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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.
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Keywords:
- Fe-C-Cr ternary alloy /
- faceted M7C3 /
- cooperative growth /
- cellular automaton
[1] Siekaniec D, Kopycinski D, Szczesny A, Guzik E, Tyraa E, Nowak A 2017 Nephron Clinical Practice 17 143
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[3] Pokusova M, Gabrisova Z, Brusilova A, Pribulova A, Futa P 2020 Mater. Sci. Forum. 998 30
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[4] Filipovic M, Kamberovic Z, Korac M, Gavrilovski M 2013 Mater. Des. 47 41
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[5] Buytoz S, Yildirim M M, Eren H 2005 Mater. Lett. 59 607
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[6] 龚沛, 赵曜, 杨浩, 王宁 2017 金属热处理 42 137
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Gong P, Zhao Y, Yang H, Wang N 2017 Heat Treatment of Metals 42 137
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[7] 陈哲, 王亮亮, 张晗, 付永红, 钟黎声, 叶芳霞 2013 热加工工艺 42 8
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Chen Z, Wang L L, Zhang H, Fu Y H, Zhong L S, Ye F X 2013 Hot Working Technology 42 8
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[9] Zhang H W, Nakajima K, Gandin C A, He J C 2013 ISIJ Int. 53 493
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[10] 王同敏, 魏晶晶, 王旭东, 姚曼 2018 金属学报 54 193
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Wang T M, Wei J J, Wang X D, Yao M 2018 Acta Metall. Sin. 54 193
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Shi Y F, Xu Q Y, Liu B C 2012 Acta Phys. Sin. 61 108101
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Zhang X W 2019 Master's Dissertation (Shenyang: Northeastern University) (in Chinese)
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[24] 付振南, 许庆彦, 熊守美 2007 中国有色金属学报 17 1567
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Fu Z N, Xu Q Y, Xiong S M 2007 J. Nonferrous Met. China 17 1567
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Google Scholar
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[29] Nastac L 1999 Acta Mater. 47 4253
Google Scholar
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Google Scholar
[31] Rappaz M, Boettinger W J 1999 Acta Mater. 47 3205
Google Scholar
[32] Burbelko A A, Gurgul D, Kaptur K W, Gorny M 2012 Arch. Foundry Eng. 12 11
Google Scholar
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Sun Y C 2012 Ph. D. Dissertation (Shandong: Shandong University) (in Chinese)
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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
Figure 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
Figure 2. Neighborhood relations for M7C3 grain.
图 3 γ元胞Moore型邻居单元
Figure 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
Figure 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 7 本模拟冷却曲线及各相质量分数演变
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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%).
Parameters Symbol Unit Value Note 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 }} $ ℃ 1266.00 GS model M7C3 nucleation temperature $ \mathop T\nolimits_{\text{M}} $ ℃ 1304.00 GS model C partition coefficient at austenite/liquid interface ${k_{ { {{\rm p}, {\mathrm{\gamma }/\mathrm{L} } , {\rm C} } } } }$ — 0.407 GS model Cr partition coefficient at austenite/liquid interface ${k_{ { {{\rm p}, {\mathrm{\gamma }/\mathrm{L} } , {\rm Cr} } } } }$ — 0.576 GS model Liquidus slope of C at austenite/liquid interface ${m_{ { { {\mathrm{L}/\mathrm{\gamma } }, {\rm C} } } } }$ ℃/% –95.49 GS model Liquidus slope of Cr at austenite/liquid interface ${m_{ { { {\mathrm{L}/\mathrm{\gamma } }, {\rm Cr} } } } }$ ℃/% 6.14 GS model Liquidus slope of C at M7C3/liquid interface ${m_{ {{\rm L/M}, \text{C} } } }$ ℃/% 90.37 GS model Liquidus slope of Cr at M7C3/liquid interface ${m_{ {{\rm L/M},\text{Cr} } } }$ ℃/% 15.29 GS model Diffusion coefficient of C in austenite ${D_{ { \mathrm{\gamma }, {\rm C} } } }$ m2/s 2.57×10–10 GS model Diffusion coefficient of Cr in austenite ${D_{ { {\mathrm{\gamma } , \rm Cr} } } }$ m2/s 3.67×10–14 GS model Diffusion coefficient of C in liquid phase ${D_{ {\text{L,C} } } }$ m2/s 9.60×10–10 GS model Diffusion coefficient of Cr in liquid phase ${D_{ {\text{L,Cr} } } }$ m2/s 8.23×10–10 GS model Diffusion coefficient of C in M7C3 ${D_{ {\text{M,C} } } }$ m2/s 0.0 Diffusion coefficient of Cr in M7C3 ${D_{ {\text{M,Cr} } } }$ m2/s 0.0 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/kg 1.86×105 GS model Latent heat of fusion for M7C3 $ \mathop L\nolimits_{\text{M}} $ J/kg 2.38×105 GS model Specific heat capacity $\mathop c\nolimits_{\rm p}$ J/(kg$ \cdot $℃) 839 GS model 
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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.
Model Alloy composition M7C3 precipitation temperature/℃ γ precipitation temperature/℃ CEM precipitation temperature or solidus /℃ Phase volume fraction at CEM precipitation
temperature or solidusGS model Fe-4%C-17%Cr 1304 1266 1194(CEM) 29.91%(M7C3) 57.22%(γ) GS model Fe-4%C-17%Cr-1.5%Ti 1288 1271 1193(CEM) 26.38%(M7C3) 63.20%(γ) Fe-C phase diagram Fe-4%C-17%Cr 1305 1266 1239(solidus) — Fe-C phase diagram Fe-4%C-17%Cr-1.5%Ti 1285 1271 1248(solidus) — GS model Fe-3.23%C-23.8%Cr 1305 1297 1193(CEM) 28.18%(M7C3) 71.62%(γ) GS model Fe-3.23%C-23.8%Cr-4%Ti 1296 1324 1296(solidus) 17.80%(M7C3) 74.28%(γ) Fe-C phase diagram Fe-3.23%C-23.8%Cr 1305 1296 1292(solidus) — Fe-C phase diagram Fe-3.23%C-23.8%Cr-4%Ti 1295 1328 1295(solidus) —
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[1] Siekaniec D, Kopycinski D, Szczesny A, Guzik E, Tyraa E, Nowak A 2017 Nephron Clinical Practice 17 143
Google Scholar
[2] Liu H N, Sakamoto M, Nomura M, Ogi K 2001 Wear 250 71
Google Scholar
[3] Pokusova M, Gabrisova Z, Brusilova A, Pribulova A, Futa P 2020 Mater. Sci. Forum. 998 30
Google Scholar
[4] Filipovic M, Kamberovic Z, Korac M, Gavrilovski M 2013 Mater. Des. 47 41
Google Scholar
[5] Buytoz S, Yildirim M M, Eren H 2005 Mater. Lett. 59 607
Google Scholar
[6] 龚沛, 赵曜, 杨浩, 王宁 2017 金属热处理 42 137
Google Scholar
Gong P, Zhao Y, Yang H, Wang N 2017 Heat Treatment of Metals 42 137
Google 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 8
Google Scholar
Chen Z, Wang L L, Zhang H, Fu Y H, Zhong L S, Ye F X 2013 Hot Working Technology 42 8
Google Scholar
[8] Tang X H, Chung R, Pang C J, Li D Y, Hinckley B, Dolman K 2011 Wear 271 1426
Google Scholar
[9] Zhang H W, Nakajima K, Gandin C A, He J C 2013 ISIJ Int. 53 493
Google Scholar
[10] 王同敏, 魏晶晶, 王旭东, 姚曼 2018 金属学报 54 193
Google Scholar
Wang T M, Wei J J, Wang X D, Yao M 2018 Acta Metall. Sin. 54 193
Google Scholar
[11] 朱鸣芳, 邢丽科, 方辉, 张庆宇, 汤倩玉, 潘诗琰 2018 金属学报 54 789
Google Scholar
Zhu M F, Xing L K, Fang H, Zhang Q Y, Tang Q Y, Pan S Y 2018 Acta. Metall. Sin. 54 789
Google Scholar
[12] Zhu M F, Cao W, Chen S L, Hong C P, Chang Y A 2007 J. Phase Equilib. Diffus. 28 130
Google Scholar
[13] 戴挺, 朱鸣芳, 陈双林, 曹伟生, 洪俊杓 2008 金属学报 10 1175
Google Scholar
Dai T, Zhu M F, Chen S L, Cao W S, Hong J Z 2008 Acta Metall. Sin. 10 1175
Google Scholar
[14] Zhang H W, Gandin C A, Hamouda H B, Tourret D, Nakajima K, He J C 2010 ISIJ Int. 50 1859
Google Scholar
[15] Zhang H W, Gandin C A, Nakajima K, He J C 2012 IOP Conf Series: Materials Science Engineering 33 012063
Google Scholar
[16] 石玉峰, 许庆彦, 柳百成 2012 物理学报 61 108101
Google Scholar
Shi Y F, Xu Q Y, Liu B C 2012 Acta Phys. Sin. 61 108101
Google Scholar
[17] Michelic S C, Thuswaldner J M, Bernhard C 2010 Acta Mater. 58 2738
Google 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)
[19] Zhu M F, Hong C P, Stefanescu D M, Chang Y A 2007 Metall. Mater. Trans. B. 38 517
Google Scholar
[20] 张蕾, 赵红蕾, 朱鸣芳 2015 金属学报 51 148
Google Scholar
Zhang L, Zhao H L, Zhu M F 2015 Acta Metall. Sin. 51 148
Google Scholar
[21] Ma S Q, Xing J, He Y, Li Y F, Huang Z F, Liu G Z, Geng Q J 2015 Mater. Chem. Phys. 161 65
Google Scholar
[22] Liu Q, Zhang H W, Wang Q, Zhou X K, Jonsson P G, Nakajima K 2012 ISIJ Int. 52 2210
Google Scholar
[23] Stefan-Kharicha M, Kharicha A, Zaidat K, Reiss G, Essl W, Goodwin F, Wu M H, Ludwig A, Mugrauer C 2020 J. Cryst. Growth 541 125667
Google Scholar
[24] 付振南, 许庆彦, 熊守美 2007 中国有色金属学报 17 1567
Google Scholar
Fu Z N, Xu Q Y, Xiong S M 2007 J. Nonferrous Met. China 17 1567
Google Scholar
[25] 董祥雷, 邢辉, 陈长乐, 沙莎, 王建元, 金克新 2016 物理学报 65 58
Google Scholar
Dong X L, Xing H, Chen C L, Sha S, Wang J Y, Jin K X 2016 Acta Phys. Sin. 65 58
Google Scholar
[26] Zhang H W, Zhang S, Wang Y C, Hao Y Z, Miao M, Nakajima K, Lei H, Wang Q, He J C 2020 IOP Conf Series: Materials Science and Engineering 861 012046
Google Scholar
[27] Gandin C A 1993 Acta Metallurgica et Materialia 41 345
Google Scholar
[28] Flemings M C, Poirier D R, Barone R V, Brody H D 1970 J. Iron Steel Inst. 208 371
[29] Nastac L 1999 Acta Mater. 47 4253
Google Scholar
[30] Eggleston J J, Mcfadden G B, Voorhees P W 2001 Phys. D 150 91
Google Scholar
[31] Rappaz M, Boettinger W J 1999 Acta Mater. 47 3205
Google Scholar
[32] Burbelko A A, Gurgul D, Kaptur K W, Gorny M 2012 Arch. Foundry Eng. 12 11
Google Scholar
[33] 孙玉成 2012 博士学位论文 (山东: 山东大学)
Sun Y C 2012 Ph. D. Dissertation (Shandong: Shandong University) (in Chinese)
[34] Wang J, Qi X, Xing X, Shi Z J, Zhou Y F, Yang Q X 2019 Mater. Res. Express 6 0865h3
Google Scholar
[35] Liu S, Zhou Y F, Xing X, Wang J B, Ren X J, Yang Q X 2016 Sci. Rep. 6 1
Google Scholar
[36] Coronado J J 2011 Wear 270 287
Google Scholar
[37] Beltran S L, Stefanescu D M 2004 Metall. Mater. Trans. A. 35 2471
Google Scholar
[38] Liu S, Wang Z, Shi Z, Zhou Y F, Yang Q X 2017 J. Alloy. Compd. 713 108
Google Scholar
[39] Kopycinski D, Guzik E, Siekaniec, Szczesny A 2015 Arch Foundry Eng 15 35
Google Scholar
[40] Liu Q 2013 Ph. D. Dissertation (Stockholm, Sweden: KTH Royal Institute of Technology)
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