The Morphology and Solute Segregation of Dendrite Growth in Ti-4.5% Al Alloy: A Phase-Field Study
Abstract
:1. Introduction
2. Phase-Field Model and Simulation Parameters
2.1. Phase-Field Model
2.2. Initial Conditions and Boundary Conditions
2.3. Other Parameters
3. Simulation Results and Discussions
3.1. Morphology of Equiaxed Dendrite Growth in Ti-Al Alloy
3.2. The Effect of Supersaturation on Dendrite Morphology
3.3. The Influence of Undercooling on Dendrite Morphology
3.4. The Influence of Thermal Disturbance on Dendrite Morphology
4. Conclusions
- (1)
- As the solidification process progresses, the first dendrite with tips and valleys is formed, and then the secondary dendrite arms begin to grow rapidly, making the dendrite morphology more complicated and having many small protrusions. When the secondary dendrite arms become coarse, the tertiary dendrite arms form and grow rapidly, and the morphology becomes more complex. Pores are formed between the secondary dendrite arms, and solute segregation is formed.
- (2)
- As the supersaturation increases, the growth rate of dendrite becomes faster, the morphology of secondary dendrite arms is developed, the morphology is complex, the dendrite necking disappears, and the solute segregation becomes more serious. As the supersaturation increases, the steady-state coefficient of the dendrite will decrease.
- (3)
- As the undercooling increases, the growth rate of dendrite accelerates, and the solute concentration in the roots of dendrite during the undercooling process is serious.
- (4)
- As the thermal disturbance increases, the influence on the morphology of the primary dendrite arms becomes smaller, and the asymmetry of the secondary dendrite arms increases significantly. When the solute segregation is serious, the thermal disturbance will not affect the steady-state of the dendrite tip.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Chen, Z.; Ding, H.; Chen, R.; Liu, S.; Guo, J.; Fu, H. An innovative method for the microstructural modification of TiAl alloy solidified via direct electric current application. J. Mater. Sci. Technol. 2019, 35, 23–28. [Google Scholar] [CrossRef]
- Wang, G.; Xu, L.; Wang, Y.; Zheng, Z.; Cui, Y.; Yang, R. Processing Maps for Hot Working Behavior of a PM TiAl Alloy. J. Mater. Sci. Technol. 2011, 27, 893–898. [Google Scholar] [CrossRef]
- Wu, S.; Guo, J.; Su, Y.; Zhao, C.; Jia, J. Numerical simulation of off-centred porosity formation of TiAl-based alloy exhaust valve during vertical centrifugal casting. Model. Simul. Mater. Sci. Eng. 2003, 11, 599. [Google Scholar]
- Daloz, D.; Hecht, U.; Zollinger, J.; Combeau, H.; Hazotte, A.; Zaloznik, M. Microsegregation, macrosegregation and related phase transformations in TiAl alloys. Intermetallic 2011, 19, 749–756. [Google Scholar] [CrossRef]
- Won, Y.M.; Thomas, B.G. Simple model of microsegregation during solidification of steels. Metall. Mater. Trans. A 2001, 32, 1755–1767. [Google Scholar] [CrossRef]
- Kang, Y.; Jin, Y.; Zhao, Y.; Hou, H.; Chen, L. Phase-field simulation of tip splitting in dendritic growth of Fe-C alloy. J. Iron Steel Res. Int. 2017, 24, 171–176. [Google Scholar] [CrossRef]
- Kang, Y.; Zhao, Y.; Hou, H.; Jin, Y.; Chen, L. Simulation of liquid channel of Fe-C alloy directional solidification by phase-field method. Acta Phys. Sin. 2016, 65, 188102. [Google Scholar]
- Wang, J.; Li, J.; Yang, Y.; Zhang, Y.; Yang, G. Phase field simulation of the interface morphology evolution and its stability during directional solidification of binary alloys. Sci. China Ser. E Technol. Sci. 2008, 51, 362–370. [Google Scholar] [CrossRef]
- Zhang, B.; Zhao, Y.; Chen, W.; Xu, Q.; Wang, M.; Hou, H.; Wang, S. Phase field simulation of dendrite sidebranching during directional solidification of Al-Si alloy. J. Cryst. Growth 2019, 522, 183–190. [Google Scholar] [CrossRef]
- Zhao, Y.; Zhang, B.; Hou, H.; Chen, W.; Wang, M. Phase-field simulation for the evolution of solid/liquid interface front in directional solidification process. J. Mater. Sci. Technol. 2019, 35, 1044–1052. [Google Scholar] [CrossRef]
- Mi, G.; Xiong, L.; Wang, C.; Ping, J.; Zhu, G. Two-dimensional phase-field simulations of competitive dendritic growth during laser welding. Mater. Des. 2019, 181, 107980. [Google Scholar]
- Meng, S.; Zhang, A.; Guo, Z.; Wang, Q. Phase-field-lattice Boltzmann simulation of dendrite motion using an immersed boundary method. Comput. Mater. Sci. 2020, 184, 109784. [Google Scholar] [CrossRef]
- Laxmipathy, V.P.; Wang, F.; Selzer, M.; Nestler, B. A two-dimensional phase-field study on dendritic growth competition under convective conditions. Comput. Mater. Sci. 2021, 186, 109964. [Google Scholar] [CrossRef]
- Zhang, A.; Meng, S.; Guo, Z.; Du, J.; Wang, Q.; Xiong, S. 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 2019, 50, 1514–1526. [Google Scholar] [CrossRef]
- Karma, A.; Rappel, W.J. Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys. Rev. E 1996, 53, 3017–3020. [Google Scholar] [CrossRef] [PubMed]
- Karma, A.; Rappel, W.J. Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E 1998, 57, 4323–4349. [Google Scholar] [CrossRef] [Green Version]
- Ohno, M. Quantitative phase-field modeling of nonisothermal solidification in dilute multicomponent alloys with arbitrary diffusivities. Phys. Rev. E 2012, 86, 051603. [Google Scholar] [CrossRef] [Green Version]
- Ohno, M.; Matsuura, K. Quantitative phase-field modeling for dilute alloy solidification involving diffusion in the solid. Phys. Rev. E 2009, 79, 031603. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Liu, D.; Wang, Y. Mesoscale multi-physics simulation of rapid solidification of Ti-6Al-4V alloy. Addit. Manuf. 2019, 25, 551–562. [Google Scholar] [CrossRef]
- Sun, W.; Yan, R.; Zhang, Y.; Dong, H.; Jing, T. GPU-accelerated three-dimensional large-scale simulation of dendrite growth for Ti6Al4V alloy based on multi-component phase-field model. Comput. Mater. Sci. 2019, 160, 149–158. [Google Scholar] [CrossRef]
- Feng, L.; Wang, Z.; Zhu, C.; Lu, Y. Phase-field model of isothermal solidification with multiple grain growth. Chin. Phys. B 2009, 18, 1985–1990. [Google Scholar]
- Chen, Y.; Li, D.; Billia, B.; Nguyen-Thi, H.; Qi, X.; Xiao, N. Quantitative Phase-field Simulation of Dendritic Equiaxed Growth and Comparison with in Situ Observation on Al-4 wt.% Cu Alloy by Means of Synchrotron X-ray Radiography. ISIJ Int. 2014, 54, 445–451. [Google Scholar] [CrossRef] [Green Version]
- Zhao, Y.; Liu, W.; Hou, H. Phase-Field Simulation for Dendritic Growth Behavior of Pure Ni under Different Temperature Coupling Strength. Rare Metal Mat. Eng. 2014, 43, 841–845. [Google Scholar]
- Zhang, B.; Zhao, Y.; Wang, H.; Chen, W.; Hou, H. Three-Dimensional Phase Field Simulation of Dendritic Morphology of Al-Si Alloy. Rare Metal Mat. Eng. 2019, 48, 2835–2840. [Google Scholar]
- Boukellal, A.K.; Rouby, M.; Debierre, J.M. Tip dynamics for equiaxed Al-Cu dendrites in thin samples: Phase-field study of thermodynamic effects. Comput. Mater. Sci. 2021, 186, 110051. [Google Scholar] [CrossRef]
- Zhang, Y.; Chi, Y.; Hu, C. Phase-field simulation of solidification dendritic segregation in Ti-45Al alloy. China Foundry 2017, 14, 184–187. [Google Scholar] [CrossRef] [Green Version]
- Li, X.; Guo, J.; Su, Y.; Wu, S.; Fu, H. Phase-field simulation of dendritic growth for binary alloys with complicated solution models. Trans. Nonferrous Met. Soc. China 2005, 15, 769–776. [Google Scholar]
- Viardin, A.; Souhar, Y.; Fernandez, M.; Apel, M.; Zaloznik, M. Mesoscopic modeling of equiaxed and columnar solidification microstructures under forced flow and buoyancy-driven flow in hypergravity: Envelope versus phase-field model. Acta Mater. 2020, 199, 680–694. [Google Scholar] [CrossRef]
- Becker, M.; Dantzig, J.; Kolbe, M.; Wiese, S.T.; Kargl, F. Dendrite orientation transition in Al Ge alloys. Acta Mater. 2019, 165, 666–677. [Google Scholar] [CrossRef]
- Dantzig, J.; Di Napoli, P.; Friedli, J.; Rappaz, M. Dendritic growth morphologies in Al-Zn alloys—Part II: Phase-field computations. Metall. Mater. Trans. A 2013, 44, 5532–5543. [Google Scholar] [CrossRef]
- Xing, H.; Dong, X.; Wang, J.; Jin, K. Orientation Dependence of Columnar Dendritic Growth with Sidebranching Behaviors in Directional Solidification: Insights from Phase-Field Simulations. Metall. Mater. Trans. B 2018, 49, 1547–1559. [Google Scholar] [CrossRef]
- Karma, A. Phase-field formulation for quantitative modeling of alloy solidification. Phys. Rev. Lett. 2001, 87, 115701. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Echebarria, B.; Folch, R.; Karma, A.; Plapp, M. Quantitative phase-field model of alloy solidification. Phys. Rev. E 2004, 70, 061604. [Google Scholar] [CrossRef] [Green Version]
- Chen, L.; Zhao, Y. From Classical Thermodynamics to Phase-field Method. Prog. Mater. Sci. 2021, 100868. [Google Scholar] [CrossRef]
- Xin, T.; Zhao, Y.; Mahjoub, R.; Jiang, J.; Yadav, A.; Nomoto, K.; Niu, R.; Tang, S.; Ji, F.; Quadir, Z.; et al. Ultrahigh specific strength in a magnesium alloy strengthened by spinodal decomposition. Sci. Adv. 2021, 7, eabf3039. [Google Scholar] [CrossRef] [PubMed]
- Chen, W.; Zhao, Y.; Yang, S.; Zhang, D.; Hou, H. Three-dimensional phase-field simulations of the influence of diffusion interface width on dendritic growth of Fe-0.5 wt.%C alloy. Adv. Compos. Hybrid Mater. 2021, 4, 371–378. [Google Scholar] [CrossRef]
- Zhao, Y.; Zhang, B.; Chen, W.; Wang, H.; Wang, M.; Hou, H. Simulation for the Influence of Interface Thickness on the Dendritic Growth of Nickel-Copper Alloy by a Phase-Field Method. ES Mater. Manuf. 2018, 2, 45–50. [Google Scholar]
- Zhang, J.; Wang, H.; Kuang, W.; Zhang, Y.; Li, S.; Zhao, Y.; Herlach, D.M. Rapid solidification of non-stoichiometric intermetallic compounds: Modeling and experimental verification. Acta Mater. 2018, 148, 86–99. [Google Scholar] [CrossRef]
- Kuang, W.; Wang, H.; Li, X.; Zhang, J.; Zhou, Q.; Zhao, Y. Application of the thermodynamic extremal principle to diffusion-controlled phase transformations in Fe-C-X alloys: Modeling and applications. Acta Mater. 2018, 159, 16–30. [Google Scholar] [CrossRef]
- Zhao, Y.; Jing, J.; Chen, L.; Xu, F.; Hou, H. Current Research Status of Interface of Ceramic-Metal Laminated Composite Material for Armor Protection. Acta Metall. Sin. 2021, 57, 1107–1125. [Google Scholar]
- Yang, Y.; Zhao, Y.; Tian, X.; Hou, H. Microscopic phase-field simulation for the precipitation process of Ni60Al20V20 medium entropy alloy. Acta Phys. Sin. 2020, 69, 14201. [Google Scholar]
- Qi, K.; Zhao, Y.; Tian, X.; Peng, D.; Sun, Y.; Hou, H. Phase field crystal simulation of the effect of misorientation angle on the low-angle asymmetric tilt grain boundary dislocation motion. Acta Phys. Sin. 2020, 69, 14504. [Google Scholar] [CrossRef]
- Karma, A.; Rappel, W.J. Phase-field model of dendritic sidebranching with thermal noise. Phys. Rev. E 1999, 60, 3614–3625. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Guo, J.; Li, X.; Su, Y.; Wu, S.; Liu, B.; Fu, H. Phase-field simulation of structure evolution at high growth velocities during directional solidification of Ti55Al45 alloy. Intermetallics 2005, 13, 275–279. [Google Scholar] [CrossRef]
- Kurz, W.; Fisher, D.J. Fundamentals of Solidification, 4th ed.; Higher Education Press: Beijing, China, 2010; pp. 60–64. [Google Scholar]
- Shibkov, A.A.; Zheltov, M.A.; Korolev, A.A.; Kazakow, A.A.; Leonov, A.A. Crossover from diffusion-limited to kinetics-limited growth of ice crystals. J. Cryst. Growth 2005, 285, 215–227. [Google Scholar] [CrossRef]
- Zhu, C.; Wang, Z.; Jing, T.; Liu, B. Phase-field simulation of dendritic sidebranching induced by thermal noise. Trans. Nonferrous Met. Soc. China 2004, 14, 1106–1110. [Google Scholar]
Physical Parameter | Values | Unit |
---|---|---|
- | ||
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhang, Y.; Wang, X.; Yang, S.; Chen, W.; Hou, H. The Morphology and Solute Segregation of Dendrite Growth in Ti-4.5% Al Alloy: A Phase-Field Study. Materials 2021, 14, 7257. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14237257
Zhang Y, Wang X, Yang S, Chen W, Hou H. The Morphology and Solute Segregation of Dendrite Growth in Ti-4.5% Al Alloy: A Phase-Field Study. Materials. 2021; 14(23):7257. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14237257
Chicago/Turabian StyleZhang, Yongmei, Xiaona Wang, Shuai Yang, Weipeng Chen, and Hua Hou. 2021. "The Morphology and Solute Segregation of Dendrite Growth in Ti-4.5% Al Alloy: A Phase-Field Study" Materials 14, no. 23: 7257. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14237257