Precipitation Behavior of Nitride Inclusions in K418 Alloy under the Continuous Unidirectional Solidification Process

Abstract

Adopting effective routs to control the precipitation and size of nitride inclusions in superalloys during the solidification is a very interesting subject for metallurgists. The precipitation behavior of nitride inclusions in K418 alloy under the continuous unidirectional solidification process was investigated by scanning electron microscopy, ASPEX Explorer, and LECO ONH-836. The results show that there were two types of nitride inclusions in the K418 alloy ingot: TiN and complex inclusion of Al₂O₃–TiN. There were gradient distributions of the number density, average and max sizes of nitride inclusions along the casting direction, as well as the contents of Ti and N. Based on the thermodynamic and kinetic calculations, the precipitation time of TiN inclusion changed from mushy to liquid zones under different initial contents of Ti and N. Al₂O₃ inclusion began to precipitate in liquid zone and acted as the nucleation site for TiN inclusion. The radius of TiN inclusion increased from 3.2 µm at 0.36 K/s to 8.6 µm at 0.08 K/s when the fraction of solid approached 1. The nitride inclusions can be refined and reduced in the K418 alloy ingot under the continuous unidirectional solidification process compared with those in revert K418 alloy. The methods to control the precipitation and size of nitride inclusions were reducing the contents of N and O and increasing the cooling rates.

1. Introduction

The nickel-base superalloys have been widely used in the aerospace and aviation engineering due to elevated temperature creep strengths and good resistance to oxidation.^1,2) However, the average yields for general machined components are approximately 40%.^3,4) A large number of scraps are increasingly generated by the wide production and usage of the Ni-base superalloys.⁵⁾ Due to contamination from the mold and furnace environment, there are changes of minor elements compared with the virgin alloys, such as Zr, Si, O, and N.³⁾ While there existed many strong nitride-forming elements in the Nickel-base superalloys, the nitride inclusion would precipitate within or nearby the interdendritic regions during solidification.⁶⁾ The nitride inclusions are recognized as TiN phase with cubic structure and density of 5.43 g/cm³, or complex inclusions, as reported in literature. It has been also suggested that the fatigue fracture behavior generally initiates from the cracking of inclusions during the deformation process, due to the significant difference in ductility between the inclusions and the matrix of superalloy.⁷⁾ The different recycling techniques are applied to revert superalloys depending on the amounts of impurities, such as remelting, downgraded use and hydrometallurgy process.⁸⁾ Revert superalloys with a few impurities are usually remelted with virgin superalloys. Pu et al.⁹⁾ found that there is a large fluctuation range of compression and yield strength at 25°C due to the increased quantity and size of Al₂O₃ inclusion by the addition of revert GH4169 alloy. Due to the strict composition control of the turbine blades, the addition amount of revert superalloys for remelting is restricted. The main drawback of the remelting process is high burn-out losses up to 20% of the alloying elements.^10,11) Revert superalloys with a large number of impurities are mainly downgraded to the additions in steel or other metal production processes.¹²⁾ However, the scarce and expensive metals such as rhenium and tantalum cannot be recycled. Revert superalloys with a considerable amount of impurities are reused by the hydrometallurgy process, which can provide pure metals from the leach solutions.^13,14) To improve the efficiency of the reaction, revert superalloys are firstly pulverized to increase the surface area and then decomposed by strong acid and finally refined to individual metals. However, the drawbacks of the hydrometallurgy process are huge energy and long-time consuming.

Above all, one of the main restrictions of revert superalloys is the nonmetallic inclusions, which are harmful to the mechanical properties.¹⁵⁾ Many studies have reported the precipitation and removal behaviors of inclusions during solidification of steel.^{16,17,18,19,20)} A variety of techniques have been employed to remove inclusions from alloys, including vacuum induction melting (VIM),^21,22) elctroslag remelting (ESR),^23,24,25) Vacuum arc remelting (VAR),^26,27,28) Electron beam melting (EBM),^29,30) Hydrogen plasma arc melting (HPAM)^31,32) and double-melting or triple-melting processes.³³⁾ Although most of the inclusions can be removed by these methods, there are drawbacks to these processes, such as the solidification defects, high energy consumption, time-consuming, and losses of high vapor pressure alloying elements. The oxide, nitride and sulfide inclusions can be removed by a foam ceramic filter.^34,35) However, the control of strict pouring temperature is difficult. Shi et al.³⁶⁾ have investigated the effect of supergravity-induced separation on the removal of oxide and nitride inclusions from IN718 alloy melt. The removal behavior of inclusions is dependent on the gravity coefficients (G) and separation times (t). However, there are higher requirements for equipment under mass melt and big gravity coefficients. The inclusions concentrated at the top of the sample produced by the directional solidification (DS) process.³⁷⁾ However, the length of samples is limited by its mold. To avoid the drawback of the DS process, a new process named continuous unidirectional solidification was developed. There are two styles of the continuous unidirectional solidification process, such as the Ohno continuous casting (OCC)^38,39) and the heating-cooling combined mold (HCCM).^40,41) Yang et al.⁴²⁾ have reported that the tensile strength and elongation of the K418 alloy produced by the continuous unidirectional solidification were higher than those of conventional casting ingot. However, few works have been performed to control the precipitation and size of nitride inclusions in revert superalloys under the continuous unidirectional solidification process.

In this work, we explored the precipitation behavior of nitride inclusions in K418 alloy under the continuous unidirectional solidification process. The morphology and sizes distribution of nitride inclusions at different distances from the bottom of the K418 alloy ingot were determined by scanning electron microscopy (SEM) and ASPEX Explorer, respectively. Under the thermodynamic and kinetic calculations, the precipitation and growth mechanisms of nitride inclusions were discussed under the continuous unidirectional solidification process.

2. Experimental Procedures

2.1. Experimental Setup

Revert K418 alloy was produced by the VIM process and its chemical compositions were given in Table 1. The liquidus and solidus temperatures of the K418 alloy were reported by Shi et al.⁴³⁾ Their DSC testing showed that liquidus and solidus temperatures of the K418 alloy were 1618 K and 1570 K, respectively.

Table 1. Chemical compositions of revert K418 alloy (wt.%).

N	O	C	B	Cr	Mo	Nb	Al	Ti	Ni
0.0088	0.0013	0.12	0.01	12.4	3.9	2. 1	5.5	1	Bal.

The continuous unidirectional solidification process was conducted by self-designed downward apparatus. A schematic illustration of this apparatus was shown in Fig. 1, including systems of heating, cooling, and traction. The small piece of revert K418 alloy was heated to 1773 K at a speed of 7.5 K/min and maintained for 15 minutes under argon gas with a purity of 99.6%. The melt solidified and then was drawn out by the dummy bar, 304 austenitic stainless steel. The chemical composition (wt.%) is 18.3 Cr, 8.5 Ni, 0.6 Si, 1.0 Mn, 0.05 C, and balance of Fe. The parameters of the continuous unidirectional solidification process were given in Table 2. The schematic diagram of specimens taken from the K418 alloy ingot was shown in Fig. 2.

Fig. 1.

Schematic illustration of the continuous unidirectional solidification process apparatus. (Online version in color.)

Table 2. Parameters of the continuous unidirectional solidification process.

Parameters	Unit	Value
Withdrawal length	mm	3
Duration of drawing stroke	s	2
Pause time	s	18
Withdrawal speed	mm/s	1.5
Casting temperature	K	1773
Water flowing rate	L/min	1.8

Fig. 2.

Schematic diagram of the K418 alloy ingot cutting (a), specimens for microstructure of the K418 alloy ingot (b) and contents of nitrogen (c). (Online version in color.)

2.2. Methods of Analysis

The microstructures at different distances from the bottom of the K418 alloy ingot was observed by optical microscopy (OM, Leica DM 6000M) after grinding, polishing, and etching with a solution of 4 g CuSO₄ + 20 ml HCl + 20 ml H₂O. The primary dendrite arm spacing (PDAS) and secondary dendrite arm spacing (SDAS) were measured on transverse and longitudinal sections, respectively. The PDAS and SDAS were measured by Eqs. (1) and (2),^44,45) respectively.   

$${\lambda }_1={\text{ n}}_p^{-1/2}$$(1)

  

$${\lambda }_2=\frac{L}{\text{n}-1}$$(2)

where λ₁ is the PDAS, μm; n_p is the number of primary dendrite cores per area; λ₂ is the SDAS, μm; L is the length of line, μm; and n is the number of the secondary dendrite. The PDAS and SDAS have been counted at least three micrographs at a magnification of 100 times. The cooling rates were obtained by the relationship between the SDAS and the local solidification time of the IN713C,⁴⁶⁾ as shown in Eq. (3).   

$${\lambda }_2=\text{A}{t}_{\text{f}}^{\text{n}}=\text{A}{\left(\frac{\mathrm{\Delta }T}{\dot{T}}\right)}^{\text{n}}$$(3)

where A= 6.79 × 10⁻⁶ m/sⁿ, n = 0.43, t_f is the local solidification time, s; ΔT is the local solidification range, K; $\dot{T}$ is the cooling rate, K/s. The morphology and composition of nitride inclusions were determined by scanning electron microscopy coupled with energy dispersive spectroscopy (SEM-EDS, FEI Quanta 450). The number and size distributions of nitride inclusions were measured by ASPEX Explorer (manufactured by FEI). The contents of nitrogen at different distances from the bottom of the K418 alloy ingot were measured by LECO ONH-836.

3. Results

3.1. Microstructure

The morphologies of γ dendrites on the transverse and longitudinal sections at different distances from the bottom of the IN713C alloy ingot are shown in Figs. 3 and 4. The γ dendrites with typical cross-shape on the transverse sections and parallel to the casting direction on the longitudinal sections are obtained. The PDAS increased from 213.2 ± 4.4 μm at 20 mm to 265.1 ± 5.7 μm at 155 mm from the bottom of the ingot, as shown in Fig. 5(a). The SDAS increased from 58.7 ± 7.3 μm at 20 mm to 80.2 ± 5.7 μm at 155 mm from the bottom of the ingot, which was smaller than that of revert K418 alloy, 106.2 μm, as shown in Fig. 5(b). Furthermore, $\dot{T}$ slightly decreased from 0.36 ± 0.06 K/s at 20 mm to 0.13 ± 0.02 K/s at 155 mm from the bottom of the ingot, which was bigger than that of revert IN713C alloy, 0.08 K/s, as shown in Fig. 5(c).

Fig. 3.

Microstructure on transverse sections at different distances from the bottom of the K418 alloy ingot. (Online version in color.)

Fig. 4.

Microstructure on longitudinal sections at different distances from the bottom of the K418 alloy ingot. (Online version in color.)

Fig. 5.

Influences of different distances from the bottom of the K418 alloy ingot on PDAS (a), SDAS (b), and $\dot{T}$ (c). (Online version in color.)

3.2. Characterization of Nitride Inclusions

The results of SEM-EDS-determined show that there were two types of nitride inclusions in the K418 alloy ingot: TiN inclusion and complex inclusion of Al₂O₃–TiN. The compositions of triangular TiN inclusion are Ti 24.3 at.% and N 24.8 at.%, as shown in Figs. 6(a) and 6(b). The elemental mappings of TiN inclusion are shown in Figs. 6(c) and 6(d). It can be seen that there was homogeneous nucleation for TiN inclusion without the distribution of Al. There are two phases of the complex inclusion of Al₂O₃–TiN with the spherical shape of inner Al₂O₃ inclusion and the cubic shape of outer TiN inclusion, as shown in Fig. 7(a). The diameter of Al₂O₃ inclusion was 1 μm and the size of each edge of TiN inclusion was about 3–5 μm. The compositions of the complex inclusion of Al₂O₃–TiN are shown in Fig. 7(b), with Al 24.2 at.%, O 41.6 at.%, Ti 29.8 at.%, and N 25.9 at.%. The elemental mappings of the complex inclusion of Al₂O₃–TiN are shown in Figs. 7(c)–7(f). It can be seen that the compositions of the inclusion were heterogeneous, meaning that the Al₂O₃ inclusion acted as the nucleation core of the TiN inclusion.

Fig. 6.

Morphology and elemental mappings of TiN inclusion. (Online version in color.)

Fig. 7.

Morphology and elemental mappings of complex inclusion of Al₂O₃–TiN. (Online version in color.)

3.3. Distribution of Nitride Inclusions

Figure 8 shows the number density and average size distributions of nitride inclusions at different distances from the bottom of the K418 alloy ingot and in revert K418 alloy. The nitride inclusions were divided by sizes: 1–3 μm, 3–5 μm, 5–15 μm, and bigger than 15 μm. Due to the contaminated by the alumina crucible and the melting of dummy bar, the number densities of nitride inclusions at 20 mm and 40 mm from the bottom of ingot were 0.9 mm⁻² and 10.9 mm⁻², respectively. The average sizes of nitride inclusions at 20 mm and 40 mm from the bottom of ingot were 6.5 μm and 2.6 μm, respectively. The number density of nitride inclusions increased from 5.3 mm⁻² at 57 mm to 15.2 mm⁻² at 137 mm from the bottom of ingot, which were smaller than that of revert K418 alloy, 28.2 mm⁻². Meanwhile, the number densities of each size between 57 mm and 137 mm from the bottom of ingot were also smaller than those of revert K418 alloy, as shown in Fig. 8 (a). However, the number density at 155 mm from the bottom of ingot, 34.2 mm⁻², was more than that of revert K418 alloy. The average size of nitride inclusions increased from 3.9 μm at 57 mm to 4.3 μm at 137 mm from the bottom of ingot, which was homogeneous and smaller than that of revert K418 alloy, 5.5 μm, as shown in Fig. 8(b). However, the average size at 155 mm from the bottom of ingot, 6.4 μm, was more than that of revert K418 alloy. There were gradient distributions of the number density and average size of nitride inclusions along the casting direction in the K418 alloy ingot. The nitride inclusions can be efficiently reduced and refined by the continuous unidirectional solidification process.

Fig. 8.

Number density (a) and average size (b) distributions of nitride inclusions at different distances from the bottom of the K418 alloy ingot and in revert K418 alloy. (Online version in color.)

Figure 9 shows the max sizes distribution of nitride inclusion at different distances from the bottom of the K418 alloy ingot and in revert K418 alloy. The max sizes of nitride inclusions increased from 14.5 μm at 20 mm to 25.4 μm at 137 mm from the bottom of ingot, which were much smaller than that in revert K418 alloy, 71.6 μm, as shown in Fig. 9. Due to the effect of flotation on the large inclusions, however, the max size of nitride inclusion was 71.1 μm at 155 mm from the bottom of ingot, which was roughly same as that in revert K418 alloy. There was a gradient distribution of the max sizes distribution of nitride inclusions along the casting direction. Meanwhile, the max sizes distribution of nitride inclusions was also refined by the continuous unidirectional solidification process.

Fig. 9.

Max sizes distribution of nitride inclusions at different distances from the bottom of the K418 alloy ingot and in revert K418 alloy. (Online version in color.)

3.4. Contents Distribution of Ti and N

Figure 10 shows the contents of Ti and N at different distances from the bottom of the K418 alloy ingot and in revert K418 alloy. Due to the contaminated by the melting of dummy bar and burn-out losses of elements, the contents of Ti and N were 0.44% and 56 ppm, respectively, at 20 mm from the bottom of ingot. Due to the microsegregation during the solidification process, the content of Ti slightly increased from 0.92% at 40 mm to 1.02% at 155 mm, as well as the content of N increased from 73 ppm at 40 mm to 110 ppm at 155 mm from the bottom of ingot, as shown in Figs. 10(a) and 10(b), respectively. The contents of N at the distances between 40 mm and 120 mm from the bottom of ingot were smaller than that of revert K418 alloy, 88 ppm, except for the contents of N at 137 mm and 155 mm from the bottom of ingot. The contents of Ti and N showed a gradient distribution along the casting direction. The content of N was reduced by the continuous unidirectional solidification process.

Fig. 10.

Content distributions of Ti (a) and N (b) at different distances from the bottom of the K418 alloy ingot and in revert K418 alloy. (Online version in color.)

4. Discussions

4.1. Morphology of Microstructure

There is no nucleation on the mold wall due to the mold heated above the liquidus temperature of the K418 alloy during the continuous unidirectional solidification process. The heat is only extracted out through the ingot due to the cooling zone located out of the mold. The solidification microstructure greatly depended on the flow condition of heat.⁴⁷⁾ The preferred-growth direction of <001> in cubic crystals was a result of the anisotropy of the surface energy.⁴⁸⁾ It was easier for grains with preferred-growth direction to grow along the direction of the thermal gradient.⁴⁹⁾ The surviving grains parallel to the casting direction were obtained under the continuous unidirectional solidification process.

Due to the smaller thermal conductivity of K418 ingot compared with that of dummy bar, the cooling rate and temperature gradient slightly decreased during the solidification process. The PDAS was indeed proportional to G^−1/2V^−1/4 when the microstructure was dendrite structure for nickel-base superalloys, as shown in Eq. (4).   

$${\lambda }_1=\text{K}{G}^{-1/2}{V}^{-1/4}$$(4)

where K is an alloy constant, G is the temperature gradient, and V is the solidification rate. According to Eqs. (3) and (4), the PDAS and SDAS were slightly increased from the bottom to the top of the K418 alloy ingot, as shown in Fig. 5.

4.2. Thermodynamic Analysis of TiN and Al₂O₃ Precipitations

The essential reactions and thermodynamic conditions of TiN and Al₂O₃ precipitations are shown in Eqs. (5), (6), (7), (8).^37,50)   

$$\text{TiN(s)}=[\text{Ti}]+[\text{N}]$$(5)

  

$$\mathrm{\Delta }{G}_{\text{TiN}}^{°}=-RT\cdot ln{K}_{\text{TiN}}=267\mathrm{\hspace{0.17em} }645-108.72T(J/mol)$$(6)

  

$${\text{Al}}_2{\text{O}}_3(\text{s})=2[\text{Al}]+3[\text{O}]$$(7)

  

$$\mathrm{\Delta }{G}_{{\text{Al}}_2{\text{O}}_3}^{°}=-RT\cdot ln{K}_{{\text{Al}}_2{\text{O}}_3}=1\mathrm{\hspace{0.17em} }157\mathrm{\hspace{0.17em} }000-356.2T(J/mol)$$(8)

The equal to the reaction equilibrium constants K_TiN and K_Al2O3 are shown in Eqs. (9) and (10).   

$$K_{{\text{T}}_{\text{i}}\text{N}}=\frac{\alpha (\text{Ti})\cdot \alpha (\text{N})}{\alpha (\text{TiN})}=\frac{[\text{wt}.\text{\%Ti}]f_{{\text{T}}_{\text{i}}}\cdot [\text{wt}.\text{\%N}]f_{\text{N}}}{\alpha (\text{TiN})}$$(9)

  

$$K_{{\text{Al}}_2{\text{O}}_3}=\frac{{\alpha }_{\text{Al}}^2\cdot {\alpha }_{\text{O}}^3}{\alpha ({\text{Al}}_2{\text{O}}_3)}=\frac{{[\text{wt}.\text{\%Al}]}^2{f}_{\text{Al}}^2\cdot {[\text{wt}.\text{\%O}]}^3{f}_{\text{O}}^3}{\alpha ({\text{Al}}_2{\text{O}}_3)}$$(10)

where R is the ideal gas constant. α(TiN), α(Ti), α(N), α(Al₂O₃), α(Al), and α(O) are the activities of TiN, Ti, N, Al₂O₃, Al, and O in the K418 alloy, respectively. [wt.%Ti], [wt.%N], [wt.%Al], and [wt.%O] are the contents of Ti, N, Al, and O in the K418 alloy. f_Ti, f_N, f_Al, and f_O are the Henrian activity coefficients of Ti, N, Al, and O, respectively. In Eqs. (9) and (10), when α(TiN) = 1 and α(Al₂O₃) = 1, both sides take the logarithm of 10 at the same time and Eqs. (9) and (10) can be simplified to Eqs. (11) and (12).   

$$log{K}_{\text{TiN}}=log[\text{wt}.\text{\%Ti}][\text{wt}.\text{\%N}]+\text{log}{f}_{\text{Ti}}+\text{log}{f}_{\text{N}}$$(11)

  

$$log{K}_{{\text{Al}}_2{\text{O}}_3}=log{[\text{wt}.\text{\%Al}]}^2{[\text{wt}.\text{\%O}]}^3+2\text{log}{f}_{\text{Al}}+3\text{log}{f}_{\text{O}}$$(12)

The first-order interaction coefficients of $e_{\text{i}}^j$,^51,52,53,54) as shown in Table 3, can be used to calculate the activity coefficient by Eq. (13).   

$$\text{log}{f}_{\text{i}}={\sum }_j{e}_{\text{i}}^j[\text{wt}.\text{\%}j]$$(13)

Table 3. First-order activity coefficients in liquid nickel at 1873 K.

j	Cr	Nb	Mo	Al	Ti	B	N	O	C
$e_{\mathrm{N}}^j$	−0.09751)	−0.07552)	−0.0453)	0.0151)	−0.2154)	0.01551)	0	–	–
$e_{\mathrm{T}\mathrm{i}}^j$	0.05554)	–	–	–	0.0854)	–	−0.6754)	−0.4654)	−0.02251)
$e_{\mathrm{O}}^j$	−0.254)	−	−0.02451)	−0.010651)	−0.4654)	–	–	0	0.21654)
$e_{\mathrm{A}\mathrm{l}}^j$	0.009654)	–	–	0.0854)	–	–	−0.00454)	−1.7954)	0.05654)

Taking the content products of Ti, N, Al, and O as $K_{\mathrm{T}\mathrm{i}\mathrm{N}}^{\prime }$ ($K_{\mathrm{T}\mathrm{i}\mathrm{N}}^{\prime }$=[wt.%Ti][wt.%N]) and $K_{{\text{Al}}_2{\text{O}}_3}^{\prime }$ ($K_{{\text{Al}}_2{\text{O}}_3}^{\prime }$ = [wt.%Al]²[wt.%O]³), respectively, Eqs. (6), (8), (9), (10), (11), (12), (13) can be combined. The relationship between content products and temperature can be expressed as follows:   

$$\text{log}{K}_{\text{TiN}}^{\prime }=-\frac{13\mathrm{\hspace{0.17em} }998}{T}+6.62$$(14)

  

$$\text{log}{K}_{{\text{Al}}_2{\text{O}}_3}^{\prime }=-\frac{60\mathrm{\hspace{0.17em} }512}{T}+26.91$$(15)

The calculated contents of Ti, N, Al, and O in equilibrium at liquidus and solidus temperatures are shown in Fig. 11. The calculated contents of N in equilibrium decreased from 92 ppm at 1618 K to 50 ppm at 1570 K, with the content of Ti, 1%, as shown in Fig. 11(a). The content of N in revert K418 alloy, 88 ppm, was smaller than that of the calculated content of N in equilibrium for the stability of TiN inclusions at 1618 K, 92 ppm. The TiN inclusion began to precipitate at the mushy zone during the solidification process. The calculated content of O in equilibrium decreased from 1 ppm at 1618 K to 0.4 ppm at 1570 K with the content of Al, 5.5%, as shown in Fig. 11(b). The content of O in revert alloy, 13 ppm, was more than that of the calculated content of O in equilibrium for the stability of Al₂O₃ inclusion at 1618 K, 1 ppm. The Al₂O₃ inclusion began to precipitate at the liquid zone. Additionallly, the calculated contents of N and O in equilibrium slightly decreased due to the microsegregation of Ti and Al at the same temperature.

Fig. 11.

Stability diagrams of TiN (a) and Al₂O₃ (b) inclusions at different temperatures in the K418 alloy T_L – Liquidus temperature, T_S – Solidus temperature, and Re. – Revert K418 alloy. (Online version in color.)

The elements will enrich in the liquid phase to cause selective crystallization resulting in segregation and precipitation at the solidification front. The contents of Ti and N at the solidification front can be expressed by the Eqs. (16)⁵⁵⁾ and (17).⁵⁶⁾   

$$C_{\text{L}}^{\text{Ti}}=C_0^{\text{Ti}}\cdot {(1-f_{\text{s}})}^{k_{\text{Ti}}-1}$$(16)

  

$$C_{\text{L}}^{\text{N}}=\frac{C_0^{\text{N}}}{1-(1-k_{\text{N}})f_{\text{s}}}$$(17)

where $C_{\text{L}}^{\text{Ti}}$, $C_{\text{L}}^{\text{N}}$, $C_0^{\text{Ti}}$, and $C_0^{\text{N}}$ are the contents of Ti and N at the solidification front and the initial contents of Ti and N, respectively. f_s is the fraction of solid of the K418 alloy. k_Ti and k_N are the equilibrium distribution coefficients of Ti, 0.75,⁴²⁾ and N, 0.48,⁵⁷⁾ respectively. The actual solubility product of TiN and Q_TiN can be calculated by the Eq. (18).   

$$Q_{\text{TiN}}=C_{\text{L}}^{\text{Ti}}\cdot C_{\text{L}}^{\text{N}}=\frac{C_0^{\text{Ti}}\cdot C_0^{\text{N}}\cdot (1-f_{\text{s}}){ }^{k_{\text{Ti}}-1}}{1-(1-k_{\text{N}})f_{\text{s}}}$$(18)

The relationship between the temperature at the solidification front and the fraction of solid can be shown by Eq. (19).⁵⁷⁾   

$$T=T_{\text{Ni}}-\frac{T_{\text{Ni}}-T_{\text{L}}}{1-f_{\text{s}}\frac{T_{\text{L}}-T_{\text{S}}}{T_{\text{Ni}}-T_{\text{S}}}}$$(19)

where T is the temperature of the K418 alloy during solidification; T_Ni, T_L, and T_S are the melting temperature of pure Ni (1728 K), the liquidus temperature (1618 K), and the solidus temperature (1570 K), respectively, of the K418 alloy.

The initial contents of Ti and N at different distances from the bottom of ingot were shown in Figs. 10(a) and 10(b). The contents of Ti and N gradually increased in the K418 alloy melt due to segregation during solidification process. When the actual solubility product in melt is more than the equilibrium solubility product, the TiN inclusion will precipitate. The relationships between the solubility product of [Ti][N] and fraction of solid at different distances from the bottom are shown in Fig. 12. The cross points between the $\text{log}{K}_{\text{TiN}}^{\prime }$ and $\text{log}{Q}_{\text{TiN}}$ are the fraction of solid which the TiN inclusion start to precipitate at different distances from the bottom of the K418 alloy ingot and in revert K418 alloy. The TiN inclusion started to precipitate gradually reduced from f_s = 0.252 at the 40 mm to f_s = 0.142 at the 120 mm, which were later than that in the revert K418 alloy, f_s = 0.046. The corresponding precipitation temperatures of the TiN inclusion were obtained by substituting the f_s into the Eq. (19): T_{20 mm} = 1583.9 K, T_{40 mm} = 1608.9 K, T_{57 mm} = 1609.2 K, T_{75 mm} = 1609.4 K, T_{100 mm} = 1610.3 K, T_{120 mm} = 1613 K, and T_revert = 1616.4 K. Those precipitation temperatures lie between the liquidus and solidus temperatures, meaning that the TiN inclusion precipitated in the mushy zone at defined contents of Ti and N. However, there were no cross points at the 137 mm and 155 mm from the bottom, meaning that the TiN started to precipitate in the liquid zone.

Fig. 12.

Relationships between the solubility product of [Ti][N] and the fraction of solid at different distances from the bottom of the K418 alloy. (Online version in color.)

4.3. Kinetic Calculations of TiN Inclusion Growth

Due to the content of Ti far greater than that of N, the content of N is the limiting factor for the growth of TiN inclusion. The theoretical precipitation size of TiN inclusion in the solidification front of the K418 alloy can be calculated by Eq. (20).^58,59)   

$$r\frac{\text{d}r}{\text{d}t}=\frac{M_{\text{s}}}{100M_{\text{m}}}\cdot \frac{{\rho }_{\text{m}}}{{\rho }_{\text{s}}}{D}_{\text{N}}\left({[\text{wt}.\text{\%N}]}_{\text{L}}-{[\text{wt}.\text{\%N}]}_{\text{e}}\right)$$(20)

The integral equation of Eq. (20) is shown below:   

$$r=\sqrt{\frac{M_{\text{s}}}{50M_{\text{m}}}\cdot \frac{{\rho }_{\text{m}}}{{\rho }_{\text{s}}}{D}_{\text{N}}\left({[\text{wt}.\text{\%N}]}_{\text{L}}-{[\text{wt}.\text{\%N}]}_{\text{e}}\right)\cdot t_{\text{f}}}$$(21)

where r is the radius of the TiN inclusion, cm; M_s is the molar mass of TiN, 62 g/mol; M_m is the molar mass of the K418 alloy, 55 g/mol; ρ_s is the density of the TiN inclusion, 5.43 g/cm³; ρ_m is the density of the K418 alloy, 8 g/cm³; D_N is the diffusion coefficient of nitrogen in the K418 melting alloy, 0.91exp(−168490/RT),⁵⁷⁾ cm²/s; [wt.%N]_L and [wt.%N]_e are the mass fractions of nitrogen during the solidification of K418 alloy and in equilibrium with TiN inclusion, respectively. The actual and equilibrium nitrogen contents, [wt.%N]_L and [wt.%N]_e, at the solidification front were obtained by the Eqs. (17) and (14), respectively. The actual content of Ti at the solidification front, [wt.%Ti]_L, was obtained by the Eq. (16).

Figure 13 shows the relationship between the radius of TiN inclusion and the fraction of solid under different cooling rates and the initial contents of Ti and N. The radius of TiN inclusion increased from 3.2 μm to 8.6 μm when the fraction of solid approached to 1. The fraction of solid of starting precipitation and radius of TiN inclusion were determined by the initial contents of Ti and N and cooling rates, as shown in Fig. 13. The radius of TiN inclusion was gradually increased by increasing the initial contents of Ti and N, and decreasing the cooling rates. Furthermore, the cooling rate had a great effect on the radius of the TiN inclusion. Additionally, the collision and agglomerating mechanisms of inclusions removal process were investigated.^60,61,62) Due to the Stokes flotation and agglomeration at the steel/gas surface, the larger size inclusions could be easily moved to the top of ingot. There was a gradient distribution of the sizes of nitride inclusions along the casting direction.

Fig. 13.

Relationships between the radius of TiN inclusion and the fraction of solid of the K418 alloy under different cooling rates and the initial contents of Ti and N. (Online version in color.)

Due to no consideration of heterogeneous nucleation behavior of TiN inclusion, the calculated radius of TiN inclusion was smaller than those of actual sizes of complex inclusion Al₂O₃–TiN. The former precipitation of Al₂O₃ inclusion in the melting process could act as the nucleation sites and provide nucleation energy for TiN precipitation. The complex inclusion of Al₂O₃–TiN can precipitate easily and grow longer compared with TiN inclusion. So, the complex inclusion of Al₂O₃–TiN is the main type of nitride inclusions in the K418 alloy ingot and revert K418 alloy.

5. Conclusions

(1) The morphology of γ dendrite is a typical cross-shape on the transverse sections and parallel to the casting direction on the longitudinal sections. There was a dendritic coarsening phenomenon from bottom to top of the K418 alloy ingot.

(2) There are two types of nitride inclusions in the K418 alloy ingot: TiN and complex inclusion of Al₂O₃–TiN. There are gradient distributions of the number density, average and max sizes of nitride inclusions, and the contents of Ti and N along the casting direction.

(3) Based on the thermodynamic calculation, it was found that the fraction of solid of starting precipitation for nitride inclusions was dependent on the initial contents of Ti and N. The fraction of solid of starting precipitation for TiN inclusion gradually reduced from 0.252 at the 40 mm to 0.142 at the 120 mm, and even to the liquid zone at the top of the K418 alloy ingot.

(4) Based on the kinetic calculation, the cooling rate had a great effect on the radius of the TiN inclusion. The sizes of TiN inclusion increased from 3.2 μm to 8.6 μm when the fraction of solid approached to 1. The calculated size of TiN inclusion was smaller than those of actual sizes of complex inclusion Al₂O₃–TiN.

(5) The size and quantity of nitride inclusions can be refined and reduced in the K418 alloy ingot under the continuous unidirectional solidification process compared with those in revert K418 alloy. The methods to control the precipitation and size of nitride inclusions were reducing the contents of N and O and increasing the cooling rates.

Acknowledgments

This work is financially supported by the Project of the Ministry of Science and Technology of China (No. 2017YFB0405902), the National Science and Technology Major Project “Aeroengine and Gas Turbine” (No. 2017-VII-0008-0102), and the Shanghai Municipal Science and Technology Commission (Nos. 19DZ1100704, 17JC1400602).

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