# Solidified Structure Refinement of H13 Tool Steel under a Multi-Rotational Speed Super Gravity Field

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}).

## 2. Experimental Procedures

_{2}, 20 wt% CaO and 20 wt% Al

_{2}O

_{3}to prevent oxidation of molten steel as much as possible during the experiment.

_{2}O (150 mL). The samples were cut from the observed area, as shown in Figure 3a. These samples were mechanically flattened, polished, and chemically etched in a solution of HNO3 (4 mL) + absolute ethanol (96 mL) for 30 s to reveal the dendritic structures and the prior austenite grains. The secondary dendrite arm spacing (SDAS) and the average diameter of the austenite grains were measured based on multiple optical micrographs (OM; Leica-DM4M) using the linear intercept method [18].

## 3. Results and Discussion

#### 3.1. Macro- and Micro-Structures of As-Cast H13 Samples in Super-Gravity Fields

#### 3.2. The Refinement Mechanism of the H13 Solidified Structure in the Super-Gravity Field

_{7}C

_{3}and MC.

_{V}is the solid–liquid difference of Gibbs free energy per unit volume; G

_{g}and G

_{b}represent energy per volume exerted on the nucleus provided by normal gravity and super-gravity, respectively; σ is the solid–liquid interfacial tension; V is the volume of the solid; and A is the interfacial area.

- The contact angle between the nucleation of austenite and the δ-ferrite grain boundary is 180°; the nucleation energy required for heterogeneous nucleation is equal to that for homogeneous nucleation [20].
- Body shrinkage rate ε, surface tension σ (N/m) and the change of chemical potential ΔF
_{T}are independent of super-gravity [10]. - The change in the chemical potential of the test material was replaced by a change in the Gibbs free energy of the pure iron from 1600 °C to 1500 °C (0.002575 J/m
^{3}) [21]. - G
_{g}can be ignored under the super-gravity field.

_{T}is the change in the chemical potential of the solidification system at the temperature of T (J/m

^{3}, i.e., ΔG

_{V}); k is the conversion factor; ε is the body shrinkage rate, 0.95 [22]; p the is external pressure (N); and σ is the solid–liquid interfacial tension (N/m). In the super-gravity field, the external pressure is centrifugal force and can be obtained by calculus. A cubic micro-volume (dR

^{3}) is extracted from the radius R of the liquid metal section, as shown in Figure 8a. The particle position of the micro-volume is R-dR/2, and the value of dR is so small that it can be ignored.

^{3}). By substituting Equation (4) into Equation (5), Equation (6) can be obtained [10].

^{3}; ω, rotational angular speed, rad/s; R, the distance from observation position to centrifugal center (i.e., rotational radius), m; and R

_{0}, the inner radius, m.

^{*}of Sample A, B, and C was, respectively, calculated by Equation (12), as shown in Figure 8c. Figure 8c shows that when R decreases from 0.225 m to 0.152 m, the value of ΔG* for Sample A increases from 1.5 × 10

^{−14}J/mol to 7 × 10

^{−14}J/mol, which means that as R decreases in the super-gravity field, the energy required for austenite nucleation increases, and the amount of austenite nucleated decreases. Compared with Sample A, the maximum value of ΔG* for Sample B evidently decreases, which makes austenite easy to nucleate. It also can be found that as the value of R decreases, ΔG* decreases at the range of increasing rotational speed, which can be also proved in the variations trend of ΔG* with R in Sample C. In short, during the process of solidification in the super-gravity field, increasing the number of rotational speeds is beneficial to refine the austenite grains.

_{l}and ρ

_{p}are the densities of the liquid and fragment (kg/m

^{3}); η is the dynamic viscosity of the liquid (Pa·s); and s is the displacement of the fragment (m).

_{r}can be expressed as

^{−10}m [20], and the viscosity of the molten steel is 0.0025 Pa·s [25]. According to the calculation results of Jmat-Pro 7.0 of thermo-physical properties, the difference value of the solid–liquid two-phase density was discussed.

^{3}, respectively. In the middle of solidification, the liquid phase ratio is less than 50% and greater than 5%, and the solid phase is austenite. The densities of austenite and liquid are 6.98 and 7.28 g/cm

^{3}, respectively. At the end of solidification, the liquid phase ratio is less than 5%, and the solid phase is austenite. The density of austenite slightly elevated but not exceeding 7.3 g/cm

^{3}. The density of liquid decreased to 6.93 from 6.98 g/cm

^{3}. The super-gravity treatment at the nucleation stage had the best refining effect, while the solidified structures were slightly refined with treatment at the beginning and end of crystal growth [26]. The ranges of refinement super-gravity are a solidification fraction of less than 59.18 wt% for Al-4.5 wt% Cu alloys and 23.16% for Al-8 wt% Cu alloys [11]. We assumed that with the liquid phase ratio of more than 50% in H13 steel, the super-gravity can refine the solidified structure. Within this range, the difference value of ρ

_{l}and ρ

_{p}almost unchanged, and the value of ρ

_{l}ρ

_{p}is defined as 0.26 g/cm

^{3}. The moving speed of the fragment was calculated by the crystal rain mechanism, as shown in Figure 9b.

_{r}for Sample A decreases from 1.4 × 10

^{−13}to 1.0 × 10

^{−13}m/s. For Samples B and C, v

_{r}increases with the decrease in R in the range of increasing rotational speed, which leads to the reduction of secondary dendrite spacings. For Samples B and C, the variations trends of secondary dendrite spacings with R are opposite to the variation trends of v

_{r}with R. If the refinement mechanism of the dendritic structure is only the “heavy crystal rain” mechanism, the difference in SDAS depends on that of v

_{r}. Combined with Figure 6a, the differences of SDAS between R = 0.225 m and R = 0.152 m for Samples A and C are 50 and 24 μm, respectively, and the corresponding differences of v

_{r}between R = 0.225 m and R = 0.152 m for Samples A and C are 0.5 × 10

^{−13}and 3.2 × 10

^{−13}m/s, respectively. Obviously, the values of SDAS are not completely related to v

_{r}, which means that other mechanisms have an effect on SDAS.

^{2}/s). In the super-gravity casting process, v quickly becomes smaller, and Re also becomes smaller. At the moment, the flow of the liquid steel to the inner wall of the mold is laminar, and the crystal front is in the laminar layer, which will promote the precipitation of small grains along the solid–liquid interface in one direction, thus forming inclined columnar crystals.

_{a}) and the distance from its center of gravity to the axis of rotation (R)

^{3}), the density difference between the solid and liquid phases of H13 (0.27 g/cm

^{3}) is smaller.

#### 3.3. Tensile Properties of As-Cast H13 Samples in Super-Gravity Fields

## 4. Conclusions

- (1)
- Compared to a single rotational speed super-gravity field, the solidified structure of H13 steel can be significantly refined in a multi-rotational speed (speed increased in stages) super-gravity field.
- (2)
- The decrease in critical nucleation work for austenite in the multi-rotational speed super-gravity field promotes the grain multiplication, resulting in the refinement of the austenite grain size. The tangential force produced by increasing the rotational speed in the super-gravity field breaks dendrites at the solidification front and finally causes the solidified structure refinement. Due to the smaller density difference between the solid and liquid phases of H13 steel, the “crystal rain” mechanism does not contribute much more to the refinement effect of the H13 solidified structure than binary alloys.
- (3)
- The increasing super-gravity can greatly enhance the tensile properties of as-cast H13 steel through refining austenite grains size and secondary dendrites. Both the tensile strength and plasticity at the inner position of the super-gravity samples are greatly enhanced with the increasing rotational speed.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Zhu, J.; Zhang, Z.H.; Xie, J.X. Improving strength and ductility of H13 die steel by pre-tempering treatment and its mechanism. Mater. Sci. Eng. A
**2019**, 752, 101–114. [Google Scholar] [CrossRef] - Zhou, H.; Zhang, H.F.; Tong, X.; Cong, D.L.; Wang, C.W.; Ren, L.Q. The comparative study of thermal fatigue behavior of H13 die steel with biomimetic non-smooth surface processed by laser surface melting and laser cladding. Mater. Des.
**2013**, 51, 886–893. [Google Scholar] - Kurz, W.; Fisher, D.J.; Li, J.G.; Hu, Q.D. Fundamentals of Solidification, 4th ed.; Higher Education Press: Beijing, China, 1998; pp. 71–73. [Google Scholar]
- Cicutti, C.; Boeri, R.; Cicutti, C.; Boeri, R. On the relationship between primary and secondary dendrite arm spacing in continuous casting products. Scr. Mater.
**2001**, 45, 1455–1460. [Google Scholar] [CrossRef] - Ferreira, A.F.; Melo, E.G.; Ferreira, L.O. Prediction of Secondary-Dendrite Arm Spacing for Binary Alloys by Means of a Phase-Field Model. Steel Res. Int.
**2015**, 86, 58–64. [Google Scholar] [CrossRef] - Liao, X.; Zhai, Q.; Luo, J.; Chen, W.; Gong, Y. Refining mechanism of the electric current pulse on the solidification structure of pure aluminum. Acta Mater.
**2007**, 55, 3103–3109. [Google Scholar] [CrossRef] - Song, W.X. Metal Science, 2nd ed.; Metallurgical Industry Press: Beijing, China, 2008; pp. 125–127. [Google Scholar]
- Gong, Y.Y.; Luo, J.; Jing, J.X.; Xia, Z.Q.; Zhai, Q.J. Structure refinement of pure aluminum by pulse magneto-oscillation. Mater. Sci. Eng. A
**2008**, 497, 147–152. [Google Scholar] [CrossRef] - Qi, F.P.; Zhang, H.B.; Gao, S.L.; Zhai, Q.J. Microstructure refinement of Sn-Sb peritectic alloy under high-intensity ultrasound treatment. J. Shanghai Univ.
**2005**, 9, 74–77. [Google Scholar] [CrossRef] - Jia, S.J.; Song, B.; Song, G.Y.; Yang, Y.H.; Huang, C.G. Effect of Super-gravity Field on Solidification Structure of Al−6%Cu Alloy. Chin. J. Process Eng.
**2014**, 14, 881–885. [Google Scholar] - Yang, Y.H.; Song, B.; Yang, Z.B.; Song, G.Y.; Cai, Z.Y.; Guo, Z.C. The Refining Mechanism of Super Gravity on the Solidification Structure of Al-Cu Alloys. Materials
**2016**, 9, 1001. [Google Scholar] [CrossRef] [Green Version] - Zhao, L.X.; Guo, Z.C.; Wang, Z.; Wang, M.Y. Influences of super-gravity field on aluminum grain refining. Metall. Mater. Trans. A
**2010**, 41, 670–675. [Google Scholar] [CrossRef] - Yang, Y.H.; Song, B.; Yang, Z.B.; Cheng, J.; Song, G.Y.; Li, L.F. Macrosegregation behavior of solute Cu in the solidifying Al-Cu alloys in super-gravity field. Metall. Res. Technol.
**2018**, 115, 1–12. [Google Scholar] [CrossRef] [Green Version] - Yang, Y.H.; Song, B.; Cheng, J.; Song, G.Y.; Yang, Z.B.; Cai, Z.Y. Effect of Super-gravity Field on Grain Refinement and Tensile Properties of Cu–Sn Alloys. ISIJ Int.
**2018**, 58, 98–106. [Google Scholar] [CrossRef] [Green Version] - Melgarejo, Z.H.; Suἁrez, O.M.; Sridharan, K. Microstructure and properties of functionally graded Al–Mg–B composites fabricated by centrifugal casting. Compos. Part A
**2008**, 39, 1150–1158. [Google Scholar] [CrossRef] - Liu, X.K.; Wang, Q.S.; Wang, Z.D.; Feng, Z.Q.; Zhang, H.; Zhu, J.J.; Fan, M. Effects of Centrifugalization on Behavior of Precipitated Phases in ZCuSn3Zn8Pb6Ni1FeCo Alloy. Foundry
**2010**, 4, 351–354. [Google Scholar] - Zhang, X.Z.; Yu, M.; Xia, R.Z. Cause Reaches Casting Crack Formation Guarding Against Method. Coal Mine Mach.
**2007**, 11, 104–106. [Google Scholar] - Wei, X.Z. Discussion on area method and cross-section method for determining the number of grains per unit area on the polished metal surface. Phys. Test
**1989**, 2, 55–60. [Google Scholar] - Cheng, X.Y. Application analysis of room temperature tensile test standard GB/T 228.1-2010. Phys. Chem. Insp. Phys. Div.
**2018**, 2, 122–124. [Google Scholar] - Cui, Z.Q.; Qin, Y.C. Metal Science and Heat Treatment, 2nd ed.; China Machine Press: Beijing, China, 2007; p. 39. [Google Scholar]
- Barin, I.; Knacke, O.; Kubaschewski, O. Thermochemical Data of Pure Substances, 3rd ed.; Springer: Berlin, Germany, 2008; p. 675. [Google Scholar]
- Chen, X.C. New Process Development and Finite Element Simulation of Induction Electroslag Centrifugal Casting. Ph.D. Thesis, University of Science and Technology Beijing, Beijing, China, 2001. [Google Scholar]
- Watanabe, Y.; Inaguma, Y.; Sato, H.; Miura-Fujiwara, E. A novel fabrication method for functionally graded materials under centrifugal force: The centrifugal mixed-powder method. Materials
**2009**, 2, 2510–2525. [Google Scholar] [CrossRef] [Green Version] - Watanabe, Y.; Kawamoto, A.; Matsuda, K. Particle size distributions in functionally graded materials fabricated by the centrifugal solid-particle method. Compos. Sci. Technol.
**2002**, 62, 881–888. [Google Scholar] [CrossRef] - Chen, J.X. General Steelmaking Chart Data Sheet, 2nd ed.; Higher Education Press: Beijing, China, 2010; p. 534. [Google Scholar]
- Yang, Y.H. Fundamental Study on Solidified Structure Refinement and Elements Segregation of Metals by Super Gravity. Ph.D. Thesis, University of Science and Technology Beijing, Beijing, China, 2017. [Google Scholar]
- Lin, G.W.; Li, Z.B.; Cheng, M.T. Research on Dynamic Effect of Electroslag Centrifugal Casting Pipe. Foundry
**1998**, 1, 1–7. [Google Scholar] - Lin, G.W.; Li, Z.B.; Cheng, M.T. Influence of dynamic effects on solidification structure of heat-resistant alloy by electroslag centrifugal casting. Iron Steel
**1997**, 32, 21–25. [Google Scholar] - Jiang, H.S.; Zheng, M.Y.; Qiao, X.G.; Wu, K.; Peng, Q.Y.; Yang, S.H.; Yuan, Y.H.; Luo, J.H. Microstructure and mechanical properties of WE43 magnesium alloy fabricated by direct-chill casting. Mater. Sci. Eng. A
**2017**, 684, 158–164. [Google Scholar] [CrossRef] - Pourbahari, B.; Mirzadeh, H.; Emamy, M. Toward unraveling the effects of intermetallic compounds on the microstructure and mechanical properties of Mg–Gd–Al–Zn magnesium alloys in the as-cast, homogenized, and extruded conditions. Mater. Sci. Eng. A
**2017**, 680, 39–46. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Schematic diagram of super-gravity apparatus; (

**b**) schematic diagram of super-gravity casting.

**Figure 3.**Macro-structure of the as-cast H13 steel samples obtained in conventional super-gravity and composite super-gravity fields: (

**a**) observed area of (

**b**); (

**b**) macro-structure at different positions in the observation area of Samples A, B and C.

**Figure 4.**Dendrite structures at different locations in the longitudinal section of Samples A, B, and C. Notes: the blue arrow points to the primary dendrite; the yellow arrow points to the secondary dendrite.

**Figure 5.**Prior austenite grains at R = 0.149 m in the longitudinal section of the samples. Notes: Due that the fact that the prior austenite grain boundaries eroded by enchant are not very clear in the micrograph, yellow curves were drawn on the prior austenite grain boundary by Photoshop software for clear observation; (

**a**) Sample A: a small number of prior austenite grains; (

**b**) Sample B: a large number of prior austenite grains; (

**c**) Sample C: the number of prior austenite grains is the largest here.

**Figure 6.**(

**a**) Secondary dendrite arm spacing (SDAS), (

**b**) grain size, and (

**c**) super-gravity coefficients of different samples solidified in the conventional super-gravity field and multi-speed super-gravity fields.

**Figure 7.**(

**a**) The phase assemblage diagram for the mole fraction of different equilibrium phases. (

**b**) The phase assemblage diagram for the non-equilibrium phase of H13 steel during solidification Notes: δ-Fe is high-temperature ferrite; γ-Fe is austenite; α-Fe is ferrite; M

_{23}C

_{6}, M

_{7}C

_{3}, and MC are carbide types.

**Figure 8.**(

**a**) Schematic diagram of centrifugal force analysis; (

**b**) effect of conversion factor (k = 1 and 100) on the relationship between critical nucleation work and the outer radius (

**c**) ΔG* at different positions of Sample A, B, and C.

**Figure 9.**(

**a**) Density change of solid and remaining liquid in the H13 steel in the solidification process calculated via Jmatpro7.0 software; (

**b**) the fragment’s moving speed at different positions of Samples A, B, and C; (

**c**) the tangential acceleration at different positions of Samples A, B and C.

**Figure 10.**Tensile strength (

**a**) and elongation (

**b**) at the outer, middle, and inner positions of Samples A, B and C.

C | Si | Mn | Cr | Mo | V | Al | W | O | N | Fe |
---|---|---|---|---|---|---|---|---|---|---|

0.46 | 0.9 | 0.3 | 4.6 | 1.4 | 0.9 | 0.03 | 0.02 | 0.0025 | 0.0104 | Bal. |

**Table 2.**Rotational speed(r∙min

^{−1}) and time (min) of each stage during super-gravity solidification.

No. | First Stage Speed/Time | Second Stage Speed/Time | Third Stage Speed/Time | Fourth Stage Speed/Time | Fifth Stage Speed/Time |
---|---|---|---|---|---|

A | 500/8.2 | - | - | - | - |

B | 500/0.2 | 600/4 | 750/4 | - | - |

C | 500/0.2 | 600/2 | 750/2 | 850/2 | 950/2 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, S.-Y.; Qin, S.-Y.; Xi, X.-J.; Sun, G.-Y.; Yang, W.-S.; Guo, J.; Guo, H.-J.
Solidified Structure Refinement of H13 Tool Steel under a Multi-Rotational Speed Super Gravity Field. *Metals* **2020**, *10*, 1428.
https://doi.org/10.3390/met10111428

**AMA Style**

Li S-Y, Qin S-Y, Xi X-J, Sun G-Y, Yang W-S, Guo J, Guo H-J.
Solidified Structure Refinement of H13 Tool Steel under a Multi-Rotational Speed Super Gravity Field. *Metals*. 2020; 10(11):1428.
https://doi.org/10.3390/met10111428

**Chicago/Turabian Style**

Li, Shao-Ying, Shu-Yang Qin, Xiao-Jun Xi, Guan-Yong Sun, Wen-Sheng Yang, Jing Guo, and Han-Jie Guo.
2020. "Solidified Structure Refinement of H13 Tool Steel under a Multi-Rotational Speed Super Gravity Field" *Metals* 10, no. 11: 1428.
https://doi.org/10.3390/met10111428