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高Cr铸铁中M7C3碳化物与奥氏体共生长的元胞自动机模拟

张山 张红伟 苗淼 冯苗苗 雷洪 王强

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高Cr铸铁中M7C3碳化物与奥氏体共生长的元胞自动机模拟

张山, 张红伟, 苗淼, 冯苗苗, 雷洪, 王强

Cellular automaton simulation on cooperative growth of M7C3 carbide and austenite in high Cr cast irons

Zhang Shan, Zhang Hong-Wei, Miao Miao, Feng Miao-Miao, Lei Hong, Wang Qiang
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  • 高铬铸铁中M7C3碳化物大小适中、弥散均匀分布, 有利于提高合金的耐磨性. 为分析凝固过程中M7C3碳化物晶粒在基体中的形貌及分布、M7C3碳化物与奥氏体晶粒生长的相互作用、引起的溶质偏聚对最终M7C3碳化物粒径分布的影响, 本文开发了Fe-C-Cr三元合金小面晶M7C3碳化物与奥氏体晶粒共生长的二维微观元胞自动机模型, 模型中加入潜热释放对凝固过程温度场的影响, 由C, Cr两溶质界面扩散共同确定晶体生长速度, 由凝固路径数据表插值获取液相元胞的溶质平衡浓度, 设定M7C3碳化物邻胞结构并优化形状因子来保持M7C3碳化物小面晶形貌, 模拟了Fe-4%C-17%Cr三元合金(C和Cr的质量分数分别为4%和17%)初生M7C3碳化物和共晶奥氏体晶粒的生长演变过程. 研究表明, M7C3碳化物和奥氏体晶粒各自的生长速度随着界面液相中C, Cr溶质的超饱和度和贝克列数的增大而增大; 随着奥氏体的析出和晶粒生长, M7C3碳化物晶粒的生长速度明显增快; 当奥氏体晶粒逐渐接触并包围M7C3碳化物晶粒时, 两相晶粒生长速度逐渐降低. 凝固过程中, 奥氏体晶粒生长向外排出C, Cr溶质, 与吸收C, Cr溶质生长的M7C3碳化物晶粒互补, 致使二者生长互相促进, 最终奥氏体晶粒包围M7C3碳化物晶粒生长. 预测的冷却曲线与实验冷却曲线变化趋势相符; 最终凝固组织形貌和M7C3碳化物体积分数与实验相符; 剩余液相、奥氏体中C, Cr溶质浓度演变也与Gulliver-Scheil, Partial Equilibrium, Lever Rule模型预测结果相符.
    M7C3 carbide’s amount, size, morphology and distribution in the microstructure contribute much to the wear resistance of high chromium cast irons. In the present paper, a two-dimensional microscopic cellular automaton model for the growth of the faceted M7C3 carbide together with the austenitic dendrite grains in an Fe-4%C-17%Cr ternary alloy is developed to obtain the evolution of M7C3 carbide grain morphology, the concentration redistribution and their interaction during the growth of M7C3 carbide and austenite grains, and also the total influence on the final M7C3 carbides’ size. The model includes the effect of latent heat release on the temperature drop. The grain growth velocity is determined by both the diffusion of C solute and the diffusion of Cr solute at the S/L interface. The equilibrium concentration in liquid cells is interpolated from the tablulated solidification path which is prescribed by Gulliver-Scheil approximation coupling with the thermodynamic equilibrium calculation. The morphology of the faceted M7C3 carbide is maintained through setting its neighborhood relations and optimizing its shape factor at grain growth. The results show that the individual grain growth velocity for M7C3 carbide and austenite increases with the increase of the supersaturation and Peclet number of solute C and Cr. The austenite precipitation and grain growth obviously speed up the growth velocity of M7C3 carbide grains. While with the austenite grains gradually touching and enveloping the M7C3 carbide grain, the growth velocities for both kinds of grains decrease. The rejection of solute C and Cr during austenite grain growth complements the absorption of solute C and Cr during M7C3 carbide grain growth, thus promoting their growth. The predicted cooling curve fits with the evolution tendency of the experimental one. The predicted final solidification microstructure and M7C3 carbide amount in volume fraction are in agreement with the experimental ones. Furthermore, both C solute concentration distribution and Cr solute concentration distribution in both residual liquid and austenite are consistent with the predictions by the Gulliver-Scheil, partial equilibrium and lever rule model.
      通信作者: 张红伟, hongweizhang@epm.neu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 51574074, 51425401)、国家自然科学基金钢铁联合研究基金(批准号: U1460108, U1560207)和辽宁省教育厅基金 (批准号: L20150183)资助的课题.
      Corresponding author: Zhang Hong-Wei, hongweizhang@epm.neu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51574074, 51425401), the National Natural Science Foundation of China and Shanghai Baosteel (Grant Nos. U1460108, U1560207), and the Natural Science Foundations of Liaoning Province, China (Grant No. L20150183).
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  • 图 1  t = 99.99 s时, 不同系数a条件下模拟的M7C3质量分数图 (a) a = 0.25; (b) a = 0.40; (c) a = 0.50; (d) a = 0.60

    Fig. 1.  M7C3 morphology in form of mass fraction with several values of coefficient a at t = 99.99 s: (a) a = 0.25; (b) a = 0.40; (c) a = 0.50; (d) a = 0.60.

    图 2  M7C3元胞邻居单元

    Fig. 2.  Neighborhood relations for M7C3 grain.

    图 3  γ元胞Moore型邻居单元

    Fig. 3.  Moore neighborhood relations for austenite grain.

    图 4  Fe-C伪二元合金相图(A 区, 液相; B区, 液相 + TiC; C 区, 液相 + M7C3; D区, 液相+ M7C3 + γ; E 区, M7C3 + γ; F区, 液相 + TiC + M7C3; G区, 液相+ TiC + γ; H区, 液相+ TiC + M7C3 + γ; I 区, TiC + γ + M7C3) (a) Fe-C-17%Cr; (b) Fe-C-23.8%Cr; (c) Fe-C-17%Cr-1.5%Ti; (d) Fe-C-23.8%Cr-4%Ti

    Fig. 4.  Fe-C pseudo binary phase diagram: (a) Fe-C-17%Cr; (b) Fe-C-23.8%Cr; (c) Fe-C-17%Cr-1.5%Ti; (d) Fe-C-23.8%Cr-4%Ti. A zone, Liquid; B zone, Liquid + TiC; C zone, Liquid + M7C3; D zone, Liquid + M7C3 + γ; E zone, M7C3 + γ; F zone, Liquid + TiC + M7C3; G zone, Liquid + TiC + γ; H zone, Liquid + TiC + M7C3 + γ; I zone, TiC + γ + M7C3.

    图 5  预测的Fe-4%C-17%Cr合金冷却曲线及添加1.5%Ti合金石墨型实验冷却曲线[22]对比

    Fig. 5.  Comparison of predicted cooling curve for Fe-4%C-17%Cr alloy and experimental cooling curve with 1.5%Ti addition in graphite mold [22].

    图 6  Fe-3.23%C-23.8%Cr合金添加4%Ti与否砂型实验冷却曲线[39]

    Fig. 6.  Experimental cooling curves in sand mold for Fe-3.23%C-23.8%Cr alloy with or without 4%Ti addition[39].

    图 7  本模拟冷却曲线及各相质量分数演变

    Fig. 7.  Predicted cooling curves and evolution of phase mass fraction.

    图 8  本模拟与GS模型中各相质量分数随温度变化

    Fig. 8.  Evolution of phase mass fraction with temperature by present model and GS model.

    图 9  M7C3碳化物和奥氏体界面液相溶质贝克列数、平衡浓度演变 (a) M7C3界面; (b)奥氏体界面

    Fig. 9.  Evolution of solute Peclet number and equilibrium concentration in liquid at M7C3 and austenite interface cell: (a) M7C3/liquid interface; (b) austenite/liquid interface.

    图 10  M7C3碳化物/液相和奥氏体/液相界面生长速度演变: (a) M7C3界面; (b)奥氏体界面

    Fig. 10.  Evolution of growth velocity with PeCr at M7C3/liquid and austenite/liquid interface: (a) M7C3/liquid interface; (b) austenite/liquid interface.

    图 11  不同时刻奥氏体晶粒形貌 (a) t = 70.83 s; (b) t = 95.83 s; (c) t = 120.83 s; (d) t = 145.83 s

    Fig. 11.  Morphologies of austenite grains at different moment: (a) t = 70.83 s; (b) t = 95.83 s; (c) t = 120.83 s; (d) t = 145.83 s.

    图 12  不同时刻晶粒取向 (a) t = 70.83 s; (b) t = 95.83 s; (c) t = 120.83 s; (d) t = 145.83 s

    Fig. 12.  Crystallographic orientations of M7C3 and austenite grains at different moment: (a) t = 70.83 s; (b) t = 95.83 s; (c) t = 120.83 s; (d) t = 145.83 s.

    图 13  奥氏体晶粒A和邻近M7C3碳化物晶粒周围溶质浓度的演变: (a) C浓度; (b) Cr浓度

    Fig. 13.  Evolution of solute concentration around austenite grain A and adjacent M7C3 carbide grain: (a) C concentration; (b) Cr concentration.

    图 14  Fe-4%C-17%Cr合金实验[22]和预测的凝固组织 (a)实验凝固形貌; (b)本模拟奥氏体质量分数; (c)本模拟C浓度场; (d)本模拟Cr浓度场

    Fig. 14.  Experimental[22] and predicted solidification microstructure for Fe-4%C-17%Cr alloy: (a) experimental microstructure; (b) predicted austenite mass fraction; (c) predicted C concentration field; (d) predicted Cr concentration field.

    图 15  剩余液相中C, Cr溶质浓度演变

    Fig. 15.  Evolution of C and Cr concentration in residual liquid.

    图 16  奥氏体中C, Cr溶质浓度演变与凝固路径模型对比 (a) C 浓度; (b) Cr浓度

    Fig. 16.  Comparison of C and Cr solute concentration evolution in austenite with GS, PE and LR solidification path prediction: (a) C concentration; (b) Cr concentration.

    表 1  Fe-4%C-17%Cr三元合金模拟所用的物性参数(单位%是指质量分数)

    Table 1.  Physical properties used for Fe-4%C-17%Cr ternary alloy. Unit of % represents mass fraction (wt%).

    ParametersSymbolUnitValueNote
    Initial composition C$ {C_{{\text{C0}}}} $%4.00文献[22]
    Initial composition Cr$ {C_{{\text{Cr0}}}} $%17.00文献[22]
    Austenite nucleation temperature$ \mathop T\nolimits_{{\gamma }} $1266.00GS model
    M7C3 nucleation temperature$ \mathop T\nolimits_{\text{M}} $1304.00GS model
    C partition coefficient at austenite/liquid interface${k_{ { {{\rm p}, {\mathrm{\gamma }/\mathrm{L} } , {\rm C} } } } }$0.407GS model
    Cr partition coefficient at austenite/liquid interface${k_{ { {{\rm p}, {\mathrm{\gamma }/\mathrm{L} } , {\rm Cr} } } } }$0.576GS model
    Liquidus slope of C at austenite/liquid interface${m_{ { { {\mathrm{L}/\mathrm{\gamma } }, {\rm C} } } } }$℃/%–95.49GS model
    Liquidus slope of Cr at austenite/liquid interface${m_{ { { {\mathrm{L}/\mathrm{\gamma } }, {\rm Cr} } } } }$℃/%6.14GS model
    Liquidus slope of C at M7C3/liquid interface${m_{ {{\rm L/M}, \text{C} } } }$℃/%90.37GS model
    Liquidus slope of Cr at M7C3/liquid interface${m_{ {{\rm L/M},\text{Cr} } } }$℃/%15.29GS model
    Diffusion coefficient of C in austenite${D_{ { \mathrm{\gamma }, {\rm C} } } }$m2/s2.57×10–10GS model
    Diffusion coefficient of Cr in austenite${D_{ { {\mathrm{\gamma } , \rm Cr} } } }$m2/s3.67×10–14GS model
    Diffusion coefficient of C in liquid phase${D_{ {\text{L,C} } } }$m2/s9.60×10–10GS model
    Diffusion coefficient of Cr in liquid phase${D_{ {\text{L,Cr} } } }$m2/s8.23×10–10GS model
    Diffusion coefficient of C in M7C3${D_{ {\text{M,C} } } }$m2/s0.0
    Diffusion coefficient of Cr in M7C3${D_{ {\text{M,Cr} } } }$m2/s0.0
    Gibbs-Thomson coefficient at austenite/liquid interface${\varGamma _{ {\gamma } } }$$ {\text{m}} \cdot {\text{K}} $1.9×10–7文献[37]
    Gibbs-Thomson coefficient at M7C3/liquid interface${\varGamma _{\text{M} } }$$ {\text{m}} \cdot {\text{K}} $6.213×10–7文献[38]
    Latent heat of fusion for austenite$ \mathop L\nolimits_{{\gamma }} $J/kg1.86×105GS model
    Latent heat of fusion for M7C3$ \mathop L\nolimits_{\text{M}} $J/kg2.38×105GS model
    Specific heat capacity$\mathop c\nolimits_{\rm p}$J/(kg$ \cdot $℃)839GS model
    下载: 导出CSV

    表 2  GS模型和Fe-C伪二元相图中二种成分Fe-C-Cr合金析出相及析出温度

    Table 2.  Phase type and precipitation temperature in two Fe-C-Cr alloys by GS prediction and in Fe-C pseudo binary phase diagram.

    ModelAlloy compositionM7C3 precipitation temperature/℃γ precipitation temperature/℃CEM precipitation temperature or solidus /℃Phase volume fraction at CEM precipitation
    temperature or solidus
    GS modelFe-4%C-17%Cr130412661194(CEM)29.91%(M7C3) 57.22%(γ)
    GS modelFe-4%C-17%Cr-1.5%Ti128812711193(CEM)26.38%(M7C3) 63.20%(γ)
    Fe-C phase diagramFe-4%C-17%Cr130512661239(solidus)
    Fe-C phase diagramFe-4%C-17%Cr-1.5%Ti128512711248(solidus)
    GS modelFe-3.23%C-23.8%Cr130512971193(CEM)28.18%(M7C3) 71.62%(γ)
    GS modelFe-3.23%C-23.8%Cr-4%Ti129613241296(solidus)17.80%(M7C3) 74.28%(γ)
    Fe-C phase diagramFe-3.23%C-23.8%Cr130512961292(solidus)
    Fe-C phase diagramFe-3.23%C-23.8%Cr-4%Ti129513281295(solidus)
    下载: 导出CSV
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    Siekaniec D, Kopycinski D, Szczesny A, Guzik E, Tyraa E, Nowak A 2017 Nephron Clinical Practice 17 143Google Scholar

    [2]

    Liu H N, Sakamoto M, Nomura M, Ogi K 2001 Wear 250 71Google Scholar

    [3]

    Pokusova M, Gabrisova Z, Brusilova A, Pribulova A, Futa P 2020 Mater. Sci. Forum. 998 30Google Scholar

    [4]

    Filipovic M, Kamberovic Z, Korac M, Gavrilovski M 2013 Mater. Des. 47 41Google Scholar

    [5]

    Buytoz S, Yildirim M M, Eren H 2005 Mater. Lett. 59 607Google Scholar

    [6]

    龚沛, 赵曜, 杨浩, 王宁 2017 金属热处理 42 137Google Scholar

    Gong P, Zhao Y, Yang H, Wang N 2017 Heat Treatment of Metals 42 137Google Scholar

    [7]

    陈哲, 王亮亮, 张晗, 付永红, 钟黎声, 叶芳霞 2013 热加工工艺 42 8Google Scholar

    Chen Z, Wang L L, Zhang H, Fu Y H, Zhong L S, Ye F X 2013 Hot Working Technology 42 8Google Scholar

    [8]

    Tang X H, Chung R, Pang C J, Li D Y, Hinckley B, Dolman K 2011 Wear 271 1426Google Scholar

    [9]

    Zhang H W, Nakajima K, Gandin C A, He J C 2013 ISIJ Int. 53 493Google Scholar

    [10]

    王同敏, 魏晶晶, 王旭东, 姚曼 2018 金属学报 54 193Google Scholar

    Wang T M, Wei J J, Wang X D, Yao M 2018 Acta Metall. Sin. 54 193Google Scholar

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    朱鸣芳, 邢丽科, 方辉, 张庆宇, 汤倩玉, 潘诗琰 2018 金属学报 54 789Google Scholar

    Zhu M F, Xing L K, Fang H, Zhang Q Y, Tang Q Y, Pan S Y 2018 Acta. Metall. Sin. 54 789Google Scholar

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    Zhu M F, Cao W, Chen S L, Hong C P, Chang Y A 2007 J. Phase Equilib. Diffus. 28 130Google Scholar

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    戴挺, 朱鸣芳, 陈双林, 曹伟生, 洪俊杓 2008 金属学报 10 1175Google Scholar

    Dai T, Zhu M F, Chen S L, Cao W S, Hong J Z 2008 Acta Metall. Sin. 10 1175Google Scholar

    [14]

    Zhang H W, Gandin C A, Hamouda H B, Tourret D, Nakajima K, He J C 2010 ISIJ Int. 50 1859Google Scholar

    [15]

    Zhang H W, Gandin C A, Nakajima K, He J C 2012 IOP Conf Series: Materials Science Engineering 33 012063Google Scholar

    [16]

    石玉峰, 许庆彦, 柳百成 2012 物理学报 61 108101Google Scholar

    Shi Y F, Xu Q Y, Liu B C 2012 Acta Phys. Sin. 61 108101Google Scholar

    [17]

    Michelic S C, Thuswaldner J M, Bernhard C 2010 Acta Mater. 58 2738Google Scholar

    [18]

    张晛韦 2019 硕士学位论文 (沈阳: 东北大学)

    Zhang X W 2019 Master's Dissertation (Shenyang: Northeastern University) (in Chinese)

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出版历程
  • 收稿日期:  2021-04-16
  • 修回日期:  2021-06-15
  • 上网日期:  2021-08-15
  • 刊出日期:  2021-11-05

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