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Deformation Mechanism of Single-Crystal Nickel-based Superalloys During Ultra-High-Temperature Creep  PDF

  • Zhao Guoqi 1,2
  • Tian Sugui 1
  • Liu Lirong 1
  • Tian Ning 2
  • Jin Fangwei 2
1. School of Materials Science and Engineering, Shenyang University of Technology, Shenyang 110870, China; 2. School of Mechanical Engineering, Guizhou University of Engineering Science, Bijie 551700, China

Updated:2022-02-04

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Abstract

The creep behavior and deformation mechanism of the nickel-based single-crystal superalloy containing 6wt% Re and 5wt% Ru at ultra-high temperatures were studied via microstructure observation and creep property analysis. The results show that under the condition of 1160 °C/120 MPa, the Ni-based superalloy has a creep life of 206 h. During the steady state creep period, the deformation mechanism is dominated by dislocation glide in the γ matrix and dislocation climb over the γ′ raft phases. The refractory elements dissolved in the γ matrix can improve the resistance to dislocation movement. In the late creep stage, the cross-slip occurs from {111} plane to the {100} plane with the dislocations used for shearing the γ′ phase, and then the Kear-Wilsdorf (K-W) dislocation locks are formed. A large number of K-W dislocation locks can inhibit the dislocation glide and cross-slip, thus improving the creep resistance and reducing the strain rate for Ni-based superalloys. In the late creep stage, the cross-slip dislocations are initiated to twist the γ′/γ raft phases, and the crack initiation and propagation occur in the γ′/γ interfaces until fracture. These phenomena are the damage and fracture features of the Ni-based superalloys. The Ru atoms dissolved in the γ′ phase can replace the Al atoms. When Ru, Re, and W atoms react in the Ni-based superalloy, more Re and W atoms can be dissolved into the γ′ phase, which reduces the element diffusion rate and hinders the dislocation movement, thereby retaining more K-W dislocation locks and excellent creep resistance of Ni-based superalloys at ultra-high temperatures.

Science Press

With increasing the power and thrust-to-weight ratio of aeroengines, the materials for the hot-end parts of the engine are required for high-temperature bearing capacities[

1-3]. The addition of refractory elements, such as W, Mo, Ta, Re, and Ru, can enhance the temperature bearing capacity of alloys. When the Re content increases to 3wt% and 6wt%, the temperature bearing capacity of the alloys can be increased by 30 and 60 °C, respectively[4,5]. The specific Re content of 3wt% and 6wt% is the main composition feature of the second-generation and third-generation nickel-based single-crystal superalloys.

Re has a larger atomic radius and smaller diffusion coefficient than other refractory elements do. During creep, Re can maintain the structural stability and decrease the diffusion rates of other elements in the alloy[

6]. In particular, the heavy atoms Re and W are precipitated near the γ′/γ interface, which results in the lattice distortion and hindrance of dislocation movement, thereby improving the creep resistance of the alloys[7]. However, with increasing the Re content, more topologically close-packed (TCP) phases are precipitated. Once the TCP phase is precipitated from the alloys, the crack initiation and propagation occur easily in the area next to TCP phase during creep, so the creep performance can be greatly reduced[8]. The addition of Ru in Re-containing alloys can inhibit the precipitation of TCP phase[9] and greatly enhance the high-temperature creep properties[10-12]. In particular, the fourth-generation single-crystal nickel-based superalloys with 2wt%~4wt% Ru and 5wt%~6wt% Re show excellent mechanical properties and creep resistances at about 1100 °C[13]. As the Re/Ru content increases, the temperature bearing capacity of the alloys are greatly improved.

The single-crystal nickel-based superalloys have good high-temperature mechanical and creep properties with abnormal yield behavior of Ni3Al phase[

14], because during the thermal deformation, the cross-slip from the {111} plane to the {100} plane occurs with activated dislocations, forming the Kear-Wilsdorf (K-W) dislocation locks with a non-planar core structure. Because K-W dislocation locks can hinder the dislocation glide and cross-slip, the deformation resistance of superalloys is greatly improved[15]. However, as the temperature further increases, the dislocation in the K-W dislocation lock can be reactivated, causing the dislocation glide on the {111} plane again and breaking the K-W dislocation lock[16]. The addition of Re/Ru can increase the peak temperature of the abnormal yield behavior[17]. Only a small number of K-W dislocation locks are formed and retained in the single-crystal alloy containing 4.5wt% Re during creep at 1100 °C. More K-W dislocation locks are retained in the single-crystal alloy after adding 3wt% Ru[18], thereby enhancing the creep properties at high temperatures. However, with further increasing the Re/Ru content, it is still not clear whether the K-W dislocation locks are formed or retained during the ultra-high-temperature creep. It is reported that in the late creep stage of an alloy containing Re/Ru, the dislocations used for shearing the γ′ phase can be decomposed to form the incomplete dislocation+superlattice intrinsic stacking fault (SISF) configuration or the incomplete dislocation+anti-phase boundary (APB) configuration[19,20]. However, the creep behavior and deformation mechanisms of single-crystal nickel-based superalloys containing 6wt% Re and 5wt% Ru at ultra-high-temperatures are still unclear.

In this research, the single-crystal nickel-based superalloys containing 6wt% Re and 5wt% Ru were prepared to examine the creep behavior and deformation mechanisms at ultra-high temperatures. The creep tests and microstructure observations of the Ni-based superalloys under the condition of 1160 °C/120 MPa were conducted, and the dislocation configuration was also analyzed.

1 Experiment

The [001]-oriented nickel-based single-crystal superalloys with the dimension of 16 mm×190 mm were prepared via crystal selection method in a ZGD-2 vacuum directional solidification furnace under a high temperature gradient. The nominal chemical composition of the Ni-based superalloy was Ni-Al-Ta-Cr-Co-Mo-W-6.0wt% Re-5.0wt% Ru, namely 6%Re-5%Ru Ni-based superalloy. The orientation difference of all the specimens is within 7° from the [001] orientation. It is reported that the continuous heating and solution treatment of the alloy in the temperature range from the solid solution line to the solidus line can improve the homogeneity of the alloy and avoid the formation of incipient melting phase[

21].Therefore the heat treatment was as follows: 1300 °C-2 h+1310 °C-6 h+1315 °C-10 h+1323 °C-10 h+1328 °C-10 h+1332 °C-5 h+air cooling+1180 °C-4 h+air cooling+870 °C- 24 h+air cooling.

After heat treatment, the specimens were processed into sheet-like creep specimens with cross-sectional dimension of 4.5 mm×2.5 mm and gauge length of 20 mm. After mechanical grinding and polishing, the specimens were put into the CTM504A high-temperature creep/rupture testing machine before the creep tests at ultra-high-temperatures. The creep tests were conducted at 1160 °C/120 MPa for 5 and 100 h. The microstructures of the Ni-based superalloys were then observed.

After mechanical grinding and polishing, the etching solution of 5 g CuSO4, 100 mL HCl, 5 mL H2SO4, and 80 mL H2O was used. The scanning electron microscopy (SEM, S3400) was used to observe the specimen morphologies. The specimens after creep for different durations were analyzed by the transmission electron microscopy (TEM). The film specimens for TEM observation was 3 mm in length and about 60 µm in thicknesses. At -20 °C, an electrolyte of 7vol% perchloric acid and 93vol% anhydrous ethanol was used for double spray thinning. The microstructure of the Ni-based superalloy was observed via TEM (TECNAI-G20) to study the deformation mechanism during creep.

2 Results

2.1 Microstructure and creep properties

After the heat treatment, the microstructure on (001) plane of Ni-based superalloy consists of the cubic γ′ phase with a size of about 0.4 μm embedded in the γ matrix in a coherent manner, as shown in Fig.1. The cube with a dark contrast is the γ′ phase, which is arranged regularly along the [100] and [010] directions. The white structure along the vertical and horizontal directions is the γ matrix phase. The γ matrix channel has a size of about 0.1 μm.

Fig.1 Morphology of 6%Re-5%Ru Ni-based superalloy on (001) plane after entire heat treatment

The γ′ phase with fine grain can be observed in the γ matrix, as shown in the rectangular areas in Fig.1. During the long-term solution treatment at high temperature, the elements are completely dissolved into the matrix. However, during the subsequent cooling and secondary aging treatment at 870 °C, the supersaturation of solute elements Al and Ta causes the precipitation of fine particles of the γ′ phase from the matrix which has a cubic morphology and is arranged regularly along the [100] and [010] directions[

22].

Fig.2 shows the creep curve of the Ni-based superalloy after heat treatment and creep at 1160 °C/120 MPa. At the initial stage of creep, the Ni-based superalloy has a large strain, large strain rate, and a short duration. Then the creep of the Ni-based superalloy enters into the steady state stage, where the Ni-based superalloy has a strain rate of 0.0083%/h. The Ni-based superalloy has a creep life of 206 h and a creep fracture strain of 10.96%. Compared with the single-crystal Ni-based superalloy containing 4wt% Re and 4wt% Ru (creep life of 160 h at 1150 °C/100 MPa)[

23], this Ni-based superalloy shows better creep properties at ultra-high temperatures.

Fig.2 Creep curve of 6%Re-5%Ru Ni-based superalloy at 1160 °C/120 MPa

Under the applied stress at high temperature, the single-crystal Ni-based superalloy produces an instantaneous strain, which activates the dislocations to propagate rapidly, thereby filling the matrix channels between the cubic γ′ phases. With proceeding the creep process, the dislocation density of the Ni-based superalloy is increased. Furthermore, the deformation-hardening effect decreases the strain rate of the Ni-based superalloy. Meanwhile, the thermal activation causes the dislocation glide and dislocation climb, therefore releasing the stress concentration in the local area, and the recovery softening phenomenon occurs. When the deformation hardening and recovery softening effects are balanced, the creep of the Ni-based superalloy enters into the steady state stage, where the strain rate of the Ni-based superalloy is fixed, according to Dorn's law[

24].

2.2 Microstructure evolution during creep

When the Ni-based superalloy is heated to 1160 °C, the fine γ′ phases in the original heat-treated matrix are completely dissolved, and the cubic γ′ phase is regularly arranged along the <100> direction. SEM morphologies of the loaded area on the (100) crystal plane of the Ni-based superalloy treated at 1160 °C/120 MPa for different durations are shown in Fig.3. The black area represents the γ′ phase, and the gray area is the γ matrix phase. During high-temperature creep, the original cubic γ′ phase in the Ni-based superalloy is completely transformed into the raft structure, and its direction is perpendicular to the stress axis. The Ni-based superalloys have different morphologies, sizes, and distortion degrees of the γ′ phases due to different creep durations.

Fig.3 SEM morphologies of Ni-based superalloys after creep at 1160 °C/120 MPa for 5 h (a), 100 h (b), and 206 h (c)

After creep for 5 h, the original cubic γ′ phase of the Ni-based superalloy is completely transformed into an N-type raft structure perpendicular to the stress axis, as shown in Fig.3a. Both the γ′ raft phase and the γ matrix have the thicknesses of about 0.4 µm. The γ′ raft phase is relatively straight, but a few granular γ′ phases still exist. Compared with Fig.1, the area fraction of the γ′ raft phase on the (100) plane of Ni-based superalloy is significantly reduced, and more areas are occupied by the sieve-like γ′ phase on the (001) plane[

25]. After creep for 100 h, the Ni-based superalloy enters into the steady state stage of creep with the strain of about 2%. Due to the lower strain, the γ′ raft phase still retains a relatively straight morphology, but its thickness is increased to 0.6 µm (the thickness of γ matrix is still 0.4~5 µm) due to the coarsening of the γ′ phase in the Ni-based superalloy during long-term creep at high temperatures.

After creep for 206 h, due to the necking of the specimen near the fracture, the area under the applied stress is reduced, and the effective stress is further increased, resulting in the coarsening and twisting of the raft phase and increasing the thickness of γ′ raft phase to 0.7 µm. When the strain reaches 10%, the distortion of γ′ raft phase occurs, and the angle between the twisted γ′ raft phase and straight γ′ raft phase is increased to about 40°, as shown in Fig.3c.

Fig.4 shows TEM microstructures of the Ni-based superalloy after creep at 1160 °C/120 MPa for different durations. In the area A of Fig.4a, the microstructure changes significantly, and some γ′ phases show the raft structure along the direction perpendicular to the stress axis. The γ′ raft phase has a thickness of about 0.4 µm, but there are still some γ′ phases with the granular morphology, as shown in the area B of Fig.4a, which is in agreement with the results in Fig.3a. This phenomenon indicates that the element diffusion occurs in the Ni-based superalloy in the initial stage of creep, causing the transformation from the original cubic γ′ phase into the raft structure along the direction perpendicular to the stress axis. However, due to the insufficient element diffusion in a short time, some original cubic γ′ phases only suffer the corner passivation and are transformed into the spherical shape. In addition, the fine granular γ′ phases can be observed in the matrix, as shown in the rectangular area in Fig.4a, which is formed by the precipitation of supersaturated solute elements from the γ matrix during cooling. In this case, many dislocations are distributed in the γ matrix channel, no dislocations can be observed in the γ′ phase, and the γ′ phase is sheared by only a few dislocations.

Fig.4 TEM microstructures of Ni-based superalloys after creep at 1160 °C/120 MPa for 5 h (a), 100 h (b), and 206 h (c)

After creep for 100 h, the Ni-based superalloy is in the steady state stage of creep, as shown in Fig.4b. The γ′ phase exhibits the N-type raft structure perpendicular to the stress axis. The thickness of the γ′ raft phase increases to about 0.65 µm. Few dislocations can be observed in the γ′ raft phase, but there are many dislocation networks at the γ/γ′ interfaces. After creep for 206 h, the γ′ phases still retains the raft shape, but the thickness increases to about 0.8 µm in the local area. The area C in Fig.4c reveals that the γ′ raft phase is sheared by some dislocations. In the γ matrix, there are many dislocations. The fine granular γ′ phases can be observed in the γ matrix channel, as shown in area D in Fig.4c. In addition, the γ/γ′ interface has a large number of dislocation networks. The rectangular area in Fig.4c shows that the γ′ raft phase is sheared by dislocations at the interface. The dislocation network at the interface is damaged because the γ′ phase is sheared at the position of the dislocation network. The shear dislocations are along [011¯] and [011] directions at 45° to the stress axis and suffer the maximum shear stress of the applied load. These phenomena occur in the late stage of creep, and the Ni-based superalloy is considered to lose creep resistance in this area at this stage.

2.3 Contrast analysis of dislocation configuration

After creep for 206 h at 1160 °C/120 MPa, the morpho-logies far from fracture area are shown in Fig.5. The dislocations with the similar shapes along the trace direction parallel to [020] direction are marked by E, and other groups of dislocations along the same trace direction are marked as F1~F3. F4 indicates the dislocation loop with an extension direction of [020]. In addition, the dislocations with mutually perpendicular traces are denoted as G1 and G2, and their trace directions are parallel to the [022] and [022¯] directions, respectively. The trace direction of dislocation H is μH=[002].

Fig.5 Dislocation configurations of γ′ raft phase after creep for 206 h at 1160 °C/120 MPa based on different diffraction vectors:

(a) g=[020], (b) g=[002], and (c) g=[311]

Fig.5a shows that when the diffraction vector is g=[020], the dislocations E, F1~F4, and H display a contrast, whereas the dislocations G1 and G2 disappear. Based on the invisibility criterion of dislocations, the Burgers vectors of dislocations G1 and G2 are determined as bG1=bG2=a[101], and their trace directions are µG1=[022] and µG2=[02¯2], respectively. Therefore, the (111¯) plane and (111) plane are the glide planes of the dislocations G1 and G2, respectively. Fig.5c indicates that when the diffraction vector is g=[311], the dislocations G1 and G2 display a contrast, and dislocations E and F1~F4 disappear. Based on the invisibility criterion of dislocations, the Burgers vectors of dislocations E and F1~F4 are determined as bE=bF=a[011¯], and their trace directions are µE=µF=[020]. Hence, the glide planes of dislocations E and F1~F4 are bE×μE=bF×μF=(100). In addition, the dislocation E in the rectangular area in Fig.5b shows a double line contrast (denoted as dislocation E1), which is caused by the dislocation decom-position. The analysis shows that the a[011¯] dislocations activated during creep firstly glide on the {111} plane. When the dislocation glide is blocked, the cross-slip dislocation occurs from the {111} plane to the {100} plane and then the dislocations decompose on the (100) plane to form the (a/2)[011¯] incomplete dislocation. There is an APB between the two incomplete dislocations, as shown in the rectangular area in Fig.5b. The expression of the decomposition reaction can be described as follows:

a[011¯]E=(a/2)[011¯]E1+(APB) (100)
+(a/2)[011¯]E1 (1)

Other dislocations E and F1~F4 all glide on the (100) plane and show single line contrast because they do not decompose. When the diffraction vectors g=[020], g=[002], and g=[311], the dislocation H show a contrast in Fig.5a, 5b, and 5c, respectively. The trace direction of dislocation H is μH=[002]. Therefore, the Burgers vector of dislocation H can be uniquely determined as bH=a[011], and the glide plane is bH×μH=(100).

Therefore, the deformation mechanism of the 6%Re-5%Ru Ni-based superalloy in the late stage during ultra-high-temperature creep is that the γ′ phase is sheared by the dislocation glide in the matrix on the {111} plane or the {100} plane. The dislocations on the {100} plane all originate from the cross-slip of the {111} plane[

16]. The plane-angle cross-slip dislocation from the {111} plane to the {100} plane is regarded as the K-W dislocation lock, which is a fixed dislocation with the ability to inhibit the dislocations from glide and cross-slip and to enhance the creep resistance of the Ni-based superalloy. During the creep at 1160 °C, the cross-slip from the {111} plane to the {100} plane still occurs and then the dislocations decompose. Thus, the incomplete dislocation+APB configuration cannot be formed or even retained. It can be found that the number of dislocations gilding on the {111} plane is less than that on the {100} plane, and the dislocations on the {100} plane are all K-W dislocation locks formed by the cross-slip from {111} plane. Since the Ni-based superalloy can still form and retain a large number of K-W dislocation lock configurations during creep at 1160 °C, the good creep resistance of the Ni-based superalloy remains.

In the late stage of creep, the high-density dislocations accumulated in the matrix of the Ni-based superalloy cause damage to the dislocation networks on the γ/γ′ interface, as shown in Fig.4c. The stress concentration in the high-density dislocation area can cause the dislocations in the matrix to shear the γ′ phase in the damaged dislocation network area. As the creep proceeds, the dislocations suffer the bidirectional cross-slip along the direction of the largest shear stress under the maximum shear stress of the applied load, as shown in Fig.5c. In particular, the bidirectional cross-slip dislocations activated by the creep dislocations can cause the distortion of γ/γ′ raft phases in the Ni-based superalloy, leading to the crack initiation at the distorted interface. With further proceeding the creep process, the strain of Ni-based superalloy is increased and the cracks on the twisted γ/γ′ interface are further expanded along the direction perpendicular to the stress axis. Mutual connection of the crack propagation of different cross-sections via the tearing edge can cause the creep fracture of the Ni-based superalloy[

26,27].

3 Discussion

3.1 Hindrance of dislocation movement

In the early stage of ultra-high-temperature creep, the transformation from the cubic γ′ phase in the Ni-based superalloy into an N-type raft structure occurs. Fig.4b indicates that as the creep enters into the steady state stage, the phenomenon of γ′ raft phase being sheared by dislocations in the Ni-based superalloy does not happen. Meanwhile, the dislocation climb over the γ′ raft phase mainly contributes to controlling the strain rate in the steady state creep.

During the ultra-high-temperature creep, several effects hinder the dislocation movement in the Ni-based superalloy matrix: (1) the effect of the stress field produced by the high density of adjacent dislocations in the matrix (τi); (2) the barrier effect of the lattice distortion caused by the heavy atoms with large radius and Re groups dissolved in the matrix (τj). Through the combination of applied stress at high-temperature and thermal activation, the dislocation glide and dislocation climb are promoted, which proceeds the creep of the Ni-based superalloy. The force applied on the dislocation line during creep is denoted as f(x), where x denotes the dislocation glide distance. The external force is f=τRbl, where τR=τi+τj, b is the Burgers vector of the dislocation, and l is the length of dislocation line. When a thermal activation causes a dislocation to glide from position x1 to x2 and cross the barrier, the free energy change (∆G) of the system can be expressed as follows[

28]:

ΔG=x1x2fx-τbldx=ΔF-τebΔa (2)

where x1 and x2 are the starting and ending positions of the dislocation glide, τ is the external stress, τe is the effective stress, ΔF=x1x2fx-τbldx is the energy required for the dislocation to cross the barrier, and ∆a=lx is the area swept by the dislocation during the thermal activation process, namely activation area. The term τeba in Eq.(2) represents the energy provided by the effective stress. Thus, the strain rate of the Ni-based superalloy deformation caused by the dislocation glide can be expressed as follows:

ε˙=ε˙0exp-ΔGRT=ε˙0exp.-ΔF-τebΔaRT (3)

where ε0=mλv0, λ is the distance between obstacles, ρm is the dislocation density, ν0 is the vibration frequency of the dislocation, T is the thermodynamic temperature, and R is the Boltzmann constant. It can be concluded from Eq.(3) that the increase in temperature causes the gradual dissolution of fine γ′ phases in the Ni-based superalloy, the increase in spacing λ of the fine γ' phases, the decrease in dislocation density, and the increase in strain rate of the Ni-based superalloy.

3.2 Theoretical analysis of effect of Re/Ru addition on creep resistance

In the single-crystal nickel-based alloys, there are two phases with face-centered cubic (fcc) structure: the γ and the γ' phases. The dislocations activated during creep firstly glide on the {111} plane. There are dislocations on the {100} plane of the Ni-based superalloy during ultra-high-temperature creep, suggesting that the dislocations in the γ' phase can glide from the {111} plane to the {100} plane, i.e., the cross-slip occurs, and decomposes to form the K-W dislocation lock+APB configuration, as indicated bt the dislocations F1~F4 in Fig.5. The K-W dislocation lock and K-W dislocation lock+APB configurations can hinder the dislocation glide and cross-slip dislocation, thereby enhancing the deformation resistance of Ni-based superalloy. However, the thermal activation can cause the dislocation in the K-W dislocation lock to glide again on the {111} plane. So the dislocation in the K-W dislocation lock can be released. Therefore, with increasing the temperature, the retention of K-W dislocation locks in the γ′ phase is crucial for the Ni-based superalloy to maintain the good creep resistance.

Fig.6a shows the schematic diagram of the γ′ phase of rich-Re and rich-W being sheared by dislocations and the formation of K-W dislocation lock through the cross-slip from the {111} plane to the {100} plane, as indicated by the step 1, step 2, and step 3 in order.

Fig.6 Schematic diagrams of cross-slip dislocations from {111} plane to {100} plane (a) and dislocation decomposing on {100} plane before forming K-W dislocation locks+APB (b)

Under the stress field in ultra-high-temperature creep, the element diffusion and dislocation movement may occur simultaneously in the γ/γ′ phases. The refractory atoms, such as W, Mo, Re, and Ru, dissolved in the γ′ phase are precipitated in the γ/γ′ interface[

29] under high temperature and applied load, as denoted by the dotted circles in Fig.6a, which delays the element diffusion rate. During the ultra-high-temperature creep, the refractory atoms assembled near the interface can enter the γ matrix. In addition, the Ni-based superalloy suffers the plastic deformation during creep, causing many dislocations to shear the γ′ phase along the {111} plane, as shown by the step 1 and step 2 in Fig.6a. With proceeding the creep and element diffusion, the γ/γ′ interface moves to the side of the γ′ phase, and the W, Mo, Re, and Ru atoms on the {111} plane of the γ′ phase hinder the dislocation glide on the {111} plane. Thus, the cross-slip in the γ′ phase from the {111} plane to the {100} plane occurs, forming the K-W dislocation lock, as shown by the step 2 and step 3 in Fig.6a .

During the ultra-high-temperature creep, the hindrance of dislocations in the γ matrix moving to the γ/γ′ interface is improved, as the number of refractory elements remaining in the interface increases, as shown in Fig.6b. With proceeding the creep, many dislocations are stacked next to the γ/γ′interface, thereby generating the stress concentration, which promotes the dislocations to shear the γ′ phase and releases the stress concentration in the interface region[

30]. Because the Re and W atoms in the γ′ phase hinder the dislocation movement, the cross-slip from the {111} plane to the {100} plane occurs and the dislocations decompose before forming the APB, as shown in Fig.6b. Because the formed APB can also inhibit the dislocation movement, the critical shear stress (Δτ) for hindering the dislocation movement and for preventing the γ′ phase being shearing can be expressed as follows:

Δτ=Bμ(Δδ)b(cTrfηAPBt)1/2 (4)

where B is a constant related to the dislocation type (B=3 corresponds to edge dislocation; B=1 corresponds to screw dislocation), μ is the shear modulus, b is the Burgers vector of the dislocation, ∆δ is the mismatch degree, ηAPB represents the APB energy per unit area, t is the dislocation line tensor, r is the size of γ′ phase, f is the volume fraction of γ′ phase, and cT is the content of refractory element. According to Eq.(4), ∆τ is increased as the size of the γ′ phase, the volume fraction of the γ′ phase, and the content of refractory element are increased. Due to the high volume fraction of the γ′ phase and the high content of the refractory elements, the 6%Re-5%Ru Ni-based superalloy retains good creep resistance under ultra-high-temperature condition of 1160 °C/120 MPa.

4 Conclusions

1) The single-crystal nickel-based superalloy containing 6wt% Re and 5wt% Ru has good creep resistance at ultra-high temperatures. The deformation mechanism during steady state creep is the dislocation glide in the matrix and the dislocation climb over the γ′ raft phase.

2) The interaction of Ru with Re and W elements in the Ni-based superalloy with high content of Re and Ru causes a large number of Re and W atoms to dissolve into the γ′ phase, which delays the element diffusion rate and hinders the dislocation movement. This is the main reason that the Ni-based superalloys can retain a large number of Kear-Wilsdorf (K-W) dislocation locks during the creep at 1160 °C, therefore remaining the good creep resistance of Ni-based superalloy.

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