Ti6Al4V is a widely used, multi-component alloy in additive manufacturing, during which the fluid flow in the molten pool significantly affects the solidified dendrites. To predict and further control the microstructure, modeling and simulating the microstructure evolution play a critical role. In this study, a newly developed, efficient, quantitative multi-component phase-field (PF) model is coupled with a lattice Boltzmann (LB) model to simulate Ti6Al4V solidified dendrite evolution under fluid flow. The accuracy and convergence behavior of the model is validated by the Gibbs–Thomson relation at the dendrite tip. Single and multiple two-dimensional (2D) equiaxed dendrite evolution cases under forced flow were simulated. Results show that the dendrite pattern is influenced remarkably by the fluid flow. Underlying mechanisms of the asymmetrical evolution are revealed by discussing the interaction among the flow, composition distribution and dendrite morphology, quantitatively. The dendrite kinetics are also derived, which ascertains the relationship between tip velocity and undercooling and inlet velocity and is the foundation for larger-scale simulation. We believe that the coupled quantitative multi-component PF–LB framework employed in this study helps in investigating the solidified dendrite morphology evolution in a deep and quantitate manner.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
C. Leyens and M. Peters, Titanium and titanium alloys: fundamentals and applications, John Wiley & Sons, 2003.
2. T. DebRoy, H. L. Wei, J. S. Zuback, T. Mukherjee, J. W. Elmer, J. O. Milewski, A. M. Beese, A. Wilson-Heid, A. De and W. Zhang, Progress in Materials Science, 2018, 92, 112-224.
3. B. E. Carroll, T. A. Palmer and A. M. Beese, Acta Materialia, 2015, 87, 309-320.
4. Y. Ren, X. Lin, X. Fu, H. Tan, J. Chen and W. Huang, Acta Materialia, 2017, 132, 82-95.
5. A. Yamanaka, T. Aoki, S. Ogawa and T. Takaki, Journal of Crystal Growth, 2011, 318, 40-45.
6. W. Sun, R. Yan, Y. Zhang, H. Dong and T. Jing, Computational Materials Science, 2019, 160, 149-158.
7. N. Provatas, N. Goldenfeld and J. Dantzig, Physical Review Letters, 1998, 80, 3308-3311.
8. Y. Xie, H. Dong, J. Liu, R. L. Davidchack, J. A. Dantzig, G. Duggan, M. Tong and D. J. Browne, Journal of Algorithms & Computational Technology, 2013, 7, 489-507.
9. H. L. Wei, J. W. Elmer and T. DebRoy, Acta Materialia, 2017, 126, 413-425.
10. S. Chen, G. Guillemot and C.-A. Gandin, Acta Materialia, 2016, 115, 448-467.
11. X. Li and W. Tan, Computational Materials Science, 2018, 153, 159-169.
12. O. Zinovieva, A. Zinoviev and V. Ploshikhin, Computational Materials Science, 2018, 141, 207-220.
13. W. Kurz, B. Giovanola and R. Trivedi, Acta metallurgica, 1986, 34, 823-830.
14. H. Xing, X. Dong, J. Wang and K. Jin, Metallurgical and Materials Transactions B, 2018, 49, 1547-1559.
15. W.-z. Sun, R. Yan, X. Wan, H.-b. Dong and T. Jing, China Foundry, 2018, 15, 422-427.
16. D. Sun, M. Zhu, S. Pan and D. Raabe, Acta Materialia, 2009, 57, 1755-1767.
17. A. Karma, Physical Review Letters, 2001, 87, 115701.
18. B. Echebarria, R. Folch, A. Karma and M. Plapp, Physical Review E, 2004, 70, 061604.
19. B. Nestler, H. Garcke and B. Stinner, Physical Review E, 2005, 71, 041609.
20. S. G. Kim, Acta Materialia, 2007, 55, 4391-4399.
21. P. Liu, Y. Ji, Z. Wang, C. Qiu, A. Antonysamy, L.-Q. Chen, X. Cui and L. Chen, Journal of Materials Processing Technology, 2018, 257, 191-202.
22. S. Sahoo and K. Chou, Additive manufacturing, 2016, 9, 14-24.
23. X. Gong and K. Chou, Jom, 2015, 67, 1176-1182.
Y. Xie, University of Leicester, 2013.
25. M. Ohno and K. Matsuura, Physical Review E, 2009, 79, 031603.
26. T. Mukherjee, W. Zhang and T. DebRoy, Computational Materials Science, 2017, 126, 360-372.
27. J.-H. Jeong, N. Goldenfeld and J. A. Dantzig, Physical Review E, 2001, 64, 041602.
28. T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva and E. M. Viggen, Springer International Publishing, 2017, 10, 978-973.
29. M. Ohno, Physical Review E, 2012, 86, 051603.
30. S. G. Kim, W. T. Kim and T. Suzuki, Physical Review E, 1999, 60, 7186-7197.
31. C. Beckermann, H.-J. Diepers, I. Steinbach, A. Karma and X. Tong, Journal of Computational Physics, 1999, 154, 468-496.
N. Provatas and K. Elder, Phase-field methods in materials science and engineering, John Wiley & Sons, 2011.
33. A. Cartalade, A. Younsi and M. Plapp, Computers & Mathematics with Applications, 2016, 71, 1784-1798.
34. D. Sun, H. Xing, X. Dong and Y. Han, International Journal of Heat and Mass Transfer, 2019, 133, 1240-1250.
35. V. G. Ivanchenko, O. M. Ivasishin and S. L. Semiatin, Metallurgical and Materials Transactions B, 2003, 34, 911-915.
36. A. R. A. Dezfoli, W.-S. Hwang, W.-C. Huang and T.-W. Tsai, Scientific reports, 2017, 7, 41527.
37. W. S. Ping, L. D. Rong, G. J. Jie, L. C. Yun, S. Y. Qing and F. H. Zhi, Materials Science and Engineering: A, 2006, 426, 240-249.
38. J. C. Ramirez and C. Beckermann, Acta Materialia, 2005, 53, 1721-1736.
39. J. Li, Z. Wang, Y. Wang and J. Wang, Acta Materialia, 2012, 60, 1478-1493.
This research is financially supported by the National Key Research and Development Program of China No. 2017YFB1103700, the National Science Foundation of China Nos. 51575304 and 51674153.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Manuscript submitted April 22, 2019.
Electronic supplementary material
Below is the link to the electronic supplementary material.
About this article
Cite this article
Sun, W., Xie, Y., Yan, R. et al. A New Efficient Quantitative Multi-component Phase Field: Lattice Boltzmann Model for Simulating Ti6Al4V Solidified Dendrite Under Forced Flow. Metall Mater Trans B 50, 2487–2497 (2019). https://doi.org/10.1007/s11663-019-01669-y