PS. Acta metallurgica. 1984 vol. 32(9), pp. 1429-38.

    Article  Google Scholar 

  4. Ankit K, Choudhury A, Qin C, Schulz S, McDaniel M, Nestler B. Acta Mater. 2013 vol. 61(11), pp. 4245-53.

    Article  Google Scholar 

  5. Zheng C, Raabe D, Li D. Acta Mater. 2012 vol. 60(12), pp. 4768-79.

    Article  Google Scholar 

  6. Steinbach I. Model Simul Mater Sc. 2009 vol. 17(7), pp. 73001.

  7. Caleyo F, Baudin T, Penelle R. Scripta Mater. 2002 vol. 46(12), pp. 829-35.

    Article  Google Scholar 

  8. Takaki T, Yamanaka A, Higa Y, Tomita Y. Journal of Computer-Aided Materials Design. 2007 vol. 14(1), pp. 75-84.

    Article  Google Scholar 

  9. D. Raabe and R.C. Becker: Model Simul Mater Sc. 2000 vol. 8(4), pp. 445.

  10. Vertyagina Y, Mahfouf M. J Mater Sci. 2015 vol. 50(2), pp. 745-54.

    Article  Google Scholar 

  11. Ko K, Rollett AD, Hwang N. Acta Mater. 2010 vol. 58(13), pp. 4414-23.

    Article  Google Scholar 

  12. Rudnizki J, Zeislmair B, Prahl U, Bleck W. Comp Mater Sci. 2010 vol. 49(2), pp. 209-16.

    Article  Google Scholar 

  13. Ivasishin OM, Shevchenko SV, Semiatin SL. Scripta Mater. 2004 vol. 50(9), pp. 1241-45.

    Article  Google Scholar 

  14. Hallberg H. Metals. 2011 vol. 1(1), pp. 16-48.

    Article  Google Scholar 

  15. Krill Iii CE, Chen L. Acta Mater. 2002 vol. 50(12), pp. 3059-75.

    Article  Google Scholar 

  16. Hesselbarth HW, Göbel IR. Acta Metallurgica et Materialia. 1991 vol. 39(9), pp. 2135-43.

    Article  Google Scholar 

  17. Ding HL, He YZ, Liu LF, Ding WJ. J Cryst Growth. 2006 vol. 293(2), pp. 489-97.

    Article  Google Scholar 

  18. An D, Pan S, Huang L, Dai T, Krakauer B, Zhu M. ISIJ Int. 2014 vol. 54(2), pp. 422-29.

    Article  Google Scholar 

  19. R. Golab, D. Bachniak, K. Bzowski, and L. Madej: Appl. Math., 2013, vol. 4(11), p. 1531.

  20. Zheng C, Raabe D. Acta Mater. 2013 vol. 61(14), pp. 5504-17.

    Article  Google Scholar 

  21. Y.J. Lan, D.Z. Li, C.J. Huang and Y. Y. Li: Model. Simul. Mater., Sci., 2004, vol. 12(4), pp. 719.

  22. Kumar M, Sasikumar R, Nair PK. Acta Mater. 1998 vol. 46(17), pp. 6291-303.

    Article  Google Scholar 

  23. Wang C, Liu G, Wang G, Xue W. Materials Science and Engineering: A. 2007 vol. 454, pp. 547-51.

    Article  Google Scholar 

  24. Wejrzanowski T, Batorski K, Kurzydłowski KJ. Mater Charact. 2006 vol. 56(4), pp. 336-39.

    Article  Google Scholar 

  25. Vertyagina Y, Mahfouf M, Xu X. J Mater Sci. 2013 vol. 48(16), pp. 5517-27.

    Article  Google Scholar 

  26. Raabe D. Annu Rev Mater Res. 2002 vol. 32(1), pp. 53-76.

    Article  Google Scholar 

  27. Zhao Y, Chen D, Long M, Arif TT, Qin R. Metallurgical and Materials Transactions B. 2014 vol. 45(2), pp. 719-25.

    Article  Google Scholar 

  28. Natsume Y, Ohsasa K. ISIJ Int. 2014 vol. 54(2), pp. 415-21.

    Article  Google Scholar 

  29. Kamachali RD, Steinbach I. Acta Mater. 2012 vol. 60(6), pp. 2719-28.

    Article  Google Scholar 

  30. Chen R, Xu Q, Liu B. Comp Mater Sci. 2015 vol. 105, pp. 90-100.

    Article  Google Scholar 

  31. D.S. Svyetlichnyy: Model. Simul. Mater. Sci., 2014, vol. 22(8), pp. 85001.

  32. Han F, Tang B, Kou H, Cheng L, Li J, Feng Y. J Mater Sci. 2014 vol. 49(8), pp. 3253-67.

    Article  Google Scholar 

  33. Lee HW, Im Y. Int J Mech Sci. 2010 vol. 52(10), pp. 1277-89.

    Article  Google Scholar 

  34. Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D. Acta Mater. 2010 vol. 58(4), pp. 1152-211.

    Article  Google Scholar 

  35. Raabe D. Acta Mater. 2004 vol. 52(9), pp. 2653-64.

    Article  Google Scholar 

  36. Xiao N, Zheng C, Li D, Li Y. Comp Mater Sci. 2008 vol. 41(3), pp. 366-74.

    Article  Google Scholar 

  37. Chen F, Cui Z, Liu J, Chen W, Chen S. Materials Science and Engineering: A. 2010 vol. 527(21), pp. 5539-49.

    Article  Google Scholar 

  38. Wang M, Yin Y, Zhou J, Nan H, Wang T, Li W. Can J Phys. 2016 vol. 94(12), pp. 1353-64.

    Article  Google Scholar 

  39. Raghavan S, Sahay SS. Comp Mater Sci. 2009 vol. 46(1), pp. 92-99.

    Article  Google Scholar 

  40. Hua F, Yang Y, Guo D, Tong W, Hu Z. ACTA METALLURGICA SINICA-CHINESE EDITION-. 2004 vol. 40, pp. 1210-14.

    Google Scholar 

  41. Fan D, Geng C, Chen L. Acta Mater. 1997 vol. 45(3), pp. 1115-26.

    Article  Google Scholar 

  42. Chen L. Scripta Metallurgica et Materialia. 1995 vol. 32(1), pp. 115-20.

    Article  Google Scholar 

  43. Feltham P. Acta metallurgica. 1957 vol. 5(2), pp. 97-105.

    Article  Google Scholar 

  44. MacPherson RD, Srolovitz DJ. Nature. 2007 vol. 446(7139), pp. 1053-55.

    Article  Google Scholar 

  45. Rios PR, Glicksman ME. Acta Mater. 2007 vol. 55(5), pp. 1565-71.

    Article  Google Scholar 

  46. P.A. Beck, M.L. Holzworth, and H. Hu: Phys. Rev. 1948 vol. 73(5), pp. 526.

  47. Petrovic V, Ristic MM. Metallography. 1980 vol. 13(4), pp. 319-27.

    Article  Google Scholar 

  48. Grey EA, Higgins GT. Acta Metallurgica. 1973 vol. 21(4), pp. 309-21.

    Article  Google Scholar 

  49. Hu H, Rath BB. Metallurgical Transactions. 1970 vol. 1(11), pp. 3181-84.

    Google Scholar 

  50. Zhou T, O Malley RJ, Zurob HS. Metallurgical and Materials Transactions A. 2010 vol. 41(8), pp. 2112-20.

    Article  Google Scholar 

  51. Vandermeer RA, Hu H. Acta Metallurgica et Materialia. 1994 vol. 42(9), pp. 3071-75.

    Article  Google Scholar 

  52. W. Yu: Cellular Automata Modelling of Austenite Grain Coarsening During Reheating. University of Sheffield, 2002.

  53. Moon J, Lee J, Lee C. Materials Science and Engineering: A. 2007 vol. 459(1), pp. 40-46.

    Article  Google Scholar 

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Acknowledgments

This research was financially supported by the National Natural Science Foundation of China (No. 51305149), and the National Science & Technology Key Projects of Numerical Control (2012ZX04012-011). The authors are also grateful to the Investment Casting Collaborating Laboratory on Advanced Lightweight Alloy Materials.

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Authors and Affiliations

  1. State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Min Wang, Jianxin Zhou, Yajun Yin, Dongqiao Zhang & Zhixin Tu

  2. Beijing Institute of Aeronautical Materials, Aviation Industry of China, Beijing, 100095, China

    Min Wang & Hai Nan

Authors
  1. Min Wang
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  2. Jianxin Zhou
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  3. Yajun Yin
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  4. Hai Nan
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  5. Dongqiao Zhang
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Corresponding authors

Correspondence to Jianxin Zhou or Yajun Yin.

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Manuscript submitted November 21, 2016.

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Wang, M., Zhou, J., Yin, Y. et al. A Three-Dimensional Cellular Automata Model Coupling Energy and Curvature-Driven Mechanisms for Austenitic Grain Growth. Metall Mater Trans B 48, 2245–2255 (2017). https://doi.org/10.1007/s11663-017-1041-6

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  • DOI: https://doi.org/10.1007/s11663-017-1041-6

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