ISIJ International, Vol. 59 (2019), No. 5

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ISIJ International, Vol. 59 (2019), No. 5, pp. 848–857

* Corresponding author: E-mail: guohanjie@ustb.edu.cnDOI: https://doi.org/10.2355/isijinternational.ISIJINT-2018-524

1. Introduction

In hot metal forming operation, the life of hot work die is restricted due to their extreme working condition in terms of thermal and mechanical loadings.1) AISI H13 steel with high hardenability, strength, toughness and softening resis-tance can be widely applied for manufacturing of hot work mold.2) Metastable primary carbides can be easily generated by dendritic segregation during solidification of H13 steel,3) and are considered detrimental for the final mechanical properties of mold.4,5)

In as-cast H13 steel, there are two kinds of primary car-bide, namely, V-rich primary carbide and Mo-Cr-rich pri-mary carbide.6,7) Primary carbide generate in interdendritic region at high temperature and cannot be easily eliminated by the subsequent hot working process. In order to allevi-ate the negative effect of primary carbide, it is of vital importance to investigate alloying elements segregation and generation of primary carbides during solidification.

Years of research have led to the belief that the solidifica-tion cooling rate has significant effect on the solidification microstructure and primary carbide characteristics.8,9) Pryds et al.10) investigated the microstructure of a low-carbon

Effect of Cooling Rate on the Solidification Microstructure and Characteristics of Primary Carbides in H13 Steel

Mingtao MAO,1,2,3) Hanjie GUO,1,2)* Fei WANG3) and Xiaolin SUN3)

1) School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083 China.2) Beijing Key Laboratory of Special Melting and Preparation of High-End Metal Materials, Beijing, 100083 China.3) Central Iron & Steel Research Institute, Beijing, 100081 China.

(Received on August 6, 2018; accepted on December 3, 2018; J-STAGE Advance published date: January 25, 2019)

The microstructure, alloying elements segregation and characteristics of primary carbides in AISI H13 steel that solidified at different cooling rate were investigated by optical microscope (OM), field emission scanning electron microscope (FE-SEM), electro-probe microanalyzer (EPMA) and automated inclusion analyzer ASPEX. The microstructure of H13 steel samples become more refined with increased cooling rate. The equation of relationship between cooling rate (RC) and secondary dendrite arm spacing (λ) for H13 steel could be expressed as � � �175 4 0 322. .RC . Primary carbides are located in interdendritic region, where existed obvious Cr, Mo, V and C segregation. Higher cooling rate promoted higher alloying elements segregation and facilitated earlier precipitation of primary carbides during solidification process. The num-ber, size, amount and mean area of primary carbides decreased significantly with the increased cooling rate, however the shape of the primary carbides were insensitive to cooling rate. Thermodynamic calcula-tion indicated that V-rich primary carbides precipitated at solid fraction larger than 0.94, Mo-rich primary carbides precipitated at solid fraction larger than 0.99 in the cooling rate range investigated. Lower cooling rate suppressed alloying elements segregation, but the precipitation of primary carbides could not be avoided in the cooling rate range.

KEY WORDS: primary carbide; H13 steel; solidification segregation; cooling rate.

Fe-12 pct Cr alloy at different cooling rates between 40 and 105°C·s −1 and found the size of carbide decreases as cooling rate increases, but the number of carbide increases as cool-ing rate increases. Fernandez et al.11) analyzed the effect of cooling rate (between 4.98 × 10 −2 and 1.07°C·s −1) on the growth geometry of MC carbide in IN-100 dendritic mono-crystals and found carbide coarsen as cooling rate increases. Chu et al.12) investigated characteristics of a cobalt-base superalloy at a medium cooling rate from 38 to 60°C·s −1 and found that, the dendrite segregation is suppressed and the size of carbide decreases as cooling rate increases. Pre-vious studies have investigated the effect of cooling rate on the morphology and distribution of carbide as well.13,14) However, they have not analyzed the carbide characteristics statistically. Moreover, in the cooling rate range corresponds to the casting of commercial scale H13 steel, and the effect of cooling rate on the solidification microstructure and pri-mary carbide characteristics has not been clearly understood yet. In fact, the cooling rate of commercial scale casting is largely governed by the design and thermal nature of the casting procedure, and is usually much lower than the reported cooling rate, especially for ingot with diameter of larger than 1 000 mm. As for theoretical work, thermody-namic calculation softwares, such as Thermo-Calc15) and FactSage16) can predict the phase transformation of steels in equilibrium condition and simplified non-equilibrium

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condition. But the solidification process of the actual casting is significantly deviated from these conditions. At present, a few reports17) adopt the partial equilibrium (PE) approxi-mation in the Thermo-Calc to predict the solidification sequence of steels, but it cannot predict the effect of solidi-fication cooling rate on the carbide characteristics. In order to clarify the effect of cooling rate on the characteristics of primary carbide in H13 steel, it is necessary using method that combines accurately alloying elements segregation calculation and thermodynamic precipitation calculation. However, to the best of the authors’ knowledge, insufficient work has been reported on the relation between the cooling rate and the precipitated primary carbide in H13 steel by the abovementioned method.

The purpose of the investigation reported here is to correlate the cooling rate (in the range corresponding to commercial scale casting) of H13 steel with the solidifica-tion microstructure and the primary carbide characteristics. Different methods including scanning electron microscope (SEM), electron probe micro analyzer (EPMA) and auto-mated inclusion analysis system (ASPEX) were employed to examine the solidification microstructure and the primary carbide characteristics of H13 steel in detail. The alloying elements segregation and the precipitation of primary car-bide were predicted by the Clyne-Kruz segregation equation and the precipitation thermodynamic calculation. We expect that the results can be applied as a guideline for manufacture process design of H13 steel ingot with alleviated segregation and reduced primary carbide.

2. Materials and Methods

Commercial AISI H13 steel was used as original material in the experiments. The contents of the main alloying ele-ments of the used H13 steel were measured by spark-optical emission spectrometer. The inductively coupled plasma atomic emission spectroscopy (ICP-AES) was utilized to analyze the contents of Ti in the sample. The content of nitrogen was determined by an inert gas thermal conductiv-ity method using a NCS analyzer. The chemical composi-tion of the sample is listed in Table 1.

The electro-slag remelting (ESR) technology is widely used for the manufacturing of commercial H13 steel ingot. As described in the literature,18) the cooling rates of the commercial scale H13 steel ingot (with diameter ranging from 300 to 1 000 mm) that casting in the conventional ESR furnace is in the range of 3.9 and 24.3°C·min −1. Therefore, the solidification experiments of H13 steel were conducted at the cooling rates of 5, 10 and 20°C·min −1. The LasertecTM VL2000DX-SVF17SP confocal laser scanning microscopy (CLSM) was used to produce the H13 steel samples that solidified at different cooling rates. Three cylindrical samples with dimensions of φ8×3 mm were used as origi-nal material for the solidification experiments. The three

samples were taken from the commercial H13 steel by wire cut machine, then prepared by mechanical polishing and ultrasonic cleaning (in ethanol). The experimental process was described in details as follows. The prepared samples were placed in an alumina crucible that positioned on a Pt stage in the confocal laser heating furnace. The temperatures of the samples were controlled by the thermocouple that mounted on the Pt stage. High purity argon atmosphere was charged into the furnace in order to avoid oxidation of the samples at high temperature. The samples were heated from the room temperature to 1 550°C at 200°C·min −1, then held for 5 min at 1 550°C for completely fusion and homogeniza-tion. After that the liquid samples were cooled to 1 100°C at rates of 5, 10 and 20°C·min −1, respectively, followed by a cooling at 200°C·min −1 to room temperature.

The solidified samples were ground, mechanically polished and etched by volume fraction 5% Nital for microstructural characterization. The dendritic structure of the solidified samples were examined using an Olympus GX51 optical microscope (OM). JSM-7800F field emission scanning elec-tron microscope (FE-SEM) and JXA-8530F field emission electron microprobe analyzer (EPMA) was utilized to analyze the alloying elements distribution and the characteristics of primary carbides in the solidified samples. ZEISS EVO18 scanning electron microscope (SEM) equipped with ASPEX system was employed to analyze the morphology, composi-tion and number of the primary carbides in a square region with dimensions of 4×4 mm2 in the solidified samples.

3. Results and Discussion

3.1.  Solidification Structure and MicrosegregationFigure 1 shows the metallographic images of the solidi-

fied samples. Dendritic structure in the solidified samples were observed and shown in Figs. 1(a)–1(c). The micro-structure of the samples become more refined with increased cooling rate. The average secondary dendrite arm spacing (SDAS) of the samples decreased as cooling rate increased. The measured average SDAS of the samples cooling at 5, 10 and 20°C·min −1 were 104.8±2.5, 82.5±3.2 and 67.4±3.4 μm, respectively. Large primary carbides were observed in the interdendritic region of the solidified samples as shown in Figs. 1(d)–1(f), and it’s worthwhile mentioning that less primary carbides were observed in the samples that solidi-fied at higher cooling rate.

Given that the thermal conductivity of H13 steel is high and the solidified samples are small (about 1 gram), a relatively homogeneous temperature distribution within the samples during solidification were achieved. Therefore, we can safely assume that the applied cooling rates was consistent with the local cooling rates, the latter is the most fundamental parameter determining the microstructure of the solidified samples.19,20) It is well established that the relation between the SDAS (λ, μm) and the local cooling rate (RC,°C·min −1) could be written:21)

� � b R n� �C ................................. (1)

Where b, n is constant of the alloys. The power function fitting was conducted for the measured λ and RC as shown in Fig. 2. The coefficients b and n were calculated to be 175.4 μm·(°C·min)0.322 and 0.322. Hence, the prediction formula

Table 1. Chemical composition of the commercial H13 steel sam-ple used (mass%).

C Si Mn Cr Mo V Ti N

0.40 0.94 0.28 5.06 1.54 0.98 0.0086 0.006

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of the λ for H13 steel was established as:

� �175 4 0 322. .� �RC ........................... (2)

Generally speaking, the determination or measurement of the local cooling rate of the commercial scale ingot is not an easy task, because the solidification system is complicated and the local cooling rate in different position of the solidi-fication system is different. However, it is relatively easier to measure the λ of the commercial scale ingot. Based on the Eq. (2), the local cooling rate of the commercial scale H13 steel ingot can be easily determined by measuring the corresponding λ. Therefore, the conclusions of the present research can be used to speculate the solidification charac-teristics of the commercial scale H13 steel.

The alloying elements distribution in the interdendritic region of the solidified samples were determined by the line scan mode of the wavelength-dispersive spectrometer (WDS) that in conjunction with the EPMA. The measured segregation ratio (SR) was used to describe the microsegre-gation in the interdendritic region and defined as:12)

SRcc

= max

min

.................................. (3)

Where cmax is the maximum concentration of alloying ele-ments in the interdendritic region and cmin is the minimum concentration of alloying elements in the neighbouring dendrite arm.

The result of the line scan alloying elements distribution indicates that there existed obvious alloying elements seg-regation in the interdendritic zone of the solidified samples, but the measured SR of different alloying elements were different. The segregation of Cr, Mo, V and C were signifi-cantly, however, the segregation of other alloying elements (Si, N and Ti for instance) were ignorable. Figure 3 shows the measured SR of Cr, Mo, V and C as a function of cool-ing rates. It can be concluded from Fig. 3 that Cr, Mo, V and C were all rich interdendritically. Despite different cool-ing rates, the measured SR of Mo was largest, followed by V, C and Cr. The partition coefficients (between solid and liquid) of Mo, V, C and Cr are 0.585, 0.63, 0.34 and 0.86, respectively.21) Smaller partition coefficient will result in an increase in the measured SR. This is the reason why the measured SR of Mo was larger than that of V and Cr. As for the alloying element C, the inconsistent relation between the partition coefficient and the measured SR can be ascribed to the larger diffusion coefficient of C in the solid phase. The measured SR of alloying elements increased with the increased cooling rate. It is obvious that the measured SR of Mo and V were sensitive to cooling rate, however, the measured SR of C and Cr changed little with cooling rate. Therefore, a higher cooling rates are detrimental for the performance of the material from the standpoint of alloying elements segregation.

Fig. 1. The dendritic structure and the morphology of primary carbides in the solidified samples: (a), (d) 5°C·min −1; (b), (e) 10°C·min −1; (c), (f) 20°C·min −1.

Fig. 2. Relation between the average SDAS and R. Fig. 3. The relation between the cooling rate and the measured segregation ratio of Cr, Mo, V and C.

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3.2. Characteristics of Primary CarbidesThe morphology and composition of typical primary car-

bides in the solidified samples are presented in Fig. 4. Plenty of primary carbides were observed in the three samples. Primary carbides are composed of Cr, Mo, V, C and a trace amount of Fe. Based on the metallic element contents, the primary carbides in the samples could be categorized into two different groups, namely, the V-rich primary carbides (or V-PC, for short) and the Mo-Cr-rich primary carbides (or M-PC, for short). V-PC contained more C, V and less Cr, Mo than M-PC, and some of the V-PC contained a trace amount of Ti and N. The compositional differences between these primary carbides can be easily seen through different colors in the backscatter electron (BSE) mode of the FE-SEM. The V-PC are more dark, while the M-PC are more bright. Primary carbides were usually formed individually but also found in coexistence as shown in Fig. 4(b). The shape of primary carbides could be stripy or blocky and the length of primary carbides could be up to tens of microns.Figure 5 shows the location distribution of the primary

carbides in the sample that cooling at 20°C·min −1. The white arrows indicate the location of M-PC and the black arrows indicate the location of V-PC. It is obvious that primary carbides can only precipitated in the interdendritic region, which indicates that the primary carbides were gen-

erated in the liquid steel at the end of solidification process.Statistical analysis of the M-PC and V-PC in the three

samples was conducted by the ASPEX system. The differ-ence in composition were used as criterion for the identifica-tion of different primary carbides here. The primary carbide with V contents value (mass percent) larger than 40% was classed as V-PC, the primary carbide with Mo contents value (mass percent) larger than 40% was classed as M-PC. The carbide with length less than 1 μm was not taken into account because it might be secondary carbide. Detailed information regarding the analysis process of the ASPEX system can be found in the literatures.22,23) The geometry of the primary car-bides was characterized by the length and length-width ratio.Figure 6 shows the relation between the quantity of dif-

ferent primary carbides and the cooling rates. In the chosen district of the three samples, there existed 181, 219 and 241 primary carbides, respectively, among which more than 70% were M-PC. The number of V-PC increased with the increased cooling rate whereas that of M-PC exhibited the inverse variation. The total quantity of primary carbides decreased with the increased cooling rate because the dec-rement of M-PC was more significantly. This phenomenon will be explained in the next chapter.

The details regarding the size, shape and quantity of the primary carbides in the three samples are plotted in Fig. 7.

Fig. 4. Typical primary carbides in the samples that solidified at different cooling rate: (a), (b): 5°C·min −1; (c), (d): 10°C·min −1; (e), (f): 20°C·min −1.

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As shown in Fig. 7(a), the number of large primary carbides (with length larger than 5 μm) decreased from 63 to 17 as the cooling rate increased from 5 to 20°C·min −1, but the number of small primary carbides (with length less than 5 μm) was insensitive to the cooling rate. The quantity propor-tion of large primary carbides decreased with the increased cooling rate. More than 70% of the primary carbides were less than 5 μm in length and more than 85% of the primary carbides were less than 10 μm in length, as shown in Fig. 7(b). The maximum length-width ratio of the primary car-bides decreased with the increased cooling rate, as shown in Fig. 7(c). The quantity proportion of the primary carbides with length-width ratio less than 2 was larger than 65%, and the quantity proportion of the primary carbides with length-width ratio less than 3 was larger than 85%. However, the quantity proportion of the primary carbides with different length-width ratio was insensitive to cooling rate, as shown in Fig. 7(d). The statistical results indicate that most of the primary carbides in the three samples were blocky with length less than 10 μm. The size of the primary carbides decreased significantly with the increased cooling rate,

but the length-width ratio of the primary carbides changed little with the cooling rate. The reason of this phenomenon could be ascribed to the fact that as cooling rate increased, the growth of the primary carbides was suppressed because the local solidification time and the space of interdendritic region decreased.12) But the shape of the primary carbides was determined by the shape of interdendritic region, hence it was insensitive to cooling rate.

The area covered by the primary carbides were also ana-lyzed and the result is plotted in Fig. 8. The area covered by M-PC was more than five times larger than that covered by V-PC, as shown in Fig. 8(a). Moreover, the area covered by these two kinds of primary carbides decreased significantly with the increased cooling rate. This means the total amount of the precipitated primary carbides decreased with the increased cooling rate. The mean area of M-PC was larger than that of V-PC in the three samples, as shown in Fig. 8(b). However, the mean area of M-PC and V-PC decreased with the increased cooling rate and were almost identical at high cooling rate.

Despite that the measured SR of the alloying elements in

Fig. 5. Location distribution of primary carbides in the sample that solidified at 20°C·min −1. Fig. 6. Quantity of primary carbides as a function of cooling rate.

Fig. 7. Effect of cooling rate on the characteristics of primary carbides: (a) length; (b) quantity proportion of different length; (c) length-width ratio; (d) quantity proportion of different length-width ratio.

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the interdendritic zone of the solidified samples increased with the increased cooling rate, the statistical result of the primary carbide indicates that the number, area and size of the primary carbide decreased significantly with the increased cooling rate. Hence it is reasonable to believe that higher solidification cooling rate is favorable for the better performance of the solidified H13 steel because it suppressed the precipitation of primary carbides. In order to explain the obtained experimental result, the alloying ele-ments segregation and the precipitation process of primary carbides were analyzed theoretically next.

4.  Analysis and Discussion

4.1.  Identification of Primary CarbidesThe Thermo-Calc software with the TCFE6 database

was used to determine the equilibrium phase transforma-tion process of H13 steel and the result is shown in Fig. 9. The calculated liquidus and solidus temperature during equilibrium solidification was 1 478 and 1 377°C, respec-tively. Four kinds of carbides, namely, MC, M2C, M7C3 and M23C6, precipitated at temperature between 1 600 and 600°C. The calculation result indicates that MC was V-rich carbide contains a trace amount of Ti and N, M2C was Mo-Cr-rich carbide, M7C3 and M23C6 was Cr-Fe-rich carbide. The composition of the precipitated carbides changed with temperature. Table 2 displays the calculated composition of the precipitated carbides. EBSD analysis was employed to identify the structure of the primary carbides in the solidi-fied samples, and the observed V-PC was identified as MC, while the M-PC was identified as M2C.

4.2.  Microsegregation of Alloying ElementsDuring the solidification of iron alloys, solute atoms are

released into the liquid phase continuously from the solidifi-cation interface because of the solubility difference between the liquid and solid phase. The alloy elements concentration in the liquid phase can be speculated theoretically by the segregation equation.

The Scheil equation and the Lever-rule equation19) are widely used for the prediction of the alloy elements con-centration in the liquid phase during the solidification of iron alloys. However, the solute concentration in the liquid phase is overestimated by the Scheil equation and underesti-mated by the Lever rule equation. This is because the Scheil equation ignores the diffusion of alloying elements in the solid phase during the solidification process, which is rea-sonable only when the cooling rate of the steel is very fast (approaching to infinity). Whereas the Lever-rule equation assumes that the alloying elements are uniformly distributed in the solid phase during the solidification process, which is reasonable only when the cooling rate of the steel is very slow (approaching to zero). In order to speculate the solute concentration in the liquid phase more accurate, the widely used Clyne-Kurz equation24) was used for the calculation. The model assumes that the alloying elements are homo-geneous in the liquid phase and the back diffusion of the alloying elements (limited diffusion of alloying elements in the solid phase) is taken into account. Hence, the model was also used to determine the effect of the cooling rate on the solidification segregation. The model predicts the solute concentration as a function of solid fraction given by:

Fig. 9. Equilibrium phase transformation diagram calculated by Thermo-Calc: (a) mole fraction of different phase; (b) sectional representation of the rectangular region in (a).

Fig. 8. Area of primary carbides: (a) Total area of the primary carbides; (b) Mean area of the primary carbides.

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CL S� � ��

�C k fk

k0

1

1 21 1 2[ ( ( ) ) ] ( )� �� � ............. (4)

�( ) exp exp� �� �

� � � � ����

���

�

��

�

��

���

���1

1 12

12

........ (5)

tT TR

f ��L S

C

................................ (6)

��

�D t fS

( . )0 5 22

............................... (7)

Where CL is the concentration (mass percentages) of the solute elements in liquid steel, C0 is the initial solute con-centration (mass percentages) in liquid phase, fS is the frac-tion of solid phase, k is the partition coefficient of solute ele-ments, tf is the local solidification time (LST), RC is the local cooling rate, DS is the solute diffusivity in the solid phase, λ2 is the secondary dendrite arm spacing, TL and TS is the liquidus temperature and solidus temperature, respectively, which can be calculated using the following relationships.25)

T TL Cr� 0 88 8 5 1 5

2 2

� � � �� �

[pct C] [pct Si] [pct Mn] . [pct ]

[pct Mo] [pct VV] [pct Ti]�18

.......................................... (8)

T TS

Cr

� 0 200 12 3

6 8 1 4

� �� �

[pct C] . [pct Si]

. [pct Mn] . [pct ] .............. (9)

Where T0 represent the melting point of pure iron, which is 1 538°C.

The temperature of the solidification interface, T, is given as follow:26)

T TT T

fT TT T

� � �

� ��

00

0

1

L

SL S

S

...................... (10)

Extended data needed for this model are listed in Table 322,27) and include the partition coefficients, k, and diffusion coefficients of solute elements in solid phase, DS, for each alloy element.

The variation of the calculated segregation ratio (named as calculated SR, the expression is CL/C0) of Cr, Mo, V and C that calculated by the Clyne-Kurz equation are shown in Fig.  10. The local cooling rate were set as 5, 10 and 20°C·min −1. The Scheil equation and the Lever-rule equa-tion were also adopted to speculate the variation of the SR. The result calculated by the Scheil equation represent the maximum SR during solidification, while the result calcu-lated by the Lever-rule equation represent the minimum SR

during solidification.It can be concluded from Fig. 10 that the calculated

SR of the alloying elements increased with solid fraction and the increment become more significant at the end of solidification (at solid fraction larger than 0.8). The SR of Cr, Mo and V that calculated by the Clyne-Kurz equation were close to that calculated by the Scheil equation, which means the back diffusion of Cr, Mo and V are suppressed in the cooling rate range investigated. However, the SR of C that calculated by the Clyne-Kurz equation was close to that calculated by the Lever-rule equation and the reason can be ascribed to the large DS of C, as shown in Table 3. Therefore, C is relatively homogeneous distributed in the interdendritic region. The calculated concentration of the alloying elements were two times larger than the initial concentration at the end of solidification process. Among the four alloying elements, the calculated SR of Mo was largest, followed by V, C and Cr.

The calculated SR of the alloying elements increased with the increased cooling rate. In the cooling rate range investi-gated, the SR of Mo and V dependent largely on the cooling rate as shown in Figs. 10(a) and 10(b). However, the SR of C and Cr were insensitive to the cooling rate, which can be concluded from Figs. 10(c) and 10(d). Comparing the SR calculated by the Clyne-Kurz equation with that calculated by the Scheil equation and the Lever-rule equation, the effect of the cooling rate on the segregation of the alloying elements can be concluded as follows: Slower cooling rate is favorable for the segregation suppression of V and Mo, and the segregation of V and Mo will become more significant with the increased cooling rate. The SR of Cr is insensitive to the cooling rate but still can be reduced by lowering the cooling rate, because it is higher than that calculated by the Lever-rule equation. However, the SR of Cr will not increase with cooling rate in the investigated cooling rate range because it is close to that calculated by the Scheil equation.

Table 2. Composition of the precipitated carbides during equilibrium solidification (mass%).

Type C N Fe Cr Mo V Ti

MC 10.5–15.2 1.0–7.1 0.8–4.2 0–5.8 0–13.0 62.6–83 0–4.2

M2C 7.4 – 1.9–2.5 8.4–8.6 63.5 18.3–18.6 –

M7C3 8.5 – 25.5–28.9 48.2–52.9 5.8–7.4 7.1–7.9 –

M23C6 5.1 – 2.8–38.1 41.3–64.6 14.6–20.6 0.8–6.9 –

Table 3. Partition coefficients k and diffusion coefficients of solute elements in solid phase DS.

Solute element k DS, cm2/s

C 0.34 0.0761 exp (−143 511/RT)

Si 0.52 0.3 exp (−251 470/RT)

Mn 0.785 0.055 exp (−249 378/RT)

Cr 0.86 0.0012 exp (−219 001/RT)

Mo 0.585 0.068 exp (−246 868/RT)

Ti 0.33 0.15 exp (−250 968/RT)

V 0.63 0.284 exp (−259 002/RT)

N 0.48 0.91 exp (−168 498/RT)

Note: R is the gas constant of 8.314 J·(mol·K) −1, and T is the temperature in Kelvin.

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The SR of C is insensitive to the cooling rate as well but cannot be relieved by adjusting the cooling rate, because it is close to the SR that calculated by the Lever-rule equation.

During the solidification of iron alloys, the back diffu-sion of alloying elements is the key factor determining the solidification segregation. The LST decreases as the cooling rate increases, which suppress the back diffusion of alloying elements. Therefore, the SR of alloying element increases with cooling rate.

The relation between the cooling rate and the SR of alloy-ing elements that calculated is consistent with the experi-mental result that shown in Fig. 3. However, the measured SR was smaller than the calculated SR. This is because the precipitation of the primary carbides consumed alloy atoms in the liquid phase.

4.3.  Thermodynamic Calculation  for  the Precipitation of Primary Carbides

During the solidification of H13 steel, the concentration of the primary carbides forming elements increase with solid fraction. Primary carbides will precipitate in the liquid phase when the contents of primary carbides forming elements reach the precipitating condition. Based on the calculated alloying elements concentration, the precipitation of the primary carbides can be speculated through thermodynamic calculation. In order to simplify the calculation, the precipi-tated V-rich MC and Mo-rich M2C were assumed to be VC and Mo2C, respectively. The precipitation of the primary carbide, taking VC as an example, starts immediately after the V and C contents in solution reach the equilibrium solu-bility limit in the liquid phase. Table 428,29) lists expressions

for the Gibbs free energy of the formation of Mo2C and VC compounds, where fMo, fV and fC are the activity coefficients of Mo, V and C in the liquid steel, respectively, and can be calculated by the Wagner’s equation as follows:30)

log [% ] [% ]f e i e ji ii

ij� �� ................... (11)

Where eij is the activity interaction coefficients that j imposed on i, and can be found in literature.29)

The Gibbs free energy of VC and Mo2C formation in the liquid phase, ΔGVC and ∆GMo C2 , were calculated and plotted in Fig. 11 as a function of solid fraction. The alloying ele-ments concentration that calculated by the Scheil equation (solid line in Fig. 11) and Lever-rule equation (dot line in Fig. 11) were also used for the precipitation calculation. Where the result calculated by the Scheil equation and Lever-rule equation represent the minimum and maximum Gibbs free energy of the primary carbide formation reac-tion at different cooling rates, respectively. The calculation result indicates that VC and Mo2C will not precipitate in liquid phase during the equilibrium solidification process (calculated by the Lever-rule equation). When the cooling rate of the liquid steel was set as 5, 10 and 20°C·min −1, VC and Mo2C precipitated at the end of solidification process, where VC precipitated at fS larger than 0.94 and Mo2C pre-cipitated at fS larger than 0.99. Primary carbides precipitated earlier at higher cooling rate. As cooling rate increased from 5 to 20°C·min −1, the solid fraction that Mo2C precipitated decreased from 0.999 to 0.995, while the solid fraction that VC precipitated decreased from 0.95 to 0.94. However, the result calculated by the Scheil equation indicates that VC will not precipitate at fS less than 0.87 and Mo2C will not

Fig. 10. Effect of cooling rate on calculated SR of alloy elements during solidification: (a) Mo; (b) V; (c) C; (d) Cr.

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precipitate at fS less than 0.97. Lower cooling rate can result in VC and Mo2C forming at higher solid fraction, but it is hard to avoid the precipitation of VC and Mo2C entirely, because the Gibbs free energy of the primary carbides for-mation reaction changed little with cooling rate.

Based on the result of thermodynamic calculation, the experimental result in Fig. 6 can be explained as follows: As cooling rate increases, V-PC generate earlier and the number of effective nuclei increases, which is favored for the quantity increase of V-PC. Moreover, the generation of more V-PC suppress the effective nuclei of M-PC because V-PC precipitate prior to M-PC.

In order to elucidate the effect of cooling rate on the growth of VC and Mo2C during the solidification of H13 steel, the solid fraction dependence of the diameter of VC and Mo2C were calculated by Eqs. (12)–(15).31) The driv-ing force for VC growth was assumed to be the difference between the V concentration in the liquid phase (CL,V) and the V concentration (Ce,V) that in equilibrium with VC particle, and that for Mo2C growth was assumed to be the difference between the C concentration in the liquid phase (CL,C) and the C concentration (Ce,C) that in equilibrium with Mo2C particle.

r D C C tVC

VC Fe

Fe VCVL

L V e V VCMM

� ���50

( ), , ........ (12)

r D C C teMo CMo C Fe

C Mo CCL

L C C Mo C2

2

2

2

MM

� ���50

( ), , .... (13)

t f t fVC S� �[ ],VC1 .......................... (14)

t f t fMo C S Mo C2 2� �[ ],1 ....................... (15)

Where rVC and rMo C2 is the radius of the precipitated VC and Mo2C, MVC, MMo C2 and MC is the molecular weight of VC, Mo2C and C respectively, ρVC, ρMo C2 and ρFe is the density of VC, Mo2C and liquid iron, DV

L and DCL is the

diffusion coefficient of V and C in liquid steel, CL,V and CL,C is the concentration of V and C in liquid steel that calculated by the Clyne-Kruz equation, fS,VC is the solid fraction that VC precipitate, fS Mo C, 2 is the solid fraction that Mo2C precipitate.Figure 12 shows the calculated radius of the precipitated

VC and Mo2C as a function of solid fraction. As above-mentioned, the solid fraction that primary carbides in H13 steel precipitate was larger than 0.87. Therefore, the growth of primary carbide is restricted by the limited space of the unsolidified liquid. Moreover, the growth of the primary carbide is further restricted because the precipitation of primary carbide consumes alloying elements in the liquid phase. Hence, the calculation result overestimated the size of the primary carbides. But relative comparison of the growth of primary carbides at different cooling rates is pos-sible. It can be concluded from Fig. 12 that the radius of VC and Mo2C increases with the increase of solid fraction whereas decreases with the increase of cooling rate. This is because that although the concentration of the primary car-bides forming elements increased with the increased cooling rate, tVC and tMo C2 decreased with the increased cooling rate significantly, which suppressed the growth of the primary carbides. The calculation result is consistent with the experi-mental result as shown in Figs. 7 and 8. The number, quan-tity proportion of large primary carbide, as well as the mean area of primary carbide decreases significantly with the increase of cooling rate, which means higher cooling rate are favored for the precipitation of smaller primary carbides.

Fig. 11. The Gibbs free energy of the formation of primary carbides: (a) VC; (b) Mo2C.

Table 4. The Gibbs free energy of the formation reaction of Mo2C and VC.

Reaction ��G (J·mol −1) ΔG (J·mol −1)

2[Mo] + [C] = Mo2C(s) −123 410 + 142.84T �� �G RTf f

ln[%Mo] [% ]

12

Mo2

C C

[V] + [C] = VC(s) −103 990 + 78.28T �� �G RTf f

ln[% ] [% ]

1

v CV C

Note: R is the gas constant of 8.314 J·(mol·K) −1, and T is the temperature in Kelvin.

ISIJ International, Vol. 59 (2019), No. 5

© 2019 ISIJ857

5.  Conclusions

In the present research, the alloying elements segrega-tion and the characteristics of primary carbides in the H13 steel samples that solidified at 5–20°C·min −1 were investi-gated. The precipitation of primary carbides was elucidated with the help of thermodynamics and kinetics. The results obtained are as follows:

(1) The microstructure of the solidified H13 steel samples become more refined with the increased solidifica-tion cooling rate. The secondary dendrite arm spacing (λ, μm) of H13 steel decreased with the increased cooling rate. The prediction formula of λ as a function of local cool-ing rate (RC,°C·min −1) for H13 steel was established as � � 175 4 0 322. .RC

� .(2) There were obvious Mo, V, C and Cr segregation

in the interdendritic zone of the solidified H13 steel and the segregation ratio of these alloying elements increased with the increased cooling rate. The experimental and theoretical calculation result indicated that the segregation of Mo and V were dependent largely on cooling rate, but the segregation of C and Cr were relatively insensitive to cooling rate. The segregation ratio of Mo is largest, followed by V, C and Cr.

(3) Two kinds of primary carbides precipitated during the solidification of H13 steel, namely, the V-rich MC and Mo-rich M2C. The primary carbides precipitated at lower solid fraction as cooling rate increased. However, the V-rich primary carbides will not precipitate at solid fraction less than 0.87 and the Mo-rich primary carbides will not pre-cipitate at solid fraction less than 0.97.

(4) The number, size, amount and mean area of the primary carbides decreased significantly with the increased cooling rate, but the length-width ratio of the primary car-bides changed little with cooling rate. In the cooling rate range investigated, most of the primary carbides in the solid-ified H13 steel samples were Mo-Cr-rich primary carbides. The Mo-rich primary carbides were relatively larger than the V-rich primary carbides. However, the mean area of the M-PC and V-PC were almost identical at high cooling rate.

AcknowledgementsThe authors are thankful to the support from the National

Natural Science Foundation of China (NSFC) (Nos. U 1560203, and 51274031), and the Beijing Key Laboratory of Special Melting and Preparation of High-End Metal Mate-

rials at the School of Metallurgical and Ecological Engi-neering at University of Science and Technology Beijing (USTB), China.

REFERENCES

1) Y. G. Zhao, Y. H. Liang, W. Zhou, Q. D. Qin and Q. C. Jiang: ISIJ Int., 45 (2005), 410.

2) J. Li, J. Li, L. Wang and L. Li: High Temp. Mater. Process., 34 (2015), 593.

3) X. L. Sun, H. J. Guo, X. C. Chen, A. G. Ning, G. W. Du and C. B. Shi: Kang Tieh/Iron Steel, 49 (2014), 68.

4) K. Ozaki: Denki Seiko, 76 (2005), 249 (in Japanese).5) L. L. Mishnaevsky, N. Lippmann and S. Schmauder: Z. Metallkd., 94

(2003), 676.6) Y. Xie, G. G. Cheng, L. Chen, Y. Zhang and Q. Yan: ISIJ Int., 56

(2016), 995.7) Y. Xie, G. G. Cheng, X. Meng, L. Chen and Y. Zhang: ISIJ Int., 56

(2016), 1996.8) S. N. Tewari: Metall. Trans. A, 17 (1986), 2279.9) B. S. Terry and O. S. Chinyamakobvu: J. Mater. Sci., 27 (1992),

5666.10) N. H. Pryds and X. Huang: Metall. Mater. Trans. A, 31 (2000), 3155.11) R. Fernandez, J. C. Lecomte and T. Z. Kattamis: Metall. Trans. A, 9

(1978), 1381.12) S. Chu, J. Li, Z. Liu, Z. Shi and H. Fu: Metall. Mater. Trans. A, 25

(1994), 637.13) X. F. Zhou, F. Fang, F. Li and J. Q. Jiang: J. Mater. Sci., 46 (2011),

1196.14) G. Du, J. Li and Z. B. Wang: Metall. Mater. Trans. B, 48 (2017), 2873.15) J. O. Andersson, T. Helander, L. Höglund, P. Shi and S. Bo: Calphad,

26 (2002), 273.16) C. W. Bale, P. Chartrand, S. A. Degterov, G. Eriksson, K. Hack, R.

Ben Mahfoud, J. Melancon, A. D. Pelton and S. Petersen: Calphad, 26 (2002), 189.

17) Q. Liu, H. W. Zhang, Q. Wang, X. K. Zhou, P. G. Jonsson and K. J. Nakajima: ISIJ Int., 52 (2012), 2210.

18) Z. B. Li: Foreign Electro-slag Remelting, Shanghai Industries Intel-ligence Services Press, Shanghai, (1978), 32.

19) M. C. Flemings: Solidification Processing, McGraw-Hill, New York, (1974), 146.

20) Z. H. Jiang: The Physical Chemistry and Transport Phenomena in Electroslag Metallurgy, Northeastern University Publishers, Shenyang, (2000), 278.

21) R. J. Su, R. A. Overfelt and W. A. Jemian: Metall. Mater. Trans. A, 29 (1998), 2375.

22) Y. Meng and B. G. Thomas: Metall. Mater. Trans. B, 34 (2003), 685.23) Q. Li, X. H. Wang, H. B. Li, F. X. Huang, G. S. Zhu, M. Jiang, W.

J. Wang: J. Univ. Sci. Technol. Beijing, 34 (2012), 1262.24) T. W. Clyne and W. Kurz: Metall. Trans. A, 12 (1981), 965.25) B. G. Thomas, I. V. Samarasekera and J. K. Brimacombe: Metall.

Trans. B, 18 (1987), 119.26) Z. Ma and D. Janke: ISIJ Int., 38 (1998), 46.27) Y. Ueshima, S. Mizoguchi, T. Matsumiya and H. Kajioka: Metall.

Trans. B, 17 (1986), 845.28) L. L. Seigle, C. L. Chang and T. P. Sharma: Metall. Trans. A, 10

(1979), 1223.29) J. X. Chen: Databook of Steelmaking, Metallurgical Industry Press,

Beijing, (2010), 840.30) Z. Liu, J. Wei and K. Cai: ISIJ Int., 42 (2002), 958.31) Y. N. Wang, J. Yang, X. L. Xin, R. Z. Wang and L. Y. Xu: Metall.

Mater. Trans. B, 47 (2016), 1378.

Fig. 12. Variations of the radius of VC (a) and Mo2C (b).