Influence of Various Elements on Primary Crystal Temperature and Carbon Equivalent in Hypo-Eutectic Cast Iron

Abstract

Generally, carbon equivalent is calculated with the following equation; CE = [%C] + (1/3) [%Si]. However, the value calculated with chemical analysis method such as emission spectrochemical analysis is different from that calculated with the primary crystal temperature (Hereafter T_L) of the CE meter. In this study, the influence of elements on primary crystal temperature and carbon equivalent in cast iron was examined, and a more accurate equation for calculating carbon equivalent was suggested.

The relationship between the various element content and T_L from hypo-eutectic to eutectic composition is as follows; T_L (°C) = 1625 − 110 [%C] − 25 [%Si] + 3 [%Mn] − 35 [%P] − 71 [%S] − 2 [%Ni] − 7 [%Cr] Dividing this equation with carbon coefficient, a carbon equivalent equation from hypo to eutectic composition is obtained, as follow; CE_L = [%C] + 0.23 [%Si] − 0.03 [%Mn] + 0.32 [%P] + 0.64 [%S] + 0.02 [%Ni] + 0.06 [%Cr]. This is calculated from the drop in the solidification temperature and is different from the generally used CE = [%C] + (1/3) [%Si]. We investigated which causes the difference and which is more correct from hypo to eutectic composition.

From the review of references, it is assumed that CE = [%C] + (1/3) [%Si] is calculated from the carbon solubility in hyper-eutectic composition. Compared to this, as for the references in which carbon equivalent are calculated from the solidification temperature from hypo to eutectic composition, Si coefficient is not (1/3) but 0.22 to 0.25.

From all the following viewpoints, it can be said that CE_L = [%C] + 0.23 [%Si] is more correct than CE = [%C] + (1/3) [%Si]: (a) experimental result, (b) cooling curve of CE meter, (c) carbon floatation result, (d) T_L and chemical analysis, (e) internal shrinkage test result, and (f) thermodynamic simulation with JMatPro. The silicon coefficient (α) is constant as 0.23 until 3.65% silicon, but it increases linearly if the silicon content exceeds 3.65%.

 

This Paper was Originally Published in Japanese in J. JFS 91 (2019) 87–93. Figure 12 was slightly modified.

1. Introduction

Primary crystal temperature (Here after T_L) is measured with CE meter and carbon equivalent is calculated from this temperature. The carbon equivalent is calculated generally with the following equation; CE = [%C] + (1/3) [%Si]. There is a similar word to the carbon equivalent, which is called carbon saturation degree (Here after Sc). Considering the influence of Si and P on carbon equivalent, P.A. Heller and H. Jungbluth suggested the following equation; Sc = [%C]/(4.23 − ([%Si] + [%P])/3.2) in 1955.¹⁾ As for the silicon coefficient in this equation, we cannot find its reference.

As for the carbon equivalent, F. Neumann and W. Patterson suggested the following equation;²⁾ CE = [%C] + 0.31 [%Si] + 0.33 [%P] + 0.4 [%S] − 0.028 [%Mn], when investigating the carbon solubility in hyper-eutectic composition. Even though it shows the influence of various elements on the carbon solubility in hyper-eutectic composition, which is related to the carbon solubility in hyper-eutectic composition, the description that this equation also can be used in hypo-eutectic composition suddenly appears in the latter half of their papers. W. Patterson also suggested similar equation in 1961.³⁾

From these references, it can be assumed that the silicon coefficient (1/3) is the silicon activity coefficient which is concerned with the carbon solubility in hyper-eutectic composition. Generally, as the elements solubility is concerned in its activity coefficient, the carbon solubility shows a strong relationship with silicon activity coefficient (1/3) in hyper-eutectic composition. However, the liquidus from hypo to eutectic composition shows the temperature at which solidification begins to start, that gradient is called solidification temperature drop. In the chemical field, it is said that the solidification temperature drop is proportional to molar fraction. Therefore, it is a contradiction for using activity coefficient to solidification temperature drop which is not solubility curve. Compared to it, there were several studies which investigated the liquidus within the range of hypo-eutectic composition⁴⁾ (Fig. 1-(B)). For example, Dietert investigated into the influence of pouring temperature and chemical composition on flowability and suggested as follows; CE_L = [%C] + (1/4) [%Si] + (1/2) [%P],⁵⁾ T_L = [%C] + (1/4) [%Si] + (1/2) [%P].⁵⁾ L.F. Porte investigated into the liquidus temperature and derived the following experimental equation; T_L (°C) = 1599 − 107 [%C] − 26.6 [%Si] − 61.4 [%P] + 9.7 [%Mn] + 7.6 [%S] + 0.5 [%Ni] − 21.7 [%Cr].⁶⁾ Dividing this equation by the carbon coefficient of 107, the following equation is obtained; CE_L = [%C] + 0.25 [%Si] + 0.57 [%P]. Daido steel reported the liquidus calculation equation as follows; T_L (°C) = 1536 − 91 [%C] + 21 [%Si].⁷⁾ Dividing this by 91 (carbon coefficient) makes the following equation; CE_L = [%C] + 0.23 [%Si]. Summarizing the papers which investigated the carbon equivalent from the solidification temperature drop, the silicon coefficient in the carbon equivalent is not 0.33 but 0.22 to 0.25.

Fig. 1

Concept of calculating carbon equivalent.

In Europe, the carbon equivalent is expressed generally as CE_L and as following equation; CE_L = [%C] + (1/4) [%Si]. In USA and in Japan, the carbon equivalent is expressed as CE and as following equation; CE = [%C] + (1/3) [%Si]. Among foundry companies, it is often said that a little hyper-eutectic composition (such as about 4.5 of CE) minimizes the internal shrinkage of ductile cast iron, which sounds like illogical.

As mentioned above, even though carbon equivalent is the basis index for manufacturing cast iron, the method of determining the carbon equivalent from hypo to eutectic composition is uncertain. It is also unclear which composition is the eutectic composition, in which the shrinkage defects become minimum.

Therefore, in this study, we investigated the influence of various elements on the primary crystal temperature and the method for calculating the carbon equivalent. In addition, from the following viewpoints, we considered the carbon equivalent equation for calculating the accurate eutectic composition; (a) experimental results, (b) cooling curve of CE meter, (c) carbon floatation result, (d) T_L and chemical analysis, (e) internal shrinkage test result, and (f) thermodynamic simulation with JMatPro.

2. Experimental Method

Melting was carried out in a silica lined high frequency induction furnace of 50 kg, 3000 Hz. As shown in Table 1, after making basic composition of molten metal (3.1% C, 1.7% Si, 0.75% Mn, 0.07% P, 0.05% S), changed the addition amount of target elements. For adjusting the composition, graphite electrode and the following Fe-alloys were used; Fe–75%Si, Fe–73%Mn, Fe–26%P, Fe–35%S.

Table 1 Chemical composition (%).

Holding the molten metal at 1430°C ± 10°C in induction furnace, CE cup samples were taken at 1400°C ± 10°C. Simultaneously, chill specimens for emission spectrochemical analysis were sampled with 700 g of graphite cup. The CE cup is consisted of a shell mold of 30 mm diameter and 50 mm in height, and a Chromel-Alumel thermocouple of 0.6 mm in diameter protected by quarts tube. By pouring the melt into the cup until the melt flowed out, 250 g ± 10 g of melt remained in the cup.

We investigated the relationship between the various elements content and T_L, with the following methods. Table 1 shows the basic composition; 3.1% C, 1.7% Si, 0.75% Mn, 0.07% P, 0.05% S. With changing only one element content among the basic composition, the effect of various elements on T_L was investigated. As shown in Fig. 1, there is a linear relationship between carbon content and solidification temperature drop within hypo-eutectic (2.4% C) to eutectic composition. Therefore, we adjusted the carbon composition in the molten metal from 2.4% to 4.0%, poured it into the CE cup and measured T_L. Figure 2 shows the principle of measuring T_L from cooling curve.⁸⁾ As shown in Fig. 2(b), on the case of slow cooling (large cup), the peak of the exothermic curve moves to slow temperature. Therefore, both the transition temperature (T_L) and the finishing point of primary crystal temperature (T_F) become lower as the cooling rate decreases. The starting point (T_S) rarely changes.

Fig. 2

Principle of measuring primary crystal temperature (T_L) from cooling curve.

However, in this study T_S is not used as primary crystal temperature, but T_L as primary crystal temperature. The reason is as follows; (a) In the foundry field, the transition point (T_L) of CE cup cooling curve is used as primary crystal temperature, (b) Since it becomes zero value in the exothermic curve, it is easy to distinguish.

From the relationship between the various elements content and the change of primary crystal temperature, the influence of various elements on primary crystal temperature was investigated. Finally, dividing the relationship equation by carbon coefficient, the accurate carbon equivalent equation is obtained within the range of hypo-eutectic to eutectic composition.

3. Experimental Result

Figure 3 shows the relationship between carbon content and primary crystal temperature, with excluding the influence of other elements. The relationship between carbon and the liquidus gradient becomes eq. (1). The carbon liquidus gradient is −117 K/% in the reference of M. Hansen,⁹⁾ and that is −104 K/% in the reference of Okamoto.⁴⁾ In this study, the gradient is almost middle of both results (−110 K/%). Though the details are omitted, the intercept (1625°C) of this study is also intermediate between those of M. Hansen and H. Okamoto in their phase diagrams.

Fig. 3

Relationship between C amount and T_L.

Figure 4 shows the relationship between silicon content and T_L, with excluding the influence of the other elements. The relationship between silicon content and T_L becomes eq. (2). The influences of other elements, from manganese to chromium, on T_L become eq. (3) to (7) as well. Except for manganese, all the elements lower the solidification temperature.   

\begin{equation} \text{(C):}\ \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) = - 110\ \text{[%C]} + 1625 \end{equation} (1)

  

\begin{equation} \text{(Si):}\ \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) = - 25\ \text{[%Si]} + 1625 \end{equation} (2)

  

\begin{equation} \text{(Mn):}\ \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) = 3\ \text{[%Mn]} + 1625 \end{equation} (3)

  

\begin{equation} \text{(P):}\ \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) = - 35\ \text{[%P]} + 1625 \end{equation} (4)

  

\begin{equation} \text{(S):}\ \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) = - 71\ \text{[%S]} + 1625 \end{equation} (5)

  

\begin{equation} \text{(Ni):}\ \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) = - 2\ \text{[%Ni]} + 1625 \end{equation} (6)

  

\begin{equation} \text{(Cr):}\ \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) = - 7\ \text{[%Cr]} + 1625 \end{equation} (7)

Figure 5 shows the influence of manganese on T_L. According to the report of Kanno,¹⁰⁾ in the molten metal of S0.05%, Mn bonds S to make with S to form MnS till Mn0.45%. During Mn bonding S to form MnS, it is thought that the solidification drop does not occur, because both Mn amount and S amount reduce at the same time. However, as for primary as shown in Fig. 5 and Fig. 6, the transition point resulted from the MnS formation is not shown. The reason why the transition resulted from the MnS formation is not shown, or the reason why Mn increases the solidification temperature is uncertain.

Fig. 4

Relationship between Si amount and T_L.

Fig. 5

Relationship between Mn amount and T_L.

Fig. 6

Influence of each elements on T_L.

From eq. (1) to eq. (7), the influence of the various elements on the T_L becomes eq. (8).   

\begin{align} \mathrm{T}_{\text{L}}({{}^{\circ}\text{C}}) &= 1625 - 110\ \text{[%C]} - 25\ \text{[%Si]} + 3\ \text{[%Mn]}\\ &\quad - 35\ \text{[%P]} - 71\ \text{[%S]} - 2\ \text{[%Ni]} - 7\ \text{[%Cr]} \end{align} (8)

The order of elements that lowers liquidus temperature of iron is as follows; C > S > P > Si > Cr > Ni

This equation shows the influence of various elements on T_L, in the range of hypo-eutectic to eutectic composition. Therefore, CE_L which is calculated from the liquidus of the phase diagram can be shown with dividing various element coefficient in eq. (8) by carbon coefficient of −110. Equation (9) shows the result. Here, L means that the carbon equivalent is not calculated from the carbon solubility in hyper-eutectic composition but it is calculated from liquidus in the range of hypo-eutectic to eutectic composition.   

\begin{align} \mathrm{CE}_{\text{L}} &= \text{[%C]} + 0.23\ \text{[%Si]} - 0.03\ \text{[%Mn]} + 0.32\ \text{[%P]} \\ &\quad + 0.64\ \text{[%S]} + 0.02\ \text{[%Ni]} + 0.06\ \text{[%Cr]} \end{align} (9)

It can be shown that the eq. (9) is different from the conventional equation (CE = [%C] + (1/3) [%Si] + (1/4) [%P]). In the basic composition of this study or in the common composition of gray cast iron, as the (−0.03 [%Mn]) is cancelled by the (+0.32 [%P]), the influence of all the elements on carbon equivalent except for carbon and silicon is as small as 0.03 of value. In the same way, as the influence of Mn on carbon equivalent is cancelled by P in the spheroidal graphite cast iron, in the case of five elements alloys, CE_L is determined by carbon and silicon. However, in the case of high nickel alloy such as Niresist or high manganese special alloy, eq. (9) should be used.

4. Comparison between CE and CE_L

There is a problem that silicon coefficient (1/3) in the conventional equation is different from the silicon coefficient (0.23) calculated with T_L. In order to investigate which is accurate, we consider based on past experimental result we did.

4.1 Consideration with cooling curve of CE meter

Figure 7 shows cooling curves from hypo-eutectic composition to hyper-eutectic composition, with changing CE or CE_L. In the case of (a) cooling curve, even though the primary crystal point (a sign of hypo-eutectic composition) appears, CE is 4.41 (> 4.3), suggesting a hyper-eutectic composition. On the other hand, CE_L is 4.2 (< 4.3) and it suggests hypo-eutectic composition. That is, CE_L is more accurate. In the case of (b) cooling curve, it is considered as eutectic composition because the super cooling is large and primary crystal point is not shown. However, the calculated CE (= 4.5) suggests that its composition is a hyper-eutectic (> 4.3). The CE (4.5) is reported as an ideal composition and is recommended at the foundry field, because the internal shrinkage defects is minimized Compared to it, CE_L is 4.28, which is consistent with the eutectic composition at graphite eutectic temperature (dotted line) shown in Fig. 1. Primary graphite temperature appears on the cooling curve of (c). Owing to the primary graphite formation, super cooling temperature is high and the eutectic solidification temperature is high.

Fig. 7

Relationship between carbon equivalent and cooling curve of CE cup¹¹⁾ (T.P.: ϕ30 × H50 mm).

From the result considering based on CE meter cooling curve, it is clear that the carbon equivalent calculated from the CE_L is more accurate than that calculated by the CE.

4.2 Difference between CE and CE_L based on the carbon floatation

Figure 8 shows the relationship between carbon equivalent and graphite structure of CE cup. These T.P.s were used also for the cooling curves in Fig. 7. In (a) upper side, even though there is no carbon floatation, CE = 4.41 (> 4.3) means that it is hyper-eutectic composition. Compared to it, CE_L (= 4.20) means that it is hypo-eutectic composition.

Fig. 8

Relationship between carbon equivalent and graphite structure of CE cup¹¹⁾ (T.P.: ϕ30 × H50 mm).

In (b) upper side, even though carbon floatation is not shown, CE = 4.50 (> 4.3) means that it is hyper-eutectic composition. Compared to it, CE_L (= 4.28) means that it is near eutectic composition.

In (c), carbon floatation is shown, and so CE_L (= 4.49) means it is hyper-eutectic composition.

From the carbon floatation, it can be said that carbon equivalent calculated with CE_L is more accurate than that calculated with CE. For your reference, in the bottom side of (c) in which carbon floatation occurs, C3.77% and Si2.19% mean CE = 4.5 (> 4.3), hyper-eutectic and CE_L (= 4.27), eutectic composition.

4.3 The difference of Si calculated from the Emission Spectro Chemical analysis and calculated from the primary temperature (T_L)

Figure 9 shows the comparison of Si content obtained from chemical analysis and that obtained from T_L. The calculating method of this study is as follow.

1. a)    Calculating CE_L from measured T_L. (°C) = 1625 − 110 [CE_L]
2. b)    Substituting the analyzed carbon content into the carbon equivalent equation and calculate Si content. (CE_L) = [%C] + 0.23 [%Si]

Comparing the calculated Si with the analyzed Si by Emission Spectro Chemical analysis.

Fig. 9

Si amount obtained from chemical analysis and that obtained from T_L.¹²⁾

Then, the past calculating method is as follow.

1. a)    Calculating carbon equivalent (CE) from the measured T_L. T_L = 1632 − 111 [CE]
2. b)    Substituting the analyzed carbon content into the carbon equivalent equation and calculating Si content. (CE = [%C] + (1/3) [%Si])
3. c)    Comparing the calculated Si with the analyzed Si by Emission Spectro Chemical analysis.

As for (a) CE_L = [%C] + 0.23 [%Si], Si content calculated with chemical analysis shows the same with T_L. However, the past calculating method CE = [%C] + (1/3) [%Si] shows large difference between Si content calculated with chemical analysis and that calculated with T_L.

That means that in the case of calculating Si content from T_L and CE = [%C] + (1/3) [%Si], it is impossible to Si content accurately. This is a question occasionally asked from the foundry field and brings birth to misunderstand. It is only in the case of CE_L = [%C] + 0.23 [%Si] that the Si content calculated with chemical analysis shows the same with T_L. From this result, it can be said that as for the carbon equivalent within the range of hypo-eutectic to eutectic composition, CE_L = [%C] + 0.23 [%Si] should be used, rather than CE = [%C] + (1/3) [%Si].

4.4 Si coefficient considered from the viewpoint of internal shrinkage test

Figure 10 shows the relationship between carbon equivalent and the internal shrinkage volume.¹¹⁾ The shape of test piece is a column and its size as follows; ϕ200 × H200 mm (45 kg). The shrinkage volume formed in the test piece was measured with filling water into the empty in the test piece. As internal shrinkage is minimum at near 4.28, eutectic composition is 4.28 in the case of CE_L. As internal shrinkage is minimum at near 4.49, eutectic composition is 4.49 in the case of CE.

Fig. 10

Relationship between carbon equivalent and shrinkage volume.¹¹⁾

Therefore, it can be said that the eutectic composition is not CE = 4.3 but CE_L = 4.28.

4.5 Si coefficient considered from the viewpoint of thermodynamic simulation (JMatPro)

Figure 11 shows the relationship between Si content and primary crystal temperature in this study (a) or simulation (b). Figure 12 shows the relationship between Si content and Si parameter (d), calculated from this study (a) or with JMatPro (b). Calculating method for Si coefficient (α) is as follows.

Fig. 11

Relationship between Si amount and primary crystal temperature in this study (a) or simulation software (b).

Fig. 12

Relationship between Si and Si parameter, calculated from this study T_L (a) or with JMatPro (b).

In this study:

1. a)    From the measured T_L, carbon equivalent [CE_L] was calculated. (T_L = 1625 − 110 [CE_L])
2. b)    Substituting the analyzed C and the analyzed Si into carbon equivalent CE_L = [%C] + α [%Si], α is calculated.   
   \begin{equation*} \alpha = (1625 - \mathrm{T}_{\text{L}} - 110\ \text{[%C]})/(110\ \text{[%Si]}) \end{equation*}

In the case of JMatPro;

1. a)    Inputting the basic composition (3.1%C, 0.75%Mn, 0.07%P, 0.05%S)
2. b)    Calculating the changing of T_L with varied Si content from zero to 5% with JMatPro.
3. c)    Substituting T_L into the T_L = 1625 − 110 [CE_L], then CE_L is calculated.
4. d)    Substituting the analyzed C and the analyzed Si into carbon equivalent CE_L = [%C] + α [%Si], α is calculated.   
   \begin{equation*} \alpha = (1625 - \mathrm{T}_{\text{L}} - 110\ \text{[%C]}/(110\ \text{[%Si]}) \end{equation*}

As shown in Fig. 11, the T_L calculated from the thermodynamic simulation (JMatPro) (b) shows higher inclination than that of this study. As T_L becomes high, following to the eq. (10), Si coefficient becomes low. As shown in Fig. 12(b), the silicon coefficient (α) is 0.20 to 0.23 and it is smaller than that of this study. The simulation method is omitted.   

\begin{equation} \alpha = \frac{1625 - \mathrm{T}_{\text{L}} - 110\text{C}}{110 \times \text{Si}} \end{equation} (10)

As shown in Fig. 12(a), the silicon coefficient (α) is constant as 0.23 until 3.65% Si, but it increases linearly also if Si exceeds 3.65%.

4.6 Problem in the relationship between carbon equivalent and T_L widely used in melting field

Figure 13 shows the data widely used in melting field. This data shows the relationship carbon equivalent and T_L.¹³⁾

Fig. 13

CE and T_L widely used in melting field.¹³⁾

It was reported by Leeds & Northrup in 1966, in order to summarize the relationship between T_L and carbon equivalent in malleable cast iron and low phosphorus hypo-eutectic composition gray cast iron. The relationship between T_L and carbon equivalent equations are summarized in hypo-eutectic, eutectic and hyper-eutectic composition. That is, the relationship between T_L and carbon equivalent in hypo-eutectic composition is; T_L = 1632 − 111 [CE], and the relationship between T_L and carbon equivalent in hyper-eutectic composition is; T_L = 1534 − 90 [CE].

5. Conclusions

The influence of various element on primary crystal temperature and carbon equivalent is investigated. The following results are obtained.

1. (1)    The relationship between various elements content and T_L within the range of hypo-eutectic to eutectic composition are as follows; T_L (°C) = 1625 − 110 [%C] − 25 [%Si] + 3 [%Mn] − 35 [%P] − 71 [%S] − 2 [%Ni] − 7 [%Cr]
2. (2)    The coefficient of various element which is calculated from the liquidus in hypo-eutectic to eutectic composition is as follows; CE_L = [%C] + 0.23 [%Si] − 0.03 [%Mn] + 0.32 [%P] + 0.64 [%S] + 0.02 [%Ni] + 0.06 [%Cr]
3. (3)    CE (= [%C] + (1/3) [%Si]) is calculated equation from carbon solubility in hyper-eutectic composition, so it slides out of usual phenomenon. By the way, CE_L (= [%C] + 0.23 [%Si]) is calculated equation from solidification temperature drop in hypo-eutectic to eutectic composition, so it coincides with field information such as phase diagram or shrinkage defect.
4. (4)    Si coefficient of carbon equivalent CE_L within the range of hypo-eutectic to eutectic composition is assumed to be 0.23.
5. (5)    Si coefficient (α) is constant as 0.23 (CE_L = [%C] + 0.23 [%Si]), but it increases straightly if Si content exceeds 3.65%.

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