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Acta Metall Sin  2021, Vol. 57 Issue (8): 1057-1072    DOI: 10.11900/0412.1961.2020.00358
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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
Cite this article: 

FENG Miaomiao, ZHANG Hongwei, SHAO Jingxia, LI Tie, LEI Hong, WANG Qiang. Prediction of Macrosegregation of Fe-C Peritectic Alloy Ingot Through Coupling with Thermodynamic Phase Transformation Path. Acta Metall Sin, 2021, 57(8): 1057-1072.

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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     
Received:  09 September 2020     
ZTFLH:  TG111.4  
Fund: National Natural Science Foundation of China(51574074);National Natural Science Foundation of China and Shanghai Baosteel(U1460108);Natural Science Foundation of Liaoning Province(L20150183)
About author:  ZHANG Hongwei, professor, Tel: (024)83683985, E-mail: hongweizhang@epm.neu.edu.cn

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2020.00358     OR     https://www.ams.org.cn/EN/Y2021/V57/I8/1057

Fig.1  Phase transformation paths of Fe-0.1%C alloy predicted by LR-TEC (a) and LR Analytical (b) models (LR—lever rule, TEC—thermodynamic equilibrium calculation, CEM—cementite, L— liquid, S—solid, T—temperature)
Parameter descriptionSymbolUnitSn-5%PbFe-0.1%C
Initial concentrationc0%5.00.1
Initial temperatureT0oC2261550
Pure solvent melting temperatureTmoC2321538
Partition coefficientkp-0.0656[5]0.2[8]
Liquidus temperatureTliqoC224.861530.12
Liquidus slopemoC·%-1-1.286[5]-80.579[8]
Eutectic/peritectic temperatureTeoC181.411494.63
Liquid phase concentration at eutectic/peritectic pointce%38.10.53
Solid phase concentration at eutectic/peritectic pointces%2.20.09
Thermal expansion coefficientβToC-16 × 10-5[5]1 × 10-4[8]
Solute expansion coefficientβs%-1-5.3 × 10-3[5]4 × 10-5[8]
Reference concentrationcref%5.00.1
Reference temperatureTrefoC2261550
Ambient temperatureTextoC2525
Liquid densityρkg·m-37000[5]7020[8]
Dynamic viscosityμlPa·s1.0 × 10-3[5]6.2 × 10-3[8]
Latent heat of solidificationLJ·kg-161000[5]270000[8]
Specific heat capacity at constant pressurecpJ·kg-1·K-1260[5]680[8]
Thermal conductivity of alloyλW·m-1·K-155[5]34[8]
Liquid diffusion coefficientDlm2·s-11 × 10-8[5]1 × 10-8[8]
Secondary dendrite arm spacingλ2μm6550
Heat transfer coefficientαW·m-2·K-1300800
Time stepΔts0.010.05
Table1  The alloy physical properties used in the calculation
Fig.2  Variances of enthalpy (h), release of latent heat (ΔL) and cp of Sn-5%Pb alloy with T
Fig.3  Illustrated linear interpolations for temperature via h and concentration (c) in tabulated phase transformation path
ConditionTfl
h > hliq (Liquid zone)T = (h - L) / cpfl = 1
he < hhliq (Mushy zone)T = (h - Lfl) / cpfl=1-11-kpT-TliqT-Tm
hsol < hhe (Mushy zone)T = Tefl = (h - cpTe) / L
hhsol (Solid zone)T = h / cpfl = 0
Table 2  Relations between h, T and mass fraction of liquid (fl)
Fig.4  Dependences of kp on temperature in Fe-0.1%C alloy
Fig.5  Phase transformation paths of Sn-5%Pb alloy predicted by LR-TEC and LR Analytical models
Fig.6  Dependences of kp on temperature in Sn-5%Pb alloy predicted by LR-TEC and LR Analytical models
Fig.7  Mass fraction of liquid and velocity field solidified at 400 s for Sn-5%Pb alloy predicted by LR-TEC (|V|max = 0.79 mm/s) (a) and LR Analytical (|V|max = 0.67 mm/s) (b) models (|V|max—maximum absolute value of velocity in the flow field)
Fig.8  Distributions of relative solute concentration [(c - c0) / c0] × 100 for solute Pb solidified at 400 s for Sn-5%Pb alloy predicted by LR-TEC (a) and LR Analytical (b) models
Fig.9  Distributions of [(c - c0) / c0] × 100 for solute Pb at the end of solidification calculation for Sn-5%Pb alloy predicted by LR-TEC (t = 991.82 s) (a) and LR Analytical (t = 1202.37 s) (b) models
Fig.10  Distributions of [(c - c0) / c0] × 100 for solute Pb on the plane at heights of y = 5 mm (a), y = 25 mm (b), y = 35 mm (c), and y = 55 mm (d) from bottom of the ingot at end of solidification for Sn-5%Pb alloy
Fig.11  Phase distributions in 2D ingot section during cooling process of Fe-0.1%C alloy predicted by LR-TEC model (Calculation finishing at 570.2 s)
Fig.12  Distributions of predicted [(c - c0) / c0] × 100 for solute C during solidification of Fe-0.1%C alloy ingot
Fig.13  Influences of storage mode of temperature in tabulation on distributions of [(c - c0) / c0] × 100 for solute C at cross section of the Fe-0.1%C alloy ingot (Mode 1—intitial temperature Tini = Tliq (int type) + overheat 30oC, temperature step ΔT = -1oC; Mode 2—Tini = Tliq (real type) + overheat 30oC, ΔT = -1oC; Mode 3—Tini = Tliq (int) + overheat 30oC, ΔT = -1oC, with L/δ, L + δ/γ, γ/α, γ + α/CEM phase transformation points in tabulation; Mode 4—Tini = Tliq (real) + overheat 30oC, with temperature reset at each phase transformation point (real type) while keeping ΔT = -1oC in tabulation)
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