Effect of Pressure on Dendrite Structure and Characteristics of Carbides during Solidification Process of H13 Die Steel Ingot

Abstract

In this paper, the effect of solidification pressure on the dendrite structure and characteristics of carbides in H13 die steel ingot was investigated by experimental and calculational methods. Based on the effect of pressure on the cooling rate, a formula is proposed to calculate the secondary dendrite arm spacing: λ₂ = 71.45 × R^−0.37. It is applicable when the maximum value of pressure is around 2 MPa and the cooling rate is between 0.5 and 3 K/s. With increasing pressure from 0.1 to 2 MPa, the effects of pressure on the segregation ratio of V, Mo, Cr and C are little and can be neglected, which caused by the combined effect of equilibrium partition coefficient, diffusion coefficient and cooling rate. Therefore, the characteristics of carbides are determined by the decreasing the secondary dendrite arm spacing and increasing cooling rate with the increment of pressure. With increasing pressure from 0.1 to 2 MPa, the types of carbides are not change, which are MC and M₂C in H13 die steel ingot. Meanwhile, the mean area of carbides decreases obviously with increasing pressure, and the decrement in mean area at the edge is larger than that at the center of ingot.

1. Introduction

Mold is an extremely important and special basic technological equipment in industrial production and plays a very important role. As the most widely used hot work die steel, H13 die steel has excellent high hardenability, strength, toughness and softening resistance, etc.^1,2,3,4) Thus, it can be employed to produce operating tools, which are repeatedly subjected to high temperatures and loads.^5,6) such as die casting molds, hot rolling, hot extrusion and hot forging.^7,8) However, characteristics of carbides, especially type and size, have significant effects on the mechanical properties of H13 die steel, such as toughness, yield strength and fatigue cracks, etc.^4,6,9) So refining the characteristics of carbides is crucial in the manufacture process of H13 die steel.

Carbide precipitates easily during solidification process due to the high V, Mo, Cr and C content,⁴⁾ including MC (M=V mainly), M₂C (M=Mo mainly), M₇C₃ (M=Cr mainly) and M₂₃C₆ (M= Fe and Cr mainly).^7,10,11) Large carbides are mainly MC and M₂C in H13 die steel.²⁾ There are some researches have been studied on refining carbides (MC and M₂C) in H13 die steel. Toshio Okuno¹²⁾ analyzed the microstructural contributions to the toughness of H13 steel during tempering and found the toughness was improved by refining the morphology of MC and M₂C. Song¹³⁾ et al. found that the pseudo-eutectic carbides of H13 steel can be broken and partially dissolved in the matrix after forging and annealing, which suppressed the segregation of C, V, Mo and Cr. Ning⁶⁾ found the increment in yield strength of H13 steel was determined by the decrements in size and volume fraction of MC during tempering. However, negative effects of carbides cannot be completely eliminated in the heat treatment process, and the performance of H13 die steel cannot be significantly improved by heat treatment alone.^4,14) Therefore, in order to reduce negative effects of carbides, it is also vital to take measures to refine the carbides in H13 ingot during solidification process, in addition to heat treatment process.

Pressurized metallurgy technology is a highly promising special smelting method for producing high-quality steel. The increment of pressure can speed up the reaction rate, improve the cooling rate, refine the solidification structure and eliminate the solidification defects, etc.^{15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)} In addition, increasing pressure can effectively refine carbides to alleviate the negative effect. Li¹⁶⁾ et al. found that average thickness of eutectic ledeburite decrease in M42 steel with increases pressure and higher solidification pressure is beneficial to reduce the volume fraction of M₆C. Therefore, it is worth exploring a new method to improve quality of H13 ingot using the pressurized metallurgy technology.

As discussed above, this research is aimed to reveal the effect of solidification pressure on dendrite structure and carbides. H13 ingots were manufactured under different solidification pressure (0.1, 1 and 2 MPa) using pressurized metallurgy technology. With increasing pressure from 0.1 to 2 MPa, changes in cooling rate, dendrite arm spacing, and element segregation were investigated in detail by experimental and calculational methods. Combing with these investigations, effect mechanisms of pressure on the type and area of carbides were clarified clearly.

2. Experimental Procedures

Three H13 ingots were smelt by a 25 kg pressurized induction furnace and the smelting process was carried under 5 Pa to proceed vacuum deoxygenation for 10 minutes. Then Al was added into the molten steel to deoxidize deeply. After deoxidation process, Ar was filled into the furnace for obtaining solidification pressure (P_s). Then the molten steel was poured into cast mold at 1773 K, and solidified under different argon pressure (0.1, 1 and 2 MPa). Elements of ingots were measured by optical emission spectrometry (OES), as shown in Table 1.

Table 1. Chemical composition and solidification pressure of H13 die steel ingots.

Ingots	Ps/MPa	C/%	Si/%	Mn/%	Cr/%	V/%	Mo/%	O/%	Al/%
H1	0.1	0.38	0.96	0.31	5.10	0.96	1.43	0.00049	0.02515
H2	1.0	0.37	0.93	0.31	5.32	0.93	1.44	0.00032	0.02791
H3	2.0	0.37	0.92	0.31	5.36	0.83	1.47	0.00070	0.02561

Figure 1 shows positions of specimens. For each ingot, five specimens with the size of 10 mm×10 mm×10 mm were cut out at the 130 mm height, which were used to investigate dendrite structure and characteristics of carbides. The five specimens were numbered from 1 to 5 form the edge to the center, respectively. The five specimens were ground, mechanically polished and etched by volume fraction 4% Nital for microstructural characterization. The dendritic structure was observed by Olympus DXS 510 digital microscope. OLYCIA m3 image-analysis software was used for the statistics of secondary dendrite arm spacing. Types of carbides were detected by X-ray diffraction (XRD) in a range of 30–90 deg and at a scan rate of 2°/min. Scanning electron microscopes (SEM) was employed to analyze the morphology and composition of the carbides. The automated inclusion analysis system (ASPEX) was employed to investigate the area of carbides in detail.

Fig. 1.

Positions of specimens. (Online version in color.)

3. Calculation Process of Cooling Rate

3.1. Mathematical Model

The cooling rate is the rate of temperature change.³⁰⁾ It can be obtained by the heat transfer model of ProCAST software. The heat transfer model is as follows:   

$$\rho \frac{\partial H}{\partial t}=\frac{\partial }{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left(\lambda \frac{\partial T}{\partial z}\right)$$(1)

where, ρ is the density of steel, kg/m³; λ is the heat conductivity coefficient, W/(m·K); C_P is the specific heat, J/(kg·K). The latent heat of solidification is obtained by enthalpy method, which is as follow:²⁸⁾   

$$H\left(T\right)={\int }_0^T{C}_{P}dT+L\left[1-f_s\left(T\right)\right]$$(2)

where, H(T) is the enthalpy, J/mol; L is the latent heat of solidification, J/kg. f_s(T) is the solid fraction.

During the calculation process, a 3-D domain with a scale that matches that of the H13 die steel ingot is used, as shown in Fig. 2. The domain was divided into 109921 hexahedral meshes. According to the previous study,³¹⁾ key properties used for the temperature calculations are almost independent of pressure, and interface heat transfer coefficients between the ingot and the mold under three pressure are listed in Table 2.³¹⁾ Additionally, the heat transfer coefficient between the top of ingot and air was set to 100 W/(m²·K) under three pressure.²⁸⁾

Fig. 2.

Schematic of the calculated steel ingot and mold. (Online version in color.)

Table 2. Properties used for the calculation.

Parameter	Value
Liquidus temperature TL, K	1750.5
Solidus temperature Ts, K	1649.1
Specific heat of liquid Cp, J/(kg·K)	822.8
Latent heat of solidification L, kJ/kg	221.3
Heat conductivity coefficient λ, W/(m·K)	33.94
Density ρ, kg/m3	7100
Interface heat transfer coefficient h0.1 (for 0.1 MPa), W/(m2·K)	h0.1 = 1137.4t−0.23
Interface heat transfer coefficient h1.0(for 1 MPa), W/(m2·K)	h1.0 = 1294.3t−0.23
Interface heat transfer coefficient h2.0 (for 2 MPa), W/(m2·K)	h2.0 = 1501.6t−0.23

3.2. Model Validation and Cooling Rate

The mathematical model was verified by the experimental values of cooling curves at 15 mm from the edge of ingot reported by Li.³¹⁾ Due to preheating of thermocouple in contact with the molten steel and the turbulence of molten steel caused by pouring, the initial temperature measurement was inaccurate.¹⁸⁾ Therefore, experimental values of cooling curves after pouring 20 s are used to validate calculation values, which are shown in Figs. 3(a), (b) and (c). Both calculation and experimental values of cooling curves are roughly identical, and have the same change trend as solidification progress under 0.1, 1 and 2 MPa. It indicates that the mathematical model can provide enough accurate cooling curves to calculate the cooling rate of H13 die steel ingot under different pressure. In addition, there are small gaps between calculation and experimental values because of measurement error and accuracy of 16-channel data acquisition system and double platinum-rhodium thermocouples of “B” type.³¹⁾

Fig. 3.

Experimental and calculational results of cooling curves and cooling rate under different pressure: (a) 0.1 MPa; (b) 1 MPa; (c) 2 MPa and (d) cooling rate. (Online version in color.)

Changes in cooling rate with pressure are shown in Fig. 3(d). The cooling rate decreased with the increment in distance away from the edge of ingot. There exist increments in cooling rate with pressure in the whole ingot. In addition, since the distance from the heat exchange interface, the increment of temperature gradient at the edge is greatly larger than that at the center, and the change trend of cooling rate is consistent with that of temperature gradient. So, the increment of cooling rate at the edge is larger than that at the center with increasing pressure.²⁸⁾

4. Results and Discussion

4.1. Effect of Pressure on Dendrite Structure

Figure 4(a) shows the measured secondary dendrite arm spacing (SDAS) λ₂ in specimens under three pressure (0.1, 1 and 2 MPa). There exhibits an increasing tendency of secondary dendrite arm spacing from the edge to the center of three ingots. And the SDAS decreased with increasing pressure. For example, the SDAS at the edge are 59.34 (for 0.1 MPa), 54.89 (for 1 MPa) and 50.63 μm (for 2 MPa), and that at the center are 90.24 (for 0.1 MPa), 87.17 (for 1 MPa) and 85.04 μm (for 2 MPa). Correspondingly, diagrams of dendritic structure in 1# specimen at the edge of ingot at the 130 mm height are showed in Figs. 4(b), (c) and (d). Figure 4(e) shows the microstructure for longitudinal cross-section of ingot at the 130 mm height. It can be found that the edge and center of ingot are entirely composed of the columnar and equiaxed dendrite under 0.1, 1 and 2 MPa, respectively. These results indicate that the dendrite structure is refined with increasing pressure from 0.1 to 2 MPa.

Fig. 4.

Dendrite structure under different pressure: (a) SDAS, (b) 0.1 MPa, (c) 1 MPa, (d) 2 MPa, (e) cross-section. (Online version in color.)

It is well established that the relation between dendrite arm spacing and cooling rate is crucial to investigate the effect of pressure on dendrite structure.¹⁷⁾ The relation between the SDAS λ₂ and cooling rate R can be written as follow:^32,33)   

$${\lambda }_2=M\cdot R^{-n}$$(4)

where n and M, mainly depending on alloy compositions, can be regarded as constant.^32,33) Curves represented the quantitative correlation between λ₂ and R (the cooling rate is between 0.5 and 3 K/s) were fitted as shown in Fig. 5. And fitting formulas are λ₂ = 72.58 × R^−0.37 (for 0.1 MPa) shown in Fig. 5(a), λ₂ = 71.52 × R^−0.37 (for 1 MPa) shown in Fig. 5(b) and λ₂ = 70.24 × R^−0.37 (for 2 MPa) shown in Fig. 5(c), respectively. The corresponding R-squares are 0.906, 0.907 and 0.904. It indicates fitting formulas are accurate to describe the change in SDAS with cooling rate under different pressure. M are 72.58, 71.52 and 70.24 under 0.1, 1 and 2 MPa, respectively. There is tiny change in the values of M with pressure. In order to derive the general formula, the universal value of M is defined to 71.48 by fit method. The general formula (λ₂ = 71.48 × R^−0.37) and fitting curve are shown in Fig. 5(d). The Corresponding R-squares is 0.903. According to the relation between the values of log (SDAS) and log (Cooling rate) under three pressure, M is corrected to 71.45, and its R-squares is 0.908, the fitting formula and curve are shown in Eq. (5) and Fig. 5(e), respectively. It suggests that the fitting formula can be applicable when the maximum value of pressure is around 2 MPa and the cooling rate ranges from 0.5 to 3 K/s. These results indicate that pressure refine dendrite structure mainly through increasing the cooling rate of ingot, and SDAS increases with the decrement in cooling rate from the edge to the center.   

$${\lambda }_2=71.45\times R^{-0.37}$$(5)

Fig. 5.

Relation between the SDAS and cooling rate: (a) 0.1 MPa, (b) 1 MPa, (c) 2 MPa, (d) three pressure, (e) log (SDAS)-log (Cooling rate). (Online version in color.)

4.2. Effect of Pressure on Element Segregation

During the solidification process of ingot, the redistribution of solute elements leads to segregation, which can reduce the impact toughness and plasticity of the ingot. Meanwhile, element segregation is a key factor in the formation of carbides. In order to investigate element segregation in H13 ingot under 0.1, 1 and 2 MPa, the Clyne-Kurz equation was used. It indicates element segregation is a function of cooling rate, secondary dendrite arm spacing, diffusion coefficient and equilibrium partition coefficient.^34,35,36) The Clyne-Kurz equation is as follow:   

$$t_f=\frac{T_{\text{L}}-T_{\text{S}}}{R}$$(6)

  

$$\alpha =\frac{D_s{t}_f}{{\left(0.5{\lambda }_2\right)}^2}$$(7)

  

$$\mathrm{\Omega }\left(\alpha \right)=\alpha \left[1-exp\left(-\frac{1}{\alpha }\right)\right]-\frac{1}{2}exp\left(-\frac{1}{2\alpha }\right)$$(8)

  

$$C_{\text{L}}=C_{\text{0}}{\left[1-\left(1-2\mathrm{\Omega }\left(\alpha \right)k\right)f_{\text{s}}\right]}^{\frac{k-1}{1-2\mathrm{\Omega }\left(\alpha \right)k}}$$(9)

where t_f is the local solidification time(LST), s; D_S is the diffusion coefficient of solute element, cm²/s; k_i is the equilibrium partition coefficient; C_L is the mass percentages of solute element in the liquid, and C₀ is the initial mass percentages of solute element. Substituting Eq. (5) into Eq. (7) yields:   

$$\alpha =\frac{D_s\left(T_{\text{L}}-T_{\text{S}}\right)}{1\mathrm{\hspace{0.17em} }276.28\times R^{0.26}}$$(10)

According to the Eqs. (6), (8), (9) and (10), solidification pressure changes the element segregation by affecting the cooling rate, diffusion coefficient, and equilibrium partition coefficient. Since V, Mo, Cr and C are main forming elements of carbides in H13 ingot,⁴⁾ changes in both equilibrium partition coefficients and diffusion coefficients of V, Mo, Cr and C with pressure were investigated. Equilibrium partition coefficients for each solidification process are calculated using the Eq. (11):^37,38,39,40)   

$$k_{i,\text{(}\delta +\gamma \text{)}/\text{L}}=w_{\delta }{k}_{i,\delta \text{/L}}+w_{\gamma }{k}_{i,\gamma \text{/L}}$$(11)

where, k_i,(δ+γ)/L, k_i,δ/L and k_i,γ/L are the partition coefficient in the (δ+γ)/L, δ/L, and γ/L interface obtained by the Thermo-calc, respectively. w_δ and w_γ are the mass fraction of austenite phase (δ) and ferrite phase (γ) in the solid phase, and the sum of w_δ and w_γ is 1.⁴⁰⁾ When solid phase is entirely composed of the austenite phase (w_δ=1 and w_γ=0), k_i,(δ+γ)/L is equal to the k_i,δ/L. In contrast, when solid phase is entirely composed of the ferrite phase (w_γ=1 and w_δ=0), k_i,(δ+γ)/L is equal to the k_i,γ/L. Otherwise, when peritectic reaction occurs during solidification, the k_i,(δ+γ)/L is determined by k_i,δ/L and k_i,γ/L using Eq. (11).^38,40) Taking partition coefficient of C (k_C,(δ+γ)/L, k_C,δ/L and k_C,γ/L) under 0.1 MPa as an example, k_C,(δ+γ)/L is obtained with the Eq. (11) for H13 ingot as shown in Fig. 6(a).

Fig. 6.

Equilibrium partition coefficient of V, Mo, Cr and C: (a) partition coefficient of C (k_C,(δ+γ)/L, k_C,δ/L and k_C,γ/L) under 0.1 MPa; (b) k_i,(δ+γ)/L under three pressure. (Online version in color.)

There exists same change trend of equilibrium partition coefficients of V, Mo, Cr and C under 0.1, 1 and 2 MPa, as shown in Fig. 6(b). The corresponding solidification mode is same, and phase transition sequences can be illustrated as: L → L + δ → L + δ + γ → L + γ → γ.³¹⁾ Equilibrium partition coefficients of V, Mo, Cr and C are 0.716, 0.717, 0.940 and 0.142 in the initial stage of solidification process under 0.1 MPa, respectively. And at the end of solidification process, equilibrium partition coefficients of V, Mo, Cr and C are 0.352, 0.470, 0.864 and 0.296. It indicates that the equilibrium partition coefficient of C in the austenite phase is greater than that in the ferrite phase, while equilibrium partition coefficients of V, Mo and Cr in the ferrite phase are greater than that in the austenite phase. These lead to the equilibrium partition coefficient of C gradually increases and that of V, Mo and Cr gradually decreases with the decrease of liquid fraction. However, when the pressure is below 2 MPa, equilibrium partition coefficients of V, Mo, Cr and C are insensitive to solidification pressure as shown in Fig. 6(b).

With increasing pressure from 0.1 to 200 MPa, changes in diffusion coefficients of V, Mo, Cr and C at 1650 K were calculated by DICTRA software, as shown in Fig. 7. It can be found that diffusion coefficients of C and Cr increase with the increment of pressure, while diffusion coefficients of V and Mo decrease. However, for the experimental pressure range (from 0.1 to 2 MPa), there is tiny change in diffusion coefficient of all elements, which can be neglected.¹⁶⁾

Fig. 7.

Diffusion coefficients under different pressure: (a) V, (b) Mo, (c) Cr, (d) C. (Online version in color.)

In summary, since equilibrium partition coefficients and diffusion coefficients used for the Clyne-Kurz equation are invariable when the pressure is below 2 MPa, the pressure influences element segregation by the change in the cooling rate of H13 ingot. Segregation ratios $\left(\text{SR}=\frac{C_{\text{L}}}{C_0}\right)$ of V, Mo, Cr and C were calculated using the Clyne-Kurz equation as shown in the Fig. 8. Under 0.1 MPa, the maximum value SR of V at edge is 3.459, and that at the center is 3.193. Meanwhile, the maximum value of SR of Mo at the edge and center are 3.859 and 3.560, that of Cr at the edge and center are 1.289 and 1.268, that of C at the edge and center are 7.074 and 7.060, respectively. It indicates that there exist decrements in element segregation caused by the decrease of cooling rate from the edge to the center.⁴¹⁾ When the equilibrium partition coefficient is less than 1, the larger equilibrium partition coefficient will decrease the segregation.²⁶⁾ Thus, the SR of Cr is smallest. However, the SR of Mo is greater than that of V, the main reason is that the diffusion coefficient of Mo is less than that of V with approximately equal equilibrium partition coefficient.³⁴⁾

Fig. 8.

SR of elements during solidification under different pressure: (a) V, (c) Mo, (e) Cr and (g) C at the edge; (b) V, (d) Mo, (f) Cr and (h) C at the center. (Online version in color.)

Due to the enhancement of cooing rate, the SR of V, Mo, Cr and C increase with increasing pressure based on Clyne-Kurz equation. Taking the SR of V as an example, the SR of V at the edge and the center under 0.1 MPa are 3.459 and 3.193, and that under 2 MPa are 3.527 and 3.212, respectively. The increment in SR at the edge is large than that at the center with increasing pressure from 0.1 to 2 MPa. It is caused by the larger increment of cooling rate at edge than that of center.²⁶⁾ However, increments in SR of V, Mo, Cr and C are all tiny and can be neglect.

It is well known that there are four key factors to change the characteristics of carbides, including dendrite structure, element segregation, diffusion coefficient and cooling rate.^{4,7,16,34,42,43)} According to the effect of pressure on those key factors, increasing pressure affects characteristics of carbides primarily through enhancing cooling rate and refining dendrite structure.

4.3. Effect of Pressure on Characteristics of Carbides

4.3.1. Types of Carbides

Types of carbides are shown in Fig. 9(a). There were two different kinds of carbides (MC and M₂C) in H13 ingot. Pressure has little effect on types of carbides in H13 ingot when the pressure is blow 2 MPa. In order to further investigate the effect of pressure on types of carbides, the precipitation behavior of carbides was investigated by the Thermo-Calc software, based on the element segregation obtained by the Clyne-Kurz equation, as shown in Fig. 9(b). Under 0.1, 1 and 2 MPa, precipitation temperatures of MC are 1526.72, 1526.74 and 1526.76 K, respectively; and that of M₂C are 1527.75, 1527.77 and 1527.79 K, respectively. Those results indicate that effects of pressure (less than 2 MPa) on types and the precipitation temperature of carbides in H13 die steel ingot can be ignored.

Fig. 9.

XRD and precipitation temperature of carbides under different pressure: (a) XRD, (b) precipitation temperature. (Online version in color.)

Morphologies and compositions of carbides in 3# specimen under 0.1, 1 and 2 MPa are shown in Fig. 10. The 3# specimen is at the 1/2 radius of ingot, which is entirely composed of the columnar dendrites under 0.1, 1 and 2 MPa, as shown in Fig. 4(e). There are two main kinds morphologies and compositions of carbides: one is the V-rich carbide and the other is Mo-rich carbide. The V-rich carbides have more V and C than Mo-rich carbides, which are MC. The Mo-rich carbides have more Mo and Cr than V-rich carbides, which are M₂C. Carbides are mostly blocky or stripy, and their sizes are about a few microns.^4,44) Carbides were usually formed individually but also may coexist with other carbides or inclusions.⁴⁴⁾

Fig. 10.

Carbides under different pressure: (a) and (d) under 0.1 MPa, (b) and (e) under 1 MPa, (c) and (f) under 2 MPa. (Online version in color.)

4.3.2. Effect of Pressure on Characteristics of Carbides

The MC (V-rich carbides) and M₂C (Mo-rich carbides) was counted at the edge,1/2 radius and the center in three ingots by the ASPEX system. The mean area of MC and M₂C in three ingots are shown in Fig. 11. The mean area of M₂C was larger than that of MC, except that the mean area of MC was approximately equal to that of M₂C at the edge of ingot under 2 MPa.³⁴⁾ The mean area of MC and M₂C both increased from the edge to the center. Taking 2 MPa as an example, the mean area of MC increased from 2.64 μm² at the edge to 3.02 μm² at the center, and that of M₂C increased from 2.63 μm² at the edge to 4.18 μm² at the center. The main reason is that there is comparatively sufficient time and space for MC and M₂C to grow with decrement in cooling rate and increment in dendrite arm spacing from edge to center.^34,41)

Fig. 11.

Change in mean area of carbides under different pressure: (a) MC, (b) M₂C. (Online version in color.)

With increasing pressure from 0.1 to 2 MPa, the mean area of MC and M₂C decreased. The decrement in mean area of M₂C at the edge was large than that at the center, and decrements of mean area of MC were roughly equal. With increasing pressure, there exists the increment in cooling rate and decrement in SDAS. Therefore, the increment in pressure leads to the insufficient time and space for the growth of MC and M₂C. At the same time, with increment in cooling rate and decrement in SDAS, the insufficient degree of growth time and space are larger at the edge than those at the center for MC and M₂C.^28,41) It results that the decrement in the mean area of carbides at the edge is greater than that at the center.

5. Conclusions

The dendrite structure and characteristics of carbides in H13 die steel ingot under three pressure (0.1, 1 and 2 MPa) were investigated by the experimental and calculational methods. According to changes in cooling rate, secondary dendrite arm spacing (SDAS), diffusion coefficients, equilibrium distribution coefficients and element segregation, the effect mechanisms of pressure on the characteristics of carbides were revealed. The main conclusions are as follow:

(1) Increasing pressure can obviously decrease SDAS. A formula is proposed to calculate the SDAS of H13 die steel ingot: λ₂ = 71.45 × R^−0.37, which is applicable for low pressure (≤ 2 MPa) and low cooling rate (0.5–3 K/s).

(2) Effects of pressure on the segregation ratio of C, V, Mo and Cr are little and can be neglected, which caused by the combined effect of equilibrium partition coefficient, diffusion coefficient and cooling rate.

(3) Under 0.1, 1 and 2 MPa, there are two kind types of carbides in H13 die steel ingot, including MC (V-rich carbides) and M₂C (Mo-rich carbides). Increasing pressure has small effects on types and the precipitation temperature of carbides.

(4) Increasing pressure can decrease the mean area of carbides by enhancing cooling rate and refining SDAS. In addition, with increment in cooling rate and decrement in SDAS, the insufficient degree of growth time and space are larger at the edge than those at the center, which resulting in the larger mean area of MC and M₂C at the center.

Acknowledgments

The present research was financially supported by National Natural Science Foundation of China (No. U1960203, 51904065 and 51774074), Project funded by China Postdoctoral Science Foundation (No. 2019M651133), Talent Project of Revitalizing Liaoning (XLYC1902046), and China National Postdoctoral Program for Innovative Talents (Grant No. BX20200076).

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