NUMERICAL STUDY ON FREE-CUTTING PHASE PRECIPITATION BEHAVIOR IN Fe-Bi-Mn TERNARY ALLOY MULTIPHASE TRANSFORMATION- DIFFUSION SYSTEM

doi:10.11900/0412.1961.2014.00200

Acta Metall Sin

2014, Vol. 50

Issue (11): 1393-1402 DOI: 10.11900/0412.1961.2014.00200

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NUMERICAL STUDY ON FREE-CUTTING PHASE PRECIPITATION BEHAVIOR IN Fe-Bi-Mn TERNARY ALLOY MULTIPHASE TRANSFORMATION- DIFFUSION SYSTEM

WANG Zhe¹, WANG Fazhan^1,²(

), HE Yinhua¹, WANG Xin¹, MA Shan², WANG Huimian³

1 College of Materials and Mineral Resources, Xi′an University of Architecture and Technology, Xi′an 710055
2 School of Mechanical and Electrical Engineering, Xi′an University of Architecture and Technology, Xi′an 710055
3 Technology Center, Shanxi Taigang Stainless Steel Co. Ltd., Taiyuan 030003

Cite this article:

WANG Zhe, WANG Fazhan, HE Yinhua, WANG Xin, MA Shan, WANG Huimian. NUMERICAL STUDY ON FREE-CUTTING PHASE PRECIPITATION BEHAVIOR IN Fe-Bi-Mn TERNARY ALLOY MULTIPHASE TRANSFORMATION- DIFFUSION SYSTEM. Acta Metall Sin, 2014, 50(11): 1393-1402.

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Abstract

The solidification process of alloys are not just liquid to solid phase transformation, in fact in some alloys liquid to gas and gas to liquid phase transformation processes happen. A method incorporating the full diffusion-governed phase transformation kinetics into a multiphase volume average solidification model is presented. The motivation to develop such a model is to predict the multiple effect of inclusions precipitation behavior in castings. A key feature of this model, different from most previous ones which usually assume an infinite solute mixing in liquid lead to erroneous estimation of the multiphase diffusion path, is that diffusions in solid, liquid and gas phases are considered. Here solidification of Fe-Bi-Mn ternary alloy is examined. As MnS and Bi have large differences in the solute partition coefficient, diffusion coefficient and liquidus slope, the multiphase diffusion path shows differently from those predicted by infinite liquid mixing models. In this work, a three-dimensional mathematical model for a three-phase flow during its horizontai solidification was studied based on diffusion-governed phase transformation kinetics. Effects of Fe-Bi-Mn ternary alloy solidification on solid-liquid-gas phase transformation were considered. The free-cutting phase precipitation behavior was studied and multiphase transformation and multiphase diffusion path of free-cutting phase precipitation behavior were analyzed. Results show that the multiphase transformation-diffusion is strongly influenced by free-cutting phases precipitation behavior: MnS has a relatively large partition coefficient and small diffusion coefficient with larger M_ls,MnS (solid-liquid mass transfer rate of MnS). During solidification, C^*_s,MnS (solid interface concentration of MnS) may become even larger than C_l,MnS (liquid concentration of MnS), MnS in liquid is assumed to be fully ‘trapped’ in solid and there is no longer any enrichment of MnS; however Bi has a relatively small partition coefficient and large diffusion coefficient with smaller M_ls,Bi (solid-liquid mass transfer rate of Bi) and negative M_gl,Bi (liquid-gas mass transfer rate of Bi), during solidification, C_l,Bi (liquid concentration of Bi) always greater than C^*_s,Bi (solid interface concentration of Bi). In addition, due to the existence of Bi-gas phase, Bi continuous to flow, enriched in the solidified around MnS. Calculated results show good agreement with experimental data.

Key words: Fe-Bi-Mn ternary alloy solidification multiphase transformation multiphase diffusion path numerical study

Received: 25 July 2014

ZTFLH:	TG111.4
	TG146

Fund: National Science and Technology Pillar Program During the Twelfth Five-Year Plan Period (No.2011BAE31B02) and Preparation and Processing of Non-ferrous Materials of High Performance for Innovative Research of Xi′an University of Architecture and Technology of China

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	Zhe WANG
	Fazhan WANG
	Yinhua HE
	Xin WANG
	Shan MA
	Huimian WANG

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https://www.ams.org.cn/EN/10.11900/0412.1961.2014.00200 OR https://www.ams.org.cn/EN/Y2014/V50/I11/1393

Name	Equation	Number
Conservative equation
Solid-liquid mass conservative	$? ? t (f s ρ s) = M l s$	(1)
	$? ? t (f l ρ l) + ? ? (f l ρ l u l) = M s l$	(2)
Liquid-gas mass conservative	$? ? t (f l ρ l) + ? ? (f l ρ l u l) = M g l$	(3)
	$? ? t (f g ρ g) + ? ? (f g ρ g u g) = M l g$	(4)
Solid-liquid momentum conservative	$? ? t (f l ρ l u l) + ? ? (f l ρ l u l ? u l) = - f l ? p + ? ? τ l + f l ρ l g - U l s M - U l s D τ l = u l (? ? (f l μ l) + (? ? (f l μ l)) T)$	(5)
		(5)
Liquid-gas momentum conservative	$? ? t (f g ρ g u g) + ? ? (f g ρ g u g ? u g) = - f g ? p + ? ? τ g + f g ρ g g - U g l M - U g l D τ g = u g (? ? (f g μ g) + (? ? (f g μ g)) T)$	(6)
		(6)
Solid-liquid species conservative	$? ? t (f s ρ s c s) = C l s M$	(7)
	$? ? t (f l ρ l c l) + ? ? (f l ρ l u l c l) = C s l M$	(8)
Liquid-gas species conservative	$? ? t (f l ρ l c l) + ? ? (f l ρ l u l c l) = C g l M$	(9)
	$? ? t (f g ρ g c g) + ? ? (f g ρ g u g c g) = C l g M$	(10)
Solid enthalpy conservative	$? ? t (f s ρ s h s) = ? ? (f s k s ? T s) + Q s M + Q l s D h s = ∫ T r e f T s c p s d T + h s r e f$	(11)
		(11)
Liquid enthalpy conservative	$? ? t (f l ρ l h l) + ? ? (f l ρ l u l h l) = ? ? (f l k l ? T l) + Q l M - Q l s D h l = ∫ T r e f T l c p l d T + h l r e f$	(12)
		(12)
Gas enthalpy conservative	$? ? t (f g ρ g h g) + ? ? (f g ρ g u g h g) = ? ? (f g k g ? T g) + Q g M - Q g l D h g = ∫ T r e f T g c p g d T + h g r e f$	(13)
		(13)
Transfer rate equation
Solid-liquid mass transfer rate	$M l s = v R l ? S l s ? ρ s$	(14)
Liquid-gas mass transfer rate	$M g l = v R g ? S g l ? ρ l$	(15)
Solid-liquid interface diffusion-phase transformation rate	$ν R l = d f s d t ? 1 S l s$	(16)
Liquid-gas interface diffusion-phase transformation rate	$ν R g = d f l d t ? 1 S g l$	(17)

Table 1 Conservative equations and transfer rate equations^[10,14,16]

Fig.1 Schematic of solidification process of the Fe-Bi-Mn ternary alloy (l, m, s represent liquid zone, solid zone, mushy zone, respectively)

Fig.2 Schematic of multiphase transformation-diffusion system (The interfacial transfer of different species are indicated by Z₁~Z₁₂)

Table 2 Physical parameters used in simulation

Fig.3 Schematic of 3D model with boundary and initial conditions

Fig.4 3D distributions of Bi and MnS isosurfaces of solidified Fe-0.3%Bi-0.9%Mn ternary alloy

Fig.5 Section zone IV shown in Fig.4 at 900 s of alloy solidification

Fig.6 Isolines in section zone I shown in Fig.4 at 900 s of alloy solidification

Fig.7 Section zone IV shown in Fig.4 at 1500 s of alloy solidification

(a) isolines of liquid fraction and nephograms of mass fraction of MnS

(b) isolines of liquid fraction and nephograms of mass fraction of Bi

Fig.8 (C_l,MnS, C_l,Bi) , (C^*_l,MnS, C^*_l,Bi) and (C^*_s,MnS, C^*_s,Bi) multiphase diffusion paths of path I

Fig.9 Curves of solid, liquid and gas-phase solute concentration and their interfacial concentration with volume fraction of solid caused by multiphase diffusion

(a) mass fraction of Bi (b) mass fraction of MnS

Fig.10 Experimental (a, c) and simulated (b, d) microstructures in transversal (a, b) and vertical (c, d) directions of Fe-0.3%Bi-0.9%Mn free-cuting stainless steel ingot

Fig.11 Experimental (a) and simulated (b) COV_d (coefficient-of-variance of the mean near-neighbor distance) of Bi and MnS on ingot section

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