Materials Science & Engineering A 701 (2017) 111–119
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Effect of N content on microsegregation, microstructure and mechanical property of cast Ni-base superalloy K417G
MARK
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Li Gong, Bo Chen , Yaqian Yang, Zhanhui Du, Kui Liu Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenhe District, Shenyang 110016, China
A R T I C L E I N F O
A B S T R A C T
Keywords: K417G cast superalloy Nitrogen content Microsegregation Microstructure Mechanical property
This study investigates the effects of nitrogen (N) content (0.0005–0.0045 wt%) on the microsegregation, microstructures and high temperature mechanical properties of cast superalloy K417G. The results show that the segregation of Ti to interdendritic region becomes very serious with increased N content. In all three samples with different N contents, the alloys are typically dendritic morphology and γ′ phases show good cubic structure. With the N content increasing from 0.0005 wt% to 0.0045 wt%, the volume fraction of γ′ phase in the dendrite decreases, the sizes of γ/γ′ eutectic and MC carbide increase, and the volume fractions of γ/γ′ eutectic, MC carbide and micro-porosity firstly increase but then decrease. N addition changes the morphology of MC carbide from script-like shape to blocky shape, and Ti(C, N) is identified in the alloy with 0.0045 wt% N. With the N content increasing, the ultimate and yield strength decrease at elevated temperature, and the ductile and stress rupture life firstly have a sharp decrease and then have a slight increase. The specimen with the minimal content of N shows the best comprehensive mechanical properties.
1. Introduction Nickel-base cast superalloys are typically used as the aeroengine turbine blades, which work under critical conditions of elevated temperature, sever creep, and great stress and fatigue [1–4]. In order to meet the rigorous demands, there are more than seven kinds of alloying elements in these superalloys for excellent performance and efficiency [5,6]. Therefore, the segregation of alloying elements during casting is very serious. Studies show that microsegregation has a significant effect on the mechanical properties of cast or wrought materials, and controlling the content of trace elements can alleviate the microsegregation [7,8]. Nitrogen (N), as a minor element in superalloys, is not easily removed during vacuum induction melting (VIM), because of its strong affinity for strengthening elements (such as Cr, Al, Ti and Nb). It is usually controlled by strictly selecting raw materials and improving the vacuum level. N has low solubility in nickel-base superalloys and it is easy to form Ti(C, N) carbonitride during solidification [9,10]. When the content of N is above the saturated solubility in the melt, TiN or other nitride particles will precipitate. Many investigations have proved that N has a positive effect on enhancing the corrosion resistance and mechanical properties [11–14]. Many studies [15–18] suggest that micro-porosity has a close relationship with the N content, but the mechanism has not been fully understood. It is widely believed that the
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Corresponding author. E-mail address:
[email protected] (B. Chen).
http://dx.doi.org/10.1016/j.msea.2017.06.044 Received 20 March 2017; Received in revised form 9 June 2017; Accepted 11 June 2017 Available online 19 June 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
increased N content will have negative effects on the tensile strength and ductility of nickel-base superalloys [10,15,16,19,20]. Especially, the effects of N content have been investigated in nickel-base alloy and stainless steels for solidification characteristics, segregation behavior, lowering the micro-porosity and strengthening mechanical properties [7–19]. However, the effects of N content on different alloys are different because of their different kinds and contents of alloying elements and multi-components. K417G superalloy belongs to the family of cast nickel-base superalloy and is widely used in turbine blades because of its excellent yield and tensile strength, high-temperature oxidation resistance and good microstructure stability at elevated temperature. K417G alloy contains amounts of alloying elements, such as Ti, Al, Co and Cr, which would appeal to N and promote the formation of nitrides. Therefore, the content of N would have an influence on microstructures and properties of K417G alloy. The main object of this study is to develop a specific understanding of effects of N content on the microsegregation, microstructures, and mechanical properties of K417G superalloy. 2. Materials and experimental procedures A 10 kg master ingot of K417G alloy used in this study was prepared by vacuum induced melting (VIM). The ingot was divided into 3 parts, re-melted with the addition of high-purity CrN, and then casted into
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Table 1 Chemical compositions of K417G superalloy (wt%). Alloy no.
N
O
C
Co
Mo
Al
Cr
V
Ti
Ni
N5 N28 N45
0.0005 0.0028 0.0045
0.0006 0.0010 0.0009
0.17 0.17 0.16
9.93 10.0 9.97
3.06 3.00 3.02
5.12 5.16 5.18
9.21 9.28 9.23
0.80 0.78 0.78
4.43 4.48 4.45
Bal. Bal. Bal.
round bars (ϕ10 × 100 mm) to produce 3 experimental alloys. The compositions of these 3 alloys are listed in Table 1. The round bars were machined into gauge of ϕ5 mm × 25 mm for high temperature tensile test and stress rupture test. High temperature tensile test was performed at 900 °C on WDW-T100 test machine with the initial strain rate of 0.15 mm/min, and then the rate increased to 3 mm/min after yielding. Rupture test was performed at 950 °C with the stress of 235 MPa on RDL-50 test machine. Metallographic examinations were made on the longitudinal section at the gauge location of high temperature tensile specimens. The samples were observed by Olympus optical microscopy (OM), and 15 images were captured continuously at each sample. Then the images were measured by Sisc IAS image analysis system to quantitatively determine the volume fraction and the size of γ/γ′ eutectic and cast porosity. To confirm the volume fraction and the size of γ′ phase and carbide, the samples were observed by FEI XL-30FEG scanning electron microscopy (SEM). 10 images captured at different areas of each specimen were analyzed and the average was taken. Transmission electron microscopy (TEM) samples were prepared by jet-beam electro-polishing in a solution of 10% perchloric acid and 90% ethanol maintained between − 18 and − 23 °C, and observed on FEI G2 20 TEM. The element concentrations and distributions on the un-etched samples were investigated with JEOL JXA8530F electron probe microanalysis (EPMA). The fracture surfaces at 900 °C tensile tests with various N contents were observed by SEM after ultrasonic cleaning.
Fig. 1. Segregation coefficient (k) on the alloys with different N contents.
of Al and Mo were fluctuating around 1, so they can be considered as neutral elements. It is noted that the segregation of Ti became much more serious with increased N content. Meanwhile, the k values of V and Co slightly increased with increased N content.
3.2. Microstructure analysis After etching with the solution of 20 g CuSO4 + 100 ml HCl + 5 ml H2SO4 + 100 ml H2O, the microstructures at the gauge location of high temperature tensile specimens with different N contents were analyzed by OM. As shown in Fig. 2, K417G superalloy has a typical dendritic morphology with γ matrix, γ′ reinforced phase, γ/γ′ eutectic, carbides and cast porosity. The dendrite arm spacing, as a critical microstructure parameter, has an important effect on the mechanical properties [24]. From quantitative calculation listed in Table 3, the secondary dendrite arm spacing (λ) with different N contents were 51.3 µm, 49.5 µm and 50.9 µm, respectively. In the range of 0.0005–0.0045 wt%, N content had no significant effect on the morphology and secondary dendrite arm spacing in K417G superalloy. The γ′ phase is the main strengthening phase of Ni-base superalloys. As shown in Fig. 3, the typical morphology of γ′ particles showed good cubic structure both in the dendritic and interdendritic regions with different N contents. After calculation, the volume fraction of the γ′ phase in the dendrite cores varied from 63.5% to 61.9%, and the average sizes were 561 nm, 565 nm and 563 nm, as detailedly listed in Table 3 respectively. The volume fraction of the γ′ phase in the interdendrite varied from 64.3% to 64.7%, and the average sizes were 573 nm, 570 nm and 571 nm. With increased N content, the average size of the γ′ phase both in the dendrite and interdendrite had little changed, but the volume fraction in the dendrite had a decrease. For better studying the γ/γ′ eutectic, the samples were electrolyzed with 10% phosphoric acid. As shown in Fig. 4, lots of γ/γ′ eutectics precipitated in the interdendritic regions with various N contents. As the N content changed, the average volume fraction of the γ/γ′ eutectic varied from 2.9% to 6.3%, and the average size varied from 34.3 µm to 36.9 µm. It can be seen that the volume fraction and size of the γ/γ′ eutectic tended to be larger with relatively greater N content. In the last stage of solidification, K417G is subject to forming cast porosity because of feeding difficulties. As shown in Fig. 2, most of the micro-porosities distributed at dendrite boundaries, and the γ/γ′ eutectics generally could be observed nearby. As the N content changed from 5 ppm to 45 ppm, the volume fraction of cast porosity changed from 0.19% to 0.28%. It indicated that the volume fraction of microporosity had an obvious increase with greater N content. Meanwhile, the size of micro-porosity tended to be larger with increased N content. As is known, MC carbide is a kind of common carbides in Ni-base superalloy, and usually precipitate at the initial stage of solidification
3. Results 3.1. Microsegregation analysis The chemical compositions in the dendritic and interdendritic regions were determined by EPMA. The values of elemental segregation coefficient (k) in three alloys are listed in Table 2, which is defined as the ratio of average concentration of alloying elements in the dendrite core to that in the interdendritic region, i.e., k = Cd/Ci [21,22]. The value of k less than 1 indicates that the elements segregate to the interdendritic region, while k greater than 1 indicates that the elements segregate to the dendrite core [23]. As clearly shown in Fig. 1, Ti was positive segregation element, which tended to gather in the residual liquid during solidification process. Co, V and Cr were negative elements, which tended to segregate towards the solid phase. The k values Table 2 Element segregation analysis of different N contents between dendrite core and interdendritic region (wt%). Alloy no.
Element segregation V
Co
Al
Cr
Mo
Ti
N5
Cd Ci k
0.78 0.76 1.03
10.86 10.67 1.02
4.70 4.83 0.97
9.38 8.93 1.05
2.80 2.84 0.99
2.66 3.20 0.83
N28
Cd Ci k
0.80 0.74 1.08
11.05 10.60 1.04
4.91 4.86 1.01
9.48 8.86 1.07
2.76 2.75 1.00
2.46 3.18 0.77
N45
Cd Ci k
0.83 0.76 1.09
11.33 10.60 1.07
4.33 4.47 0.97
9.86 9.31 1.06
3.04 2.89 1.05
2.39 3.29 0.73
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Fig. 2. The microstructure and dendrite arm spacing (λ) with different N contents: (a) and (d) N5, (b) and (e) N28, (c) and (f) N45.
decreased C/N ratio [26].
[25]. As shown in Fig. 5, the carbides mainly distributed in dendrite boundaries or near the γ/γ′ eutectic region with different N contents, but they showed different morphologies. In alloy N5, the carbide showed blocky and script-like shape, and its volume fraction was 1.02%. In alloy N28 and N45, the carbide simply showed blocky shape, and their volume fractions were 1.35% and 1.26% respectively. With increased N content, the average size of the carbide increased from 1.99 µm to 2.26 µm. According to EPMA maps in the sample N5 and N28, Ti and Mo were significantly enriched in the carbides, while Cr, Al and Co were depleted, as illustrated in Figs. 6 and 7. It is well known that Mo and Ti are strong carbides former [25]. Moreover, as illustrated in Fig. 8, the carbide was fcc crystal structure with the lattice constant a of 0.429 nm, which fell intermediately between MoC (0.4273 nm) and TiC (0.4327 nm), so the probability was that the carbides were MC ((Ti, Mo)C) carbides. It can be seen in Fig. 9 that there were bits of dark black phases precipitating among the MC carbides in alloy N45. As shown in the EPMA map, the dark black phase was rich with Ti, C and N, but poor with Mo, Cr, Co and Al. The MC carbides nearby were rich with Ti, Mo and C, but poor with N. It can be deduced that dark black phases were not MC carbides. The EDS spectrum showed that the average chemical compositions of this phase were 74.4% Ti, 35.7% N, 7.9% C, 0.4% Cr, 0.5% Co, 1.1% Ni and 0.5% Mo (at%). Therefore, the compound was identified as Ti(C, N). As reported previously, the C/N ration in the TiCxN1−x carbonitride can vary continuously from zero to one, and the lattice constant a of the TiCxN1−x carbonitride decreases linearly with
3.3. Mechanical property The ultimate and yield tensile strength, elongation and reduction of area in tensile tests at 900 °C and the typical rupture life in rupture tests at 950 °C with the stress of 235 MPa were listed in Table 4. With the N content increasing from 0.0005 wt% to 0.0045 wt%, the yield and ultimate tensile strength had slight decrease, while the plastic property had obviously decrease. When the N content increased from 0.0005 wt % to 0.0028 wt%, the elongation and reduction of area decreased from 29.5% to 6.8% and 15.8% to 4.0%, respectively. Although the elongation and reduction of area increased to 13.0% and 7.8% when the N content was 0.0045 wt%, they were still far lower than those of alloy N5. Meanwhile, the N content had a significant effect on the rupture life of K417G alloy. With the N content increasing from 0.0005 wt% to 0.0045 wt%, the rupture life firstly decreased from 62.2 h to 24.7 h, and then increased to 38.1 h. The full view morphology of fracture surfaces at 900 °C tensile tests with different N contents were shown in Fig. 10. In all specimens, the fracture surface was perpendicular to the tensile stress, and the deformation of fracture surface was obvious. Therefore, the specimens with different N contents all had a ductile fracture manner. As shown in Fig. 11(a), (d) and (g), the crack expanded in the interdendrite in all specimens. Fig. 11(c), (e) and (h) exhibited that there were cast porosities on all fracture surfaces. Therefore, the N content had no obvious
Table 3 Microstructure features at the gauge location of specimens with different N contents. No.
N5 N28 N45
λ (μm)
51.3 ± 0.4 49.5 ± 0.3 50.9 ± 0.3
The size of γ′ phase (nm)
The volume fraction of γ′ phase (%)
dendrite
interdendrite
dendrite
interdendrite
561 ± 13 565 ± 14 563 ± 10
573 ± 9 570 ± 13 571 ± 11
63.5 ± 0.7 62.4 ± 0.5 61.9 ± 0.4
64.5 ± 0.6 64.3 ± 0.8 64.7 ± 0.6
The size of γ/γ′ eutectic (μm)
The volume fraction of γ/γ′ eutectic (%)
The volume fraction of cast porosity (%)
The size of carbides (μm)
The volume fraction of carbides (%)
34.3 ± 2.0 36.5 ± 2.2 36.9. ± 1.9
2.9 ± 1.1 6.3 ± 1.0 4.4 ± 1.2
0.19 ± 0.1 0.28 ± 0.1 0.25 ± 0.1
1.99 ± 0.4 2.22 ± 0.3 2.26 ± 0.4
1.02 ± 0.2 1.35 ± 0.2 1.26 ± 0.1
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Fig. 3. The morphology of γ′ phase in the dendrite and interdendrite with different N contents: (a) N5 at the dendrite; (b) N5 at the interdendrite; (c) N28 at the dendrite; (d) N28 at the interdendrite; (e) N45 at the dendrite; (d) N45 at interdendrite.
Meanwhile, because of its strong affinity for Ti, the k value of Ti had a great decrease. The standard Gibbs formation free energy (ΔG°) of TiC and TiN are as following formulas [27]:
effect on the fracture manners. From Fig. 11(b) and (c), shallow dimples can be obviously identified on the fracture surface of alloy N5, which meant that the crystal lattice of alloy N5 generated larger deformation under high tensile test than the others. Therefore, the plastic property of alloy N5 (elongation and reduction of area) was higher than that of the other specimens. From Fig. 11(e) and (f), there were lots of microporosities on the fracture surface of alloy N28, which resulted poor mechanical properties. Fig. 11(i) showed that the fracture surface of alloy N45 was relatively smooth, so its deformation was relatively small.
[Ti] + [C] = TiC(s), ΔG0 = −189110 + 100.44 T J/mol
(1)
[Ti] + [N] = TiN(s), ΔG0 = −379000 + 149 T J/mol
(2)
As listed above, both values of the ΔG are far below 0, so TiC and TiN are easy to precipitate during solidification. As the ΔG0 of TiN is smaller than TiC, TiN will preferentially form when the content of N is large enough. In these three alloys, the content of C (0.17 wt%) is 35–340 times of N content. Therefore, Ti atom is much easier to meet with C atom and form TiC. In alloy N5 and N28, there are only TiC precipitates. When the alloy contains 0.0045 wt% N, Ti atoms capture some N atoms, whereas the void N sites of TiN lattice will be substituted by surrounding amount of C atoms. Therefore, Ti(C, N) came into being in alloy N45. With increased N content, the segregation of Ti to the interdendritic region is more sever, which results in larger volume fraction and size of MC carbide, as listed in Table 3. However, Ti(C, N) 0
4. Discussion 4.1. Effects of N content on the segregation and microstructures It is well known that segregation level strongly depends on the liquidus and solidus temperatures and larger solidification temperature range would result in more severe segregation. N addition in nickelbase alloys can decrease the solidus temperature [9,27], so the segregation of Ti, V and Co becomes more serious with increased N content. 114
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Fig. 4. The morphology and distribution of the γ/γ′ eutectic with different N contents: (a) and (b) N5, (c) and (d) N28, (e) and (f) N45.
Fig. 5. The morphology and distribution of the carbides with different N contents: (a) N5, (b) N28 and (c) N45.
carbonitrides precipitating in alloy N45 would consume Ti and reduce the precipitation of γ/γ′ eutectic. Therefore, the volume fraction of γ/γ′ eutectic in N45 is smaller than in N28. Micro-porosity is formed at the last stage of solidification, which is related to the solidification parameters, such as grain size, precipitation and development of secondary phase, elements segregation, temperature gradient and solidification velocity [28,29]. In this work, a large number of MC carbides and γ/γ′ eutectics will serve as bridging obstacles in the dendritic regions and hinder the smooth flow of feed metal. Therefore, plenty of micro-porosities will generate around the carbides and γ/γ′ eutectics. The γ′ phases coherently precipitate from the supersaturated γ matrix during the solidification process. With increased N content, the content of Ti in
carbonitrides precipitating in alloy N45 consume a portion of Ti, so the volume fraction of MC carbides in alloy N45 is slightly less than that in N28. Meanwhile, because of severe segregation of Ti into the interdendrite with increased N content, the morphology of MC carbide changes from small script-shape to large blocky-shape. The γ/γ′ eutectic, enriched with Al and Ti, is one of common phases in multicomponent nickel-base superalloys. It is brittle and always as the initiation site of crack, so it should be avoided as much as possible [28]. The formation of the γ/γ′ eutectic is strongly related to the microsegregation. As the N content increases and more contents of Ti gather into the interdendrite, larger size and volume fraction of γ/γ′ eutectics form in the last stage of solidification. In addition, Ti(C, N) 115
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Fig. 6. Qualitative elemental mapping images of Ti, Mo, Cr, Al, Co and N in alloy N5.
Fig. 7. Qualitative elemental mapping images of Ti, Mo, Cr, Al, Co and N in alloy N28.
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Table 4 High temperature tensile properties and stress rupture properties of K417G superalloy with different N contents. Alloy no.
Ultimate tensile strength (MPa)
Yield tensile strength (MPa)
Elongation (%)
Reduction of area (%)
Rupture life (h)
N5 N28 N45
720.0 692.5 670.5
520.0 507.5 470.2
29.5 6.8 13.0
15.8 4.0 7.8
62.2 24.7 38.1
interdendrite. Because of Ti enriched in the interdendrite, the average size and volume fraction of the γ′ phase in the interdendrite are slightly larger than those in the dendrite. 4.2. Effects of N content on the mechanical properties The longitudinal profiles of three fractures at 900 °C tensile tests with different N contents are shown in Fig. 12. In all specimens, cracks expended along the grain boundary and the interdendrite, and the direction of tensile stress axis and the direction of crack propagation are about 45°. Under the action of shear stress, the slip and deformation in the grain boundary and the interdendrite lead to microcracks. The expansion of microcracks along the grain boundary and the interdendrite leads to the fracture of materials. The γ/γ′ eutectic is a phase with lower strength and is prone to form cracks, which has a very detrimental influence on the mechanical properties of the testing alloy [28]. It can be seen from Fig. 12 that there are γ/γ′ eutectics on all the fracture sections. The γ/γ′ eutectic will hinder the movement of dislocations, and deformation will generate because of stress concentration. When the stress concentration is great enough, the microcrack will form and propagate around brittle γ/γ′ eutectics. Micro-porosity, which is one of the main defects in
Fig. 8. TEM photograph and selected-area diffraction pattern of MC carbide in alloy N5.
the dendrite decreases, which results in decreasing volume fraction of γ′ phase in the dendrite. In the solidification process, Ti-γ′ phase forming element has been sufficiently consumed by MC carbides, Ti(C, N) carbonitrides and γ/γ′ eutectics, so the volume fraction of γ′ phase in the interdendrite is not obviously affected by the segregation of Ti to the
Fig. 9. The morphology of precipitates and qualitative elemental mapping images of Ti, Mo, N, C, Cr, Co, Al and Ni in alloy N45.
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Fig. 10. Full view morphology of fracture surfaces in tensile test at 900 °C with different N contents: (a) N5, (b) N28 and (c) N45.
dislocation. With the N content increasing from 0.0005 wt% to 0.0045 wt%, N content has no obvious effect on the morphology and size of γ′ phase in K417G superalloy. So the way that the dislocations shear γ′ phase is the same. However, its volume faction in the dendrite decreases with increased N content, which leads to the decrease on the yield and ultimate tension strength. The carbide plays an important part on superalloys and its morphology, size and volume fraction have the decisive effect on mechanical properties [35–37]. The fine MC carbide effectively obstructs the movement of dislocations and inhibits the GB sliding, and thus it would contribute to strengthening grain boundaries and effectively improve the mechanical properties of superalloys [38]. With the
superalloys, would facilitate the creep cavity during high temperature conditions and thus lead to poor mechanical properties [30,31]. As shown in Fig. 11, amount of micro-porosities could be observed on the fractures in all specimens. Under the action of tensile stress, the microporosity is easy to provide the microcrack and promotes the fracture of alloys. Therefore, with the content of N increasing, the volume fractions of γ/γ′ eutectic and micro-porosity increase a lot in the grain boundary and the interdendritic region, which results in low tensile strength, ductility property and rupture life of K417G alloy. The high temperature strength of Ni-base superalloy is primarily determined by the morphology, size and volume fraction of the γ′ phase [32–34]. The γ′ particles act as barriers against movement of
Fig. 11. SEM morphology of fracture surfaces in tensile tests at 900 °C with different N contents: (a), (b) and (c) N5, (d), (e) and (f) N28, (g), (h) and (i) N45.
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Fig. 12. OM morphology of fracture surfaces in tensile tests at 900 °C with different N contents: (a) N5, (b) N28 and (c) N45.
References
content of N increasing, the size of MC carbide becomes lager and larger, which will alleviate its effect of reinforcement on grain boundaries. So the tensile strength of K471G alloy decreases with increased N content. The fine Ti(C, N) also strengthens the grain boundary. Because of very small numbers of Ti(C, N) in N45 alloy, it has little effect on mechanical properties.
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5. Conclusion After analyzing K417G alloys with N content of 0.0005, 0.0028 and 0.0045 wt% the microsegregation, microstructures, and mechanical properties varied evidently with different N contents. The results obtained are as following: 1. With increased N content, V and Co have a slight increase on segregating to the dendrite cores, while the segregation of Ti to interdendritic region becomes much more serious. 2. The N content has no significant effects on the dendritic morphology, secondary dendrite arm spacing and γ′ phase. With the N content increasing from 0.0005 wt% to 0.0045 wt%, the γ′ phase shows good cubic structure in all specimens and the size of γ′ phase has no obvious change, but its volume fraction in the dendrite decreases. 3. The N content plays a significant role on the γ/γ′ eutectic and microporosity. With the N content increasing from 0.0005 wt% to 0.0045 wt%, the size of γ/γ′ eutectic increases, and the volume fractions of γ/γ′ eutectic and micro-porosity firstly increase but then decrease. 4. With the N content increasing from 0.0005 wt% to 0.0045 wt%, the morphology of MC carbide changes from script-like shape to blocky shape, the size increases and the volume fraction firstly increases but then decreases. Ti(C, N) is identified in the alloy with 0.0045 wt % N. 5. With the N content increasing from 0.0005 wt% to 0.0045 wt%, the ultimate and yield strength decrease at elevated temperature, and the ductile and stress rupture life firstly have a sharp decrease and then have a slight increase. The γ/γ′ eutectics and micro-porosities are prone to form cracks, and fine MC carbide can strengthen grain boundaries. Alloy N45 shows good mechanical properties due to the minimal volume fraction of γ/γ′ eutectic and porosity, and the minimal size of MC carbide. 6. Considering the microstructures and mechanical properties, the N content should be controlled as less as possible. Acknowledgements The authors would like to thank Northeastern University for the electron probe microanalysis facilities. This research did not receive any specific grant from agencies in the public, commercial, or not-for-profit sectors.
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