Effect of directional solidification of electroslag remelting on the microstructure and primary carbides in an austenitic hot-work die steel

Effect of directional solidification of electroslag remelting on the microstructure and primary carbides in an austenitic hot-work die steel

Journal of Materials Processing Tech. 249 (2017) 32–38 Contents lists available at ScienceDirect Journal of Materials Processing Tech. journal homep...

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Journal of Materials Processing Tech. 249 (2017) 32–38

Contents lists available at ScienceDirect

Journal of Materials Processing Tech. journal homepage: www.elsevier.com/locate/jmatprotec

Effect of directional solidification of electroslag remelting on the microstructure and primary carbides in an austenitic hot-work die steel

MARK



Yong-feng Qi, Jing Li , Cheng-bin Shi, Yi Zhang, Qin-tian Zhu, Hao Wang State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing (USTB), 30 Xueyuan Road, Haidian District, Beijing 100083, PR China

A R T I C L E I N F O

A B S T R A C T

Keywords: Directional solidification Austenite Primary carbides Hot-work die steel

The microstructure of as-cast ingot and three-dimensional microstructure of carbides were analyzed by optical microscope and scanning electron microscope. The types of carbides were identified by X-ray diffraction. Directional solidification of electroslag remelting effectively reduced the segregation of alloying elements in ascast ingot. The growing direction of dendrites in as-cast ingot refined by directional solidification of electroslag remelting was paralleled to < 001 > crystallographic orientation. The solidification microstructure of austenitic hot-work die steel was composed of austenite and primary carbides (V8C7-type and Mo2C-type) which distributed along grain boundaries. Compared with conventional electroslag remelting, the directional solidification of electroslag remelting process reduced the size of primary carbides and improved dispersed distribution of carbides, but not changed the types and compositions of carbides. The direction of driving force for carbides growth was irregular in conventional electroslag remelting, while that was nearly parallel to crystal < 001 > in directional solidification of electroslag remelting.

1. Introduction The working temperatures for molding cavities served as copper extrusion die range from 700 °C to 900 °C. The service conditions of extruding dies for copper alloys are very rigorous. Conventional hotwork die steels are widely applied in hot forging, hot extrusion and die casting. In fact, hot-work die steels with martensite matrix, including 3Cr2W8V, H13, THG2000 and QRO90, are widely used in industrial applications (Li et al., 2015). Zhou et al. (2011) reported that the temperature at the surface of dies may reaches up to 600 °C or exceeds the tempering temperature of steel, inevitably leading to the cumulative effect of tempering and certainly affect properties of dies such as hot hardness, temper resistance and high-temperature fatigue strength. In order to prevent the decrease of strength and the premature failure caused by coarsening carbides and the recovery of martensite, a high-strength insulating coating on the functional surface of die steels (such as a layer of zirconium oxide) was employed, but it has been confirmed to be invalid for service temperature above 600 °C (Grabovskii, 2000). In recent years, austenitic hot-work die steels have attracted researchers’ attentions in order to improve the strength of die steels at the temperatures higher than 600 °C. Xie et al. (1990) reported that the more austenite there was in the matrix, the better was the hot strength for hot-work die steel at elevated temperature. Baglyuk et al. (2006) suggested that the possibility of using powder metallurgy to



Corresponding author. E-mail addresses: [email protected], [email protected] (J. Li).

http://dx.doi.org/10.1016/j.jmatprotec.2017.05.034 Received 14 February 2017; Received in revised form 25 May 2017; Accepted 26 May 2017 Available online 29 May 2017 0924-0136/ © 2017 Published by Elsevier B.V.

prepare effective die steels that exhibit increased hardness and heat resistance at temperature not less than 850 °C. Wang et al. (2015) investigated effects of B on high temperature mechanical properties and thermal fatigue behavior of austenitic die-casting die steel, they found that thermal fatigue resistance of austenitic die steel was much better than that of martensitic die steel H13. The microstructure of austenitic hot-work die steels keeps a stable austenite phase, and there is no phase transformation during high temperature services. Therefore, these die steels have longer service life and better thermal stability, but lower hardness. These steels are strengthened by solid solution strengthening and precipitation strengthening with intermetallic, carbides and carbonitrides phases. The stable austenitic structure is composited by Fe-Cr-Ni, Fe-Cr-Mn and Fe-Mn-C alloy system. Grabovskii and Kanyuka (2001) reported that austenitic hot-work die steels ÉK39 and ÉK40 provided by Fe-Cr-Ni matrix have good hot-hardness, good impact toughness and good thermal stability, and these steels can preferably meet requirements of extrusion for copper at service temperature above 700 °C. The elements such as carbon, nitrogen and nickel, are austenite phase forming elements. At the same time, nitrogen is always added to form VN, CV and Cr2N precipitations to provide precipitation strengthening (Wang et al., 2010.). In order to save precious nickel, manganese is used to replace nickel to obtain stable austenitic matrix. Austentic hot-work steel with low thermal conductivity, tends to produce solidification mushy zone in

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some carbides were observed by SEM for the three-dimensional morphology.

the casting process, which will lead to the center segregation, porosity and the shrinkage cavity. Electroslag remelting (ESR) could significantly improve the cleanliness, solidification structure, and transverse mechanical properties of steel (Shi et al., 2013). However, the increasing demands on steel mechanical properties urge metallurgists to make greater efforts to eliminate the defects of steel microstructure, such as shrinkage and segregation. Fu et al. (2015) demonstrates that the combination of directionally solidification technology with electroslag remelting technology effectively eliminates macro-segregation in as-cast ingot through the shallow molten metal pool controlled by directional solidification. Compared to ESR process, the amount and size of inclusions in ESR-CDS process could be reduced. Shallow flat pool caused by ESRCDS process was more conductive to the removal of inclusions. Meanwhile, smaller secondary dendritic spacing and smaller non-equilibrium precipitated phases could be controlled by a higher cooling rate in ESRCDS process. High cooling rate with spraying water at bottom of ingots could provide stable temperature gradient nearly parallel to axis of ingots (Li et al., 2016). In recent years, the studies on the directional solidification of ESR were focused on the production of superalloy. In this work, the effect of directional solidification of ESR on the segregation, microstructure and primary carbides evolution in as-cast ingot was studied. Moreover, the mechanism of the effect of directional solidification of ESR on primary carbides distribution and morphology was discussed.

3. Results and discussion 3.1. Macrosegregation of as-cast ingot Eliminating macro-segregation in as-cast ingots was a critical factor for precipitation-hardened steel used at elevated temperature (Zhou et al., 2013). Inhomogeneous structure owing to the segregation of alloying elements during solidification played an important role on impact toughness of cast steel (Lan et al., 2000). Auburtin et al. (2000) showed that the flow of solute-rich interdendritic liquid in the mushy zone during solidification was responsible for most types of macrosegregation such as freckles. The freckles were common in ESR ingots on account of deep molten pool with steeper sides, large mushy zones and long local solidification time. During the conventional ESR process, the cooling rate was slow relatively, opposing thermal and solute buoyancy forces led to the remelting and the plume in the mushy zone, and then the segregation channel formed. The deep V-shaped pool profile with a prolonged mushy zone enhanced the intensity of liquid flow in an ESR ingot, so the macro-segregation was more likely to be formed. The ESR-CDS process was developed on the base of the traditional ESR technique. In ESR-CDS process, the macro-segregation was effectively eliminated because of the shallow metal pool with a uniformly distributed mushy zone. At the same time, the severe segregated region existing in the interfaces of columnar grains with different orientations in center of ESR ingot was eliminated. Fig. 1 presents the principle diagram of ESR-CDS, and the longitudinal macrostructure of the ESR-CDS ingot is shown in Fig. 2. Fig. 2 presents the macrostructure of S2 ingot showing columnar crystals growing nearly parallel to the axis. The direction of some columnar grains deviated a little from the axis of the ingot, and the maximum deviation was about 13°. Deviation of the growth direction may be due to the temperature fluctuation at the solid/liquid interface. It could be seen that the ESR-CDS technique completely eliminated the solidification mushy zone in as-cast ingot. The element segregation was reduced, and the homogeneity of the structure was improved. In addition, the growing direction of columnar grain was nearly parallel to < 001 > crystallographic orientation. Li et al. (2016) pointed out that this parallel oriented columnar grain boundaries avoided the maximum shear stress direction of 45° to the axis of ingot during deformation, which greatly improved hot-workability. While in conventional ESR ingot, there were coarse equiaxed grains and interfaces of columnar grains with various orientations, so processability of ingot with non-oriented columnar grain obviously worsened. The direction of maximum shear stress was consistent with the slip crystallographic orientation of {111} < 110 > slip system during longitudinal

2. Experimental 2.1. Experimental materials The austenitic hot-work die steel was obtained by melting pure alloy ingredients in a 200 kg vacuum induction furnace. The liquid steel was cast into a rod, and then forged into two rods of 120 mm in diameter. Then the electrodes were remelted using conventional ESR and ESRCDS for comparison. The remelting process was conducted in the argon gas atmosphere. The produced as-cast ingots of 160 mm in diameter remelted by ESR and ESR-CDS were sampled as S1 and S2, respectively. The chemical compositions of remelted ingots S1 and S2 were determined by inductively coupled plasma optical emission spectrometer, and the results are shown in Table 1. 2.2. Microscopic observation The samples with the dimension of 15 mm × 15 mm × 12 mm were taken from as-cast ingots S1 and S2, respectively. The metallographic samples were analyzed by optimal microscope (LEICA DM2500M, OM) and scanning electron microscope (FEI MLA250, FEI, Hillsboro, OR, USA, SEM), after grinding, polishing and etching with 6% nitric acid alcohol. The precipitated phases in austenitic hot-work die steel were calculated by Thermo-Calc software. 2.3. Carbides collection using electrolytic extraction technique The samples taken from S1 and S2 ingots, were machined into a rod of Ø15 mm × 90 mm. Carbides were extracted from steel matrix in organic solution (methanol, tetramethylammonium chloride, glycerin, diethanol amine) by electrolysis. Some of the carbides were analyzed by XRD (Rigaku Dmax-RB, Rigaku, Tokyo, Japan) to confirm the types, and Table 1 Chemical composition of steel (wt/%).

S1 S2

C

Si

Mn

Cr

Mo

V

P

S

Fe

0.70 0.698

0.55 0.544

14.95 14.90

3.45 3.53

1.57 1.55

1.723 1.726

0.0085 0.0088

0.0023 0.0021

Bal. Bal. Fig. 1. Schematic diagram of ESR-CDS.

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Fig. 2. Macrostructure of solidification ingot at longitudinal direction.

Fig. 3(a)–(c) shows that the dendrites in S1 ingot grew with different direction, and dendritic spacings were larger than those in S2 ingot. Fig. 3(d)–(f) shows that the primary dendrites were compact and the secondary dendrites were fine in position C, while the positions A and B were parallel columnar crystals. The secondary dendrite had a certain degree of coarsening. The dendrite spacings gradually decreased from the center to the edge, and the difference of dendrite spacing between area A and B were smaller than 1 μm. As shown in Fig. 4, the primary dendritic spacing (dI) and secondary dendritic spacing (dII) in S2 ingot were smaller than those in S1 ingot. There was a quantitative relationship between dendrite spacing and local solidification time

compression, so S2 ingot had lower resistance of deformation and higher plasticity than that of non-oriented S1 ingot. The primary dendrite spacing, secondary dendrite spacing and columnar dendritic growth direction were important parameters to characterize the quality of electroslag remelting process (Dong et al., 2009). To further observe details of columnar dendrites in Fig. 2A–C, three specimens were sampled to observe the metallographic structure in vertical direction to in comparition with specimens at same position in S1 ingot, which were shown in Fig. 3. The dendritic spacings were measured using statistical software. The standard values were averages of 15 measurements. The results are shown in Fig. 4.

Fig. 3. Optical microscope metallographic images in different positions of as-cast S1 and S2 ingots: (a)–(c) S1; (d)–(f) S2; (a), (d) at edge C; (b), (e) at 1/ 4 diameter B; (c), (f) at center A.

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nonmetallic inclusion and morphological characteristics of precipitates. The direction of temperature gradient was perpendicular to the solid/ liquid interface, which led to a certain growing direction of primary dendritic axis (Fu et al., 2015). Closed mushy zone was bound to form owing to the crossing primary dendritic arms. Shallow molten pool was obtained during the ESR-CDS process by controlling the direction of thermal flow, the temperature gradient of solidification front and the solidification rate. The growing direction of primary dendritic axis was nearly parallel to the axis of solidifying ingot, which could avoid the formation of closed mushy zone. The schematic diagrams of the solidification behavior during ESR and ESR-CDS process are shown in Fig. 6(a) and (b), respectively. The effect of ESR-CDS compared to conventional ESR on the microstructure of Rene88DT (Li et al., 2016) and M2 high speel steel (Zhan et al., 2013) ingots have been verified elsewhere. It could be obtained from above analysis that, compared to the conventional ESR process, ESR-CDS process greatly reduced the level of segregation and solidification shrinkage. It was commonly known that the secondary dendritic spacing had a great influence on the size, quantity and distribution of the precipitates in the interdendritic region of ingots. Flemings revealed that local solidification time and dendritical axial spacing have the following relation (Flemings, 1981):

Fig. 4. Inter-dendritic spacing at different positions of S1 and S2 ingots.

(Hernandez-Morales and Mitchell, 1999), which indicated that the ingots had similar local solidification time except the edge chill zone during ESR-CDS process. It indicated that the molten pool was shallow, and element segregation was effectively reduced.

log d = k1 + k2 log T

(1)

where d represents the dendritic axial spacing, μm; k1 and k2 are constant and determined by the content of alloy element; T is the local solidification time, min. In order to further study the effect of ESR and ESR-CDS technique on primary carbides in as-cast ingots, the microstructure of specimens taken from S1 and S2 ingots and carbides extracted from as-cast ingots were analyzed by SEM-EDS. The microstructure of as-cast ingots and three-dimensional structure of carbides were shown in Fig. 7. Fig. 7(a) and (b) displayed the distributions of primary carbides in Fig. 5(a), (b), respectively. Fig. 7(a) shows that some phases precipitated along the equiaxed grain boundaries and distributed densely. Fig. 7(b) shows that the some phases precipitated along the columnar grain boundaries and distributed dispersedly, and their size was smaller than that in Fig. 7(a). The basic parameters and characteristic parameters of primary carbides were analyzed by image analysis software. The characteristic parameters include: volume fraction Vv, the number of carbides per unit volume VN, the average diameter of carbides D (Qin, 1987). The relationship among them was shown in Table 2. The following parameters could be obtained: length (l) and width (w) of the carbides, length (L) and width (W) of the metallography, the number (N) of carbides, the area (A) of carbides, the average diameter (D ), as shown in Table 2. According to the data in Tables 2 and 3, characteristic parameters of carbides could be calculated, as listed in Table 3. Comparing characteristic parameters of carbides, it could be found that not only the amount, but also the size of carbides decreased when using ESR-CDS

3.2. Microsegregation of as-cast ingot During solidification, the segregation of alloying elements occurs due to selective crystallization. According to dendritic solidification mode, the elements Cr and Mn were enriched in the dendritic axis because their solute partition coefficients (k) exceeded 1. The primary carbide forming elements, such as C, Mo and V, were enriched in the interdendritic regions due to their solute partition coefficients (k) was smaller than 1 (Wang et al., 2014). The microstructures of conventional S1 and S2 ingots are shown in Fig. 5. The microstructure of S1 ingot was consisted of equiaxed grains with chaotic dendrites, coarse dendritic arms and large secondary dendritic spacing (about 80 μm). Fig. 5(b) revealed that the primary dendrites were parallel to each other and secondary dendritic arms arranged in neat rows in S2 ingot. The secondary dendritic arms crossed with each other, and the dendritic spacings were smaller than 40 μm. ESR and ESR-CDS experiments were conducted at the same melting rate. The difference in the microstructure of S1 and S2 ingots could be attributed to the following aspects: (1) different local solidification time caused by the shape of the metal molten pool; (2) different cooling rate controlled by external conditions; (3) concentration gradient at the solid/liquid interface. A deep V-shape molten pool formed during the ESR process influenced the growing direction of dendrite, removal of

Fig. 5. Dendritic structures of conventional S1 and S2 ingots: (a) S1; (b) S2.

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Fig. 6. Schematic diagrams for the solidification behavior during ESR and ESR-CDS process: (a) ESR; (b) ESR-CDS.

process. This illustrated that finer primary carbides and more diffuse carbides could be obtained by ESR-CDS process. Fig. 7(c) and (d) shows the three-dimensional structure of carbides extracted from as-cast S1 and S2 ingots. The composition of the precipitated phases analyzed by EDS was shown in Table 4. It could be seen from Table 4 that carbides extracted from as-cast S1 and S2 could be divided into two categories: the first type (such as “I”, in Fig. 7) was primary MC-type carbides which were vanadium-rich containing a certain amount of Cr and Mo elements; the other type (such as “II”, in Fig. 7) was M2C-type eutectic carbides which were molybdenum-rich containing a certain amount of Mn, Cr and V elements. In order to further confirm the type of carbides and the matrix phase in as-cast ingot, XRD was used for phase analysis. The results were shown in Fig. 8. Fig. 8(a) shows that matrix phase in as-cast ingot was single austenite phase. Fig. 8(b) shows that the MC-type and M2C-type carbides were V8C7 and Mo2C, respectively. The intensity of main diffraction peak do not change significantly, which proved that the crystallography surface do not change greatly. According to three-

Table 2 Characteristic parameters of carbides. Relation

Unit

The meaning of space characteristic parameters

Vv = AA Nv = NA/D

% –

Volume fraction of carbides The number of carbides per unit volume

dimensional structures of carbides shown in Fig. 7(c) and (d), the morphology of carbides of type I in S1 was short rod-shaped, while that of type I in S2 was disc-shaped with multi-angles. The morphology of carbides of type II in S1 was lamellar fish-skeleton-like, while that of type II in S2 was thin-leaf skeleton-like and it was similar to that of type II in S1, which were typical eutectic carbides. Compared to ESR process, ESR-CDS process effectively reduced the sizes of primary carbides, improved dispersed distribution of carbides, and also changed the morphology of MC-type carbides.

Fig. 7. The microstructure of remelted ingots and three-dimensional carbides structure in S1 and S2 ingots: (a), (c) S1; (b), (d) S2.

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Table 3 Basic parameters and characteristic parameters of carbides. Sample

The basic parameters of quantitative metallography

Characteristic parameters of carbides

Statistic of carbides parameters

S1 S2

Size of photo

N

A/μm

D /μm

l//μm

w/μm

L//μm

W/μm

Vv/%

Nv

527 521

12226.43 5517.55

5.85 3.94

9.35 5.65

3.65 2.44

595.92 595.92

507.29 507.29

4.04 1.83

0.035 0.016

solidification of liquid steel, primary carbides precipitated along preexisted austenite. Due to the difference in the concentration gradient of carbon content, the premiere carbides might grow up from one grain boundary to other grain boundaries. The driving force for carbides growing located in the grain boundaries. Therefore, the directions of driving force for carbides growth in conventional ESR process were irregular. On the contrary, those were single direction nearly parallel to crystal < 001 > in ESR-CDS process. This was the reason for the difference in morphologies of eutectic carbides obtained in ESR and ESRCDS process, as shown in Fig. 7(c) and (d). This result was similar with the findings reported elsewhere. Yu et al. (2016) verified that the cooling rates of ESR affected not only the dendritic spacing, but also the morphology of eutectic carbides. Trivedi et al. (1991) obtained a similar trend based on their experimental work. The present study shows that the combination of directional solidification with electroslag remelting not only reduced segregation of solute atoms, but also refined the size and distribution of carbides.

Table 4 Compositions of the precipitated phases in S1 and S2 samples (wt/%). Element

Precipitated Phase

C

Fe

Mo

Mn

Cr

V

S1

Point I Point II

15.27 13.68

4.39 25.24

10.72 30.33

1.95 10.93

2.36 10.02

65.31 9.80

S2

Point I Point II

13.61 14.82

3.80 12.27

19.16 33.90

1.67 10.78

6.47 13.57

55.28 12.19

3.3. Phases formation calculated with Thermo-Calc software According to solidification principle, the preliminary analysis suggested that the dendritic structure of the ingots and morphology of carbides were affected by the shape of molten metal pool, cooling intensity and segregation degree. The equilibrium and non-equilibrium phase diagram of austenitic hot-work die steel were calculated by Thermo-Calc software. The calculated results were shown in Fig. 9. It could be seen from Fig. 9(a) that the primary austenite phase precipitated from liquid steel first and then served as the single stable matrix in austenitic hot-work die steel. With decreasing temperature, different types of carbides such as MC, M2C, M7C3 and M23C6 precipitated in sequence. In practical solidification process, the carbides forming elements with solute partition coefficients (k) smaller than 1 would segregate at the solid/liquid interface, which would lead to eutectic reaction in the interdendritic regions. Fig. 9(b) shows that MC and M2C carbides precipitated from liquid steel directly in non-equilibrium condition. With the precipitation of austenite, the eutectic reaction (L → γ + M2C) would gradually take place. These calculated results were in agreement with the experimental results. The modes of dendritic growth during solidification in ESR and ESRCDS process are schematically presented in Fig. 10. The growing direction of dendrites in ESR-CDS process was parallel to each other throughout the whole ingot as shown in Fig. 10(b), whereas dendrites in conventional ESR process were chaotic even in the small areas as shown in Fig. 10(a). Compared to the microstructure in ESR process, the dendritic arm was finer and the dendritic spacing was narrower in the ESR-CDS process, as shown in Fig. 5. The shadow area around dendritic crystal represented solute enrichment area. When the composition of residual liquid steel reached eutectic point during

4. Conclusions (1) Compared to conventional ESR, directional solidification of ESR is more favorable to eliminate macro-segregation of ingot, which is attributed to the shallower molten pool. The growing direction of dendritite in the as-cast ingot produced by directional solidification of ESR is paralleled to < 001 > crystallographic orientation. (2) The as-cast ingot refined by directional solidification of ESR process exhibits less micro-segregation than that of conventional ESR process, which is due to the finer secondary dendritic spacing. The secondary dendritic spacings in ESR-CDS ingot are less than 40 μm, while those in conventional ESR ingot are about 80 μm. (3) The solidification microstructure of austenitic hot-work die steel is composed of single austenite phase and primary carbides (V8C7 and Mo2C) located along grain boundaries. The finer primary carbides and more diffuse carbides could be obtained through ESR-CDS process, compared to that in ESR process. (4) Compared to conventional ESR process, the directional solidification of ESR process do not change the type and compositions of carbides, but improves the distribution and morphology carbides in as-cast ingot. The differences in the distribution and morphology of Fig. 8. XRD patterns of the steel matrix and carbides powder: (a) steel matrix; (b) carbides powder.

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Fig. 9. Phase precipitated in austenitic hot-work die steel calculated by Thermo-Calc: (a) equilibrium phase diagram; (b) non-equilibrium phase diagram.

Fig. 10. Schematic diagram for the dendritic growth during solidification in ESR and ESR-CDS process: (a) ESR; (b) ESR-CDS.

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carbides in ESR and ESR-CDS ingots are due to different directions of driving force for carbides growth at the grain boundaries. Acknowledgment The financial support by the National Natural Science Foundation of China (Grant Nos. 51504019 and 51574025) was greatly acknowledged. This work was also financially supported by the Project of Hightech Ships of Ministry of Industry and Information Technology of the Peoples Republic of China (Grant Nos. [2014] 508) References Auburtin, P., Wang, T., Cockcroft, S.L., Mitchell, A., 2000. Freckle formation and freckle criterion in superalloy castings. Metall. Mater. Trans. B 31 (4), 801–811. Baglyuk, G.A., Terekhov, V.N., Ternovoi, Y.F., 2006. Structure and properties of power austenitic die steels. Powder Metall. Met. Ceram. 45 (7–8), 317–320. Dong, Y.W., Jiang, Z.H., Xiao, Z.X., Li, Z.B., 2009. Influence of ESR process parameters on solidification quality of remelting ingots. J. Northeast Univ. 30 (11), 1598–1601. Fu, R., Li, F.L., Yin, F.J., Feng, D., Tian, Z.L., Chang, L.T., 2015. Microstructure evolution and deformation mechanisms of the electroslag refined-continuous directionally solidified (ESR-CDS®) superalloy Rene88DT during isothermal compression. Mater. Sci. Eng. A 638, 152–164. Flemings, M.C., 1981. Solidification Process. Mtallurgical Industry Press, Beijing (In Chinese). Grabovskii, V.Y., Kanyuka, V.I., 2001. Austenitic die steels and alloys for hot deformation of metals. Met. Sci. Heat Treat. 43 (9–10), 402–405. Grabovskii, V.Y., 2000. Structural transformations of matrices in hot pressing of titanium and steel shapes. Metalloved. Term. Obrab. Met. 3, 17–20. Hernandez-Morales, B., Mitchell, A., 1999. Review of mathematical models of fluid flow, heat transfer, and mass transfer in electroslag remelting process. Ironmaking Steelmaking 26 (6), 423–437.

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