Abstract
The distinctions of dendritic morphology and sidebranching behavior when solidified under atmosphere pressure, constant pressure which is higher than atmosphere pressure (hereinafter referred to as constant pressure) and periodic pressure were investigated using 3-D phase field method. When growing at atmosphere pressure, side branches (secondary dendritic arms) are irregular. When solidified under constant pressure with a relatively high value, side branches are much more luxuriant, with more developed high-order side branches. When applied with periodic pressure, resonant sidebranching happens, leading to many more regular side branches and the smallest secondary dendritic arm spacing (SDAS) in the three cases. The significant difference in dendritic morphology is associated with tip velocity modulated by total undercooling including pressure and temperature undercooling. In the case of constant pressure, tip velocity increases linearly with total undercooling, and it varies periodically in periodic pressure case. The different variation trend in tip velocity is the reason for the distinct dendrite growth behavior in different cases. Unlike the phenomenon in constant pressure case where the dendrite grows faster with higher pressure, the dendrite grows slower under periodic pressure with higher amplitude, resulting in less developed primary dendrite and side branches. This is influenced by tip remelting due to low undercooling or even negative undercooling. It is revealed that the accelerated velocity of tip remelting increases with the decline of undercooling. The greater the amplitude of periodic pressure, the faster the tip remelting velocity during one period. This is the reason why the average tip velocity decreases with the rise of amplitude of periodic pressure.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Sawada T, Takemura K, Kitamura K, et al. Crystal growth by pressure control using a diamond anvil cell. Journal of Crystal Growth, 1988, 88(4): 535–536.
Sawada T, Takemura K, Shigematsu K, et al. Dynamic pressure control for solution growth and its microgravity application. Journal of Crystal Growth, 1996, 158(3): 328–335.
Sawada T, Takemura K, Shigematsu K, et al. Effects of gravity on a free dendrite of NH4Cl grown by dynamic pressure control. Journal of Crystal Growth, 1998, 191(1–2): 225–233.
LaCombe J C, Koss M B, Tennenhouse L A, et al. The Clapeyron effect in succinonitrile: Applications to crystal growth. Journal of Crystal Growth, 1998, 194(1): 143–148.
Kar P, LaCombe J C, Koss M B. Velocity and radius transients during pressure mediated dendritic growth of succinonitrile. Materials Science and Technology, 2004, 20(10): 1273–1280.
Koss M B, LaCombe J C, Chait A, et al. Pressure-mediated effects on thermal dendrites. Journal of Crystal Growth, 2005, 279(1–2): 170–185.
Yokoyama C, Tamura Y, Nishiyama Y. Crystal growth rates of tricaprin and trilaurin under high pressures. Journal of Crystal Growth, 1998, 191(4): 827–833.
Sachdeva D, Tiwari S, Sundarraj S, et al. Microstructure and corrosion characterization of squeeze cast AM50 magnesium alloys. Metallurgical and Materials Transactions B, 2010, 41(6): 1375–1383.
Masoumi M, Hu H. Influence of applied pressure on microstructure and tensile properties of squeeze cast magnesium Mg-Al-Ca alloy. Materials Science and Engineering: A, 2011, 528(10–11): 3589–3593.
Han Z Q, Pan H W, Li Y, et al. Study on pressurized solidification behavior and microstructure characteristics of squeeze casting magnesium alloy AZ91D. Metallurgical and Materials Transactions B, 2015, 46(1): 328–336.
Huang X R, Han Z Q, Liu B C. Study on the effect of pressure on the equilibrium and stability of the solid-liquid interface in solidification of binary alloys. Science China Technological Sciences, 2011, 54(2): 479–483.
Han G M, Han Z Q, Luo A A, et al. A phase field model for simulating the precipitation of multi-variant β-Mg17Al12 in Mg-Al-based alloys. Scripta Materialia, 2013, 68(9): 691–694.
Han Z Q, Zhu W, Liu B C. Thermomechanical modeling of solidification process of squeeze casting I. Mathematic model and solution methodology. Acta Metallurgica Sinica, 2009, 45(3): 356–362.
Kim S G. A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties. Acta Materialia, 2007, 55(13): 4391–4399.
Kim S G, Kim W T, Suzuki T. Phase-field model for binary alloys. Physical Review E, 1999, 60(6): 7186–7197.
Echebarria B, Folch R, Karma A, et al. Quantitative phase-field model of alloy solidification. Physical Review E, 2004, 70: 61604.
Karma A. Phase-field formulation for quantitative modeling of alloy solidification. Physical Review Letters, 2001, 87(11): 115701.
Eiken J, Böttger B, Steinbach I. Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Physical Review E, 2006, 73(6): 066122.
Pan H W, Han Z Q, Liu B C. Study on dendritic growth in pressurized solidification of Mg-Al alloy using phase field simulation. Journal of Materials Science & Technology, 2016, 32: 68–75.
Shang S, Guo Z P, Han Z Q. On the kinetics of dendritic sidebranching: A three dimensional phase field study. Journal of Applied Physics, 2016, 119(16): 164305.
Shang S, Han Z Q, Sun W H, et al. A phase field model coupled with pressure-effect-embedded thermodynamic modeling for describing microstructure and microsegregation in pressurized solidification of a ternary magnesium alloy. Computational Materials Science, 2017, 136: 264–270.
Börzsönyi T, Tóth-Katona T, Buka Á, et al. Dendrites regularized by spatially homogeneous time-periodic forcing. Physical Review Letters, 1999, 83(14): 2853–2856.
Börzsönyi T, Tóth-Katona T, Buka Á, et al. Regular dendritic patterns induced by nonlocal time-periodic forcing. Physical Review E, 2000, 62(6): 7817–7827.
Guo Z P, Xiong S M. On solving the 3-D phase field equations by employing a parallel-adaptive mesh refinement (Para-AMR) algorithm. Computer Physics Communications, 2015, 190: 89–97.
Shang S, Guo Z P, Han Z Q, et al. Influence of periodic pressure on dendritic morphology and sidebranching. China Foundry, 2020, 17(4): 279–285.
Acknowledgements
This work was supported by the National High Technology Research and Development Program of China (Grant No. 2018YFE0204300) and Institute Guo Qiang, Tsinghua University (Grant No. 2019GQG1010).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Xin-yu Zhang Male, Master, Senior Engineer. His research interests mainly focus on the intelligent vehicles and robotics, machine learning, deep learning, and driving safety.
Rights and permissions
About this article
Cite this article
Shang, S., Guo, Zp., Han, Zq. et al. Distinctions of dendritic behavior influenced by constant pressure and periodic pressure. China Foundry 18, 94–100 (2021). https://doi.org/10.1007/s41230-021-0149-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41230-021-0149-0