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Dendritic Growth Under Natural and Forced Convection in Al-Cu Alloys: From Equiaxed to Columnar Dendrites and from 2D to 3D Phase-Field Simulations

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Abstract

The interaction between convection and solute transport during solidification has significant influence on the dendritic evolution. By employing the phase-field lattice-Boltzmann approach together with the parallel and adaptive-mesh-refinement algorithm, the dendritic evolution under convection is simulated in both 2D and 3D cases. The flow-induced redistribution of the solute alters both tip velocity and the development of dendritic arms. The effect of both convection and undercooling is quantified and compared using the length ratio of the dendritic arms. The effect of convection behavior (i.e., natural and forced) and domain dimension (i.e., 2D and 3D) on dendritic growth is discussed. Results show that the convection effect is mainly dominated by the convection mode, and the melt flow in 2D can produce biased results comparing with those in 3D.

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References

  1. J.A. Dantzig and M. Rappaz. Solidification, EPFL Press, Lausanne, 2009.

    Book  Google Scholar 

  2. N. Shevchenko, S. Boden, S. Eckert, and G. Gerbeth. Observation of segregation freckle formation under the influence of melt convection., in IOP Conference Series-Materials Science and Engineering, 2012.

  3. S. Wang, Z.P. Guo, X.P. Zhang, A. Zhang and J.W. Kang, Ultrason Sonochem, 2019, vol. 51, pp. 160-65.

    Article  Google Scholar 

  4. M. Zhang and T. Maxworthy, J Fluid Mech, 2002, vol. 470, pp. 247-68.

    Article  Google Scholar 

  5. L. Yuan and P.D. Lee: Model. Simul. Mater. Sci. Eng., 2010, vol. 18, art. id 055008.

    Article  Google Scholar 

  6. W.J. Boettinger, J.A. Warren, C. Beckermann and A. Karma, Annu Rev Mater Res, 2002, vol. 32, pp. 163–94.

    Article  Google Scholar 

  7. I. Steinbach: Simul. Mater. Sci. Eng., 2009, vol. 17, art. id 073001.

    Article  Google Scholar 

  8. X. Fan, A. Zhang, Z. Guo, X. Wang, J. Yang and J. Zou, J Mater Sci, 2019, vol. 54, pp. 2680-89.

    Article  Google Scholar 

  9. A. Zhang, J. Du, Z. Guo, Q. Wang and S. Xiong, Scripta Mater, 2019, vol. 165, pp. 64-67.

    Article  Google Scholar 

  10. D. Sun, M. Zhu, S. Pan and D. Raabe, Acta Mater, 2009, vol. 57, pp. 1755-67.

    Article  Google Scholar 

  11. M.F. Zhu and C.P. Hong, Isij Int, 2001, vol. 41, pp. 436-45.

    Article  Google Scholar 

  12. J. Du, Z. Guo, A. Zhang, M. Yang, M. Li, and S. Xiong: Sci. Rep., 2017, vol. 7, art. id 13600.

    Article  Google Scholar 

  13. J. Du, D. Xiao, B. Wen, R. Melnik and Y. Kawazoe, J. Phys. Chem. Lett., 2016, vol. 7, pp. 567-71.

    Article  Google Scholar 

  14. J. Du, A. Zhang, Z. Guo, M. Yang, M. Li, F. Liu and S. Xiong, J Alloy Compd, 2019, vol. 775, pp. 322-29.

    Article  Google Scholar 

  15. J. Du, A. Zhang, Z. Guo, M. Yang, M. Li and S. Xiong, Intermetallics, 2018, vol. 95, pp. 119-29.

    Article  Google Scholar 

  16. A Zhang, Z. Guo and S.M. Xiong, Phys. Rev. E, 2018, vol. 97, pp. 053302.

    Article  Google Scholar 

  17. A. Zhang, Z. Guo and S.M. Xiong, J. Appl. Phys., 2017, vol. 121, pp. 125101.

    Article  Google Scholar 

  18. J. Du, A. Zhang, Z. Guo, M. Yang, M. Li, F. Liu and S. Xiong, Acta Mater, 2018, vol. 161, pp. 35-46.

    Article  Google Scholar 

  19. J. Du, A. Zhang, Z. Guo, M. Yang, M. Li and S. Xiong, ACS Omega, 2017, vol. 2, pp. 8803-09.

    Article  Google Scholar 

  20. C. Chen, E. Bouchbinder and A. Karma, Nat. Phys., 2017, vol. 13, pp. 1186–90.

    Article  Google Scholar 

  21. Y. Lu, C. Beckermann and J.C. Ramirez, J Cryst Growth, 2005, vol. 280, pp. 320-34.

    Article  Google Scholar 

  22. X. Tong, C. Beckermann, A. Karma and Q. Li, Phys. Rev. E, 2001, vol. 63, pp. 061601.

    Article  Google Scholar 

  23. J. Jun-Ho, N. Goldenfeld and J.A. Dantzig, Phys. Rev. E, 2001, vol. 64, pp. 041602.

    Article  Google Scholar 

  24. C.W. Lan and C.J. Shih, J Cryst Growth, 2004, vol. 264, pp. 472-82.

    Article  Google Scholar 

  25. C.W. Lan, C.M. Hsu, C.C. Liu and Y.C. Chang, Phys. Rev. E, 2002, vol. 65, pp. 061601.

    Article  Google Scholar 

  26. Z. Guo, J. Mi, S. Xiong and P.S. Grant, J Comput Phys, 2014, vol. 257, pp. 278-97.

    Article  Google Scholar 

  27. X. Zhang, J. Kang, Z. Guo, S. Xiong and Q. Han, Comput Phys Commun, 2018, vol. 223, pp. 18-27.

    Article  Google Scholar 

  28. Zhang, J. Du, Z. Guo, Q. Wang and S. Xiong, Metallurgical and Materials Transactions B, 2018, vol. 49, pp. 3603-15.

    Article  Google Scholar 

  29. T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva and E.M. Viggen. The Lattice Boltzmann Method Principles and Practice, Springer, Cham, Switzerland, 2017.

    Book  Google Scholar 

  30. W. Miller, S. Succi and D. Mansutti, Phys Rev Lett, 2001, vol. 86, pp. 3578-81.

    Article  Google Scholar 

  31. D. Medvedev, T. Fischaleck and K. Kassner, Phys. Rev. E, 2006, vol. 74, pp. 031606.

    Article  Google Scholar 

  32. T. Takaki, R. Rojas, S. Sakane, M. Ohno, Y. Shibuta, T. Shimokawabe and T. Aoki, J Cryst Growth, 2017, vol. 474, pp. 146-53.

    Article  Google Scholar 

  33. S. Sakane, T. Takaki, M. Ohno, Y. Shibuta, T. Shimokawabe and T. Aoki, J Cryst Growth, 2018, vol. 483, pp. 147-55.

    Article  Google Scholar 

  34. M. Eshraghi, M. Hashemi, B. Jelinek and S.D. Felicelli, Metals-Basel, 2017, vol. 7, pp. 474-95.

    Google Scholar 

  35. Z. Guo and S.M. Xiong, Comput Phys Commun, 2015, vol. 190, pp. 89-97.

    Article  Google Scholar 

  36. J. Du, A. Zhang, Z. Guo, M. Yang, M. Li and S. Xiong, Phys. Rev. Mater. 2018, vol. 2, pp. 083402.

    Article  Google Scholar 

  37. J.C. Ramirez, C. Beckermann, A. Karma and H.J. Diepers, Phys. Rev. E, 2004, vol. 69, pp. 051607.

    Article  Google Scholar 

  38. Karma, Phys Rev Lett, 2001, vol. 87, pp. 115701.

    Article  Google Scholar 

  39. Zhang, Z. Guo and S. Xiong, China Foundry, 2017, vol. 14, pp. 373-78.

    Article  Google Scholar 

  40. Z. Guo, C. Zheng and B. Shi, Phys. Rev. E, 2002, vol. 65, pp. 046308.

    Article  Google Scholar 

  41. C. Beckermann, H.J. Diepers, I. Steinbach, A. Karma and X. Tong, J. Comput. Phys., 1999, vol. 154, pp. 468-96.

    Article  Google Scholar 

  42. A. Zhang, J. Du, Z. Guo and S. Xiong, Phys. Rev. E, 2018, vol. 98, pp. 043301.

    Article  Google Scholar 

  43. Zhang, J. Du, Z. Guo, Q. Wang and S. Xiong, Metall. Mater. Trans. B, 2019, vol. 50, pp. 517-30.

    Article  Google Scholar 

  44. R.S. Maier, R.S. Bernard and D.W. Grunau, Phys Fluids, 1996, vol. 8, pp. 1788-801.

    Article  Google Scholar 

  45. R. Tönhardt and G. Amberg, Phys Rev E, 2000, vol. 62, pp. 828-36.

    Article  Google Scholar 

  46. C.J. Vreeman and F.P. Incropera, Int. J. Heat Mass Trans., 2000, vol. 43, pp. 687-704.

    Article  Google Scholar 

  47. N. Shevchenko, O. Roshchupkina, O. Sokolova and S. Eckert, J. Cryst. Growth, 2015, vol. 417, pp. 1-8.

    Article  Google Scholar 

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Acknowledgments

This work was financially supported by the Joint Funds of the National Natural Science Foundation of China (Grant Number U1537202), the Tsinghua-General Motors International Collaboration Project (Grant Number 20153000354), the Tsinghua University Initiative Scientific Research Program (Grant Number 20151080370), and the Tsinghua Qingfeng Scholarship (THQF-2015). The authors would also like to thank the National Laboratory for Information Science and Technology in Tsinghua University for access to supercomputing facilities.

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Authors and Affiliations

  1. School of Materials Science and Engineering, Tsinghua University, Beijing, 100084, China

    Ang Zhang, Shaoxing Meng, Zhipeng Guo, Jinglian Du & Shoumei Xiong

  2. Materials Technology, GM Global Propulsion Systems, Pontiac, MI, 48340-2920, USA

    Qigui Wang

  3. Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Tsinghua University, Beijing, 100084, China

    Shoumei Xiong

Authors
  1. Ang Zhang
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  2. Shaoxing Meng
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  3. Zhipeng Guo
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  4. Jinglian Du
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Correspondence to Zhipeng Guo or Shoumei Xiong.

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Manuscript submitted December 5, 2018.

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Zhang, A., Meng, S., Guo, Z. et al. Dendritic Growth Under Natural and Forced Convection in Al-Cu Alloys: From Equiaxed to Columnar Dendrites and from 2D to 3D Phase-Field Simulations. Metall Mater Trans B 50, 1514–1526 (2019). https://doi.org/10.1007/s11663-019-01549-5

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