高温镍基合金电渣重熔过程中的<bold>Al</bold>、<bold>Ti</bold>成分控制

巨建涛; 朱智洪; 杨康帅; 棘广恒; 安家良; 史成斌; Ju Jiantao; Zhu Zhihong; Yang Kangshuai; Ji Guangheng; An Jialiang; Shi Cheng- bin

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Control of Al and Ti Contents During Electroslag Remelting of High-Temperature Ni-based Alloys PDF

- ORCID：
Ju Jiantao ^1,2
✉
- ORCID：
Zhu Zhihong ^1,2
- ORCID：
Yang Kangshuai ^1,2
- ORCID：
Ji Guangheng ^1,2
- ORCID：
An Jialiang ^1,2
- ORCID：
Shi Cheng- bin ³

1. School of Metallurgical Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China； 2. Metallurgical Engineering Technology Research Centre of Shaanxi Province, Xi'an 710055, China； 3. State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China

Updated：2021-10-28

Abstract

The oxidation of Al and Ti in the electroslag remelting process causes an uneven axial composition of the electroslag ingot, which adversely affects its performance, including corrosion resistance and mechanical properties. To control the uniformity of Al and Ti content in electroslag ingots, it is necessary to clarify the change in Al and Ti content during the high-temperature electroslag remelting and to reduce the oxidation of Al and Ti in the alloy by optimizing the slag system ratio and smelting conditions. The research status of Al and Ti element control in the electroslag remelting process was reviewed based on the existing literature, taking the low-fluorine slag CaF₂-CaO-Al₂O₃-MgO-TiO₂ and Incoloy 825 alloy as examples. The ion and molecular coexistence theory of slag (IMCT) was used along with FactSage software to summarize the thermodynamic and kinetic research methods. The effects of temperature and components of slag on the equilibrium Al and Ti contents in the alloy were discussed. Based on the film-penetration theory, a kinetics model for predicting Al and Ti contents in the alloy was proposed, and the mathematical equation of the Al and Ti contents vs time in the electroslag process and the slag-metal reaction rate-limiting method were obtained. Results show that the optimum TiO₂ addition during the electroslag remelting for Incoloy 825 alloy is determined to be approximately 10%. The slag-metal equilibrium experimental results were compared and analyzed using IMCT and FactSage. It is found that the FactSage calculation results are more accurate than the IMCT calculation results. The higher the TiO₂ content, the smaller the deviation between the calculated and experimental results.

Keywords

electroslag remelting; Al, Ti content; thermodynamics; IMCT; kinetics

Science Press

Alloys and steels refined by electroslag remelting are commonly used in aerospace and petrochemical fields^[

1], so there are strict requirements on all aspects of their perfor-mance, and the alloying elements Al and Ti in the metal are the key elements that determine their performance. For example, the high-temperature nickel-based alloys are solid solution-strengthened Fe-Cr-Ni-based corrosion-resistant alloys. The Al and Ti contents in the alloy determine the strengthening phase γ'-Ni₃(Al, Ti), the precipitation tempe-rature, and the amount of Ti(C, N), which in turn affect the alloy’s structure, mechanics, corrosion resistance, and melting point of the alloy^{[Reference 2-4}2-4]. At present, the main production methods for most high-temperature nickel-based alloys are vacuum melting and electroslag remelting. However, the oxidation-reduction reaction between the slag and the metal during the electroslag remelting process causes the metal elements Al and Ti in the electroslag ingot to be oxidized. This results in their uneven distribution in the axial direction, and seriously affects the quality of the electroslag ingot^{[Reference 5-8}5-8].

Current research methods of component content control in the electroslag process rely upon theoretical calculations combined with experimental verification. Researchers have proposed a large number of reaction models, including thermodynamic models, kinetic models, deoxidation models, and desulphurisation models, to predict the content changes of various components^[

9-13]. The study of the control of Al and Ti content employs mainly a thermodynamic model and a kinetic model. In the case of an argon atmosphere or addition of a deoxidizer, the oxidation reaction equation of Al and Ti in the alloy is as follows^{[Reference 14

Baidu Scholar}14,15]:

4[Al]+3(TiO₂)=3[Ti]+2(Al₂O₃)

(1)

The Al₂O₃ content in the slag is high, and the Ti content in the high-titanium and low-aluminium alloy is much higher than the Al content, which causes the Ti element to be easily oxidized. At present, the focus of thermodynamics research is to determine the optimal amount of TiO₂ in the slag when the content of Al and Ti in the alloy is controlled. However, the TiO₂ content required for smelting is not only related to the type of alloy but also affected by the content of other components in the slag. For different alloys, the optimal TiO₂ content in the slag is variable. The focus of kinetics research is to predict the distribution of Al and Ti elements in electroslag ingots based on actual electroslag process parameters and slag composition^[

16-18]. This more closely represents actual conditions. The influence of slag composition and smelting conditions on Al and Ti content can be determined, and the formulation of process parameters in the electroslag process can be clarified. Therefore, it is important to summarize the previous research methods and results to obtain the change regularity and mechanism of Al and Ti content during the electroslag remelting process.

This paper summarizes the research progress on the control of Al and Ti content during the electroslag remelting process. In addition, based on the ion and molecular coexistence theory of slag (IMCT) and FactSage (GTT-Technologies, DE) software calculations, the changes in the equilibrium Al and Ti contents of the CaF₂-CaO-Al₂O₃-MgO-TiO₂ slag reaction with Incoloy 825 alloy were identified. The oxidation regularity of Al and Ti during the electroslag remelting of the Incoloy 825 alloy reveals the optimal TiO₂ content in the slag. To provide theoretical guidance for the control of Al and Ti content in the process of electroslag remelting, a kinetic model for predicting Al and Ti contents was proposed based on the film permeation theory.

1 Thermodynamic Calculation Method

The thermodynamic calculation of Al and Ti contents during the electroslag remelting process can provide theoretical support for the slag system design, and the key in the calculation is the component activity in the slag. The reaction of Al and Ti vs Al₂O₃ and TiO₂ in the slag during the electroslag remelting process under the protection of argon has been shown in Eq.(1), and the equilibrium constant of the reaction is shown in Eq.(2)^[

19]:

l g K = l g \frac{a_{T i}^{3} \cdot a_{A l_{2} O_{3}}^{2}}{a_{A l}^{4} \cdot a_{T i O_{2}}^{3}} = l g \frac{f_{T i}^{3} [T i]}{f_{A l}^{4} [A l]} + l g \frac{a_{A l_{2} O_{3}}^{2}}{a_{T i O_{2}}^{3}} = \frac{35300}{T} - 9.94

(2)

where $a_{A l}$ and $a_{T i}$ are the activities of Al and Ti in the alloy, and $a_{T i O_{2}}$ and $a_{A l_{2} O_{3}}$ are the activities of TiO₂ and Al₂O₃ in the slag, respectively; the coefficients $f_{A l}$ and $f_{T i}$ are the activity coefficients of Al and Ti elements, respectively, and are calculated using Wagner's equation in the alloy with 1% as the standard state, as shown in Eq.(3):

l g f_{i} = \sum e_{i}^{j} [% j]

(3)

where $f_{i}$ represents the activity coefficient of element i in the alloy; $e_{i}^{j}$ represents the activity interaction coefficient of element j with respect to element i in the alloy. The activity interaction coefficients of the components in the alloy are listed in Table 1. The Incoloy 825 alloy composition is shown in Table 2.

Table 1 Activity interaction coefficient e

_{i}^{j}

of the alloying ele-ments in Incoloy 825 alloy^{[Reference 20-23}20-23]

Element	Mn	Cr	Ni	Al	Ti	Cu	Mo
Al	0.034	0.045	-0.0376	0.040	-	-	-
Ti	-0.120	0.025	-0.0166	-	0.048	0.014	0.016

Table 2 Chemical composition of the Incoloy 825 alloy (wt%)

C	Mn	Si	P	S	Cr	Mo	Ni	Cu	Al	Ti	O	Fe
0.010	0.107	0.131	0.009	0.009	20.620	3.180	38.880	1.660	0.120	1.000	0.0026	Bal.

1.1 IMCT calculation of component activity in slag

According to the theoretical assumption of IMCT, the structural units existing in the slag system include four simple ions of Ca²⁺, Mg²⁺, F^-, and O^2-, two simple molecules of Al₂O₃ and TiO₂ ^[

24,25], other related compounds (Table 3), and related chemical reactions (Table 4). The mole fraction of oxide in the slag can be expressed as

b_{1} = n_{C a O}^{0}

b_{2} = n_{C a F_{2}}^{0}

b_{3} = n_{M g O}^{0}

b_{4} = n_{A l_{2} O_{3}}^{0}

b_{5} = n_{T i O_{2}}^{0}

. According to the definition of IMCT, Eq.(4~9) can be acquired by defining N₁, N₂, N₃, N₄, and N₅ as the active concentrations of the components. MATLAB R2017b (MathWorks, USA) was used to perform the calculations based on Eq.(4~9).

N_{1} + N_{2} + \dots + N_{5} + N_{c 1} + N_{c 2} + \dots + N_{c 15} = \sum N_{i} = 1

(4)

\begin{array}{l} b_{1} = (0.5 N_{1} + N_{c 1} + 3 N_{c 3} + 12 N_{c 4} + N_{c 5} + N_{c 6} + N_{c 7} \\ + 3 N_{c 8} + 4 N_{c 9} + 3 N_{c 14} + 11 N_{c 15}) \sum n_{i} = n_{C a O}^{0} \end{array}

(5)

b_{2} = (1 / 3 N_{2} + N_{c 15} + N_{c 16}) \sum n_{i} = n_{C a F_{2}}^{0}

(6)

b_{3} = (0.5 N_{3} + N_{c 2} + N_{c 11} + N_{c 12} + 2 N_{c 13}) \sum n_{i} = n_{M g O}^{0}

(7)

\begin{array}{l} b_{4} = (N_{4} + N_{c 1} + N_{c 2} + N_{c 3} + 7 N_{c 4} + 2 N_{c 5} + 6 N_{c 6} + N_{c 10} \\ + N_{c 14} + 3 N_{c 15} + 7 N_{c 16}) \sum n_{i} = n_{A l_{2} O_{3}}^{0} \end{array}

(8)

\begin{array}{l} b_{5} = (N_{5} + N_{c 7} + 2 N_{c 8} + 3 N_{c 9} + N_{c 10} + N_{c 11} + \\ 2 N_{c 12} + N_{c 13}) \sum n_{i} = n_{T i O_{2}}^{0} \end{array}

(9)

Table 3 Expression of structural units as ion couples or complex molecules, their mole numbers, and mass action concentrations in 100 g CaF₂-CaO-Al₂O₃-MgO-TiO₂ slags based on IMCT

Item	Structural units as ion couples or molecules	Number of structural units or ion couples	Mole number of structural unit, n_i/mol	Mass action concentration of structural unit or ion couple, N_i
Simple cation	Ca²⁺+ O^2-	1	$n_{1} = n_{C a^{2 +}, C a O} = n_{O^{2 -}, C a O}$	$N_{1} = \frac{2 n_{1}}{\sum n_{i}} = N_{C a O}$
	Ca²⁺+ 2F^2-	2	$n_{2} = n_{C a^{2 +}, C a F_{2}} = 2 n_{F^{-}, C a F_{2}}$	$N_{2} = \frac{3 n_{2}}{\sum n_{i}} = N_{C a F_{2}}$
	Mg²⁺+ O^2-	3	$n_{3} = n_{M g^{2 +}, M g O} = n_{O^{2 -}, M g O}$	$N_{3} = \frac{2 n_{3}}{\sum n_{i}} = N_{M g O}$
Simple molecule	Al₂O₃	4	$n_{4} = n_{A l_{2} O_{3}}$	$N_{4} = \frac{n_{4}}{\sum n_{i}} = N_{A l_{2} O_{3}}$
Simple molecule	TiO₂	5	$n_{5} = n_{T i O_{2}}$	$N_{5} = \frac{n_{5}}{\sum n_{i}} = N_{T i O_{2}}$
Complex molecule	CaO·Al₂O₃	c1	$n_{c 1} = n_{C a O \cdot A l_{2} O_{3}}$	$N_{c 1} = \frac{n_{c 1}}{\sum n_{i}} = N_{C a O \cdot A l_{2} O_{3}}$
	MgO·Al₂O₃	c2	$n_{c 2} = n_{M g O \cdot A l_{2} O_{3}}$	$N_{c 2} = \frac{n_{c 2}}{\sum n_{i}} = N_{M g O \cdot A l_{2} O_{3}}$
	3CaO·Al₂O₃	c3	$n_{c 3} = n_{3 C a O \cdot A l_{2} O_{3}}$	$N_{c 3} = \frac{n_{c 3}}{\sum n_{i}} = N_{3 C a O \cdot A l_{2} O_{3}}$
	12CaO·7Al₂O₃	c4	$n_{c 4} = n_{12 C a O \cdot 7 A l_{2} O_{3}}$	$N_{c 4} = \frac{n_{c 4}}{\sum n_{i}} = N_{12 C a O \cdot 7 A l_{2} O_{3}}$
	CaO·2Al₂O₃	c5	$n_{c 5} = n_{C a O \cdot 2 A l_{2} O_{3}}$	$N_{c 5} = \frac{n_{c 5}}{\sum n_{i}} = N_{C a O \cdot 2 A l_{2} O_{3}}$
	CaO·6Al₂O₃	c6	$n_{c 6} = n_{C a O \cdot 6 A l_{2} O_{3}}$	$N_{c 6} = \frac{n_{c 6}}{\sum n_{i}} = N_{C a O \cdot 6 A l_{2} O_{3}}$
	CaO·TiO₂	c7	$n_{c 7} = n_{C a O \cdot T i O_{2}}$	$N_{c 7} = \frac{n_{c 7}}{\sum n_{i}} = N_{C a O \cdot T i O_{2}}$
	3CaO·2TiO₂	c8	$n_{c 8} = n_{3 C a O \cdot 2 T i O_{2}}$	$N_{c 8} = \frac{n_{c 8}}{\sum n_{i}} = N_{3 C a O \cdot 2 T i O_{2}}$
	4CaO·3TiO₂	c9	$n_{c 9} = n_{4 C a O \cdot 3 T i O_{2}}$	$N_{c 9} = \frac{n_{c 9}}{\sum n_{i}} = N_{4 C a O \cdot 3 T i O_{2}}$
	Al₂O₃·TiO₂	c10	$n_{c 10} = n_{A l_{2} O_{3} \cdot T i O_{2}}$	$N_{c 10} = \frac{n_{c 10}}{\sum n_{i}} = N_{A l_{2} O_{3} \cdot T i O_{2}}$
	MgO·TiO₂	c11	$n_{c 11} = n_{M g O \cdot T i O_{2}}$	$N_{c 11} = \frac{n_{c 11}}{\sum n_{i}} = N_{M g O \cdot T i O_{2}}$
	MgO·2TiO₂	c12	$n_{c 12} = n_{M g O \cdot 2 T i O_{2}}$	$N_{c 12} = \frac{n_{c 12}}{\sum n_{i}} = N_{M g O \cdot 2 T i O_{2}}$
	2MgO·TiO₂	c13	$n_{c 13} = n_{2 M g O \cdot T i O_{2}}$	$N_{c 13} = \frac{n_{c 13}}{\sum n_{i}} = N_{2 M g O \cdot T i O_{2}}$
	3CaO·3Al₂O₃·CaF₂	c14	$n_{c 14} = n_{3 C a O \cdot 3 A l_{2} O_{3} \cdot C a F_{2}}$	$N_{c 14} = \frac{n_{c 14}}{\sum n_{i}} = N_{3 C a O \cdot 3 A l_{2} O_{3} \cdot C a F_{2}}$
	11CaO·7Al₂O₃·CaF₂	c15	$n_{c 15} = n_{11 C a O \cdot 7 A l_{2} O_{3} \cdot C a F_{2}}$	$N_{c 15} = \frac{n_{c 15}}{\sum n_{i}} = N_{11 C a O \cdot 7 A l_{2} O_{3} \cdot C a F_{2}}$

Table 4 Chemical reaction formulas of possibly formed complex molecules^{[Reference 26-28}26-28]

Reaction	ΔG_i^θ/J·mol^-1	N_i
(Ca²⁺+O^2-) + (Al₂O₃) = (CaO·Al₂O₃)	59413 - 59.413T	$N_{c 1} = K_{c 1} N_{1} N_{4}$
(Mg²⁺ + O^2-) + (Al₂O₃) = (MgO·Al₂O₃)	-18828 - 6.276T	$N_{c 2} = K_{c 2} N_{3} N_{4}$
3(Ca^{2 +}+ O^2-) + (Al₂O₃) = (3CaO·Al₂O₃)	-21757 - 29.288T	$N_{c 3} = K_{c 3} N_{1}^{3} N_{4}$
12(Ca²⁺ + O^2-) + 7(Al₂O₃) = (12CaO·7Al₂O₃)	617977 - 612.119T	$N_{c 4} = K_{c 4} N_{1}^{12} N_{4}^{7}$
(Ca²⁺ + O^2-) + 2(Al₂O₃) = (CaO·2Al₂O₃)	-16736 - 25.522T	$N_{c 5} = K_{c 5} N_{1} N_{4}^{2}$
(Ca²⁺ + O^2-) + 6(Al₂O₃) = (CaO·6Al₂O₃)	-22594 - 31.798T	$N_{c 6} = K_{c 6} N_{1} N_{4}^{6}$
(Ca²⁺ + O^2-) + (TiO₂) = (CaO·TiO₂)	-79900 - 3.35T	$N_{c 7} = K_{c 7} N_{1} N_{5}$
3(Ca²⁺ + O^2-) + 2(TiO²) = (3CaO·2TiO₂)	-207100 - 11.35T	$N_{c 8} = K_{c 8} N_{1}^{3} N_{5}^{2}$
4(Ca²⁺ + O^2-) + 3(TiO²) = (4CaO·3TiO₂)	-292880 - 17.573T	$N_{c 9} = K_{c 9} N_{1}^{4} N_{5}^{3}$
(Al₂O₃) + (TiO₂) = (Al₂O₃·TiO₂)	-25270 + 3.924T	$N_{c 10} = K_{c 10} N_{4} N_{5}$
(Mg²⁺ + O^2-) + (TiO₂) = (MgO·TiO₂)	-26400 + 3.14T	$N_{c 11} = K_{c 11} N_{3} N_{5}$
(Mg²⁺ + O^2-) + 2(TiO₂) = (MgO·2TiO₂)	-27600 + 0.63T	$N_{c 12} = K_{c 12} N_{3} N_{5}^{2}$
2(Mg²⁺+ O^2-) + (TiO₂) = (2MgO·TiO₂)	-25500 + 1.26T	$N_{c 13} = K_{c 13} N_{3}^{2} N_{5}$
3(Ca²⁺+ O^2-) + 3(Al₂O₃) + (Ca²⁺+ 2F^-) = (3CaO·3Al₂O₃·CaF₂)	-44492 - 73.15T	$N_{c 14} = K_{c 14} N_{1}^{3} N_{2} N_{4}^{3}$
11(Ca²⁺+ O^2-) + 7(Al₂O₃) + (Ca²⁺+2F^-) = (11CaO·7Al₂O₃·CaF₂)	-228760 - 155.8T	$N_{c 15} = K_{c 15} N_{1}^{11} N_{2} N_{4}^{7}$

1.2 FactSage calculation of component activity in slag

FactSage 7.3 thermodynamic software was used to calculate the Al₂O₃ and TiO₂ activities in the slag at 1773 K. The FactPS and FToxid databases were used in the software. The pure solid standard state was selected for the calculation results.

The expressions of the equilibrium Al and Ti contents in the alloy are shown in Eq.(10) and Eq.(11), respectively:

l g X_{T i}^{'} = \frac{1}{3} (\begin{array}{l} l g \frac{a_{T i O_{2}}^{3}}{a_{A l_{2} O_{3}}^{2}} + 4 l g f_{A l} + 4 l g X_{A l} \\ - 3 l g f_{T i} + \frac{35300}{T} - 9.94 \end{array})

(10)

l g X_{A l}^{'} = \frac{1}{4} (\begin{array}{l} l g \frac{a_{A l_{2} O_{3}}^{2}}{a_{T i O_{2}}^{3}} - 4 l g f_{A l} + 3 l g X_{T i} \\ + 3 l g f_{T i} - \frac{35300}{T} + 9.94 \end{array})

(11)

where $X_{T i}^{}$ and $X_{A l}^{}$ are the initial Ti and Al contents in the alloy, and $X_{T i}^{'}$ and $X_{A l}^{'}$ are the equilibrium Ti and Al contents in the alloy, respectively.

2 Oxidation Regularity of Al and Ti Content in Alloy

A thermodynamic study of the electroslag remelting process can obtain the equilibrium Al and Ti content in the alloy at the end of the slag-metal reaction under the condition that the alloy and slag compositions are fixed. It is usually used to determine the optimal amount of TiO₂ in the slag to provide a theoretical basis for further research. Pateisky et al^[

19] used different slags for electroslag remelting experiments, and the changes in Al, Ti, and Si contents during the electroslag remelting process were studied. It was found that the reaction of Ti and Si in steel with Al₂O₃ in slag does not cause a uniform distribution of axial components in the ingot. Appropriate addition of TiO₂ and SiO₂ to the slag can reduce the loss of Ti and Si. Duan et al^{[Reference 29

Baidu Scholar}29] systematically studied the effects of components and temperature of the slag on the equilibrium Al and Ti content in the alloy with the help of IMCT, and summarized the effects of the slag components on the oxidation behavior of Al and Ti elements in the alloy. The calculation result of equilibrium Ti content and component of slag is shown in Fig.1. And the relative importance of factors controlling the oxidation of Al and Ti is in the following order: TiO₂>Al₂O₃>CaO>CaF₂>MgO. It can be observed that as the temperature increases, the equilibrium Ti content gradually decreases. At the same time, the kinetic model proves that the mass transfer rate of Al and Ti in the alloy is much greater than that of Al₂O₃ and TiO₂ in the slag. Hou et al^{[Reference 30

Baidu Scholar}30] proposed a thermodynamic model for the deoxidation of 1Cr21Ni5Ti stainless steel during electroslag remelting. When the amount of Al added is 0.15%, and the amount of TiO₂ added to the slag is 4wt%, the Ti element of the steel can be ensured not to lose.

Fig.10 Mass transfer diagram of slag-metal interface

According to Eq.(10) and Eq.(11), the relationship of the equilibrium Ti and Al content in the alloy with the component content in the slag at different temperatures as calculated by both IMCT and FactSage is shown in Fig.2 and Fig.3, respectively. As the temperature increases from 1773 K to 1973 K, the oxidation of Ti in the alloy increases. The main reason is that as the temperature increases, the Gibbs free energy of Eq.(1) increases continuously, and the tendency of the reaction to proceed in the reverse direction increases. Yang and Park et al^[

31] studied the slag-metal equilibrium experiment of CaF₂-CaO-Al₂O₃-TiO₂ and Ni-based alloys from 1773 K to 1873 K, and calculated the activity-composition relationship of Al₂O₃ and TiO₂ in slag from 1823 K to 1873 K using FactSage software. The relationship is shown in Fig.4. Fig.4a indicates that when the activity ratio of Al₂O₃ and TiO₂ is constant, the higher the temperature, the larger the ratio of Al₂O₃ to TiO₂. More TiO₂ is then needed to prevent Ti loss.

From Fig.2a, 2b, 3a and 3b, it can be observed that as the slag increases (0% to 35%), the equilibrium Ti content in the alloy decreases significantly, and the Al content increases significantly. When the content of Al or CaO is less than 15%, the degree of influence is Al₂O₃>CaO, but the loss of the equilibrium Ti content in the alloy is significantly slowed as the content of Al₂O₃ increases to larger than 15wt%. This is because as the Al₂O₃ content increases to 15wt%, the reaction between Al₂O₃ and CaO is strengthened, the activity of Al₂O₃ in the slag decreases, and the reaction strength of Al₂O₃ and Ti in the alloy is reduced, causing a decrease in the Ti content. Jiang et al^[

32] proved that CaO can promote the oxidation of Ti in GH8825 alloy through experiments and calculations of CaF₂-CaO-Al₂O₃-MgO-TiO₂-SiO₂ slag and GH8825 alloy slag at 1823 K. As shown in Fig.5a, as the CaO content increases, the Ti is oxidized and the Al content is increased. The main reason is that the optical basicity of TiO₂ is smaller than that of Al₂O₃, and CaO is more easily combined with TiO₂. With the increase in CaO content, the activity of TiO₂ evidently decreases. Hou et al^{[Reference 33

Baidu Scholar}33] reported that the increase in CaO content during the reaction of CaF₂-Al₂O₃-CaO-MgO-TiO₂-SiO₂ slag with 1Cr21Ni5Ti stainless steel significantly inhibits Al oxidation in the alloy and intensifies Ti oxidation. Therefore, when the content of CaO in the slag is high, it is necessary to increase the content of TiO₂ to inhibit the oxidation of Ti in the alloy. This is especially true for low-fluorine slag, where the content of CaO and Al₂O₃ in the slag is higher, and control of the Ti element requires more TiO₂ in the slag. At the same time, the relationship between Al₂O₃ and TiO₂ in the slag and the content of Al and Ti in the steel under different temperatures and CaO contents is established. Fig.6 shows that the contents of Al and Ti remain unchanged and they are the corresponding components of the slag.

From Fig.2c~2e and Fig.3c~3e, one can see that as the content of TiO₂, CaF₂, and MgO in the slag increases, the content of Ti in the alloy increases, and the content of Al decreases. The relative magnitudes of their effects are TiO₂>CaF₂>MgO. Increasing the TiO₂ content can significantly inhibit the loss of Ti in the alloy. This is due to the increased reactivity of the TiO₂ content with Al in the alloy. The Al in the alloy is oxidized to Al₂O₃ in the slag, and the Ti is reduced in the alloy. However, the initial Al and Ti contents in different alloys differ, and the optimal TiO₂ addition also differs. Duan et al^[

34] showed that during the reaction of the CaF₂-Al₂O₃-CaO-MgO-TiO₂ slag system and the Inconel 718 alloy (Al and Ti contents are 0.43wt% and 1.13wt%, respectively) at 1773 K, the optimal TiO₂ content in the slag is 4wt%. The results are shown in Fig.7. The optimal TiO₂ addition for smelting the Incoloy 825 alloy at 1773 K is shown in Fig.2c. The calculated result using IMCT is 10%, and the calculated result using FactSage7.1 is 12%. Compared with the Inconel 718 alloy, the optimal content of TiO₂ for the Incoloy 825 alloy is higher. Because the contents of Al and Ti in the alloy differ greatly, more TiO₂ is required to control the loss of Ti in the alloy. Moreover, the appropriate addition of TiO₂ to the slag can not only control the loss of Ti in the alloy,

but also reduce the viscosity of the slag^[

35], which is beneficial for optimizing the kinetic conditions of the slag-metal reaction. From the calculation results of Jiang et al^{[Reference 32

Baidu Scholar}32] highlighted in Fig.5b, it can be observed that the value of

l g [(γ_{T i O_{2}})^{3} / (γ_{A l_{2} O_{3}})^{2}]

changes with the increase in MgO content is very small (

γ_{i O_{x}}^{}

represents the activity coefficient of component in slag). This shows that the change in MgO content has little effect on the equilibrium Al and Ti content in the alloy. From the experimental results of Yang and Park^{[Reference 31

Baidu Scholar}31] in Fig.4b, we can see that the effect of CaF₂ content on the changes in Al and Ti content in the alloy is small. The CaF₂ content improves the fluidity and conductivity of the slag.

Comparing the calculated results of IMCT with those of FactSage in Fig.2 and Fig.3, it is observed that the oxidation of Ti in the alloy is greater than that obtained using FactSage. As can be seen from Fig.2c and Fig.3c, the FactSage results show that the optimal TiO₂ content for controlling Al and Ti content in the alloy at 1773 K is 10%, while the IMCT calculation results show that it is 12%. The higher calculated result of IMCT indicates that the Ti element in the alloy has excessive loss when calculated by IMCT. In a previous study, the author conducted a high-temperature slag-metal equilibrium experiment on CaF₂-CaO-Al₂O₃-MgO-Li₂O-TiO₂ low-fluorine slag and Incoloy 825 alloy at 1773 K^[

36]. The experimental results are shown in Fig.8. The deviation between the calculated results of FactSage/IMCT and the experimental result is shown in Fig.9. It can be observed that the calculated result of FactSage has small deviation from the experimental result, while the calculated result of IMCT has a slightly larger deviation from the experimental result. There are two reasons for this result. First, loop iteration method in MATLAB is used in the IMCT calculation process, and certain errors occur during the process. Second, the FactSage database is relatively larger than the dataset used for IMCT. All IMCT data come from the data obtained in previous studies, but the data quantity is relatively less. This may be the main reason for the error; however, the calculation principle used for both data sets is the same, based on the Gibbs free energy of the component reaction in the slag. The calculation results indicate that as the TiO₂ content is higher, the calculation results are closer to the experimental results. Summarizing the calculation and experimental results, it can be concluded that the optimal TiO₂ addition amount in the slag is approximately 10% to prevent the oxidation of Al and Ti elements in the alloy during electroslag remelting of the Incoloy 825 alloy.

3 Mass Transfer of Al and Ti Elements During Electroslag Remelting

A kinetic study of the electroslag remelting process was used to predict the changes in the Al and Ti elements in the alloy. In the industrial electroslag process, the slag-metal reaction is more complicated and the thermodynamic applicability is reduced, but analysis is conducted mainly using kinetics. The mass transfer process of Al, Ti, TiO₂, and Al₂O₃ during the electroslag remelting process is shown in Fig.10.

The mass transfer of slag and alloy components occurs in three regions of the slag, i.e. the metal interface at the electrode tip, the droplet-slag interface in the process of droplet dropping, and the molten metal pool-slag interface. The reaction formulas of Al and Ti in the alloy with Al₂O₃ and TiO₂ in the slag are as shown in Eq.(12) and Eq.(13):

[A l] + 1.5 [O] = (A l O_{1.5})

(12)

[T i] + 2 [O] = (T i O_{2})

(13)

The expressions for the equilibrium constants are shown in Eq.(14) and Eq.(15).

l g K_{A l} = l g \frac{a_{A l O_{1.5}}^{*}}{a_{A l}^{*} {a_{O}^{*}}^{1.5}} = \frac{32000}{T} - 10.29

(14)

l g K_{T i} = l g \frac{a_{T i O_{2}}^{*}}{a_{T i}^{*} {a_{O}^{*}}^{2}} = \frac{34458}{T} - 11.96

(15)

According to the film-penetration theory, the diffusion flux of component i can be expressed as Eq.(16):

J_{i} = \frac{k_{i, m} ρ_{m}}{100 M_{i}} \{[% i] - {[% i]}^{*}\} = \frac{k_{i, s} ρ_{s}}{100 M_{i O_{x}}} \{{(% i O_{x})}^{*} - (% i O_{x})\}

(16)

where $J_{i}$ is the diffusion flux of i; $k_{i, m}$ and $k_{i, s}$ are the mass tran-sfer coefficients of i and iO_x in the alloy and slag, respectively; $M_{i}$ and $M_{i O_{x}}$ are the relative atomic masses of i and iO_x, respec-tively; $ρ_{m}$ and $ρ_{s}$ are the densities of the alloy and slag, respec-tively; ${[% i]}^{*}$ and ${(% i O_{x})}^{*}$ are the interfacial concentrations of the components in the molten alloy and slag, respectively.

According to Eq.(16), the interface concentration of element i in the alloy can be expressed as Eq.(17) and Eq.(18):

{[% i]}^{*} = \frac{\frac{k_{i, m} ρ_{m} M_{i O_{x}}}{k_{i, s} ρ_{s} M_{i}} [% i] + (% i O_{x})}{\frac{k_{i, m} ρ_{m} M_{i O_{x}}}{k_{i, s} ρ_{s} M_{i}} + B_{i} a_{O}^{* x}}

(17)

B_{i} = \frac{{(% i O_{x})}^{*}}{{[% i]}^{*} {a_{O}^{*}}^{x}} = \frac{M_{i O_{x}} f_{i} K_{M} \{\frac{(% C a F_{2})}{M_{C a F_{2}}} + \sum \frac{(% i O_{x})}{M_{i O_{x}}}\}}{γ_{i O_{x}}}

(18)

where $a_{O}^{*}$ is the interface oxygen activity and $K_{M}$ is the equilibrium constant. The activity coefficient of the components in the alloy, $f_{M}$ , and the activity coefficient of component $i O_{x}$ in the slag, $γ_{i O_{x}}$ , are calculated using Eq.(19) and Eq.(20), respectively:

l g f_{i} = \sum (e_{i}^{j} [% j] + r_{i}^{j} {[% j]}^{2})

(19)

γ_{i O_{x}} = \frac{a_{i O_{x}}}{(% i O_{x})}

(20)

where $e_{i}^{j}$ and $r_{i}^{j}$ are the first-order and second-order interaction parameters in the alloy, respectively. The first-order interac-tion coefficients are listed in Table 1. The currently available second-order interaction coefficients are summarized as: $r_{A l}^{C} = - 0.004$ , $r_{A l}^{A l} = (- 0.0011 + 0.17 / T)$ , $r_{A l}^{S i} = - 0.0006$ , $r_{A l}^{N i} = 0.000164$ , $r_{S i}^{S i} = (- 0.0055 + 6.5 / T)$ , $r_{S i}^{C r} = 0.00043$ , $r_{T i}^{T i} = - 0.001$ , $r_{T i}^{N i} = 0.0005$ ^[

37]. The activity of the components in the slag is represented by

a_{i O_{x}}

- \frac{d [% A l]}{d t} = (\frac{A}{W_{m}} k_{A l}) \{[% A l] - \frac{(% A l O_{1.5})}{B_{A l} {a_{O}^{*}}^{1.5}}\}

(21)

- \frac{d [% T i]}{d t} = (\frac{A}{W_{m}} k_{T i}) \{[% T i] - \frac{(% T i O_{2})}{B_{T i} {a_{O}^{*}}^{2}}\}

(22)

- \frac{d [% O]}{d t} = (\frac{A}{W_{m}} k_{O}) \{[% O] - \frac{a_{O}^{*}}{f_{O}}\}

(23)

\frac{1}{k_{i}} = \frac{1}{k_{i, m} ρ_{m}} + \frac{M_{i O_{x}}}{B_{i} k_{i, s} ρ_{s} M_{i} {a_{O}^{*}}^{x}}

(24)

where $W_{m}$ is the mass of molten steel and $k_{i}$ is the comprehensive mass transfer coefficient. The interfacial oxygen activity can be determined according to the mass conservation of elements at the interface, as shown in Eq.(25).

\frac{1.5}{M_{A l}} \cdot \frac{d [% A l]}{d t} + \frac{2}{M_{T i}} \cdot \frac{d [% T i]}{d t} - \frac{1}{M_{O}} \frac{d [% O]}{d t} = 0

(25)

According to Eq.(21~25), mathematical expressions for the change in Al and Ti contents in the alloy can be obtained, and expressed as Eq.(26) and Eq.(27):

[% A l] = E X P (- \frac{A}{W_{m}} k_{A l} t) \{[% A l] - \frac{(% A l O_{1.5})}{B_{A l} {a_{O}^{*}}^{1.5}}\} + \frac{(% A l O_{1.5})}{B_{A l} {a_{O}^{*}}^{1.5}}

(26)

[% T i] = E X P (- \frac{A}{W_{m}} k_{T i} t) \times \{[% T i] - \frac{(% T i O_{2})}{B_{T i} {a_{O}^{*}}^{2}}\} + \frac{(% T i O_{2})}{B_{T i} {a_{O}^{*}}^{2}}

(27)

According to the conservation of mass, the contents of Al₂O₃ and TiO₂ in the slag can be obtained. The mass transfer coefficients for different regions are obtained using Eq.(28) and Eq.(29):

k_{i, m} = 2 \frac{\sqrt[]{D_{i}}}{\sqrt[]{π t}}

(28)

k_{i, s} = 2 \frac{\sqrt[]{D_{i O_{x}}}}{\sqrt[]{π t}}

(29)

where $D_{i}$ and $D_{i O_{x}}$ are the diffusion coefficients of the components in the alloy and slag, respectively, and t is the slag-metal reaction time at different reaction regions. The values of the diffusion coefficients are listed in Table 5.

Table 5 Relevant component diffusion coefficients of alloy and slag^{[Reference 38

Baidu Scholar}38]

Temperature/K	D_Al/× 10^-5 cm²·s^-1	D_Ti/× 10^-5 cm²·s^-1	D_O/× 10^-5 cm²·s^-1	$D_{A l_{2} O_{3}}$ /×10^-6 cm²·s^-1	$D_{T i O_{2}}$ /×10^-5 cm²·s^-1
1750	1.5	1.5	1.5	7.1	2.7
1773	2.7	2.7	2.7	7.8	3.0
1798	4.4	4.4	4.4	9.0	3.5
1923	57	57	57	35	6.0
1938	77	77	77	42	7.2
1950	92	92	92	50	8.0

The mathematical expressions for calculating the mass transfer resistance of the Al and Ti elements in the alloy and Al₂O₃ and TiO₂ in the slag are shown in Table 6. According to Table 6, the rate-determining step during the process of electroslag remelting can be obtained.

Table 6 Mass transfer resistance of components in alloy and slag

Al, Ti	Al₂O₃	TiO₂
$\frac{1}{ρ_{m} \cdot k_{i, m}}$	$\frac{M_{A l O_{1.5}}}{B_{A l} M_{A l} ρ_{s} k_{s} {a_{O}^{*}}^{1.5}}$	$\frac{M_{T i O_{2}}}{B_{T i} M_{T i} ρ_{s} k_{s} {a_{O}^{*}}^{2}}$

According to the above kinetic model results, the change of Al and Ti elements in the ingot during the electroslag remelting process can be predicted. This reduces the experiment cost, and clarifies the control factors of Al and Ti content in the reaction process, as well as the rate-determining step in the slag-metal reaction process. It can provide theoretical guidance for improving the technology conditions of electroslag remelting.

Fig.11　Variation of Ti content in consumable electrodes and electroslag ingots^[

38,44]: (a) Exp. A, (b) Exp. B, and (c) Exp. C

Fraser et al^[

39, 40] proposed a kinetic model in the electroslag remelting process using the film-penetration theory to study the mass transfer behavior between the two systems, Mn + MnO and Fe + FeO. The model is relatively simple. The mass transfer process of the electroslag remelting process was analyzed in detail, and the mass transfer coefficient and mass transfer time were derived. Based on a large number of experiments, the feasibility and rationality of the model were verified. Schwerdtfeger et al^{[Reference 41

Baidu Scholar}41] obtained a mass transfer model

of the Al+Al₂O₃, Ti+TiO₂, and Fe+FeO systems in the electroslag process based on the results of Fraser's research, and predicted the Al, Ti, and Al₂O₃ and TiO₂ contents in the steel in the electroslag remelting process. The composition change of the ingot is in good agreement with the experimental results. Wei et al^[

42,43] optimized the model of Fraser, and proposed a kinetic model of the heterogeneous reaction in the electroslag process. The optimized model used a CaF₂-Al₂O₃ (argon atmosphere) and a CaF₂-CaO-Al₂O₃ (air atmosphere) slag system to subject SAE 1020 steel to electroslag remelting on a 1t UBC 250 kVA electroslag furnace. The results show that the burning loss of Si in the steel during the electroslag remelting process under an argon atmosphere is significantly improved, and the burning loss of Al, Si, and Mn in the alloy is mainly due to the strong oxidation of FeO. The model also explains that the influence of CaO in the slag on the activity of SiO₂ and Al₂O₃ is the key to control Si/Al in the electroslag ingot. Hou et al^{[Reference 38

Baidu Scholar}38,44] proposed a kinetic model for mass transfer in Al + Al₂O₃, Ti + TiO₂, Si + SiO₂, and Fe + FeO systems and tested the model with CaF₂-CaO-Al₂O₃-SiO₂-TiO₂-MgO slag and 1Cr21Ni5Ti in electroslag remelting experiments on a 50 kg electroslag furnace. The model calculation results are in good agreement with the experimental results. The Al, Ti, and Si in the steel and Al₂O₃, TiO₂, and SiO₂ in the slag, as calculated by the model, accurately predicted the variation in the composition of the electroslag ingot. The model also identified the rate-determining steps of the reaction: mass transfer of alumina through the molten steel, silica through the slag, and titanium on both the metal and slag sides. In addition, it is found that the addition of 200 g TiO₂ during the initial heating stage of electroslag remelting can significantly inhibit the loss of Ti.

Fig.11 illustrates that even under the optimal process conditions and slag system, Ti loss inevitably occurs in the ingot. This may be due to the complex environment in the actual electroslag process and the difficulty of imposing stable controls in the process. In the initial heating stage, particularly, the fluctuation range of metal elements is relatively large. Therefore, it is necessary to use the kinetic method in the electroslag remelting process to further explore improvements in process conditions. Our current kinetic model considers relatively few actual factors, and more accurate models are needed for the future development processes. However, our model more closely represents the actual process, which not only helps to have a clearer and deeper understanding of the entire electroslag remelting process, but also further optimizes the process parameters and slag system ratio, and more accurately controls the Al and Ti content.

4 Conclusions

1) Based on previous research, our study summarizes the thermodynamic and kinetic methods to control the Al and Ti content in the process of electroslag remelting. The results of the thermodynamic calculations indicate that an increase in temperature increases the oxidation of Ti and inhibits the oxidation of Al.

2) The increase in CaO and Al₂O₃ content in the slag increases the oxidation of Ti; however, when the Al₂O₃ content is greater than 15%, the oxidation of Ti in the alloy becomes weaker. The higher content of CaO and Al₂O₃ in the low-fluorine slag system requires addition of more TiO₂ to inhibit the oxidation of Ti in the alloy. Increasing the TiO₂ content significantly inhibits Ti oxidation, but different alloys require different amounts of TiO₂.

3) The FactSage calculation result has a small deviation from the slag-metal equilibrium experiment result, while the IMCT calculation result is slightly larger than the experimental result. As the TiO₂ content in the slag increases, the calculation results are closer to the experimental results. Based on the film-penetration theory, a kinetic model is proposed for the process of electroslag remelting, and the mathematical expressions for the change in the Al and Ti element content and the rate-determining step in the process of electroslag remelting can be obtained.

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Control of Al and Ti Contents During Electroslag Remelting of High-Temperature Ni-based Alloys PDF

Abstract

Keywords

1 Thermodynamic Calculation Method

1.1 IMCT calculation of component activity in slag

1.2 FactSage calculation of component activity in slag

2 Oxidation Regularity of Al and Ti Content in Alloy

3 Mass Transfer of Al and Ti Elements During Electroslag Remelting

4 Conclusions

References

首 页

期刊简介

编委会

投稿指南

过刊浏览

联系我们

English

Control of Al and Ti Contents During Electroslag Remelting of High-Temperature Ni-based Alloys PDF

Abstract

Keywords

1 Thermodynamic Calculation Method

1.1 IMCT calculation of component activity in slag

1.2 FactSage calculation of component activity in slag

2 Oxidation Regularity of Al and Ti Content in Alloy

3 Mass Transfer of Al and Ti Elements During Electroslag Remelting

4 Conclusions

References

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