“Ʌ”-shaped trend of stress relaxation stability of Inconel718 superalloy with initial stress increasing

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“Ʌ”-Shaped Trend of Stress Relaxation Stability of Inconel718 Superalloy with Initial Stress Increasing Jing Yang , Jianxin Dong , He Jiang , Zhihao Yao PII: DOI: Reference:

S2589-1529(19)30366-7 https://doi.org/10.1016/j.mtla.2019.100570 MTLA 100570

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Materialia

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27 October 2019 14 December 2019

Please cite this article as: Jing Yang , Jianxin Dong , He Jiang , Zhihao Yao , “Ʌ”-Shaped Trend of Stress Relaxation Stability of Inconel718 Superalloy with Initial Stress Increasing, Materialia (2019), doi: https://doi.org/10.1016/j.mtla.2019.100570

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“Ʌ”-Shaped Trend of Stress Relaxation Stability of Inconel718 Superalloy with Initial Stress Increasing Jing Yang*, Jianxin Dong, He Jiang, Zhihao Yao School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China

Graphical abstract



Corresponding author

E-mail: [email protected] (Jing Yang)

ABSTRACT: Stress relaxation tests were carried out to identify stress relaxation behavior of Inconel718 superalloy under different initial stresses. Experimental results indicate that: increasing initial stress from 260 MPa to 1160 MPa, stress relaxation stability of Inconel718 superalloy rises firstly and then falls. Above all, thermodynamic models of stress relaxation under different initial stresses are constructed, and the release of elastic strain energy density (△W) and release ratio of elastic strain energy density (η) are identified to quantify thermodynamic characteristics of stress relaxation. The trends of △W and η demonstrate that plastic deformation decreases firstly and then increases with initial stress increasing. Besides, constitutive equation and relevant parameters are used to describe kinetic characteristics of stress relaxation behavior. Plastic strain rate increases continuously, but the tendency of stress exponent suggests that work hardening strengthens in the beginning and then weakens remarkably. Due to the coupling effect between the two factors, the accumulation of plastic deformation drops firstly and then rises significantly. Finally, based on microstructure evolution, it can be found that, at low initial stress, stress relaxation consists of two stages, and dislocation movement and grain boundary migration are dominant mechanisms of stress relaxation. While at high initial stress, stress relaxation can be divided into three stages. Twinning is the main mechanism in the first stage, leading to obvious plastic deformation. When it comes to the second stage, dislocation movement and grain boundary migration are dominant reasons. Eventually, stress relaxation achieves the third stage, referred to as the steady state. Key words: Inconel718; Stress relaxation; Thermodynamics; Kinetics; Mechanism

1. Introduction Inconel718 superalloy is widely used as high-temperature fasteners in the field of aerospace due to its excellent high-temperature performance, including outstanding corrosion resistance, good mechanical properties and so on [1-4]. For fasteners, loosening of the connection is a major failure mode under the long-term service conditions at high temperature [5]. In addition, the rapid development of the aerospace science and technology nowadays has already put forward tougher requirements for high-temperature fasteners in mechanical properties [6-8], especially stress

relaxation stability, which can better reflect the characteristics of fastener materials and is also an important parameter to judge whether fasteners are in the normal service condition [9]. Therefore, it is of great significance to study stress relaxation behavior and mechanisms of Inconel718 superalloy deeply and systematically. Up to now, there have already existed a considerable number of researches related to stress relaxation. Stress relaxation means that under a certain temperature and initial stress, total strain is constant, while stress drops with time. In essence, it is the process during which elastic strain transforms into plastic strain [10]. Gjestland et al. [11] and Vierreck et al. [12] pointed out that creep constitutive equation could be applied to the analysis of stress relaxation, and this equation was helpful to calculate important parameters for describing the characteristics of stress relaxation, including plastic strain rate, stress exponent, threshold stress and so on. Xusheng et al. [13] carried out stress relaxation tests on nanostructured copper and studied the effect of temperature, initial stress, and cycles number on activation energy, activation volume, and stress exponent by analyzing stress relaxation curves. They also built up a formula to quantify the time, stress, and temperature-dependent deformation. In addition, stress relaxation behavior and mechanisms differ with the variation of alloy types as well as testing conditions. Mohammad et al. [14] studied multiple-cycle stress relaxation and flow behavior of ultra-fine-grained AA 1050. For this alloy, stress relaxation stability decreased with the increase of cycles, and this was attributed to recovery softening. M.V. Nathal et al. [15] found that precipitates of CMSX-4 and EFM-102 single crystal superalloys coarsened during stress relaxation tests, and this was the dominant mechanism of stress relaxation of the two single crystal superalloys. While for copper alloys in the Cu–Ni–Sn system, recrystallisation in local regions was the main reason for stress relaxation [16]. Besides, stress relaxation tests were also used to analyze residual stress in alloys [17], describe the characterization of precipitation kinetics [18,19], and identify design stress level for turbines [20,21]. However, researches related to stress relaxation behavior and mechanisms of Inconel718 superalloy are relatively rare. What induces the occurrence of stress relaxation of Inconel718 superalloy under different testing conditions? What rules does stress relaxation behavior obey? And what is the underlying mechanism of stress relaxation? Answers to these questions are all still

unclear at present. Therefore, it is vital to conduct a series of experiments to further study stress relaxation behavior and mechanisms of Inconel718 superalloy to meet the requirements in theoretical research and practical use for high-temperature fasteners. In the present work, we then aim to cope with the above questions. Stress relaxation tests were carried out in the stress range of 260~1160 MPa to identify the basic rules of stress relaxation stability by the analysis of stress relaxation curve. Subsequently, stress relaxation behavior under different testing conditions was interpreted in terms of thermodynamics to account for the root causes of stress relaxation, and then kinetic regulations of stress relaxation under different testing conditions were summarized using constitutive equation. Finally, stress relaxation mechanisms of Inconel718 superalloy under different initial stresses were revealed after observing microstructure evolution by Field Emission Scanning Electron Microscope (FESEM) and Transmission Electron Microscope (TEM). 2. Materials and methods The investigated Inconel718 superalloy was obtained by vacuum induction melting (VIM) and vacuum arc remelting (VAR). Then, standard heat treatment was conducted on materials, including: 980°C±10°C×1h/AC → 720°C±10°C×8h/FC(50°C±10°C/h) → 620°C±10°C×8h/AC. Chemical composition (in wt %) of the Inconel718 used in this work is shown in Table 1. Table 1 Chemical composition of Inconel718 superalloy (in wt %) elements

C

Cr

Nb

Mo

Ti

Al

Fe

Ni

fraction/%

0.05

19.00

5.30

3.00

1.00

0.50

18.15

Bal.

Materials used in tests were machined into standard samples 25 mm in gauge length and 5 mm in

diameter

according

to

GB/T 10120-2013

“Metallic

Materials

–

Tensile

Stress

Relaxation-Method of Test”, and stress relaxation tests were conducted on the RMT-D5SC Electronic High-temperature Stress Relaxation Test Machine. The test could be divided into three stages, including heating to the testing temperature, loading initial stress, and carrying out stress relaxation test. After setting the testing parameters (temperature, initial stress, and time), stress relaxation test started and then RMT-D5SC Electronic High-temperature Stress Relaxation Test

Machine recorded stress variation with time automatically during the test, and these experimental data were mathematically analyzed by Origin software to quantify stress relaxation stability. Tests held for 6000 min were performed at initial stresses of 260 MPa, 380 MPa, 510 MPa, 765 MPa, 1020 MPa (σs, yield strength), 1090 MPa, 1160 MPa (σb, ultimate tensile strength) at temperature of 650 °C to explore the effect of initial stress on stress relaxation behavior of Inconel718 superalloy. After tests, specimens were divided into two parts along the middle cross section by wire-cut electrical discharge machine (WEDM). Cylindrical samples with the size ofφ5×10 mm were machined from either of the two parts, and the middle cross section was chosen as observation surface. Subsequently, cylindrical samples were electro-etched in a solution of H3PO4 (150 ml) + H2SO4 (10 ml) + CrO3 (15 g) after being ground and polished for microstructure observation using ZEISS SUPRA55 Field Emission Scanning Electron Microscope (FESEM). In addition, samples after stress relaxation were prepared for Transmission Electron Microscope (TEM) studies to gain a better understanding of stress relaxation mechanism. Slices of 0.3 mm in thickness were cut transverse to the loading direction using an electric-discharge machine (EDM), and were ground to a thickness of 0.05 mm afterwards. Disks of 3 mm in diameter were cut from the thinned wafers and TEM foils were prepared by electropolishing these disks in a Fishione twin jet unit using a solution of 10% HClO4 in ethanol with a voltage of 35V at 20 °C. Then, FEI Tecnai G2 20 TEM operating at 200 kV was employed for more detailed investigations on samples. 3. Results 3.1 stress relaxation curves Fig.1 shows stress relaxation curves of Inconel718 superalloy under different initial stresses at temperature of 650 ℃. The following characteristics can be observed: stress decreases sharply at first. Subsequently, stress relaxation rate (the slope of stress relaxation curve) slows down, and then stress relaxation curves tend to be in the steady state in the end. However, there also exist some differences among stress relaxation curves under different initial stresses.

Fig.1. Stress relaxation curves of Inconel718 superalloy under different initial stresses at temperature of 650 ℃. When initial stress is less than 510 MPa (50% σs), stress reductions during stress relaxation tests are small, and stress relaxation curves can achieve the steady state quickly, especially when initial stress is 510 MPa (achieving the steady state less than 500 min with lower stress reduction). While increasing initial stress to 765 MPa (75% σs), stress relaxation curve obtains the steady state at the 3000th min or so with larger stress reduction. Continuously increasing initial stress to 1020 MPa (σs), 1090 MPa, and even 1160 MPa (σb), stress decreases rapidly with higher stress relaxation rate in the beginning, and then there still exists a marked linear dropping trend for a long time. After that, stress relaxation curves obtain the steady state gradually almost at the 5000th min. It’s obvious that stress reduction increases remarkably when initial stress is higher than yield strength. In order to further explore the trend of stress relaxation stability of Inconel718 superalloy under different initial stresses, it’s necessary to quantify stress relaxation stability with specific parameters, including stress relaxation limit (σr), relaxation stability coefficient (S), and total relaxation stress (△σt). 3.2 stress relaxation stability Stress relaxation limit and relaxation stability coefficient are important parameters to estimate stress relaxation stability of superalloys, and the higher the value of σr and S, the better the stress relaxation stability (calculation method reference literature [5,10]). In addition, identifying total relaxation stress, △σt:

△σt = σo - σr

(1)

Where σo and σr represent initial stress and stress relaxation limit, and the higher the value of △σ t, the worse the stress relaxation stability.

Fig.2. Stress relaxation stability of Inconel718 superalloy under different initial stresses at temperature of 650 ℃: (a) stress relaxation limit (σr) and total relaxation stress (△σt); (b) relaxation stability coefficient (S). Fig.2 shows the trends of stress relaxation limit, total relaxation stress, and relaxation stability coefficient of Inconel718 superalloy under different initial stresses at temperature of 650 ℃. Increasing initial stress from 260 MPa to 510 MPa, stress relaxation limit increases (117.3 MPa to 485.7 MPa), while total relaxation stress decreases (142.7 MPa to 24.3 MPa) (Fig.2 (a)). In addition, relaxation stability coefficient increases significantly from 0.21 to 0.84 (Fig.2 (b)). These data demonstrate that stress relaxation stability of Inconel718 superalloy rises with the growth of initial stress within the stress range between 260 MPa to 510 MPa. However, when initial stress is higher than 510 MPa, the increase of initial stress leads to the rise of total relaxation stress (219.7 MPa to 613.0 MPa) but with mere changes of stress relaxation limit (Fig.2 (a)). Meanwhile, relaxation stability coefficient falls from 0.57 to 0.31 (Fig.2 (b)). On the basis of these data, it can be deduced that, increasing initial stress from 510 MPa to 1160 MPa, stress relaxation stability of Inconel718 superalloy deteriorates. To sum up, with the growth of initial stress, stress relaxation limit increases significantly at first and then changes slightly; total relaxation stress falls firstly and then rises; while relaxation stability coefficient increases remarkably in the beginning and decreases subsequently. Namely, stress relaxation stability of Inconel718 grows firstly and then drops, appearing to be a

“Ʌ”-shaped trend. 3.3 Microstructure evolution

Fig.3. Microstructures of Inconel718 superalloy before and after stress relaxation tests, showing shapes and distributions of δ phase, γ′′ phase and γ′ phase (the insets in the upper right corner of Fig.3), and grain boundary (the insets in the lower right corner of Fig.3): (a) as-heat-treated; (b) 650 ℃-510 MPa; (c) 650 ℃-1020 MPa; (d) 650 ℃-1160 MPa. Fig.3 presents microstructures of Inconel718 superalloy before and after stress relaxation tests under different initial stresses at temperature of 650 ℃. Microstructure of as-heat-treated Inconel718 superalloy has the following characteristics (Fig.3(a)): the average grain size is about 10 μm; short-rod δ phase distributes along grain boundaries or in the grains, with the average width of 0.45 μm, the average length of 0.86 μm; γ′′ phase, the main strengthening phase in the shape of ellipsoid, with the dimensions of 45 nm in length and 20 nm in width, distributes evenly in the grains; γ′ phase, in the shape of sphere with the diameter of 18 nm, also distributes evenly in the grains. Interestingly, after stress relaxation tests held for 6000 min under different initial stresses at temperature of 650 ℃, even at initial stress of 1160 MPa (σb), there are still no obvious changes in

the shapes and distributions of δ phase, γ′′ phase, and γ′ phase. With the increase of initial stress, δ phase is still in short-rod shape. The average lengths are 0.92 μm, 0.98 μm, and 0.81 μm, and the average widths are 0.48 μm, 0.41 μm, and 0.40 μm under initial stresses of 510 MPa, 1020 MPa, and 1090 MPa, respectively. γ′′ phase is in the shape of ellipsoid, with the lengths of 50 nm, 47 nm, and 49 nm and the widths of 23 nm, 19 nm, and 25 nm under different initial stresses, respectively. While for γ′ phase, it is spherical, and the diameters are 16 nm, 21 nm, and 19 nm under different initial stresses, respectively. It can be found that there are also few changes in the sizes of δ phase, γ′′ phase, and γ′ phase. However, stress relaxation curves and stress relaxation stability do vary with the increase of initial stress. Therefore, the reasons for the “Ʌ”-shaped trend of stress relaxation stability of Inconel718 superalloy with initial stress increasing are supposed to be further studied in other ways. 4. Discussions As a general rule of cognition, there are three steps to study a phenomenon [22-24]. Firstly, predicting whether the phenomenon can happen or not in terms of thermodynamics. Secondly, quantifying the rate of the whole process using kinetic parameters. Thirdly, revealing the essence of the phenomenon by microstructure evolution. Apparently, this method can also be applied to the research relevant to stress relaxation behavior, and it will be worthwhile to interpret the trend of stress relaxation stability with initial stress increasing in the three aspects respectively. 4.1Thermodynamic analysis of stress relaxation 4.1.1 Basic theory Gibbs free energy (Eq. (2)), an essential parameter in the field of thermodynamics, is used to predicate the stability of a system universally [25, 26]. △G = △H – T△S

(2)

where △G, △H, △S and T represent Gibbs free energy change, enthalpy change, entropy change, and temperature, respectively. According to the minimum energy principle [22, 26], as long as the system does not achieve the minimum Gibbs free energy under a certain condition, there will be a series of complicated changes in the system. It is the gap between Gibbs free energy of the unsteady state and that of the steady state that provides the driving force for the occurrence of changes.

For stress relaxation of Inconel718 superalloy under a certain testing condition, the value of elastic strain energy enlarges because of the applying of initial stress, which results in the increase of enthalpy and then the rise of Gibbs free energy. Under this condition, the sample is unstable, and the increase of Gibbs free energy provides the driving force for stress relaxation. Subsequently, elastic strain transforms into plastic strain with a constant total strain and the decrease of stress during stress relaxation test [10]. On the one hand, plastic deformation, including twinning, dislocation movement, and grain boundary migration and so on, consumes elastic strain energy and causes the reduction of the value of enthalpy. On the other hand, the value of entropy, namely the degree of disorder, increases due to crystal defects resulting from plastic deformation. Because of the interaction between the two factors mentioned above, stress relaxation curves tend to achieve the steady state gradually. 4. 1.2 Thermodynamic rules of stress relaxation In essence, stress relaxation behavior under different testing conditions is similar, namely elastic strain transforming into plastic strain [10]. However, there still exist some differences in stress relaxation behavior under different initial stresses, and thermodynamic diagrams of stress relaxation can be classified into two types according to the value of initial stress.

Fig.4. Thermodynamic diagrams of stress relaxation of Inconel718 superalloy under different initial stresses at temperature of 650 ℃: (a) initial stress is not higher than yield strength, and the loading process is based on linear elastic theory; (b) initial stress is over yield strength, and the loading process is based on linear elastic theory and linear reinforced plastic theory. σo, σr, and σs represent initial stress, stress relaxation limit, and yield strength, respectively. εo, εoe, εop, εre, and

εrp represent initial strain/total strain (constant during stress relaxation), initial elastic strain, initial plastic strain (caused by loading), residual elastic strain, and residual plastic strain (caused by stress relaxation), respectively. Fig.4 (a) presents thermodynamic diagram of stress relaxation of Inconel718 superalloy when initial stress is not higher than yield strength, and linear elastic theory is applicable to loading process. The applying of initial stress results in initial strain/total strain (εo) and initial elastic strain energy density, Wo: εo = εre + εrp Wo = σo εo/2 = σo2/2E

(3) (4)

Where σo, εo, εre, εrp, and E represent initial stress, initial strain, residual elastic strain, residual plastic strain (caused by stress relaxation), and Young's modulus, respectively. Subsequently, initial elastic strain energy density (Wo) works as the driving force for stress relaxation, and elastic strain gradually evolves into plastic strain. The transformation from elastic strain to plastic strain will continue with the consumption of elastic strain energy density until Gibbs free energy achieves the minimum. At that time, stress relaxation is in the steady state, and residual elastic strain energy density (Wr) and the release of elastic strain energy density (△W, red shaded area in Fig.4 (a)) caused by stress relaxation can be identified as: Wr = σr εre/2 = σr 2 /2E

(5)

△W= Wo – Wr = σo εo/2 - σr εre/2 = (σo 2 –σr 2)/2E

(6)

Increasing initial stress to over yield strength, the corresponding thermodynamic diagram is shown in Fig.4 (b), and linear elastic theory and linear reinforced plastic theory are used to describe loading process. Under this condition, initial strain caused by loading can be divided into two parts, εoe and εop. εoe represents initial elastic strain, and initial elastic strain energy density caused by initial elastic strain provides driving force for stress relaxation. εop represents initial plastic strain caused by loading, and strain energy density consumed by it is shown in Fig.4 (b) (blue shaded area). To some extent, initial plastic strain has influence on kinetic regulations of stress relaxation behavior due to work hardening, and this will be discussed in detail in the section 4.3. εo = εoe + εop

(7)

εoe = εre + εrp

(8)

Similarly, stress relaxation at initial stress of over yield strength occurs stimulated by initial elastic strain energy density which can be calculated by Eq. (4) through replacing εo with εoe under this condition. Then, plastic strain increases by consuming elastic strain energy density, which leads to the decrease of elastic strain as well as Gibbs free energy. In the end, stress relaxation realizes the steady state with the minimum of Gibbs free energy. Residual elastic strain energy density (Wr) and the release of elastic strain energy density (△W, red shaded area in Fig.4 (b)) during stress relaxation process can also be calculated by Eq. (5) and Eq. (6) through replacing εo with εoe. 4.1.3 Quantitative analysis of stress relaxation stability Based on the analyses mentioned above, elastic strain energy density plays a significant role in stress relaxation process. Firstly, initial elastic strain energy density works as driving force for stress relaxation. Secondly, the amount of the release of elastic strain energy density during stress relaxation tests demonstrates the degree of plastic deformation. The higher the release of elastic strain energy density, the more the plastic deformation. In addition, in order to compare stress relaxation stability under different initial stresses reasonably, release ratio of elastic strain energy density (η), is identified by normalization using initial elastic strain energy density: η= △W/ Wo = ((σo2 – σr2) / 2E) / (σo2 / 2E) = (σo2 –σr2) / σo2

(9)

It’s obvious that the smaller the release of elastic strain energy density (△W) and release ratio of elastic strain energy density (η), the better the stress relaxation stability. Therefore, the release of elastic strain energy density (△W) and release ratio of elastic strain energy density (η) can be used to quantify stress relaxation stability in terms of thermodynamics. Fig.5 presents the trends of the release of elastic strain energy density and release ratio of elastic strain energy density with the rise of initial stress. Increasing initial stress from 260 MPa to 510 MPa, the release of elastic strain energy density falls slightly (Fig.5 (a), from 0.16×10^6 J/m^3 to 0.07×10^6 J/m^3), and release ratio of elastic strain energy density decreases remarkably (Fig.5 (b), from 79.6% to 9.3%). This suggests not only that plastic deformation decreases, but also that stress relaxation stability gets improved with the increase of initial stress in this stress range. Increasing initial stress continuously from 765 MPa to 1160 MPa, the release of elastic

strain energy density grows from 0.79×10^6 J/m^3 to 3.17×10^6 J/m^3 (Fig.5 (a)), and release ratio of elastic strain energy density rises from 44.9% to 77.8% (Fig.5 (b)). These experimental data demonstrate the increase of plastic deformation and the deterioration of stress relaxation stability with initial stress increasing. In summary, the release and release ratio of elastic strain energy density both fall at first and then grow with the rise of initial stress, and it confirms that the amount of plastic deformation alleviates firstly and then aggravates with initial stress increasing. Therefore, stress relaxation stability of Inconel718 superalloy tends to be ameliorated in the beginning and then degrade with the growth of initial stress. This is coherent with the conclusion deduced by relaxation stability parameters (stress relaxation limit, total relaxation stress, and relaxation stability coefficient) in Fig.2.

Fig.5. Thermodynamic parameters of stress relaxation of Inconel718 superalloy under different initial stresses at temperature of 650 ℃: (a) the release of elastic strain energy density (△W); (b) release ratio of elastic strain energy density (η). 4.2 Kinetic analysis of stress relaxation 4.2.1 Basic theory The essence of creep and stress relaxation behavior is similar, namely the accumulation of plastic deformation due to the coupling effect of temperature and stress [10,14,15]. What’s more, stress relaxation is regarded as a creep process with decreasing stress normally, and it is also named as “multi-stage creep” [10]. In addition to these relevance, there are also researches [5,11,12,23] related to stress relaxation and creep indicating that creep constitutive equation (Eq. (10)) can be applied to the analysis of stress relaxation.

dεp/dt = Aσnexp (-Q/RT)

(10)

Where dεp/dt is plastic strain rate, σ is exterior stress, n is stress exponent, Q is activation energy for deformation, R is gas constant (8.314 Jmol-1K-1) and T is Kelvin temperature. Differing from creep, exterior stress applied on samples decreases during stress relaxation tests. Based on constitutive equation (Eq. (10)), there are four factors that play important roles in stress relaxation, referred to as exterior stress, temperature, activation energy, and stress exponent. Exterior stress and temperature are driving forces of stress relaxation, while activation energy is the resistance of stress relaxation. Under a certain testing condition, temperature is constant during stress relaxation test. While activation energy is a temperature-dependent function, activation energy is also a constant under a certain testing condition. As for stress exponent (the slope of ln(dεp/dt)-lnσ curve, calculation method reference literature [5,10-12]), on the one hand, it reflects the relevance between exterior stress and plastic strain rate directly (the higher the stress exponent is, the faster the plastic strain rate decreases). On the other hand, it’s a significant parameter to predicate stress relaxation mechanism accordingly [27-30]. Therefore, in order to reveal the reasons for stress relaxation stability under different initial stresses in terms of kinetics, it’s necessary to screen the regulations of stress, plastic strain rate, and stress exponent with initial stress increasing, respectively. 4.2.2 Kinetic rules of stress relaxation For calculating kinetic parameters, including stress, plastic strain rate, and stress exponent, numerical simulation method is used commonly and ln(dεp/dt)-lnσ curve is an essential tool during this process [10]. After drawing ln(dεp/dt)-lnσ curves under different initial stresses, it can be found that, ln(dεp/dt)-lnσ curves under different initial stresses can be divided into two types (Fig.6) according to the value of initial stress. When initial stress is smaller than yield strength, ln(dεp/dt)-lnσ curves are similar and schematic diagram is shown in Fig.6 (a). Based on the value of stress exponent (the slope of ln(dεp/dt)-lnσ curve), stress relaxation process consists of two stages. In the first stage, the value of stress exponent is low. While in the second stage, stress exponent approximates to +∞. This can be interpreted in terms of stress variation. At the beginning of stress relaxation, exterior stress (σe=σo) is much higher than interior stress (σi), leading to the high plastic strain rate. The

occurrence of plastic strain, on the one hand, will result in work hardening which means the increase of interior stress. On the other hand, exterior stress reduces to maintain a constant total strain. Therefore, the gap between exterior stress and interior stress falls gradually, leading to a certain decrease of plastic strain rate (the first stage). With stress relaxation carrying on, exterior stress decreases continuously. At some point (the first transition stress, σ1), exterior stress will not be high enough to activate plastic deformation, and plastic strain rate will drop sharply, namely the second stage. Meanwhile, this makes the steady state realizable (stress relaxation limit, σr). Increasing initial stress to yield strength or above, ln(dεp/dt)-lnσ curve can be summed up as shown in Fig.6 (b). According to the value of stress exponent, stress relaxation under this condition can be classified into three stages. In the first stage, the value of stress exponent is high; In the second stage, stress exponent is remarkably lower than that in the first stage; When it comes to the third stage, stress exponent is close to +∞. Similarly, the plastic strain rate is high at first due to high effective stress (σe-σi). Subsequently, plastic deformation results in work hardening as well as the reduction of exterior stress, which leads to a considerable decrease of plastic strain rate (the first stage). Because of the lasting interaction between exterior stress and interior stress, plastic strain rate decreases continuously with the falling of elastic strain and the rising of plastic strain (the second stage). Finally, plastic strain rate decreases dramatically and stress relaxation achieves the steady state (the third stage).

Fig.6. Kinetic diagrams of stress relaxation of Inconel718 superalloy under different initial stresses at temperature of 650 ℃: (a) initial stress is smaller than yield strength [5]; (b) initial stress is over yield strength. σo, σ1, σ2, and σr represent initial stress, the first transition stress, the second transition stress, and stress relaxation limit, respectively. What needs to be pointed out is

that σ2 in Fig.6 (b) is approximate to σr. 4.2.3 Quantitative analysis of stress relaxation stability Fig.7 shows the trends of kinetic parameters (plastic strain rate and stress exponent) with the rise of initial stress. Increasing initial stress from 260 MPa to 510 MPa, initial plastic strain rate climbs from 0.01×10^-6/s to 0.40×10^-6/s, while stress exponent in the first stage surges from 2.9 to 21.6. Although initial plastic strain rate rises slightly with initial stress increasing, the high stress exponent (the slope of ln(dεp/dt)-lnσ curve) in the first stage illustrates that plastic strain rate decreases sharply, and the first transition plastic strain rate is only 10^-10/s or so. This has a beneficial influence on hindering the accumulation of plastic deformation significantly and makes the realization of the steady state easier. Therefore, stress relaxation stability of Inconel718 superalloy increases in this stress range. Subsequently, increasing initial stress to 765 MPa, initial plastic strain rate rises to 0.42×10^-6/s, but stress exponent in the first stage falls to 9.5. This means that the reduction of plastic strain rate slows down, and the value of the first transition plastic strain rate (10^-9/s, increasing modestly compared to the conditions mentioned above) demonstrates it exactly right. Under this condition, stress relaxation continues with a high plastic strain rate in a long time, leading to the remarkable accumulation of plastic deformation before the realization of the steady state. Thus, stress relaxation stability of Inconel718 degrades. When initial stress is 1020 MPa (yield strength, σs) or above, initial plastic strain rate soars from 1.75×10^-6/s to 12.97×10^-6/s because of the notable increase of initial stress, while stress exponent in the first stage declines from 20.5 to 13.2. This means that plastic strain rate is high, and the reduction of plastic strain rate is slow with the decrease of stress. Namely, plastic strain rate can maintain a large value for a long time, and this causes the notable growth of plastic deformation during the first stage with the rise of initial stress. In addition, there is still a considerable plastic strain rate even though stress relaxation enters the second stage, and stress exponent in the second stage is low. Taking these factors into consideration, plastic deformation exacerbates substantially. Thus, stress relaxation stability of Inconel718 superalloy deteriorates dramatically under initial stresses of yield strength or above.

Fig.7. Kinetic parameters of stress relaxation of Inconel718 superalloy under different initial stresses at temperature of 650 ℃: (a) plastic strain rate (dεp/dt); (b) stress exponent (n) at different stages. dεpo/dt and dεp1/dt represent initial plastic strain rate and the first transition plastic strain rate, respectively. While n1 and n2 represent stress exponent in the first stage and the second stage, respectively. Plastic strain rate and stress exponent of the steady state which referred to as the second stage in Fig.6 (a) and the third stage in Fig.6 (b), approximate to 0 and +∞, respectively. Therefore, the relevant data are not given in Fig.7. To sum up, plastic strain rate increases with the growth of initial stress, but the trend of stress exponent with initial stress rising is complex and affects plastic strain rate and the accumulation of plastic deformation significantly. Due to the interaction between plastic strain rate and stress exponent, stress relaxation stability of Inconel718 superalloy increases firstly and then decreases with initial stress rising. 4.3 Stress relaxation mechanisms

Fig.8. The interactions between dislocation, δ phase, and grain boundary of Inconel718 superalloy after stress relaxation at temperature of 650 ℃ under initial stress of 260 MPa (a), 380 MPa (b), and 510M Pa (c) (The arrows in Fig.8(a) show dislocations, and the inset is an enlargement of the

local region. In addition, the arrows in Fig.8 (b) and (c) represent pinning effect of δ phase to grain boundary migration and dislocation movement.) Fig.8 shows the interactions between dislocation, δ phase, and grain boundary of Inconel718 superalloy after stress relaxation at 650 ℃ under initial stresses of 260 MPa, 380 MPa, and 510 MPa. When initial stress is 260 MPa, there already exist a certain number of dislocations caused by stress concentration in local regions, especially around grain boundary and δ phase (Fig.8 (a)), and this makes stress relaxation stability under this stress worse. Increasing initial stress to 380 MPa and 510 MPa, dislocation pile-up can be observed and results in work hardening significantly, thereby making flow stress increase and then deterring the accumulation of plastic deformation. In addition, bow-like grain boundary (Fig.8(b)) and stage-like grain boundary (Fig.8(c)) can be observed around δ phase. Normally, grain boundary always tends to be straight to reduce grain boundary area and then achieve the minimum of grain boundary energy. Because of high temperature and stress, grain boundary migration occurs. However, grain boundary mobility varies in different regions due to the differences in chemical compositions and microstructures. δ phase works as the block to grain boundary migration, so straight grain boundary transforms into bow-like grain boundary (Fig.8(b)) and stage-like grain boundary (Fig.8(c)) around δ phase. Meanwhile, this demonstrates that the changes in the shape of grain boundary can be used to judge whether grain boundary migration occurs or not. To summarize, stress relaxation stability of Inconel718 superalloy is improved with the growth of initial stress because of all the factors mentioned above. Increasing initial stress to 765 MPa, microstructure evolution under this condition is similar to that under initial stress of 510 MPa, dislocation movement and grain boundary migration are the dominant mechanisms of stress relaxation. However, stress relaxation stability under initial stress of 765 MPa degrades. The reason for this is that initial stress of 765MPa is high enough to overcome work hardening effect, namely high stress field caused by dislocation pile-up, or even destroy obstacles that hinder dislocation movement [31]. Therefore, there is the considerable accumulation of plastic deformation.

Fig.9. The interactions between dislocation, δ phase, and grain boundary of Inconel718 superalloy after stress relaxation at 650 ℃ under initial stress of 1020 MPa (a1-2), 1090 MPa (b1-2), and 1160 MPa (c1-2). (a1-c1) show dislocation pile-up, twins, and fine twins within the coarse twin, respectively. While, (a2-c2) demonstrate dislocation pile-up around δ phase, grain boundary migration, and defects in δ phase. Fig.9 presents interactions between dislocation, δ phase, and grain boundary of Inconel718 superalloy after stress relaxation at 650 ℃ under initial stress of 1020 MPa, 1090 MPa, and 1160 MPa. Increasing initial stress to 1020 MPa or above, initial stress is high enough to activate twinning, and this is the dominant stress relaxation mechanism in the first stage (Fig.9(a1-c1)). Particularly, fine twins within the coarse twins can be observed under initial stress of 1160 MPa (Fig.9(c1)). Because the boundary of the twins owns good coherency, twins can obstruct dislocation movement and cause work hardening to some extent [32-35], reflecting high value of stress exponent. However, under this condition with high initial stress, the occurrence of a considerable number of twins leads to obvious plastic deformation, and interior stress field resulting from work hardening is too weak to impede the accumulation of plastic deformation. Subsequently, Because of the continuous decline of exterior stress, the dominant stress relaxation mechanism transforms from twinning into dislocation movement and grain boundary migration in the second stage (Fig.9 (a2-c2)). Meanwhile, defects in δ phase can be observed in Fig.9 (b2),

which is a kind of stress relaxation mechanism under high initial stress as well. In the end, stress relaxation achieves the steady state due to the continuous decrease of driving force. What needs to be pointed out is that, when initial stress is higher than yield strength but lower than ultimate tensile strength, the pre-plastic deformation caused by loading can provide pre-work hardening before stress relaxation. Therefore, stress relaxation stability does not decrease obviously in that stress range (from 0.42 to 0.41). 4.4 Relevance between stress relaxation stability and mechanisms According to the discussion in the section 4.3, stress relaxation mechanism transforms from dislocation movement and grain boundary migration to twinning with the increase of initial stress. When initial stress is lower than a certain value (referred to as σc1), only dislocation movement and grain boundary migration can be activated during stress relaxation process. Subsequently, although twinning occurs in few local regions due to the increase of initial stress and stress concentration, dislocation movement and grain boundary migration are still the dominant mechanism of stress relaxation, and this is a transition zone. When initial stress is higher than another value (referred to as σc2), twinning is in charge of stress relaxation, and this process couples with dislocation movement and grain boundary migration. To sum up, σc1 and σc2 determine the forms of plastic deformation, and they can be used to judge the types of stress relaxation mechanism under different conditions. Fig.10 shows schematic diagram of stress relaxation stability and mechanisms under different initial stresses. The two important parameters: σc1 and σc2, represent the first critical stress and the second critical stress, respectively. Based on the two parameters, stress relaxation behavior of Inconel718 superalloy under different initial stresses can be divided into three cases.

Fig.10. Schematic diagram of stress relaxation stability and mechanisms of Inconel718 superalloy under different initial stresses at temperature of 650 ℃. σc1 and σc2 represent the first critical stress and the second critical stress, respectively. When initial stress is lower than the first critical stress, referred to as case 1, stress relaxation stability is improved gradually with the increase of initial stress. The main reason for this is that the driving force for stress relaxation is small at low initial stress, while there exists remarkable work hardening during stress relaxation process, making the accumulation of plastic deformation difficult and then prompting stress relaxation stability. At this time, stress relaxation process consists of two stages. In the first stage, dislocation movement and grain boundary migration are the dominant mechanisms of stress relaxation. Dislocation piles up around precipitates and δ phase hinders grain boundary migration, thereby leading to work hardening and deterring plastic deformation. So, stress relaxation realizes the steady state quickly, namely the second stage. Between the first critical stress and the second critical stress is a transition zone, namely case 2. In this stress range, stress relaxation stability degrades with the rise of initial stress. This is because high initial stress causes large driving force for stress relaxation and makes work hardening weak. In addition, stress relaxation mechanism transforms from dislocation movement and grain boundary migration to twinning gradually. Increasing initial stress to the second critical stress or above, namely case 3, stress relaxation stability deteriorates significantly with the growth of initial stress. At this time, initial stress is high enough to activate multiple forms of plastic deformation, including dislocation movement, grain boundary migration, and twinning, which leads to significant plastic deformation and then the deterioration of stress relaxation. There are three stages during the whole stress relaxation process. At the beginning, high initial stress stimulates the occurrence of mechanical twins, working as the dominant mechanism of stress relaxation. There also exists dislocation movement and grain boundary migration, but they are secondary factors in the first stage. When it comes to the second stage, stress is too low to activate twinning, and dislocation movement and grain boundary migration are in charge of stress relaxation. In the end, stress relaxation achieves the steady state due to the decrease of stress and the resistance caused by strengthening effects, referred to as the third stage.

5. Conclusions In the present work, stress relaxation behavior and mechanisms of Inconel718 superalloy were investigated in the stress range of 260~1160 MPa by the analyses of stress relaxation curve, thermodynamics, kinetics, FESEM and TEM observation, respectively. The following conclusions can be derived from the investigation and discussion: (1) Increasing initial stress from 260 MPa to 1160 MPa, stress relaxation stability of Inconel718 superalloy increases firstly and then decreases, with the peak of 0.84 under initial stress of 510MPa (50% σs), appearing to be a “Ʌ”-shaped trend. This is caused by the interaction between initial stress providing driving force and work hardening resulting from internal stress field. (2) Stress relaxation behavior is regarded as the process during which elastic strain transforms into plastic strain essentially, and the amount of transformation from elastic strain to plastic strain can be quantified in terms of thermodynamics by the release and release ratio of elastic strain energy density. The two parameters both fall at first and then rise with the growth of initial stress, which demonstrates that the accumulation of plastic deformation decreases firstly and then increases. (3) The accumulation of plastic deformation is described in terms of kinetics by plastic strain rate as well as stress exponent. Increasing initial stress from 260 MPa to 510 MPa, plastic strain rate increases slightly at first, but stress exponent rises remarkably suggesting strong work hardening effect. Therefore, the amount of plastic deformation decreases in this stress range. However, increasing initial stress to 765 MPa or above, plastic strain rate increases exponentially. Although work hardening still exists, driving force is large enough to overcome the resistance of work hardening and lead to significant plastic deformation. (4) Stress relaxation mechanisms of Inconel718 superalloy differ under different initial stresses. When initial stress is low, stress relaxation can be divided into two stages, and dislocation movement and grain boundary migration are dominant stress relaxation mechanisms. While at high initial stress, stress relaxation consists of three stages. Twinning is in charge of stress relaxation in the first stage, and dislocation movement and grain boundary migration are main stress relaxation mechanisms in the second stage. Finally, stress relaxation reaches the third stage, namely the steady state.

Acknowledgments This work is financially supported by the National Natural Science Foundation of China (No. 51771016).

Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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