Stress rupture properties and deformation mechanisms of K4750 alloy at the range of 650 °C to 800 °C

1. Introduction

As the increase of engine thrust-weight ratio, the turbine inlet temperature is enhanced for improvement of aero-engine efficiency. Nickel based superalloys consisting of γ matrix and γ′ phase are widely used in aircraft engines and gas turbines owing to their unique high-temperature mechanical properties [[1], [2], [3], [4]]. Polycrystalline nickel based superalloys such as Inconel 718 [5], RR1000 [6,7], ME3 [8], U720Li [9,10] and TMW [[11], [12], [13]] alloys have been proposed for aircraft applications in the middle service temperatures. Inconel 718 alloy represents 60% in weight of the materials used for moving parts of turbo jet engines owing to its excellent properties at elevated temperature (650 °C) [5,14]. But Inconel 718 alloy is not enough to meet the higher temperature requirements because of the presence of δ-phase [15,16]. RR1000 and ME3 alloys are produced via the power metallurgy route for the disk application at temperature up to 720 °C, but the thermo-mechanical processing steps make the manufacturing process complex [11,12]. U720Li and TMW alloys [9,12,13] have been proposed for aircraft applications at elevated temperature up to 675 °C and 725 °C, respectively. However, U720Li and TMW alloys are prohibitively expensive due to high contents of Co (15-26 wt%). Therefore, a new cast nickel based superalloy [17,18] named as K4750 (developed by Institute of Metal Research, China) is developed for the aero-engines applications, it has the excellent mechanical properties at temperatures up to 750 °C.

Stress rupture resistance is a major concern for nickel based superalloys in typical service environments. The stress rupture properties of K4750 alloy depend on the coherent, ordered, intermetallic γ′ phase. This is because γ′ phase acting as obstacles effectively hinders the dislocation motion. In general, the dislocation motion is very complex because of the different interactions between dislocation and γ′ phase, including Orowan looping, cooperative climbing, dislocation pairs cutting (APB shearing; APB: anti-phase boundary), stacking faults shearing and micro-twinning [[19], [20], [21], [22], [23]]. The γ′ size, stress, temperature usually have a significant effect on these deformation mechanisms. For example, in nickel based superalloys, dislocation pairs cutting prevails at low temperature, while stacking faults shearing or Orowan bypassing is usually observed at elevated temperature [[23], [24], [25]]. Some articles have reported that the dominant deformation mechanism transfer from Orowan looping to the shearing of γ′ phase in a Ni-Fe-based superalloy as the further increasing temperature [[26], [27], [28]]. However, it is unclear whether there is the transition of deformation mechanism in K4750 alloy at the increase of temperature or stress. How the deformation mechanism affects the stress rupture life of K4750 alloy is also unclear.

In this study, the stress rupture properties of K4750 alloy were firstly measured at 650 °C, 700 °C, 750 °C and 800 °C for various stress levels. Then the dislocation configurations of stress rupture specimens were observed by means of Transmission electron microscopy (TEM), the aim was to reveal the deformation mechanism. Based on the experimental results, the threshold stress at 650 °C, 700 °C, 750 °C and 800 °C for the transitions of deformation mechanism was proposed. And the relationship between the deformation mechanism and the stress rupture life was discussed.

2. Experimental

The cast ingot of K4750 alloy was prepared via vacuum induction melting, and then was cast into the round bars. The chemical composition of K4750 alloy was determined by Inductively Coupled Plasma Atomic Emission Spectrometer (ICP-AES) and was 19.44Cr, 5.06Fe, 4.35(W + Mo), 4.39(Al + Ti), 1.58Nb, 0.12C, 0.006B and the balance Ni (wt%). Forty-two bars were prepared in this study. After casting, the same heat treatment regime given to all bars was 1120 °C for 4 h following by air cooling and 800 °C for 20 h following by air cooling. After the heat treatment, these bars were machined into stress rupture samples with a gauge length of 25 mm and a gauge diameter of 5 mm. Stress rupture tests were performed at 650 °C, 700 °C, 750 °C and 800 °C for different stress levels. Two stress rupture samples were tested under each condition, and the average value was used to determine the stress rupture life and elongation.

After testing, stress rupture samples were cut into discs along the vertical direction of the stress axial line and mechanically thinned down to 50 μm. After grinding, TEM specimens were prepared by twin-jet polish with a chemical solution composed of 10 vol.% HClO₄ and 90 vol.% C₂H₅OH at -20 °C and at a voltage of 24 V. Dislocation configurations resulting from the stress rupture deformation were investigated with Tecnai G² 20 TEM operating at 200 kV.

3. Results and discussion

3.1. Stress rupture properties of K4750 alloy

The stress rupture tests were carried out at 650 °C, 700 °C, 750 °C and 800 °C for different stress levels. Fig. 1(a) shows the relationship between stress rupture life and stress at different temperatures. It can be seen that the stress rupture life obviously increased with the decrease of stress, as shown in Fig. 1(a). But there was no clear regularity between stress-rupture life and elongation, as shown in Fig. 1(b). Nevertheless, K4750 alloy had a certain plastic because the elongation of all stress rupture samples exceeded 4.0%.

Based on the theory of creep in metallic materials [29], the relationship between stress and the stress rupture life can be formulated as follows:

τ=Cσ^-m (1)

where τ is the stress rupture life (h), σ is the stress (MPa), C is a constant, m is the stress index and is also considered to be an constant. Eq. (1) is calculated with the logarithmic function and can be simplified as:

logσ=A+Blogτ (2)

where both A and B are constants related to the stress rupture temperature. Eq. (2) demonstrates that there is a linear relationship between logσ and logτ, thus the linear regression analysis of Origin software was applied to K4750 alloy. Based on the measured value of stress rupture life, which was marked by the different-shaped dots in Fig. 1(a), the fitting lines at 650 °C, 700 °C, 750 °C and 800 °C were obtained. Meanwhile, the value of A and B, and the corresponding standard error (SE) and coefficient of determination (R²) at different temperatures were identified, as listed in Table 1. The coefficient of determination R² indicated that the degree of linear fitting was high.

In order to establish the relationship among temperature, stress and the stress rupture life, the well-known Larson-Miller method was applied to K4750 alloy. The general formula of Larson-Miller parameter (LMP) could be written as:

LMP=(T+273.15)×(logτ+C₁)×10^-3 (3)

where T is temperature (°C), τ is the stress rupture life (h), C₁ is a constant and it is about 20 for Nickel based superalloys [3,11,30]. The data of K4750 alloy were analyzed by Eq. (3), and the relationship between stress and LMP was plotted by a scatter diagram. According to these different-shaped dots, the linear regression analysis of Origin software was carried out again. The fitting result indicated that there existed a good linear correlation between stress (σ) and LMP, as shown in Fig. 2. And the linear formula could be derived as: σ = 3166.455-119.969 × LMP, the fitting coefficient R² was 0.98. According to the fitting result, the stress rupture life of K4750 alloy could be predicted when the temperature and stress were given.

3.2. Stress rupture deformation microstructures at intermediate temperatures

After heat treatment, K4750 alloy had a typical microstructure consisting of γ matrix, fine spherical γ′ phase, blocky MC and granular M₂₃C₆ carbides [17,18]. γ′ phase was distributed uniformly in γ matrix, MC carbide was distributed randomly in the grain interiors or at grain boundaries, while M₂₃C₆ carbide was only precipitated at grain boundaries. In this work, all stress rupture samples were carried out the same heat treatment, so the microstructural characteristics were considered to be similar before stress rupture testing. Our previous studies showed that the morphology, size, distribution of MC and M₂₃C₆ carbides were basically unchanged before long-term aging at 700 °C or 750 °C for 3000 h [17,18]. The stress rupture life of most samples was lower than 3000 h in this work, so the effect of MC and M₂₃C₆ carbides on the stress rupture life was considered to be small. The γ′ size was confirmed to have a significant impact on the deformation mechanism of nickel base superalloys [23,31]. The average diameter of γ′ phase was fixed after the same heat treatment, but γ′ phase grew up gradually in the process of stress rupture testing, the influence of γ′ size on the deformation mechanism would be discussed in the following. Besides γ′ size, the temperature and stress had a significant effect on the deformation mechanism, which would be investigated first.

After stress rupture deformation at 650 °C, the microstructures were presented in Fig. 3 and Fig. 4. The dislocation features were basically the same after testing at 650 °C/650 MPa and 650 °C/680 MPa, as shown in Fig. 3. In the initial stage of deformation, the dislocations were first slipped in γ matrix, then stopped at γ/γ′ interfaces because the ordered L1₂γ′ phase acted as effective obstacles for dislocation motion. As the deformation continued, some dislocations bypassed γ′ phase and some Orowan loops were formed around these γ′ phase, as marked by blue arrows in Fig. 3. Beyond that, the loading stress could assist the a/2 < 110> matrix dislocations undergo reactions that resulted in <112 > -type dislocations that were able to penetrate into γ′ phase [21]. Thus some other dislocations sheared γ′ phase and stacking faults were left inside these γ′ phase, as indicated by red arrows in Fig. 3. Therefore, Orowan looping and stacking faults shearing were generated simultaneously during stress rupture tests at 650 °C/650 MPa and 650 °C/680 MPa.

After stress rupture testing at 650 °C/705 MPa, almost all γ′ phase were sheared by dislocations with leaving stacking faults inside them, as shown in Fig. 4(a) and (b). This might be because the resolved shear stress acting on γ/γ′ interfaces exceeded the critical interface stress when the loading stress increased. For K4750 alloy, the stress rupture life decreased significantly when stacking faults shearing acted as the dominant mechanism [18]. In some nickel based superalloys, the γ′ phase with many stacking faults staying inside was also difficult to provide the strengthening effect [[26], [27], [28]]. Hence, γ′ phase would be very difficult to impede the dislocation motion if stacking faults shearing was dominant. As the loading stress increased from 650 MPa to 680 MPa and finally to 705 MPa, stacking faults shearing gradually replaced Orowan looping and finally acted as the dominant mechanism, so the stress rupture life of K4750 alloy decreased from 844.5 h to 689.5 h and finally to 319.1 h. After stress rupture testing at 650 °C/740 MPa, numerous slip-bands resulting from a large extent of plastic deformation were generated in the grain interior, as shown in Fig. 4(c). Owing to the further increase of loading stress, γ′ phases were cut by dislocations more easily and many stacking faults were left inside these γ′ phases, so the stress rupture life was decreased greatly to 64.7 h.

After stress rupture deformation at 700 °C for 400 MPa, 530 MPa, 590 MPa and 620 MPa, the dislocation configurations of specimens were shown in Fig. 5. During testing at 700 °C for 400 MPa, 530 MPa, 590 MPa and 620 MPa. During testing at 700 °C/400 MPa, dislocations firstly bypassed around γ′ phases then many Orowan loops were formed around these γ′ phases. As dislocations continued to glide, the dislocations tended to form Orowan loops around those γ′ phases having been surrounded by Orowan loops before. In other words, double Orowan looping process occurred around single γ′ phase, as indicated by blue arrows in Fig. 5(a) and (b). The result showed that the γ′ phases surrounded by Orowan loops were still able to impede the dislocation motion effectively. In addition, some gliding dislocations with long segment formed a relatively larger dislocation loop, which surrounded two or several γ′ phases together, as denoted by yellow arrows in Fig. 5(b). These larger loops would make the movement of dislocation more difficult. That was because the large loops would need higher energies to bypass two or more γ′ phases, and then to form an individual Orowan loop around single γ′ phase again. Hence, γ′ phases acting as obstacles effectively hindered the further motion of the gliding dislocations, which could make a great strengthening effect, so K4750 alloy obtained a long stress rupture life (2727.2 h).

During testing at 700 °C/530 MPa, many Orowan loops were formed around single γ′ phase, as shown in Fig. 5(c). Similarly, some dislocations with long segment bowed out and tended to form the large loops around two or more γ′ phases. Thus lots of γ′ phases effectively hindered the dislocation motion through Orowan looping process. Besides, a few γ′ phases were cut by dislocations and stacking faults were left inside these γ′ phases, as denoted by red arrows in Fig. 5(c). In other words, a few γ′ phases impeded the dislocation motion through stacking faults shearing instead of Orowan looping. This phenomenon demonstrated that γ′ phase shearing began to generate because the resolved shear stress, which acted on the γ/γ′ interfaces, might exceed the critical interface stress. Therefore, Orowan looping still acted as the dominant deformation mechanism but γ′ phase shearing started to occur at 700 °C/530 MPa.

After testing at 700 °C/590 MPa, many γ′ phases were sheared by dislocations then left stacking faults inside them, and a few Orowan loops still generated around some γ′ phases, as shown in Fig. 5(d) and (e). The increasing loading stress helped the dislocations penetrating into γ′ phases by means of dislocation reactions. Therefore, stacking faults shearing combining Orowan looping acted as the dominant deformation mode at 700 °C/590 MPa. When the loading stress increased to 620 MPa, almost all of γ′ phases were sheared by moving dislocations with the creation of stacking faults inside these γ′ phases, as shown in Fig. 5(f). Hence, stacking faults shearing was the dominant deformation mechanism at 700 °C/620 MPa.

Based on the above results, the dominant deformation mechanism gradually changed from Orowan looping to stacking fault shearing as the increase of loading stress at 700 °C. In K4750 alloy, γ′ phases effectively hindered the dislocation motion by Orowan looping process and resulted in a great strengthening effect, but γ′ phases with stacking faults staying inside provided a low strengthening effect. Therefore, the stress rupture life of K4750 alloy was dropped from 2727.2 h to 301.1 h and finally to 59.4 h as the loading increasing from 400 MPa to 530 MPa and finally to 620 MPa at 700 °C.

After stress rupture deformation at 750 °C for 320 MPa, 360 MPa, 400 MPa, 430 MPa and 505 MPa, the dislocation configurations of specimens were shown in Fig. 6, Fig. 7. In the process of deformation at 750 °C/320 MPa, Orowan looping acted as the dominant mechanism. Specially, the large Orowan loops surrounding two or more γ′ phases could be generated, as denoted by yellow arrows in Fig. 6(a) and (b). The large Orowan loops made the subsequent movement of dislocations more difficult. Therefore, γ′ phases effectively enhanced the alloy strength, and K4750 alloy obtained a long stress rupture life (1445.2 h). After testing at 750 °C /360 MPa and 750 °C/400 MPa, Orowan loops around single γ′ phase were mainly observed, so Orowan looping was still the dominant mechanism. As the loading stress increased to 430 MPa, most of γ′ phases were bypassed by Orowan loops, but a few γ′ phases started to be cut by the gilding dislocations with leaving stacking faults inside them. The appearance of stacking faults demonstrated that the loading stress provided enough energy to help the moving dislocations penetrating into some γ′ phases. Nevertheless, most of γ′ phases were bypassed by Orowan loops. Therefore, Orowan looping combing stacking faults shearing acted as the dominant deformation mechanism at 750 °C/430 MPa.

The dislocation configurations of stress rupture specimen at 750 °C/505 MPa were given in Fig. 7. Under this high stress condition, well-defined slip bands were distributed in the grain interior owing to the large extent of plastic deformation, as shown in Fig. 7(a). Besides, extended stacking faults passing both γ matrix and γ′ phases were generated, as shown in Fig. 7(b). Dislocation pairs could be also found in the specimen, as shown in Fig. 7(c). Dislocation pairs shearing γ′ phases is one of important precipitation-hardening effects. The reason is that a a/2〈110〉{111} dislocation travelling in γ matrix cannot enter γ′ phase without APB forming when dislocations travel through γ/γ′ structure in pairs [[31], [32], [33]]. In addition, a few dislocations bypassed γ′ phases via Orowan looping process, as marked by blue arrows in Fig. 7(d). Therefore, stacking faults shearing combing Orowan looping was the dominant deformation mechanism at 750 °C/505 MPa. Fig. 6, Fig. 7 show that the dominant deformation mechanism also gradually changed from Orowan looping to stacking fault shearing as the increase of stress at 750 °C. Thus, the stress rupture life was dropped from 457.7 h to 151.2 h and finally to 37.4 h as the stress increasing from 360 MPa to 430 MPa and finally to 505 MPa at 750 °C.

Similar analyses were applied to the stress rupture tests at 800 °C for 150 MPa, 250 MPa, 300 MPa and 350 MPa, the corresponding dislocation configurations were shown in Fig. 8. The remarkable feature of dislocation configurations revealed that Orowan loops were mainly observed in the specimens after stress rupture testing at 800 °C/150 MPa, 800 °C/250 MPa and 800 °C/300 MPa. Besides, a few dislocations climbing up γ′ phases could be also observed after stress rupture deformation at 800 °C/150 MPa. One important reason was that vacancies could diffuse into the dislocation cores which allowed dislocations to climb up γ′ phases since the stress and vacancy concentrated at γ/γ′ interfaces [20,27]. Another important reason was that some activated dislocations had enough long time to climb over γ′ phases because of the long stress rupture life (5822.0 h) under this circumstance. Thus, some dislocations accumulating at γ/γ′ interfaces could move forward by means of climbing up γ′ phases. Based on these results, Orowan looping combining climb acted as the dominant mechanism at 800 °C/150 MPa, and Orowan looping was the dominant mechanism at 800 °C/250 MPa and 800 °C/300 MPa.

When the loading stress increased to 350 MPa at 800 °C, Orowan looping around γ′ phases was still active, meanwhile some γ′ phases were sheared by dislocations and stacking faults were left inside these γ′ phases. Specially, some dislocations with long segment bowed out, and tended to form a respectively large loop around two or more γ′ phases, as marked by yellow arrows in Fig. 8(e) and (f). These loops suggested that γ′ phases be able to impede the dislocation motion. However, stacking faults shearing decreased the resistance of γ′ phase to the dislocation motion. Therefore, Orowan looping combining stacking fault shearing was the dominant mechanism at 800 °C/350 MPa, and the stress rupture life dropped. Above all, the dominant mechanism gradually transformed from Orowan looping to stacking fault shearing, so the stress rupture life was decreased from 5822.0 h to 495.1 h and finally to 61.1 h as the stress increasing from 150 MPa to 250 MPa and finally to 350 MPa at 800 °C.

3.3. Relationship among deformation mechanism, stress and temperature

The γ′ precipitation strengthening of K4750 alloy was controlled by two main deformation mechanism, i.e. Orowan looping and stacking fault shearing, which mainly depended on the loading stress and temperature. Based on experimental results, the relationship among the dominant deformation mechanism, temperature and stress had been illustrated schematically, as shown in Fig. 9. At a given temperature, the deformation mechanism gradually changed from Orowan looping to stacking fault shearing with the increase of loading stress, according to which the threshold stress could be determined. Fig. 9 shows that the threshold stress for the transition of the deformation mechanism gradually decreased as temperature increasing, the value of which was estimated to decrease from 650 MPa to 350 MPa with the temperature increasing from 650 °C to 800 °C. Below the threshold stress, Orowan looping was the dominant mechanism. Slightly above the threshold stress, Orowan looping combining stacking fault shearing was the dominant mechanism. As the further increase of loading stress, stacking fault shearing was the dominant mechanism. In addition, there existed a certain linear relationship between stress and temperature, as indicated in Fig. 9 by dotted lines. Therefore, there was a threshold temperature for the transition of dominant mechanism at a given loading stress, which could be predicted by the dotted line in Fig. 9. For example, the threshold temperature at 600 MPa, 500 MPa and 400 MPa that the dominant mechanism began to transfer from Orowan looping to stacking fault shearing was inferred to be about 660 °C, 710 °C and 760 °C, respectively.

In the process of stress rupture testing, γ′ phase grew up, and the γ′ size increased gradually. According to the literature reports [21,32,34], the γ′ size-dependent critical resolved shear stress (CRSS) values have been estimated using the following equations:

$\tau_{cs}=\sqrt\frac{3}{2}\frac{Gb}{r}f^{1/2}\frac{w}{π^{3/2}}(\frac{2πγAPBr}{wGb^{2}}-1)^{1/2}$ (4)

$τ_{co}=\frac{Gb}{l}$ (5)

where τ_cs and τ_co are critical resolved shear stresses for γ′ shearing and Orowan looping, respectively, G is the shear modulus, b is the Burgers vector, r is the particle radius of γ′ phase, f is the volume fraction of γ′ phase, l is the inter-particle spacing, γ_APB is the anti-phase boundary energy, w is a dimensionless constant and it is taken to be 1 in this case.. The CRSS value for Orowan looping around fine γ′ phase was significantly higher than that for shearing fine γ′ phase. The Orowan looping mechanism was preferred when the γ′ size was beyond a critical value. When the γ′ size was comparable to the critical value, both Orowan looping and γ′ shearing mechanisms were active. During deformation, the γ′ size increased gradually as the increase of stress rupture life. Hence, the long stress rupture life was good for Orowan looping mechanism. The γ′ coarsening of K4750 alloy was affected by the elements diffusion, longer time and higher temperature were more helpful to accelerate the diffusion of elements [18]. Thus the γ′ size at high temperatures grew up faster than that at low temperatures. Hence, the CRSS value for Orowan looping was obtained more quickly during deformation at high temperatures owing to the faster coarsening rate of γ′ phase. For instance, the stress rupture life was about 61.1 h, 151.2 h and 844.5 h when specimens were tested at 800 °C/350 MPa, 750 °C/430 MPa and 650 °C/650 MPa, respectively. After testing at above three conditions, the γ′ size was basically the same, Orowan looping was the dominant mechanism and stacking fault shearing started to generate. That was to say, the CRSS value for Orowan looping could be obtained under low stress conditions when the temperature increased and the effect of γ′ size was small. Above all, the CRSS analysis could provide a good proof for explaining that the threshold stress for the transition of deformation mechanism decreased with the increasing temperature.

4. Conclusions

The stress rupture life and deformation mechanisms of K4750 alloy at 650 °C, 700 °C, 750 °C and 800 °C with different stress levels. Based to experimental results, the following conclusions were made as follow:

(1)At a given temperature, the stress rupture life (τ) of K4750 alloy obviously increased with the decrease of stress (σ), and there existed a linear relationship between logσ and logτ. There was also a linear relationship between stress (σ) and Larson-Miller Parameter (LMP), the linear fitting formula was derived as σ = 3166.455-119.969 × LMP, the fitting coefficient was 0.98.

(2)When the loading stress increased at a given temperature, the deformation mechanism gradually changed from Orowan looping to stacking fault shearing. Based on experimental results, the threshold stress that the deformation mechanism began to transfer from Orowan looping to stacking fault shearing was estimated to be about 650 MPa, 530 MPa, 430 MPa and 350 MPa at 650 °C, 700 °C, 750 °C and 800 °C, respectively.

(3)Below the threshold stress, γ′ phase effectively inhibited the dislocation motion by means of Orowan looping process, K4750 alloy had a long stress rupture life. Slightly above the threshold stress, Orowan looping combining stacking fault shearing was the dominant mechanism, the resistance of γ′ phase to the dislocation motion decreased and the stress rupture life dropped. As the further increase of loading stress, the shearing of γ′ phases was more and more easy, these γ′ phases with stacking faults staying inside provided a low strengthening effect, so the stress rupture life reduced significantly.

Acknowledgements

The authors would like to sincerely thank Prof. Shunnan Zhang for discussing the results, and thank Mr. Zhanhui Du for providing the materials.

The authors have declared that no competing interests exist.

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