耦合热力学相变路径预测<strong>Fe-C</strong>包晶合金宏观偏析

doi:10.11900/0412.1961.2020.00358

金属学报

2021, Vol. 57

Issue (8): 1057-1072 DOI: 10.11900/0412.1961.2020.00358

研究论文

本期目录 | 过刊浏览

耦合热力学相变路径预测Fe-C包晶合金宏观偏析

冯苗苗¹^,², 张红伟¹^,²(

), 邵景霞¹^,², 李铁¹^,², 雷洪¹^,², 王强¹^,²

^1.东北大学材料电磁过程研究教育部重点实验室沈阳 110819
^2.东北大学冶金学院沈阳 110819

Prediction of Macrosegregation of Fe-C Peritectic Alloy Ingot Through Coupling with Thermodynamic Phase Transformation Path

FENG Miaomiao¹^,², ZHANG Hongwei¹^,²(

), SHAO Jingxia¹^,², LI Tie¹^,², LEI Hong¹^,², WANG Qiang¹^,²

^1.Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, Shenyang 110819, China
^2.School of Metallurgy, Northeastern University, Shenyang 110819, China

引用本文:

冯苗苗, 张红伟, 邵景霞, 李铁, 雷洪, 王强. 耦合热力学相变路径预测Fe-C包晶合金宏观偏析[J]. 金属学报, 2021, 57(8): 1057-1072.
Miaomiao FENG, Hongwei ZHANG, Jingxia SHAO, Tie LI, Hong LEI, Qiang WANG. Prediction of Macrosegregation of Fe-C Peritectic Alloy Ingot Through Coupling with Thermodynamic Phase Transformation Path[J]. Acta Metall Sin, 2021, 57(8): 1057-1072.

全文: PDF(8831 KB) HTML

摘要:

针对Fe-0.1%C (质量分数)包晶合金冷却过程中多固相共存及界面分配系数实时变化的情况，由杠杆定律结合热力学平衡计算(LR-TEC)获得合金由液相冷却至室温的相变路径，制成相变路径数据表，由成分与热焓线性插值获得相应温度、相质量分数、相成分和相焓，以及凝固潜热释放量和比热容随多固相析出以及成分和温度的变化关系，与连续介质宏观传输模型相结合，预测了铸锭宏观偏析形成过程。模型采用经典的Sn-5%Pb合金凝固基准实验进行了验证。在随温度和溶质成分即时变化的分配系数及多固相的影响下，预测的Fe-0.1%C合金截面偏析变得更为严重。计算结束时，采用LR-TEC耦合宏观传输预测的最大负偏析在距铸锭左侧x = 16 mm、距底面y = 45 mm处，偏析率为-2.22%；而杠杆定律解析式(LR Analytical)预测的最大负偏析位于y = 55 mm左侧壁面处，偏析率为-1.78%。2者预测的最大正偏析都位于铸锭右侧贴壁区域，合金冷却过程中的相变路径采用LR-TEC比LR Analytical预测的偏析率大1.13%。凝固计算结束时区域内仍多固相共存，其中α、γ两固相，α、渗碳体(CEM)两固相及α、γ、CEM三固相分别共存于铸锭左侧x < 0.0342 m的低温区域，δ、γ两固相共存于区域右侧x > 0.0858 m的高温区域。

关键词 ： Fe-0.1%C合金, 宏观偏析, 热力学相变路径, 多固相, 线性插值

Abstract：

The phase transformation path is vital to enclosing the macroscopic transport equations for predicting alloy macrosegregation. However, the analytical approximations for micro-segregation, such as the lever rule (LR), are invalid because an actual alloy is a multi-component system with several coexisting solids. The LR only expresses the phase transformation between a single solid phase and a liquid phase and adopts a constant solute partition coefficient, which is insufficient for micro-segregation. In this study, a model combining the thermodynamic phase transformation path calculation with the macroscopic transport was adopted to predict the macrosegregation formation in an Fe-0.1%C (mass fraction) peritectic alloy, which considers the coexistence of multi-solids and the variance of the local partition coefficient at the solid/liquid and solid/solid phase interface with a solidification process. The phase transformation path from the liquid state cooling to room temperature within a certain range of the solute concentrations was obtained using the LR approximation combined with the thermodynamic equilibrium calculation (LR-TEC). By tabulating the phase transformation path and interpolating the local concentration and enthalpy, the corresponding temperature, phase fraction, phase concentration, and phase enthalpy required in the continuum macroscopic transport model were achieved. The latent heat released and the specific heat corresponding to the amounts of the two solid phases at the peritectic or eutectic phase transformation zone were updated along with their dependence on the local concentration and temperature. This method was validated through the benchmark macrosegregation test of the binary Sn-5%Pb alloy. Regarding the Fe-0.1%C alloy, the varied local partition coefficients and the other thermodynamic parameters with multi-solids precipitating during solidification resulted in a more severe macrosegregation profile in the ingot. At the end of the solidification calculation, the predicted minimum relative solute concentration for the Fe-0.1%C alloy was -2.22% at y = 45 mm from the bottom and x = 16 mm from the left wall of the ingot by LR-TEC. In contrast, it was -1.78% using the LR Analytical model near y = 55 mm at the left-side wall. The predicted maximum macrosegregation ratio at the right wall of the ingot by LR-TEC was 1.13% larger than that achieved using the LR Analytical model. Several solids, such as α and γ, α and cementite (CEM), or α, γ, and CEM at the left part (x < 0.0342 m), and δ and γ at the right (x > 0.0858 m), still coexisted in the region at the end of solidification calculation.

Key words： Fe-0.1%C alloy macrosegregation thermodynamic phase transformation path multi-solids linear interpolation

收稿日期: 2020-09-09

ZTFLH:

TG111.4

基金资助:国家自然科学基金项目(51574074);国家自然科学基金钢铁联合研究基金项目(U1460108);辽宁省教育厅基金项目(L20150183)

作者简介: 冯苗苗，女，1996年生，硕士生

	服务

	把本文推荐给朋友
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	冯苗苗
	张红伟
	邵景霞
	李铁
	雷洪
	王强
44.8K

链接本文:

https://www.ams.org.cn/CN/10.11900/0412.1961.2020.00358 或 https://www.ams.org.cn/CN/Y2021/V57/I8/1057

图1 采用杠杆定律结合热力学平衡计算(LR-TEC)模型和杠杆定律解析(LR Analytical)模型预测的Fe-0.1%C合金相变路径

表1 计算所用合金物性参数

图2 Sn-5%Pb合金体系热焓(h)、潜热释放(ΔL)及比热容(cp)随温度(T)的变化

图3 由h及成分(c)线性插值数据表获得温度示意图(a) interpolation for T1 from c1 and h (Hk, Hk-1—mixture enthalpy closest to h according to c1 in tabulation (Hk ≤ h < Hk-1); Tk, Tk-1—temperatures corresponding to Hk, Hk-1 in tabulation, respectively; T1—temperature corresponding to c1 in tabulation)(b) interpolation for T from c1, c2 and c (c1, c2—mixture concentrations closest to c in tabulation (c2 ≤ c < c1); T2—temperature corresponding to c2 in tabulation)

表2 h与T、液相质量分数(fl)的关系

图4 Fe-0.1%C合金液/固界面分配系数(kp)随温度的变化

图5 采用LR-TEC和LR Analytical模型得到的Sn-5%Pb合金相变路径

图6 采用LR-TEC和LR Analytical模型得到的Sn-5%Pb合金分配系数随温度的变化

图7 采用LR-TEC和LR Analytical模型模拟的Sn-5%Pb合金凝固进行到400 s时全场的液相质量分数与速度分布

图8 采用LR-TEC和LR Analytical模型模拟的Sn-5%Pb合金凝固进行到400 s时溶质Pb的相对溶质成分分布[(c - c0) / c0] × 100

图9 采用LR-TEC和LR Analytical模型模拟的Sn-5%Pb合金凝固计算结束时Pb相对溶质成分分布

图10 Sn-5%Pb合金凝固结束时，距铸锭底面不同高度水平面上Pb的相对溶质成分分布曲线

图11 采用LR-TEC模型预测的Fe-0.1%C合金铸锭冷却过程中不同时刻截面上各相分布(计算结束时间570.2 s)(a) t = 110 s, fl(b) calculation end, fCEM (fCEM—phase mass fraction of cementite)(c) t = 110 s, fγ (fγ—phase mass fraction of fcc structure austenite (γ))(d) calculation end, fγ(e) t = 110 s, fδ (fδ—phase mass fraction of bcc structure ferrite (δ))(f) calculation end, fα,δ (fα,δ —phase mass fraction of bcc structure ferrite (α and δ))(g) t = 110 s, y = 0.03 m(h) calculation finish, y = 0.03 m

图12 预测的Fe-0.1%C合金铸锭凝固过程不同时刻C的相对溶质成分分布(a) LR-TEC, t =110 s (b) LR-TEC, calculation end(c) distributions of [(c - c0) / c0] × 100 at heights of y = 5 mm (c1), y = 25 mm (c2), y = 35 mm (c3), y = 45 mm (c4), and y = 55 mm (c5) from bottom of 2D ingot cross section, respectively

图13 数据表温度数据存储方式对Fe-0.1%C合金截面C的相对溶质成分分布的影响(a) y = 5 mm, t = 110 s (b) y = 5 mm, calculation end(c) y = 25 mm, t = 110 s (d) y = 25 mm, calculation end(e) y = 35 mm, t = 110 s (f) y = 35 mm, calculation end(g) y = 45 mm, t = 110 s (h) y = 45 mm, calculation end(i) y = 55 mm, t = 110 s (j) y = 55 mm, calculation end

1	Du Q, Li D Z, Li Y Y. Quantitative prediction of macrosegregation formation caused by natural convection during solidification of steel casting [J]. Acta Metall. Sin., 2000, 36: 1197
1	杜强, 李殿中, 李依依. 铸钢件凝固过程中自然对流引起的宏观偏析模拟 [J]. 金属学报, 2000, 36: 1197
2	Brody H D, Flemings M C. Solute redistribution in dendritic solidification [J]. Trans. TMS-AIME, 1966, 236: 615
3	Clyne T W, Kurz W. Solute redistribution during solidification with rapid solid state diffusion [J]. Metall. Trans., 1981, 12A: 965
4	Ohnaka I. Mathematical analysis of solute redistribution during solidification with diffusion in solid phase [J]. Trans. Iron Steel Inst. Japan, 1986, 26: 1045
5	Ahmad N, Rappaz J, Desbiolles J L, et al. Numerical simulation of macrosegregation: A comparison between finite volume method and finite element method predictions and a confrontation with experiments [J]. Metall. Mater. Trans., 1998, 29A: 617
6	Li T. Numerical simulation on macrosegregation formation during binary alloy solidification processes [D]. Shenyang: Northeastern University, 2013
6	李铁. 二元合金凝固过程宏观偏析的数值预测 [D]. 沈阳: 东北大学, 2013
7	Založnik M, Kumar A, Combeau H. An operator splitting scheme for coupling macroscopic transport and grain growth in a two-phase multiscale solidification model: Part Ⅱ-Application of the model [J]. Comput. Mater. Sci., 2010, 48: 11
8	Aboutalebi M R, Hasan M, Guthrie R I L. Coupled turbulent flow, heat, and solute transport in continuous casting processes [J]. Metall. Mater. Trans., 1995, 26B: 731
9	Kraft T, Exner H E. Numerical simulation of solidification. 1. Microsegregation in binary alloys [J]. Z. Metallkd., 1996, 87: 598
10	Gulliver G H. The quantitative effect of rapid cooling upon the constitution of binary alloys [J]. J. Inst. Met., 1913, 9: 120
11	Scheil E. Uber die eutektische kristallisation on eutectic crystallization [J]. Z. Metallkd., 1942, 34: 70
12	Kraft T, Rettenmayr M, Exner H E. An extended numerical procedure for predicting microstructure and microsegregation of multicomponent alloys [J]. Model. Simul. Mater. Sci. Eng., 1996, 4: 161
13	Kobayashi S. A mathematical model for solute redistribution during dendritic solidification [J]. Trans. Iron Steel Inst. Japan, 1988, 28: 535
14	Sundman B, Chen Q. Thermodynamic Calculation Interface TQ-Interface V7.0 [M]. Stockholm: Thermo-Calc Software AB, 2008: 1
15	Zhu M F, Cao W, Chen S L, et al. Modeling of microstructure and microsegregation in solidification of multi-component alloys [J]. J. Phase Equilib. Diffus., 2007, 28: 130
16	Dai T, Zhu M F, Chen S L, et al. Modeling of dendritic structure and microsegregation in Al-rich quaternary alloys [J]. Acta Metall. Sin., 2008, 44: 1175
16	戴挺, 朱鸣芳, 陈双林等. 铝基四元合金枝晶组织及微观偏析的数值模拟 [J]. 金属学报, 2008, 44: 1175
17	Wang T T. Numerical modeling and simulation software development of microporosity eveolution in aluminum alloy [D]. Nanjing: Southeast University, 2016
17	王韬涛. 铝合金显微气孔演化数值模拟及其软件开发 [D]. 南京: 东南大学, 2016
18	Doré X, Combeau H, Rappaz M. Modelling of microsegregation in ternary alloys: Application to the solidification of Al-Mg-Si [J]. Acta Mater., 2000, 48: 3951
19	Carozzani T, Gandin C A, Digonnet H, et al. Direct simulation of a solidification benchmark experiment [J]. Metall. Mater. Trans., 2013, 44A: 873
20	Saad A, Gandin C A, Bellet M. Temperature-based energy solver coupled with tabulated thermodynamic properties—Application to the prediction of macrosegregation in multicomponent alloys [J]. Comput. Mater. Sci., 2015, 99: 221
21	Carman P C. Flow of Gases Through Porous Media [M]. London: Butterworths Scientific Publications, 1956: 1
22	Tu W T. Modelling and simulation of macrosegregation in large steel ingots by a multicomponent and multiphase model [D]. Beijing: Tsinghua University, 2016
22	涂武涛. 大型钢锭宏观偏析多元多相建模与仿真 [D]. 北京: 清华大学, 2016
23	Bennon W D, Incropera F P. A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems-I. Model formulation [J]. Int. J. Heat Mass Transf., 1987, 30: 2161
24	Bennon W D, Incropera F P. A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems-Ⅱ. Application to solidification in a rectangular cavity [J]. Int. J. Heat Mass Transf., 1987, 30: 2171
25	Shi P. TCS Steels/Fe-Alloys Database V60 [M]. Stockholm: Thermo-Calc Software AB, 2008:１
26	Hebditch D J, Hunt J D. Observations of ingot macrosegregation on model systems [J]. Metall. Trans., 1974, 5: 1557

[1]	张利民, 李宁, 朱龙飞, 殷鹏飞, 王建元, 吴宏景. 交流电脉冲对过共晶Al-Si合金中初生Si相偏析的作用机制[J]. 金属学报, 2023, 59(12): 1624-1632.
[2]	吴春雷,李德伟,朱晓伟,王强. 电磁旋流水口连铸技术对小方坯凝固组织形貌和宏观偏析的影响[J]. 金属学报, 2019, 55(7): 875-884.
[3]	李军, 夏明许, 胡侨丹, 李建国. 大型铸锭均质化问题及其新解[J]. 金属学报, 2018, 54(5): 773-788.
[4]	沈厚发, 陈康欣, 柳百成. 钢锭铸造过程宏观偏析数值模拟[J]. 金属学报, 2018, 54(2): 151-160.
[5]	李军, 王军格, 任凤丽, 葛鸿浩, 胡侨丹, 夏明许, 李建国. 基于成分均匀化的层状铸造方法的实验与模拟研究[J]. 金属学报, 2018, 54(1): 118-128.
[6]	李军,葛鸿浩,GE Honghao,WU Menghuai,李建国. 基于热溶质对流及晶粒运动的柱状晶-非球状等轴晶混合三相模型^*[J]. 金属学报, 2016, 52(9): 1096-1104.
[7]	赵海东; 吴朝忠; 李元元; 大中逸雄 . 垂直向上凝固Al-Cu铸件中微观孔洞形成的数值模拟[J]. 金属学报, 2008, 44(11): 1340-1347 .
[8]	王同敏; 李廷举; 曹志强; 金俊泽; T.Grimmig; A.Buhrig-Polaczek; M.Wu; A.Ludwig . 等轴球晶凝固多相体系内热溶质对流、补缩流及晶粒运动的数值建模 II．模型的应用[J]. 金属学报, 2006, 42(6): 591-598 .
[9]	李中原; 赵九洲 . 平行板型薄板坯连铸结晶器中钢液流动、凝固及溶质分布的三维耦合数值模拟[J]. 金属学报, 2006, 42(2): 211-217 .
[10]	郭大勇; 杨院生; 童文辉; 胡壮麒 . 电磁离心凝固过程中宏观偏析的数值模拟[J]. 金属学报, 2004, 40(3): 275-280 .
[11]	郭大勇; 杨院生; 童文辉; 胡壮麒 . 电磁离心凝固过程中宏观偏析的数值模拟[J]. 金属学报, 2004, 40(3): 275-280 .
[12]	张勤; 崔建忠 . 7075铝合金CREM法半连铸坯中溶质元素的的宏观分布[J]. 金属学报, 2003, 39(12): 1264-1268 .
[13]	沈厚发; C.Beckermann . 糊状区变形及浓度再分布的模拟实验[J]. 金属学报, 2002, 38(4): 352-358 .
[14]	张红伟; 王恩刚 . 方坯连铸过程中钢液流动、凝固及溶质分布的耦合数值模拟[J]. 金属学报, 2002, 38(1): 99-104 .
[15]	杜强; 李殿中 . 铸铁件凝固过程中自然对流引起的宏观偏析模拟[J]. 金属学报, 2000, 36(11): 1197-1200 .

Viewed

Full text

Abstract

Cited

Shared

Discussed