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Investigation of the liquidus temperature calculation method for medium manganese steel

  • Li Min , Liu Hongbo EMAIL logo , Xie Rongyuan EMAIL logo , Che Xiaorui , Liu Ying , Xu Hao , Zhang Caidong and Tian Zhiqiang
Published/Copyright: October 4, 2023
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High Temperature Materials and Processes
From the journal High Temperature Materials and Processes Volume 42 Issue 1

Abstract

The liquidus temperature and temperature drop coefficients of medium manganese steel were systematically studied using Factsage and differential scanning calorimetry (DSC) experiments. The results indicated that the temperature drop coefficients of C, Mn, Cr, Si, and Al were complex, while the coefficients of Mo, V, and Nb were of a constant value. Based on the temperature drop coefficients, the empirical formula for calculating the liquidus temperature of medium manganese steel was established. The liquidus temperature calculated using the empirical formula was 1422.7°C, while that obtained by the DSC experiment was 1422.9°C. By comparison with different calculation formulas, the liquidus temperature obtained from the formula that was constructed in this study was much closer to the experiment one, indicating the high accuracy of the empirical formula in predicting the liquidus temperature of medium manganese steel.

Keywords: liquidus temperature; temperature drop coefficients; DSC; medium manganese steel

1 Introduction

Medium manganese steel, with excellent wear resistance, has been widely used in mining machinery of wear-resistant lining boards [1,2,3]. However, serious shrinkage cavity and shrinkage porosity defects occur frequently in the production process of the steel [4] when high C [5,6] and high Mn [7] contents are present in the steel. In addition, other alloying elements such as Cr [8] are also added. Therefore, the liquidus temperature of medium manganese steel must be quite different from that of conventional steel. Significant progress has been achieved in the research of the microscopic structure [9,10], heat treatment process [11,12,13], rolling process [14], and wear performance [15,16] of medium manganese steel; however, the study on liquidus temperature is rarely reported.

Liquidus temperature plays a vital role during the solidification process of steel, which is closely related to the microstructure evolution and solidification quality [17]. In the steelmaking process, the confirmation of tapping temperature is based on the liquidus temperature. An appropriate liquidus temperature can not only ensure the running of the pouring process but also can improve the quality of the billet significantly [18]. At present, experimental methods including the differential thermal analysis (DTA) [19,20,21,22], differential scanning calorimetry (DSC) [23,24,25,26], thermodynamic software calculation method [22], and empirical formula method [27,28,29,30] are often adopted to determine the liquidus temperature of steel. Hamada and Karjalainen [20] investigated the liquidus temperature of Fe–22Mn–0.6C high manganese TWIP steel by DTA measurement and found that the liquidus temperature was 1378°C. Zinke et al. [21] also used DTA and reported the liquidus temperature of Fe–17.8Mn–0.59C–1.33Al–0.22Si steel to be 1,416°C. In order to reduce the experimental errors caused by Mn volatilization during the test and improve the reliability of the results, Zhuang et al. [19] found that the liquidus temperatures of Fe–20Mn–0.75C–1.5Al–0.05Si and Fe–10Mn–0.5C–1.5Al steels were 1406.5 and 1,466°C, respectively, by using the improved DTA equipment. The results obtained by DTA or DSC experiments are accurate; however, the experimental process is expensive and time-consuming, which is not suitable for industrial field production. In addition, some thermodynamic software such as Factsage and Thermo-calc [26,31] can also be used to calculate the liquidus temperature. Pierer et al. [31] pointed out that the liquidus temperature of Fe–25Mn–0.5C–1Al steel calculated with Thermo-calc was 1,411°C, which was lower than that of conventional steel. Because of convenience, the empirical formula method [27,28,29] was widely adopted during the production process. In this method, the temperature drop coefficients of the composition need to be calculated and then the liquidus temperature can be obtained by the linear sum of the temperature drop coefficients [30]. It should be noted that the temperature drop coefficients of different elements vary, and even the temperature drop coefficients of the same element also varied greatly under different steel components. It was reported that in some steels, the temperature drop coefficients are not independent but shared.

During the past few decades, some formulas have been constructed to predict the liquidus temperature. However, the vast majority of them were applicable to infinitely dilute solutions. But, high alloy content steel such as medium manganese steel does not belong to the category of dilute solution. Thus, these formulas cannot predict the liquidus temperature of high alloy content steels effectively.

Fast and accurate prediction of the liquidus temperature of high alloy content steels is of great significance to the casting temperature of ingot casting and continuous casting, which will eventually affect the quality and yield of the casting billet. Therefore, in the current study, the empirical formula that can effectively determine the liquidus temperature of medium manganese steel was constructed. The results obtained by the formula were in good agreement with the DTA/DSC experiment results. Compared with other formulae, the empirical formulae in this study can effectively predict the liquidus temperature of medium manganese steel. The present study provides theoretical guidance for industrial production, especially for the development of a continuous casting process of medium manganese. Besides, it also provides experience and reference for the accurate prediction of liquidus temperature of other high alloy steels.

2 Materials and methods

2.1 Materials

The ingot of medium manganese steel was fabricated in the ZGJ0.05–100–25 50 kg capacity vacuum induction furnace where the maximum temperature can reach 1,700°C, and the limit vacuum degree is 6.67 × 10−3 Pa. In addition, the ingot was manufactured from commercial pure materials and cast using a cast-iron mold in a vacuum. After the solidification was completed, the riser was removed from the ingot, and the specimens used in ICP and DSC experiments were cut longitudinally at the same position as the ingot. The chip samples of about 5 g were drilled from the specimens for the ICP test. The chemical composition of the experimental steel is given in Table 1.

Table 1

Composition of high-carbon medium manganese steel (wt%)

Element C Si Mn Cr Mo Nb V Alt
Content 0.95 0.20 8.5 2.1 0.32 0.035 0.065 0.01

2.2 DSC test

The liquidus temperature can be determined accurately using DSC. It shows exothermic and endothermic peaks according to the phase transformation of the sample during heating or cooling. The size of the samples in DSC was 3 mm × 2 mm and the weight was approximately 10 mg. The equipment used in this study was NETZSCH STA 449 F5, where the maximum heating temperature can reach 1,800°C, and the range of heating rates can be controlled from 0.001 to 50°C·min−1. Besides, the measurements were conducted in an inert atmosphere of pure argon with the flow rate maintained at 50 ml·min−1. In order to shorten the duration of measurement, the samples were first heated from room temperature to 1,200°C at a heating rate of 50 K·min−1. Then, after 30 min of preservation, the samples were continued to be heated above the liquidus temperature to 1,550°C with heating rates of 5, 10, and 15°C·min−1, respectively. Finally, the temperature was reduced to room temperature at a rate of 50°C·min−1. The liquidus temperature can be obtained according to the characteristic exothermic peak in the heating process of the steel.

2.3 Calculation using Factsage

The empirical formula method is based on the Fe–I phase diagram. The general formula is shown as follows [32]:

(1) T liq = M Fe − ∑ Δ t i ( 1 % ) ⋅ ω i − 6 .

where T liq is the liquidus temperature (°C), M Fe is the melting point of pure iron, which is usually selected as 1,536–1,539°C, ω i is the mass fraction of the alloying element, and t i 1 % is the temperature drop coefficient, representing the changes in the liquidus temperature when the element i increased 1%. The effect of gases such as nitrogen, oxygen, and hydrogen on the liquidus temperature is determined at −6°C. The effect of the composition of medium manganese steel on the liquidus temperature was calculated using the thermodynamic software Factsage8.0. During the calculation, the “Equilib” model was selected, and the “FS stel” was selected from data research. Then, the chemical composition was input into the software, and then select IL (equilibrium cooling) to run the program; finally, the precipitation at different temperatures was obtained. The temperature when the solid phase started to precipitate from the liquids was defined as the liquidus temperature. Figure 1 shows the precipitates during the solidification process of Fe–0.95C–8.5Mn–2.1Cr–0.32Mo–0.035Nb–0.065V–0.01Al steel. It can be seen the liquidus temperature is determined as 1422.9°C. According to the calculation results, the temperature drop coefficients ( t i 1 % ) can also be calculated. The empirical formula for calculating the liquidus temperature can be obtained by the linear sum of the coefficients.

Figure 1 The precipitates during the solidification process of Fe–0.95C–8.5Mn–2.1Cr–0.32Mo–0.035Nb–0.065V–0.01Al steel.
Figure 1

The precipitates during the solidification process of Fe–0.95C–8.5Mn–2.1Cr–0.32Mo–0.035Nb–0.065V–0.01Al steel.

3 Results

3.1 Effect of C on the liquidus temperature

Generally, the increase of C will significantly decrease the liquidus temperature of steel [28]. In this study, the influence of C on the liquidus temperature of medium manganese steel was studied with Factsage8.0. In order to ensure the accuracy and adaptability of the calculation results, the calculation was carried out in a wider range of C content. The results are shown in Table 2. It can be seen that when the content of C increased from 0 to 1.1%, the liquidus temperature of the medium manganese steel decreased from 1478.62 to 1413.12°C. In addition, the temperature drop coefficients also dropped from 91 to 67.82. Other scholars [28,29,33] pointed out the relationship between the liquidus temperature and the C content was linear, which was quite different from the results in this study. The traditional empirical formula was not applicable to predict the liquidus temperature of the medium manganese steel. The temperature drop coefficients of C were fitted, as shown in Figure 2. The relationship between coefficients and content conforms to the quadratic distribution, and the fitting degree R 2 = 0.989, indicating that the results are reliable. The formula is shown in equation (2):

(2) Δ t C 1 % = 32.52 [ % C ] 2 − 62.02 [ % C ] + 97.45 .

Table 2

The liquidus temperature and temperature drop coefficients with different C contents of the medium manganese steel

ω C (wt%) Fe–(0–1.1)C–8.5Mn–0.2Si–2.1Cr–0.01Al0.035Nb–0.065V–0.32Mo ω C (wt%) Fe–(0–1.1)C–8.5Mn–0.2Si–2.1Cr–0.01Al0.035Nb–0.065V–0.32Mo
T liq (°C) Δ t c 1 % T liq (°C) Δ t c 1 %
0.1 1478.62 91 0.9 1426.15 68.41
0.2 1470.06 88.3 0.92 1424.87 68.32
0.3 1463.12 82 0.94 1423.58 68.23
0.4 1457.13 76.48 0.95 1422.93 68.2
0.5 1451.09 73.26 0.96 1422.29 68.16
0.6 1444.98 71.23 0.98 1420.99 68.09
0.7 1438.8 69.89 1.00 1419.69 68.03
0.8 1432.52 69 1.02 1418.38 67.98
0.82 1431.26 68.85 1.04 1417.07 67.93
0.84 1429.99 68.73 1.06 1415.76 67.89
0.86 1428.71 68.62 1.08 1414.44 67.85
0.88 1427.44 68.5 1.1 1413.12 67.82
Figure 2 Relationship between the temperature drop coefficients and the C content.
Figure 2

Relationship between the temperature drop coefficients and the C content.

3.2 Effect of Mn on the liquidus temperature

To date, studies on the influence of Mn on the liquidus temperature are rare. The content of Mn in medium manganese steel is much higher than that of conventional steel [34]. Therefore, it is of significance to study the effect of Mn on the liquidus temperature. Figure 3 shows the liquidus temperature and temperature drop coefficients with different contents of Mn. It was found that when the Mn content Mn increased from 7 to 10 wt%, the liquidus temperature decreased almost linearly from 1428.49 to 1417.35°C. Besides, the temperature drop coefficients of Mn were almost constant at around 3.67 (Table 3).

Figure 3 Relationship between the temperature drop coefficients of Mn with different C contents.
Figure 3

Relationship between the temperature drop coefficients of Mn with different C contents.

Table 3

The liquidus temperature and temperature drop coefficients with different Mn contents of the medium manganese steel

ω Mn (wt%) Fe–0.95C–(7–10)Mn–0.2Si–2.1Cr–0.035Nb–0.065V–0.32Mo–0.01Al
T liq (°C) Δ t Mn 1 %
7 1428.49 3.66
7.25 1427.57 3.66
7.5 1426.64 3.66
7.75 1425.72 3.66
8 1424.79 3.67
8.25 1423.86 3.67
8.5 1422.93 3.67
8.75 1422.00 3.67
9 1421.08 3.67
9.25 1420.15 3.67
9.5 1419.22 3.67
10 1417.35 3.68

Liu et al. [35] investigated the liquidus temperature of Fe–Mn–C–Al TWIP steels and found that the influence of Mn on the liquidus temperature was closely related to the C content. Whether a similar phenomenon existed in the medium manganese steel needs to be verified. Therefore, the influence of Mn on the liquidus temperature and temperature drop coefficients with different C contents was investigated. The results are shown in Table 4. It was found that when the C content increased from 0.8 to 1.1 wt%, the coefficients decreased from 3.75 to 3.58. Although the temperature drop coefficients of Mn were lower than that of C, considering the Mn content in the medium manganese steel was much higher than C, the influence of Mn on the liquidus temperature cannot be ignored.

Table 4

The liquidus temperature and temperature drop coefficients of Mn with different C contents of the medium manganese steel

ω C (wt%) T liq (°C) Δ t Mn 1 %
Fe–(0.8–1.1)C–0.2Si–2.1Cr–0.035Nb–0.065V–0.32Mo–0.01Al Fe–(0.8–1.1)C–8.5Mn–0.2Si–2.1Cr–0.035Nb–0.065V–0.32Mo–0.01Al
0.8 1464.43 1432.52 3.75
0.85 1461.02 1429.35 3.73
0.9 1457.58 1426.15 3.70
0.95 1454.12 1422.93 3.67
1.00 1450.63 1419.69 3.64
1.05 1447.11 1416.42 3.61
1.10 1443.56 1413.12 3.58

The coefficients of Mn with different C contents were fitted. As shown in Figure 3, the variation of the curve is in agreement with the binary polynomial, as shown in equation (3):

(3) Δ t Mn 1% = − 0.07 [ % C ] 2 − 0.45 [ % C ] + 4.16 .

The fitting degree R 2 = 0.999, indicating the reliability of the results.

3.3 Effect of Cr on the liquidus temperature

An appropriate amount of Cr element added to the steel can improve the mechanical properties of steel effectively [8]. The content of Cr in the medium manganese steel was about 2%, which was lower than that of Mn and much higher than that of C. Therefore, it is of great significance to systematically study the effect of Cr on the liquidus temperature of the medium manganese steel. The liquidus temperature and temperature drop coefficients with different Cr contents were calculated. As shown in Table 5, when the Cr increased from 1 to 3%, the liquidus temperature decreased from 1487.7 to 1422.3°C. Besides, the coefficients of Cr were not constant and it increased from 1.56 to 1.69; although the degree is small, it cannot be neglected. The coefficients of Cr were fitted, as shown in Figure 4. The results demonstrated that the relationship between coefficient and content of Cr is in agreement with linear changes; the fitting degree R 2 = 0.999, indicating that the fitting degree was reliable.

(4) Δ t Cr 1 % = 1.50 + 0.06 [ % Cr ] .

Table 5

The liquidus temperature and temperature drop coefficients with different Cr contents of the medium manganese steel

ω Cr (wt%) Fe–0.95C–8.5Mn–(1–3)Cr–0.035Nb–0.065V–0.2Si–0.32Mo–0.01Al
T liq (°C) Δ t Cr 1 %
0 1426.36
1.0 1424.8 1.56
1.2 1424.47 1.57
1.4 1424.14 1.59
1.6 1423.8 1.60
1.8 1423.46 1.61
2.0 1423.11 1.63
2.2 1422.76 1.64
2.4 1422.4 1.65
2.6 1422.04 1.66
2.8 1421.67 1.67
Figure 4 Relationship between the temperature drop coefficients and the Cr content.
Figure 4

Relationship between the temperature drop coefficients and the Cr content.

3.4 Effect of Al on the liquidus temperature

The addition of Al can stabilize and expand the volume fraction of the α phase [8]. However, excessive Al will generate work hardening and deteriorate the strength and ductility of the steel [36,37]. The content of Al in medium manganese steel is lower than 0.01%; therefore, in order to ensure the applicability of the calculation results, the liquidus temperature and temperature drop coefficients with different Al contents were investigated in a wider range. The calculation results are shown in Table 6. It was found that the effect of Al on the liquidus temperature was complex. When the content of Al increased from 0.01 to 0.5%, the liquidus temperature increased from 1422.93 to 1423.29°C. However, as the Al continued to increase to 1.7%, the liquidus temperature decreased to 1421.71°C. When the Al further increased to 4%, the liquidus temperature again increased to 1428.2°C. It can be seen that when the Al content was lower than 1.7%, the coefficients increased with the increase in Al. However, when the Al content was between 1.8 and 3.5%, the coefficients decreased with an increase in Al. When the content of Al exceeded 4.0%, the coefficients showed again an increasing tendency. Generally speaking, the liquidus temperature increased with the increase in the Al content in conventional steel [30]. However, the calculation results proved that this relationship did not apply to medium manganese steel. The reason that caused this phenomenon is not clear at present. It was speculated that it may be related to the transformation of the structure in medium manganese steel, which still needs to be further confirmed. To reveal the effect of Al on the liquidus temperature of the medium manganese steel, the temperature drop coefficients with various Al contents were fitted, and the results are shown in Figure 5 and equations (5) and (6):

(5) Al:0 – 1 .7% Δ t Al 1 % = – 1 .48 + 1 .53[%Al] – 0 .12[%Al] 2 ,

(6) Al:1 .7 – 4 .0% Δ t Al 1 % = 6 .82 – 4 .91[%Al] + 0 .73[%Al] 2 .

Table 6

The liquidus temperature and temperature drop coefficients with different Al contents of the medium manganese steel

ω Al (wt%) Fe–(0–1.1)C–8.5Mn–0.2Si–2.1Cr–0.01Al0.035Nb–0.065V–0.32Mo ω Al (wt%) Fe–(0–1.1)C–8.5Mn–0.2Si–2.1Cr–0.01Al0.035Nb–0.065V–0.32Mo
T liq (°C) Δ t Al 1 % T liq (°C) Δ t Al 1 %
0.01 1422.93 −1.00 0.9 1423.09 −0.19
0.02 1422.95 −1.50 1.0 1422.98 −0.06
0.03 1422.96 −1.33 1.1 1422.84 0.07
0.04 1422.98 −1.50 1.2 1422.68 0.20
0.05 1422.99 −1.40 1.3 1422.51 0.32
0.06 1423.01 −1.50 1.4 1422.31 0.44
0.07 1423.02 −1.43 1.5 1422.1 0.55
0.08 1423.03 −1.38 1.6 1421.86 0.66
0.09 1423.05 −1.44 1.7 1421.71 0.71
0.1 1423.06 −1.40 1.8 1422.25 0.37
0.12 1423.08 −1.33 1.9 1422.77 0.08
0.14 1423.1 −1.29 2.0 1423.25 −0.17
0.16 1423.13 −1.31 2.1 1423.71 −0.38
0.18 1423.15 −1.28 2.2 1424.13 −0.55
0.2 1423.16 −1.20 2.3 1424.54 −0.70
0.3 1423.24 −1.07 2.4 1424.91 −0.83
0.4 1423.28 −0.90 2.5 1425.27 −0.94
0.5 1423.29 −0.74 3.0 1426.7 −1.26
0.6 1423.28 −0.60 3.5 1427.66 −1.35
0.7 1423.24 −0.46 4.0 1428.2 −1.32
0.8 1423.18 −0.33
Figure 5 Relationship between the temperature drop coefficients and the Al content.
Figure 5

Relationship between the temperature drop coefficients and the Al content.

The fitting degree R 2 = 0.978 and 0.982, indicating the reliability of the results.

3.5 Effect of Si on the liquidus temperature

The effect of Si added to the medium manganese steel is similar to that of Al [8]. Si is also one of the ferrite-stable elements. The formation of carbides will be inhibited when appropriate Si is added to the medium manganese steel [38]. The liquidus temperature and temperature drop coefficients were calculated with the Si content ranging from 0 to 4.0%. The results are shown in Table 7. It can be seen that the liquidus temperature decreased from 1429.01 to 1352.26°C and the coefficients decreased from 30.8 to 19.2. The temperature drop coefficients of Si were fitted. As shown in Figure 6 and equation (7), the relationship between the coefficients and the Si content was in accordance with the univariate quadratic distribution:

(7) Δ t Si 1 % = 31.50 − 5.78 [ % Si ] + 068 [ % Si ] 2 .

Table 7

Theliquidus temperature and the temperature drop coefficients with different Si contents of the medium manganese steel

ω Si (wt%) Fe–0.95C–8.5Mn–(0–1)Si–2.1Cr–0.035Nb–0.065V–0.32Mo–0.01Al
T liq (°C) Δ t Si 1 %
0 1429.01 —
0.1 1425.93 30.80
0.2 1422.93 30.40
0.3 1420.05 29.87
0.4 1417.26 29.38
0.5 1414.59 28.84
06 1412.02 28.32
0.7 1409.55 27.80
0.8 1407.17 27.30
0.9 1404.88 26.81
1.0 1402.67 26.34
1.5 1392.64 24.25
2.0 1383.81 22.6
2.5 1375.66 21.34
3.0 1367.84 20.39
3.5 1360.09 19.69
4.0 1352.26 19.19
Figure 6 Relationship between the temperature drop coefficients and the content of Si.
Figure 6

Relationship between the temperature drop coefficients and the content of Si.

3.6 Effect of other elements on the liquidus temperature

Other alloying elements such as Mo, V, and Nb were also added to the medium manganese steel [39,40], which can combine with other elements to form nano-scale precipitates and strengthen the second phase of steel, thus refining the grain, and finally, the strength of the steel can be improved by maintaining certain plasticity [41,42]. Considering that the contents of Mo, V, and Nb were less, the liquidus temperature and temperature drop coefficients were investigated in the range of 0–1, 0–0.1, and 0–0.1%, respectively. As shown in Tables 8–10, when the Mo, V, and Nb contents increased, the liquidus temperature decreased almost linearly. However, the temperature drop coefficients have no obvious changes. Because of the low content of Mo, V, and Nb in medium manganese steel, the coefficients were regarded to be constant and were equal to 4, 4, and 6, respectively.

Table 8

Theliquidus temperature and temperature drop coefficients with different Mo contents of the medium manganese steel

ω Mo (wt%) Fe–0.95C–8.5Mn–0.2Si–2.1Cr–0.035Nb–0.065V–(0–1)Mo–0.01Al
T liq (°C) Δ t Mo 1 %
0 1424.2 —
0.1 1423.81 3.90
0.2 1423.41 3.95
0.3 1423.01 3.97
0.4 1422.62 3.95
0.5 1422.22 3.96
0.6 1421.82 3.97
0.7 1421.42 3.97
0.8 1421.02 3.98
0.9 1420.61 3.99
1.0 1420.21 3.99
Table 9

The liquidus temperature and temperature drop coefficients with different V contents of the medium manganese steel

ω V (wt%) Fe–0.95C–8.5Mn–0.2Si–2.1Cr–0.035Nb–(0–0.1)V–0.32Mo–0.01Al
T liq (°C) Δ t V 1 %
0 1423.19 —
0.01 1423.15 4
0.02 1423.11 4
0.03 1423.07 4
0.04 1423.03 4
0.05 1422.99 4
0.06 1422.95 4
0.07 1422.91 4
0.08 1422.87 4
0.09 1422.84 3.89
0.1 1422.8 3.90
Table 10

The liquidus temperature and temperature drop coefficients with different Nb contents of the medium manganese steel

ω Nb (wt%) Fe–0.95C–8.5Mn–0.2Si–2.1Cr–(0–0.1)Nb–0.065V–0.32Mo–0.01Al
T liq (°C) Δ t Nb 1 %
0 1423.15 —
0.01 1423.09 6.0
0.02 1423.03 6.0
0.03 1422.97 6.0
0.04 1422.9 6.25
0.05 1422.84 6.20
0.06 1422.78 6.17
0.07 1422.71 6.29
0.08 1422.65 6.25
0.09 1422.59 6.22
0.1 1422.52 6.30

3.7 The empirical formula of the liquidus temperature of medium manganese steel

The influence of C, Mn, Cr, Al, Si, Mo, V, and Nb on the liquidus temperature and temperature drop coefficients are calculated in Sections 3.1–3.6. Then, the formula to calculate the liquidus temperature of the medium manganese steel can be obtained by the linear sum of these coefficients. It should be noted that the formula can be obtained in the sections according to the Al content. When the Al content ranged from 0 to 1.7%, the liquidus temperature can be obtained as follows:

(8) T liq = 1 , 538 − 32.52 [ % C ] 3 + 62.02 [ % C ] 2 − 97.45 [ % C ] − 0.06 [ % Cr ] 2 − 1.50 [ % Cr ] + 0.07 [ % C ] 2 × [ % Mn ] + 0.45 [ % C ] × [ % Mn ] − 4.16 [ % Mn ] − 31.50 [ % Si ] + 5.78 [ % Si ] 2 − 0.68 [ % Si ] 3 + 0.12 [ % Al ] 3 − 1.53 [ % Al ] 2 + 1.48 [ % Al ] − 4 [ % Mo ] − 4 [ % V ] − 6 [ % Nb ] − 6 .

Similarly, when the Al content was 1.7–4.0%, the liquidus temperature can be obtained as follows:

(9) T liq = 1538 − 32.52 [ % C ] 3 + 62.02 [ % C ] 2 − 97.45 [ % C ] − 0.06 [ % Cr ] 2 − 1.50 [ % Cr ] + 0.07 [ % C ] 2 × [ % Mn ] + 0.45 [ % C ] × [ % Mn ] − 4.16 [ % Mn ] − 31.50 [ % Si ] + 5.78 [ % Si ] 2 − 0.68 [ % Si ] 3 − 0.73 [ % Al ] 3 + 4.91 [ % Al ] 2 − 6.82 [ % Al ] − 4 [ % Mo ] − 4 [ % V ] − 6 [ % Nb ] − 6 .

4 Discussion

4.1 Verification of the results calculated with Factsage

Figure 7 shows the DSC curves during the heating process of the medium manganese steel at heating rates of 5, 10, and 15 K·min−1. The exothermic peak on the DSC curves is considered to be the liquidus temperature of the steel. Therefore, the liquidus temperatures at different heating rates were 1428.4, 1426.6, and 1424.6°C, respectively. That is, the liquidus temperature increased when the heating rates increased. It should be noted that there was a linear relationship between the liquidus temperature and heating rate. Thus, the liquidus temperature of medium manganese steel at a heating rate of 0 K·min−1 was 1422.7°C, which can be seen in Figure 8. It should be noted that the liquidus temperature calculated with Factsage was 1422.9°C. The error between the DSC experimental results and the calculated results was within 1%, indicating the accuracy and reliability of the calculated results using Factsage.

Figure 7 Liquidus temperatures at different heating rates.
Figure 7

Liquidus temperatures at different heating rates.

Figure 8 Linear regression analysis of liquidus temperatures.
Figure 8

Linear regression analysis of liquidus temperatures.

4.2 Verification of the empirical formula

The liquidus temperatures of the medium manganese steel obtained by DTA or DSC experiments [19,21,43] were investigated, and the results are shown in Table 11. It can be found that the liquidus temperatures calculated by the empirical formula were close to experiment results, and all of the errors were within 8°C. Besides, the different empirical formulas for calculating liquidus temperatures of steel are also given in Table 12. Figure 9 shows the liquidus temperatures obtained by different empirical formulas. On the whole, except for a few examples, most of the results obtained using the empirical formula in the current study were much closer to experiment results, indicating the accuracy and reliability of the formula to predict the liquidus temperature of the medium manganese steel. It should be noted that the composition in the table is only to verify the accuracy and adaptability of the empirical formula. Therefore, although the content of some elements exceeds the limited range of the empirical formula in this study, the calculation results still have reference value.

Table 11

Liquidus temperatures obtained by experiments and the empirical formula

Sample Composition (wt%) Liquidus temperature (°C) Errors
C Mn Al Si Results by DTA/DSC Results by empirical formula
1 0.59 17.8 1.33 0.22 1,416 1412.41 −3.59
2 0.75 20 1.5 0.05 1406.49 1401.04 −5.45.
3 0.79 13.62 — 0.39 1,419 1414.02 −4.98
4 0.8 12.95 — 0.34 1,422 1417.38 −4.62
5 0.05 19.64 3.47 2.44 1402.68 1397.65 −5.03
6 0.38 25.64 4.12 2.11 1354.9 1356.2 1.30
7 0.38 25.1 3.53 2.78 1346.5 1348.76 2.26
8 0.4 22 — — 1,405 1412.55 7.55
Table 12

Different empirical formulae for calculating liquidus temperatures

Number Empirical formulae
1 [44] T l i q = 1 , 539 ‒ 70 [ % C ] ‒ 8 [ % S i ] ‒ 5 [ % M n ] ‒ 30 [ % P ] ‒ 25 [ % S ] ‒ [ % C u ] ‒ 4 [ N i % ] ‒ 1 . 5 [ % C r ]
2 [28] T l i q = 1 , 491 ‒ 36 . 33 [ % C ] + 61 . 9 [ % C ] 2 ‒ 17 . 10 [ % S i ] ‒ 3 . 32 [ % M n ] ‒ 27 . 07 [ % P ] ‒ 30 . 40 [ % S ] ‒ 2 . 61 [ C r % ] ‒ 3 . 25 [ M o % ] ‒ 1 . 60 [ % N i ] ‒ 1 . 7 [ % C u ] ‒ 10 . 17 [ % T i ] ‒ 0 . 86 [ % C o ] ‒ 2 . 11 [ % W ]
3 [44] T l i q = 1 , 535 ‒ 73 [ % C ] ‒ 3 [ % M n ] ‒ 12 [ % S i ] ‒ 28 [ % P ] ‒ 30 [ % S ] ‒ [ % C r ] ‒ 3 [ % A l ]
4 [44] T l i q = 1 , 534 ‒ 80 [ % C ] ‒ 4 [ % M n ] ‒ 14 [ % S i ] ‒ 35 [ % P ] ‒ 1 . 4 [ % C r ] ‒ 3 . 4 [ % A l ]
5 [33] T l i q = 1 , 536 ‒ 83 [ % C ] ‒ 31 . 5 [ % S ] ‒ 32 [ % P ] ‒ 5 [ % M n + C u ] ‒ 7 . 8 [ % S i ] ‒ 3 . 6 [ % A l ] ‒ 1 . 5 [ % C r ] ‒ 2 [ % M o ] ‒ 4 [ % N i ] ‒ 18 [ % T i ] ‒ 2 [ % V ]
6 [27] T l i q = 1 , 539 ‒ 100 . 3 [ % C ] + 22 . 41 [ % C ] 2 ‒ 3 . 55 [ % S i ] + 0 . 64 [ % S i ] 2 ‒ 5 . 82 [ % M n ] ‒ 0 . 3 [ % M n ] 2 ‒ 1 . 59 [ % C r ] + 0 . 007 [ % C r ] 2 ‒ [ % M o ] ‒ 4 . 18 [ % N i ] ‒ 0 . 01 [ % N i ] ‒ 2 . 42 [ % C u ]
7 [29] T l i q = 1 , 538 ‒ 31 . 15 [ % C ] 2 ‒ 62 . 645 ‒ [ % C ] ‒ 0 . 609 [ % S i ] 2 ‒ 2 . 0678 [ % S i ] + 0 . 0674 [ % M n ] 2 ‒ 5 . 3464 [ % M n ] ‒ 20 [ % P ] 2 ‒ 9 [ % P ] + 1 . 7724 [ % S ] 2 ‒ 24 . 755 [ % S ] ‒ 1 . 1159 [ % N b ] ‒ 15 . 3326 [ % N b ] + 0 . 0758 [ % C a ] 2 ‒ 3 . 1313 [ % C a ] ‒ 0 . 0379 [ % N i ] ‒ 5 . 2917 [ % N i ] ‒ 0 . 6818 [ % C u ] 2 ‒ 2 . 5955 [ % C u ] ‒ 0 . 0214 [ % M o ] 2 ‒ 3 . 2214 [ % M o ] ‒ 0 . 0359 [ % C r ] 2 ‒ 1 . 1402 [ % C r ] + 1 . 791 .
8 [44] T l i q = 1 , 536 ‒ 83 . 9 [ % C ] ‒ 10 [ % C ] 2 ‒ 12 . 6 [ % S i ] ‒ 54 [ % M n ] ‒ 4 . 6 [ % C u ] ‒ 5 . 1 [ % N i ] ‒ 1 . 5 [ % C r ] + 33 [ % M o ] + 30 [ % P ] + 37 [ % S ] + 9 . 5 [ % N b ] ‒ 0 . 1
9 [44] T l i q = 1 , 536 ‒ 8 [ % C ] ‒ 7 . 6 [ % S i ] ‒ 3 . 9 [ % M n ] ‒ 33 . 4 [ % P ] ‒ 38 [ % S ] ‒ 1 . 3 [ % C r ] ‒ 3 . 6 [ % A l ]
10[44] T l i q = 1536 ‒ 251 [ % C ] ‒ 12 . 3 [ % S i ] ‒ 6 . 8 [ % M n ] ‒ 123 . 4 [ % P ] ‒ 183 . 9 [ % S ] ‒ 14 [ % C r ] ‒ 3 . 6 [ % A l ]
Figure 9 Errors between the liquidus temperature of experiments and formulae.
Figure 9

Errors between the liquidus temperature of experiments and formulae.

5 Conclusions

  1. The temperature drop coefficients of the medium manganese steel were calculated using Factsage. When the content of C,、Mn,、Cr, and、Si increased, the coefficients of C and Mn increased nonlinearly, and the coefficients of Cr increased linearly, while the coefficient of Si decreased. However, the coefficients of Al were complex when the Al content was lower than 1.7% and the coefficient increased with an increase in Al. When the Al content was between 1.8 and 3.5%, the coefficient decreased with an increase in Al. When the content of Al exceeded 4.0%, the coefficient showed an increasing trend again. Considering the lower contents of Mo, V, and Nb in the medium manganese steel, the temperature drop coefficients were constant and equal to 4, 4, and 6, respectively.

  2. The empirical formulae for calculating the liquidus temperature of the medium manganese steel were established by the linear sum of the corresponding temperature drop coefficients. In the current study, when the Al content ranged from 0 to 1.7%, the liquidus temperature can be obtained as

T liq = 1 , 538 − 32.52 [ % C ] 3 + 62.02 [ % C ] 2 − 97.45 [ % C ] − 0.06 [ % Cr ] 2 − 1.50 [ % Cr ] + 0.07 [ % C ] 2 × [ % Mn ] + 0.45 [ % C ] × [ % Mn ] − 4.16 [ % Mn ] − 31.50 [ % Si ] + 5.78 [ % Si ] 2 − 0.68 [ % Si ] 3 + 0.12 [ % Al ] 3 − 1.53 [ % Al ] 2 + 1.48 [ % Al ] − 4 [ % Mo ] − 4 [ % V ] − 6 [ % Nb ] − 6 .

When the content of Al was 1.7–4.0%, the liquidus temperature can be calculated as by

T liq = 1 , 538 − 32.52 [ % C ] 3 + 62.02 [ % C ] 2 − 97.45 [ % C ] − 0.06 [ % Cr ] 2 − 1.50 [ % Cr ] + 0.07 [ % C ] 2 × [ % Mn ] + 0.45 [ % C ] × [ % Mn ] − 4.16 [ % Mn ] − 31.50 [ % Si ] + 5.78 [ % Si ] 2 − 0.68 [ % Si ] 3 − 0.73 [ % Al ] 3 + 4.91 [ % Al ] 2 − 6.82 [ % Al ] − 4 [ % Mo ] − 4 [ % V ] − 6 [ % Nb ] − 6 .

  1. The reliability of the empirical formulae to predict the liquidus temperature was verified. The liquidus temperature of the medium manganese steel found by the DSC experiment was 1422.7°C, which was closer to that obtained using the empirical formula. By comparison with different empirical formulas, the results calculated by the formula in this study were closer to the experimental results, indicating the reliability of the empirical formula in determining the liquidus temperature of the medium manganese steel.

Acknowledgments

The authors gratefully acknowledge the financial support provided by the Natural Science Foundation of Hebei Province (No. E2021318004) and the Central and Local Science and Technology Development Fund Project (No. 216Z1009G).

  1. Funding information: This research was supported by: Natural Science Foundation of Hebei Province (No. E2021318004) as well as Central and Local Science and Technology Development Fund Project (No. 216Z1009G).

  2. Author contributions: Conceptualization, L.Y.; methodology, L.M. and C.X.R.; validation, X.R.Y.; formal analysis, Z.C.D.; investigation, T.Z.Q.; writing – original draft preparation, L.M.; writing – review and editing – L.H.B and L.M.; Supervision, X.H.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The data presented in this study are available on request from the corresponding author.

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Received: 2023-05-23
Revised: 2023-08-07
Accepted: 2023-08-14
Published Online: 2023-10-04

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/htmp-2022-0285
Keywords for this article
liquidus temperature; temperature drop coefficients; DSC; medium manganese steel
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  24. Research on the behaviour and mechanism of void welding based on multiple scales
  25. Preparation of CaO–SiO2–Al2O3 inorganic fibers from melting-separated red mud
  26. Study on diffusion kinetics of chromium and nickel electrochemical co-deposition in a NaCl–KCl–NaF–Cr2O3–NiO molten salt
  27. Enhancing the efficiency of polytetrafluoroethylene-modified silica hydrosols coated solar panels by using artificial neural network and response surface methodology
  28. High-temperature corrosion behaviours of nickel–iron-based alloys with different molybdenum and tungsten contents in a coal ash/flue gas environment
  29. Characteristics and purification of Himalayan salt by high temperature melting
  30. Temperature uniformity optimization with power-frequency coordinated variation in multi-source microwave based on sequential quadratic programming
  31. A novel method for CO2 injection direct smelting vanadium steel: Dephosphorization and vanadium retention
  32. A study of the void surface healing mechanism in 316LN steel
  33. Effect of chemical composition and heat treatment on intergranular corrosion and strength of AlMgSiCu alloys
  34. Soft sensor method for endpoint carbon content and temperature of BOF based on multi-cluster dynamic adaptive selection ensemble learning
  35. Evaluating thermal properties and activation energy of phthalonitrile using sulfur-containing curing agents
  36. Investigation of the liquidus temperature calculation method for medium manganese steel
  37. High-temperature corrosion model of Incoloy 800H alloy connected with Ni-201 in MgCl2–KCl heat transfer fluid
  38. Investigation of the microstructure and mechanical properties of Mg–Al–Zn alloy joints formed by different laser welding processes
  39. Effect of refining slag compositions on its melting property and desulphurization
  40. Effect of P and Ti on the agglomeration behavior of Al2O3 inclusions in Fe–P–Ti alloys
  41. Cation-doping effects on the conductivities of the mayenite Ca12Al14O33
  42. Modification of Al2O3 inclusions in SWRH82B steel by La/Y rare-earth element treatment
  43. Possibility of metallic cobalt formation in the oxide scale during high-temperature oxidation of Co-27Cr-6Mo alloy in air
  44. Multi-source microwave heating temperature uniformity study based on adaptive dynamic programming
  45. Round-robin measurement of surface tension of high-temperature liquid platinum free of oxygen adsorption by oscillating droplet method using levitation techniques
  46. High-temperature production of AlN in Mg alloys with ammonia gas
  47. Review Article
  48. Advances in ultrasonic welding of lightweight alloys: A review
  49. Topical Issue on High-temperature Phase Change Materials for Energy Storage
  50. Compositional and thermophysical study of Al–Si- and Zn–Al–Mg-based eutectic alloys for latent heat storage
  51. Corrosion behavior of a Co−Cr−Mo−Si alloy in pure Al and Al−Si melt
  52. Al–Si–Fe alloy-based phase change material for high-temperature thermal energy storage
  53. Density and surface tension measurements of molten Al–Si based alloys
  54. Graphite crucible interaction with Fe–Si–B phase change material in pilot-scale experiments
  55. Topical Issue on Nuclear Energy Application Materials
  56. Dry synthesis of brannerite (UTi2O6) by mechanochemical treatment
  57. Special Issue on Polymer and Composite Materials (PCM) and Graphene and Novel Nanomaterials - Part I
  58. Heat management of LED-based Cu2O deposits on the optimal structure of heat sink
  59. Special Issue on Recent Developments in 3D Printed Carbon Materials - Part I
  60. Porous metal foam flow field and heat evaluation in PEMFC: A review
  61. Special Issue on Advancements in Solar Energy Technologies and Systems
  62. Research on electric energy measurement system based on intelligent sensor data in artificial intelligence environment
  63. Study of photovoltaic integrated prefabricated components for assembled buildings based on sensing technology supported by solar energy
  64. Topical Issue on Focus of Hot Deformation of Metaland High Entropy Alloys - Part I
  65. Performance optimization and investigation of metal-cored filler wires for high-strength steel during gas metal arc welding
  66. Three-dimensional transient heat transfer analysis of micro-plasma arc welding process using volumetric heat source models
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