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

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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.

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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

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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)

Condition	T	f_l
h > h_liq (Liquid zone)	T = (h - L) / c_p	f_l = 1
h_e < h ≤ h_liq (Mushy zone)	T = (h - Lf_l) / c_p	$f l = 1 - 1 1 - k p T - T l i q T - T m$
h_sol < h ≤ h_e (Mushy zone)	T = T_e	f_l = (h - c_pT_e) / L
h ≤ h_sol (Solid zone)	T = h / c_p	f_l = 0

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

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