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金属基复合材料原位反应相场模型

郭灿 康晨瑞 高莹 张一弛 邓英远 马超 徐春杰 梁淑华

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金属基复合材料原位反应相场模型

郭灿, 康晨瑞, 高莹, 张一弛, 邓英远, 马超, 徐春杰, 梁淑华

A phase-field model for in-situ reaction process of metal-matrix composite materials

Guo Can, Kang Chen-Rui, Gao Ying, Zhang Yi-Chi, Deng Ying-Yuan, Ma Chao, Xu Chun-Jie, Liang Shu-Hua
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  • 原位反应法制备金属基复合材料具有增强体与基体间无杂质、无污染、颗粒分布均匀等优点, 已成为制备金属基复合材料的一种重要方法, 揭示其动力学机制及规律具有重要的理论及工业价值. 然而, 原位反应过程具有反应时间短、随机发生、温度高等特点, 目前采用原位实验观测其反应过程仍存在较大困难. 本文采用相场法模拟金属熔体内的原位反应过程, 首先建立了能够描述双束金属熔体界面反应形核的相场模型, 并采用该模型模拟了不同参数下相界反应形核过程. 结果表明, 形核率随着曲率半径及噪声强度的增大而增大, 小曲率半径及强噪声条件下新相颗粒尺寸分布更加均匀, 形核率随着过冷度的增大而先增大后减小.
    The in-situ reaction is an important method of preparing metal matrix composites: it can produce more uniform distribution of the reinforcement particles and more excellent structure of the phase boundary between the particles and the matrix. Therefore, the kinetics of in-situ reaction process deserves to be further studied. However, as the in-situ reaction is a rapid random process under high-temperature condition, it is difficult to observe the reaction process of metal-matrix composite materials experimentally. In this work, we propose a new phase-field model to describe the in-situ reaction process, and investigate the nucleation kinetic processes of in-situ reaction under different physical conditions. We find that the nucleation rate increases with the augment of curvature radius and noise intensity, and the size distribution of the particles is more uniform under the conditions of a small curvature radius and strong noise. With the increase of the undercooling, the nucleation rate first increases and then decreases, which is consistent with the classical nucleation theory.
      通信作者: 郭灿, cguo@xaut.edu.cn ; 梁淑华, liangsh@xaut.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 51801154, 51834009)、陕西省高等学校学科创新引智基地(批准号: S2021-ZC-GXYZ-0011)和西安市高校重大科技创新平台及科技成果就地转化项目(批准号: 20GXSF0003)资助的课题
      Corresponding author: Guo Can, cguo@xaut.edu.cn ; Liang Shu-Hua, liangsh@xaut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51801154, 51834009), the Higher Education Institution Discipline Innovation and Intelligence Base of Shaanxi Province, China (Grant No. S2021-ZC-GXYZ-0011), and the Project of Major Innovation Platforms for Scientific and Technological and Local Transformation of Scientific and Technological Achievements of Xi’an, China (Grant No. 20GXSF0003)
    [1]

    郭明星, 汪明朴, 申坤, 张真, 李树梅 2007 中国有色金属学报 09 1440Google Scholar

    Guo M X, Wang M P, Shen K, Zhang Z, Li S M 2007 Nonferrous Met. Soc. China 09 1440Google Scholar

    [2]

    杨滨, 王玉庆, 周本濂 1998 金属学报 01 100

    Yang B, Wang Y Q, Zhou B L 1998 Acta. Metall. Sin. 01 100

    [3]

    张来启, 孙祖庆, 张跃, 杨王玥 1998 金属学报 11 1206

    Zhang L Q, Sun Z Q, Zhang Y, Yang W Y 1998 Acta. Metall. Sin. 11 1206

    [4]

    孙靖 2015 硕士学位论文 (上海: 上海交通大学)

    Sun J 2015 M. S. Thesis (Shanghai: Shanghai Jiao Tong University) (in Chinese)

    [5]

    Qu L, Zhao N, Zhao H J, Huang M L, Ma H T 2014 Scr. Mater. 72 43

    [6]

    Li H, Jiao L, Huang X P, Li F, Lu S B, Li Y L, Qiao Y P 2021 J. Mater. Eng. Perform. 30 7295Google Scholar

    [7]

    Jiang Y H, Li D, Liang S H, Zou J T, Liu F 2017 J. Mater. Sci. 52 2957Google Scholar

    [8]

    Lan T, Jiang Y H, Zhang X J, Cao F, Liang S H 2021 Int. J. Miner., Metall. Mater. 28 1090Google Scholar

    [9]

    Kavousi S, Novak B R, Hoyt J, Moldovan D 2020 Comput. Mater. Sci. 184 854

    [10]

    方辉, 薛桦, 汤倩玉, 张庆宇, 潘诗琰, 朱鸣芳 2019 物理学报 68 048102Google Scholar

    Fang H, Xue H, Tang Q Y, Zhang Q Y, Pan S Y, Zhu M F 2019 Acta Phys. Sin. 68 048102Google Scholar

    [11]

    郭春文, 李俊杰, 马渊, 王锦程 2015 金属学报 54 657Google Scholar

    Guo C W, Li J J, Ma Y, Wang J C 2015 Acta Phys. Sin. 54 657Google Scholar

    [12]

    Zhang Z D, Cao Y T, Sun D K, Xing H, Wang J C, Ni Z H 2020 Chin. Phys. B 29 028103Google Scholar

    [13]

    魏雷, 林鑫, 王猛, 黄卫东 2015 物理学报 64 018013Google Scholar

    Wei L, Lin X, Wang M, Huang W D 2015 Acta Phys. Sin. 64 018013Google Scholar

    [14]

    Rolchigo M R, LeSar R 2019 Comput. Mater. Sci. 163 148Google Scholar

    [15]

    Chen L Q 2002 Annu. Rev. Mater. Res. 32 113Google Scholar

    [16]

    Guo C, Wang J C, Li J J, Wang Z J, Huang Y H, Gu J W, Lin X 2018 Acta Mater. 145 175Google Scholar

    [17]

    Deng Y Y, Guo C, Wang J C, Liu Q, Zhao Y P, Yang Q 2021 Chin. Phys. B 30 611Google Scholar

    [18]

    王锦程, 郭春文, 李俊杰, 王志军 2018 物理学报 54 657Google Scholar

    Wang J C, Guo C W, Li J J, Wang Z J 2018 Acta Phys. Sin. 54 657Google Scholar

    [19]

    郭灿, 王锦程, 王志军, 李俊杰, 郭耀麟, 唐赛 2015 物理学报 64 028102Google Scholar

    Guo C, Wang J C, Wang Z J, Li J J, Guo Y L, Tang S 2015 Acta Phys. Sin. 64 028102Google Scholar

    [20]

    Guo M X, Shen K, Wang M P 2009 Acta Mater. 57 4568Google Scholar

    [21]

    Pan S Y, Zhu M F, Rettenmayr M 2017 Acta Mater. 132 565Google Scholar

    [22]

    柯常波, 周敏波, 张新平 2014 金属学报 50 294Google Scholar

    Ke C B, Zhou M B, Zhang X P 2014 Metall. Sin. 50 294Google Scholar

    [23]

    Shi R P, Shen C, Dregia S A, Wang Y Z 2018 Scr. Mater. 146 276Google Scholar

    [24]

    Guo M X, Shen K, Wang M P 2012 Mater. Chem. Phys. 131 589Google Scholar

    [25]

    Guo C, Wang J C, Wang Z J, Li J J, Guo Y L, Huang Y H 2016 Soft Matter 12 4666Google Scholar

    [26]

    王巍, 付立铭 2008 金属学报 06 723Google Scholar

    Wang W, Fu L M 2008 Metall. sin. 06 723Google Scholar

  • 图 1  (a)—(c)原位反应形核过程, 红色区域为c = 1的液相, 蓝色区域为c = 0的液相, 黄色区域为c = 0.5的固相; (d) 沿图(a)中黑直线上的成分场随时间的演化曲线

    Fig. 1.  (a)–(c) Snapshots of the in-situ reactive process, the blue and red regions represent melt phases with c = 0 and c = 1, respectively. The yellow region is the new solid phase. (d) Temporal evolution of the concentration filed across the solid black line in panel (a).

    图 2  不同曲率半径下的原位反应形核过程(左侧为bnds场(${\text{bnds}} = c + \displaystyle\sum\nolimits_i {{\eta _i}}$), 右侧为成分场) (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80

    Fig. 2.  Snapshots of the in-situ reaction processes with different radius of curvatures: (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80. In each row, the left three figures show the temporal evolution of the bnds field, the right three figures show the temporal evolution of the concentration field.

    图 3  不同曲率半径下的晶核数目随时间演化图 (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80

    Fig. 3.  Temporal evolution of the particle numbers with different initial radius of curvatures: (a) ρ = 30; (b) ρ = 50; (c) ρ = 60; (d) ρ = 80

    图 4  形核率随曲率半径的变化关系

    Fig. 4.  Nucleation rate versus initial radius of curvatures.

    图 5  不同界面曲率下的颗粒粒径分布 (a) ρ = 30; (b) ρ = 60; (c) ρ = 80; (d)平直界面

    Fig. 5.  Particle size distributions with different curvatures: (a) ρ = 30; (b) ρ = 60; (c) ρ = 80; (d) ρ = ∞.

    图 6  不同噪声强度下的原位反应形核过程 (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07

    Fig. 6.  Snapshots of the in-situ reaction processes with different noise intensities: (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07.

    图 7  形核率随噪声强度的变化关系

    Fig. 7.  Nucleation rate versus initial noise intensity.

    图 8  不同噪声下的颗粒粒径分布 (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07

    Fig. 8.  Particle size distributions with different noise intensities: (a) δ = 0.03; (b) δ = 0.05; (c) δ = 0.07.

    图 9  不同过冷度参数下的原位反应形核过程 (a) A = 0.5; (b) A = 0.55; (c) A = 0.65

    Fig. 9.  Snapshots of the in-situ reaction processes with different undercoolings: (a) A = 0.5; (b) A = 0.55; (c) A = 0.65.

    图 10  形核率随过冷度参数的变化关系

    Fig. 10.  Nucleation rate versus undercoolings.

    图 11  不同过冷度参数下的颗粒粒径分布 (a) A = 0.5; (b) A = 0.55; (c) A = 0.65

    Fig. 11.  Particle size distributions with different undercoolings: (a) A = 0.5; (b) A = 0.55; (c) A = 0.65.

  • [1]

    郭明星, 汪明朴, 申坤, 张真, 李树梅 2007 中国有色金属学报 09 1440Google Scholar

    Guo M X, Wang M P, Shen K, Zhang Z, Li S M 2007 Nonferrous Met. Soc. China 09 1440Google Scholar

    [2]

    杨滨, 王玉庆, 周本濂 1998 金属学报 01 100

    Yang B, Wang Y Q, Zhou B L 1998 Acta. Metall. Sin. 01 100

    [3]

    张来启, 孙祖庆, 张跃, 杨王玥 1998 金属学报 11 1206

    Zhang L Q, Sun Z Q, Zhang Y, Yang W Y 1998 Acta. Metall. Sin. 11 1206

    [4]

    孙靖 2015 硕士学位论文 (上海: 上海交通大学)

    Sun J 2015 M. S. Thesis (Shanghai: Shanghai Jiao Tong University) (in Chinese)

    [5]

    Qu L, Zhao N, Zhao H J, Huang M L, Ma H T 2014 Scr. Mater. 72 43

    [6]

    Li H, Jiao L, Huang X P, Li F, Lu S B, Li Y L, Qiao Y P 2021 J. Mater. Eng. Perform. 30 7295Google Scholar

    [7]

    Jiang Y H, Li D, Liang S H, Zou J T, Liu F 2017 J. Mater. Sci. 52 2957Google Scholar

    [8]

    Lan T, Jiang Y H, Zhang X J, Cao F, Liang S H 2021 Int. J. Miner., Metall. Mater. 28 1090Google Scholar

    [9]

    Kavousi S, Novak B R, Hoyt J, Moldovan D 2020 Comput. Mater. Sci. 184 854

    [10]

    方辉, 薛桦, 汤倩玉, 张庆宇, 潘诗琰, 朱鸣芳 2019 物理学报 68 048102Google Scholar

    Fang H, Xue H, Tang Q Y, Zhang Q Y, Pan S Y, Zhu M F 2019 Acta Phys. Sin. 68 048102Google Scholar

    [11]

    郭春文, 李俊杰, 马渊, 王锦程 2015 金属学报 54 657Google Scholar

    Guo C W, Li J J, Ma Y, Wang J C 2015 Acta Phys. Sin. 54 657Google Scholar

    [12]

    Zhang Z D, Cao Y T, Sun D K, Xing H, Wang J C, Ni Z H 2020 Chin. Phys. B 29 028103Google Scholar

    [13]

    魏雷, 林鑫, 王猛, 黄卫东 2015 物理学报 64 018013Google Scholar

    Wei L, Lin X, Wang M, Huang W D 2015 Acta Phys. Sin. 64 018013Google Scholar

    [14]

    Rolchigo M R, LeSar R 2019 Comput. Mater. Sci. 163 148Google Scholar

    [15]

    Chen L Q 2002 Annu. Rev. Mater. Res. 32 113Google Scholar

    [16]

    Guo C, Wang J C, Li J J, Wang Z J, Huang Y H, Gu J W, Lin X 2018 Acta Mater. 145 175Google Scholar

    [17]

    Deng Y Y, Guo C, Wang J C, Liu Q, Zhao Y P, Yang Q 2021 Chin. Phys. B 30 611Google Scholar

    [18]

    王锦程, 郭春文, 李俊杰, 王志军 2018 物理学报 54 657Google Scholar

    Wang J C, Guo C W, Li J J, Wang Z J 2018 Acta Phys. Sin. 54 657Google Scholar

    [19]

    郭灿, 王锦程, 王志军, 李俊杰, 郭耀麟, 唐赛 2015 物理学报 64 028102Google Scholar

    Guo C, Wang J C, Wang Z J, Li J J, Guo Y L, Tang S 2015 Acta Phys. Sin. 64 028102Google Scholar

    [20]

    Guo M X, Shen K, Wang M P 2009 Acta Mater. 57 4568Google Scholar

    [21]

    Pan S Y, Zhu M F, Rettenmayr M 2017 Acta Mater. 132 565Google Scholar

    [22]

    柯常波, 周敏波, 张新平 2014 金属学报 50 294Google Scholar

    Ke C B, Zhou M B, Zhang X P 2014 Metall. Sin. 50 294Google Scholar

    [23]

    Shi R P, Shen C, Dregia S A, Wang Y Z 2018 Scr. Mater. 146 276Google Scholar

    [24]

    Guo M X, Shen K, Wang M P 2012 Mater. Chem. Phys. 131 589Google Scholar

    [25]

    Guo C, Wang J C, Wang Z J, Li J J, Guo Y L, Huang Y H 2016 Soft Matter 12 4666Google Scholar

    [26]

    王巍, 付立铭 2008 金属学报 06 723Google Scholar

    Wang W, Fu L M 2008 Metall. sin. 06 723Google Scholar

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出版历程
  • 收稿日期:  2021-09-17
  • 修回日期:  2021-12-16
  • 上网日期:  2022-01-26
  • 刊出日期:  2022-05-05

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