China Foundry

, Volume 16, Issue 2, pp 97–104 | Cite as

Phase-field simulation of secondary dendrite growth in directional solidification of binary alloys

  • Li FengEmail author
  • Ni-ni Lu
  • Ya-long Gao
  • Chang-sheng Zhu
  • Jun-he Zhong
  • Rong-zhen Xiao
Research & Development


Phase field method was used to simulate the effect of grains orientation angle θ11 and azimuth θA of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the simulation process, two single-factor influence experiments were designed for columnar crystal structures. The simulation results showed that, when θ11 < 45° and θA < 45°, as θ11 was enlarged, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging grain boundary (GB) presented an increasing inclination to that of preferentially growing dendrites; with increasing θA, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging GB exhibited greater deflection, and the secondary dendrites grew with branches; the secondary dendrites on the preferentially growing dendrites at diverging GBs grew along a direction vertical to the growth direction of the preferentially growing dendrites. When θA = 45° and θ11 = 45°, the secondary dendrites grew in a direction vertical to the growth direction of preferentially growing dendrites. The morphologies of the dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the effect of a grain’s orientation angle and azimuth of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites does exist and frequently appears in the practical solidification process.

Key words

phase-field method binary alloy directional solidification secondary dendrites 

CLC numbers


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This work is supported by the National Natural Science Foundation of China (Grant Nos.: 11504149, 11364024, and 51661020).


  1. [1]
    Zhou Yaohe, Hu Zhangling, and Jie Wanqi. Solidification technology. Beijing: Machinery Industry Press, 1998. (In Chinese)Google Scholar
  2. [2]
    Lu Baiping. Some Development of Directional Solidification Technique. Foundry, 2006, 55 (8): 767–771. (In Chinese)Google Scholar
  3. [3]
    Fu Hengzhi, Guo Jin Jie, and Liu Lin. Directional solidification and processing of advanced materials. Beijing: Science Press, 2008. (In Chinese)Google Scholar
  4. [4]
    Liu Lin, Huang Taiwen, Qu Min, et al. High thermal gradient directional solidification and its application in the processing of nickel based super alloys. Journal of Materials Processing Technology, 2010, 210 (1): 159–165.CrossRefGoogle Scholar
  5. [5]
    Zhamg Weiguo, Liu Lin, Zhao Xinbao, et al. Progress in Directionally Solidified Super Alloys. Foundry, 2009, 58 (1): 1–6. (In Chinese)Google Scholar
  6. [6]
    Clarke Amy J, Tourret D, Song Younggil, et al. Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations. Acta Materialia, 2017, 129: 203–216.CrossRefGoogle Scholar
  7. [7]
    Tourret D, Song Younggil, Clarke Amy J, et al. Grain growth competition during thin-sample directional solidification of dendritic microstructures: A phase-field study. Acta Materialia, 2017, 122: 220–235.CrossRefGoogle Scholar
  8. [8]
    Yu Honglie. Research on Competitive Grain Growth during Directional Solidification. Northwestern Polytechnical University, 2015. (In Chinese)Google Scholar
  9. [9]
    Lu Xing, Zeng Min, Ma Ting, et al. Simulation of metal corrosion layer growth behavior under high temperature by Cellular Automaton Method. Journal of engineering thermophysics, 2016, 37 (9): 2019–2022. (In Chinese)Google Scholar
  10. [10]
    Zuo Xiaojing, Meng Xiangning, Huang Shou, et al. Morphology simulation and mechanical analysis of primary dendrites for continuously cast low carbon steel. Acta Physica Sinica, 2016, 65(16): 166101. (In Chinese)Google Scholar
  11. [11]
    Xing Hui, Ankit Kumar, Dong Xianglei, et al. Growth direction selection of tilted dendritic arrays in directional solidification over a wide range of pulling velocity: A phase-field study. International Journal of Heat and Mass Transfer, 2018, 117: 1107–1114.CrossRefGoogle Scholar
  12. [12]
    Feng Li, Gao Yalong, Zhu Changsheng, et al. Phase-feld numerical simulation of three dimensional competitive growth of dendrites in a binary alloy. China Foundry, 2018, 15(1): 44–50.CrossRefGoogle Scholar
  13. [13]
    Shi Xiaoming, Huang Houbing, Cao Guoping, et al. Accelerating large-scale phase-field simulations with GPU. Aip Advances, 2017, 7(10): 105216.CrossRefGoogle Scholar
  14. [14]
    Zhang Ang, Guo Zhipeng, Xiong Shoumei. Phase-field-lattice Boltzmann study for lamellar eutectic growth in a natural convection melt. China Foundry, 2017, 14(5):373–378.CrossRefGoogle Scholar
  15. [15]
    Zhang Ang, Guo Zhi Peng, Xiong Shou Mei. Quantitative phase-field lattice-Boltzmann study of lamellar eutectic growth under natural convection. Physical Review E, 2018, 97(5): 053302.CrossRefGoogle Scholar
  16. [16]
    Yang Man Hong, Xiong Shou Mei, Guo Zhi Ping. Characterisation of the 3-D dendrite morphology of magnesium alloys using synchrotron X-ray tomography and 3-D phase-field modelling. Acta Materialia, 2015, 92: 8–17.CrossRefGoogle Scholar
  17. [17]
    Gong Xi Bing and Chou KiVin. Phase-Field Modeling of Microstructure Evolution in Electron Beam Additive Manufacturing. JOM, 2015, 67(5): 1176–1182.CrossRefGoogle Scholar
  18. [18]
    Tourret D and Karma A. Growth competition of columnar dendritic grains: A phase-field study. Acta Materialia, 2015, 82: 64–83.CrossRefGoogle Scholar
  19. [19]
    Guo Chunwen, Li Junjie, Yu Hongjie, et al. Branching-induced grain boundary evolution during directional solidification of columnar dendritic grains. Acta Materialia, 2017, 136: 148–163.CrossRefGoogle Scholar
  20. [20]
    Feng Li, Gao Ya-long, Lu Ni-ni, et al. An Guo Sheng, Zhon Jun He. Phase-field simulation of competitive growth of grains in a binary alloy during directional solidification. China Foundry, 2018, 15(5): 333–342.CrossRefGoogle Scholar
  21. [21]
    Feng Li, Jia Jinfang, Zhu Changsheng, et al. Research on Phase-Field Model of Three-Dimensional Dendritic Growth for Binary Alloy. Journal of Computational and Theoretical Nanoscience, 2015, 12(11): 4289–4296.CrossRefGoogle Scholar

Copyright information

© Foundry Journal Agency and Springer Singapore 2019

Authors and Affiliations

  • Li Feng
    • 1
    • 2
    Email author
  • Ni-ni Lu
    • 1
  • Ya-long Gao
    • 1
  • Chang-sheng Zhu
    • 2
  • Jun-he Zhong
    • 1
  • Rong-zhen Xiao
    • 1
    • 2
  1. 1.College of Materials and EngineeringLanzhou University of TechnologyLanzhouChina
  2. 2.State Key Laboratory of Advanced Processing and Recycling of Non-ferrous MetalsLanzhou University of TechnologyLanzhouChina

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