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Phase-field modeling of free dendritic growth of magnesium based alloy

Duan Pei-Pei Xing Hui Chen Zhi Hao Guan-Hua Wang Bi-Han Jin Ke-Xin

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Phase-field modeling of free dendritic growth of magnesium based alloy

Duan Pei-Pei, Xing Hui, Chen Zhi, Hao Guan-Hua, Wang Bi-Han, Jin Ke-Xin
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  • In this paper, the process of the free dendritic growth of Mg-0.5 wt.%Al alloy in the basal plane (0001) is simulated in two-dimensional system by using a quantitative phase-field model. A convergence study is carried out to choose the optimal coupling parameter λ and grid width Δx/W0 in simulation. Then we systematically discuss the effects of the anisotropic strength ε and the supersaturation Ω on dendritical tip growth velocity, radius, Péclet number, and stability parameter σ *. Results show that the stability parameter σ * defined by the theory of microscopic solvability is a function of the anisotropy strength ε, i.e., σ* ≅ ε1.81905, which is obviously closest to σ * (ε) ≅ ε 1.75 obtained from the analytical solution. Moreover, for Ω σ * is approximately a constant while it sharply and monotonically decreases with the augment of the value of ε for Ω > 0.6. This indicates that there is a transition from solute-controlled dendrite to kinetic dendrite as Ω increases. Furthermore, the transition of the growth pattern from the snow-like to the circle-like patterns occurs as Ω increases.
    • Funds: Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 3102014KYJD026), the National Natural Science Foundation of China (Grant Nos. 61078057, 51172183, 6147130, 11102164), the Natural Science Foundation of Shaanxi Province in China (Grant No. 2012JQ8013), NPU Foundation for Fundamental Research, China (Grant Nos. NPU-FFR-JC20110273, JC201155, JC20120246), and the Program of New Staff and Research Area Project of NPU, China (Grant No. 13GH014602).
    [1]

    Gurevich S, Amoorezaei M, Montiel D, Provatas N 2012 Acta Mater. 60 3287

    [2]

    Shi C X, Li H D, Wang D Z, Li Y Y, Zuo T Y 2001 Mater. Rev. 15 5 (in Chinese) [师昌绪, 李恒德, 王淀佐, 李依依, 左铁镛 2001 材料导报 15 5]

    [3]

    Cao R C, Ke W, Xu Y B 2001 Acta Metal. Sin. 51 2 (in Chinese) [曹荣昌, 柯伟, 徐永波 2001 金属学报 51 2]

    [4]

    Asta M, Beckermann C, Karma A, Kurz W, Napolitano R, Plapp M 2009 Acta Mater. 57 941

    [5]

    Amoorezaei M, Gurevich S, Provatas N 2012 Acta Mater. 60 657

    [6]

    Ivantsov G R, Nauk D A 1947 SSSR 58 567

    [7]

    Kessler D A, Koplik J, Levine H 1988 Adv. Phys. 37 255

    [8]

    Pomeau Y, Ben-Amar M 1992 Solids far from Equilibrium (Cambridge: Cambridge University Press) pp365-378

    [9]

    Lipton J, Glicksman M E, Kurz W 1984 Mater. Sci. Eng. 65 57

    [10]

    Lipton J, Glicksman M E, Kurz W 1987 Metall Trans. A 18 341

    [11]

    Lipton J, Kurz W, Trivedi R 1987 Acta Metall 35 957

    [12]

    Plapp M 2011 Philos. Mag. 91 25

    [13]

    Yamanaka A, Aoki T, Ogawa S, Takaki T 2011 J. Cryst. Growth 318 40

    [14]

    Du L F, Zhang R, Xing H, Zhang L M, Zhang Y, Liu L 2013 Acta Phys. Sin. 62 106401 (in Chinese) [杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘琳 2013 物理学报 62 106401]

    [15]

    Boussinot G, Brener E A, Temkin D E 2010 Acta Mater. 58 1750

    [16]

    Zhang X G, Zong Y P, Wu Y 2012 Acta Phys. Sin. 61 088104 (in Chinese) [张宪刚, 宗亚平, 吴艳 2012 物理学报 61 088104]

    [17]

    Wang X D, Ouyang J, Su J, Zhou W 2013 Chin. Phys. B 22 106103

    [18]

    Wang Z J, Wang J C, Yang G C 2010 Chin. Phys. B 19 078101

    [19]

    Li J J, Wang J C, Yang G C 2008 Chin. Phys. B 17 3516

    [20]

    Karma A, Rappel W J 1998 Phys. Rev. E 57 4323

    [21]

    Echebarria B, Folch R, Karma A, Plapp M 2004 Phys. Rev. E 70 061604

    [22]

    Bergeon N, Tourret D, Chen L, Debierre J M, Guérin R, Ramirez A, Billia B, Karma A, Trivedi R 2013 Phys. Rev. Lett. 110 226102

    [23]

    Amoorezaei M, Gurevich S, Provatas N 2010 Acta Mater. 58 6115

    [24]

    Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478

    [25]

    Wang M, Jing T, Liu B 2009 Script. Mater. 61 777

    [26]

    Eiken J 2009 Int. J. Cast. Met. Res. 22 1

    [27]

    Karma A 2001 Phys. Rev. Lett. 87 115701

    [28]

    Kara M, Kurki-Suonio K 1981 Acta Crystallogr. A: Cryst. Phys. Diffr. Theor. Gen. Crystallogr. 37 201

    [29]

    Sun D Y, Mendelev M I, Becker C A, Kudin K, Haxhimali T, Asta M, Hoyt J J, Karma A, Srolovitz D J 2006 Phys. Rev. B 73 024116

    [30]

    Fu Z, Xu Q, Xiong S 2007 Mater. Sci. Forum. 546-549 133

    [31]

    Ohno M 2012 Phys. Rev. E 86 051603

  • [1]

    Gurevich S, Amoorezaei M, Montiel D, Provatas N 2012 Acta Mater. 60 3287

    [2]

    Shi C X, Li H D, Wang D Z, Li Y Y, Zuo T Y 2001 Mater. Rev. 15 5 (in Chinese) [师昌绪, 李恒德, 王淀佐, 李依依, 左铁镛 2001 材料导报 15 5]

    [3]

    Cao R C, Ke W, Xu Y B 2001 Acta Metal. Sin. 51 2 (in Chinese) [曹荣昌, 柯伟, 徐永波 2001 金属学报 51 2]

    [4]

    Asta M, Beckermann C, Karma A, Kurz W, Napolitano R, Plapp M 2009 Acta Mater. 57 941

    [5]

    Amoorezaei M, Gurevich S, Provatas N 2012 Acta Mater. 60 657

    [6]

    Ivantsov G R, Nauk D A 1947 SSSR 58 567

    [7]

    Kessler D A, Koplik J, Levine H 1988 Adv. Phys. 37 255

    [8]

    Pomeau Y, Ben-Amar M 1992 Solids far from Equilibrium (Cambridge: Cambridge University Press) pp365-378

    [9]

    Lipton J, Glicksman M E, Kurz W 1984 Mater. Sci. Eng. 65 57

    [10]

    Lipton J, Glicksman M E, Kurz W 1987 Metall Trans. A 18 341

    [11]

    Lipton J, Kurz W, Trivedi R 1987 Acta Metall 35 957

    [12]

    Plapp M 2011 Philos. Mag. 91 25

    [13]

    Yamanaka A, Aoki T, Ogawa S, Takaki T 2011 J. Cryst. Growth 318 40

    [14]

    Du L F, Zhang R, Xing H, Zhang L M, Zhang Y, Liu L 2013 Acta Phys. Sin. 62 106401 (in Chinese) [杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘琳 2013 物理学报 62 106401]

    [15]

    Boussinot G, Brener E A, Temkin D E 2010 Acta Mater. 58 1750

    [16]

    Zhang X G, Zong Y P, Wu Y 2012 Acta Phys. Sin. 61 088104 (in Chinese) [张宪刚, 宗亚平, 吴艳 2012 物理学报 61 088104]

    [17]

    Wang X D, Ouyang J, Su J, Zhou W 2013 Chin. Phys. B 22 106103

    [18]

    Wang Z J, Wang J C, Yang G C 2010 Chin. Phys. B 19 078101

    [19]

    Li J J, Wang J C, Yang G C 2008 Chin. Phys. B 17 3516

    [20]

    Karma A, Rappel W J 1998 Phys. Rev. E 57 4323

    [21]

    Echebarria B, Folch R, Karma A, Plapp M 2004 Phys. Rev. E 70 061604

    [22]

    Bergeon N, Tourret D, Chen L, Debierre J M, Guérin R, Ramirez A, Billia B, Karma A, Trivedi R 2013 Phys. Rev. Lett. 110 226102

    [23]

    Amoorezaei M, Gurevich S, Provatas N 2010 Acta Mater. 58 6115

    [24]

    Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478

    [25]

    Wang M, Jing T, Liu B 2009 Script. Mater. 61 777

    [26]

    Eiken J 2009 Int. J. Cast. Met. Res. 22 1

    [27]

    Karma A 2001 Phys. Rev. Lett. 87 115701

    [28]

    Kara M, Kurki-Suonio K 1981 Acta Crystallogr. A: Cryst. Phys. Diffr. Theor. Gen. Crystallogr. 37 201

    [29]

    Sun D Y, Mendelev M I, Becker C A, Kudin K, Haxhimali T, Asta M, Hoyt J J, Karma A, Srolovitz D J 2006 Phys. Rev. B 73 024116

    [30]

    Fu Z, Xu Q, Xiong S 2007 Mater. Sci. Forum. 546-549 133

    [31]

    Ohno M 2012 Phys. Rev. E 86 051603

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Publishing process
  • Received Date:  09 September 2014
  • Accepted Date:  15 October 2014
  • Published Online:  05 March 2015

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