- Email: [email protected]
Low cycle fatigue and creep-fatigue interaction behavior of nickel-base superalloy GH4169 at elevated temperature of 650 °C
Materials Science & Engineering A 655 (2016) 175–182
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Low cycle fatigue and creep-fatigue interaction behavior of nickel-base superalloy GH4169 at elevated temperature of 650 °C G. Chen a,n, Y. Zhang a, D.K. Xu b, Y.C. Lin c, X. Chen a a
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Environmental Corrosion Center, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China c School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 September 2015 Received in revised form 27 December 2015 Accepted 30 December 2015 Available online 31 December 2015
Total strain-controlled low cycle fatigue (LCF) tests of a nickel based superalloy were performed at 650 °C. Various hold times were introduced at the peak tensile strain to investigate the high-temperature creepfatigue interaction (CFI) effects under the same temperature. A substantial decrease in fatigue life occurred as the total strain amplitude increased. Moreover, tensile strain holding further reduced fatigue life. The saturation phenomenon of holding effect was found when the holding period reached 120 s. Cyclic softening occurred during the LCF and CFI process and it was related to the total strain amplitude and the holding period. The relationship between life-time and total strain amplitude was obtained by combining Basquin equation and Coffin-Manson equation. The surface and fracture section of the fatigued specimens were observed via scanning electronic microscope (SEM) to determine the failure mechanism. & 2015 Elsevier B.V. All rights reserved.
Keywords: Low cycle fatigue Creep-fatigue interaction Nickel based superalloys GH4169
1. Introduction GH4169 is a nickel-base superalloy and possesses attractive high temperature mechanical properties such as exceptionally high temperature strength and good resistance to oxidation and creep. The alloy has been extensively used in aircraft engines like the fabrication of turbine discs because of these overall properties. Its working temperature ranges from 600 °C to 700 °C [1–3] as a key hot-end component in the aero-engines. High pressure turbine disc inevitably withstands hostile environment with respect to load and temperature during its service. Therefore, the material is inclined to suffer strain-controlled high temperature LCF and CFI effects [4]. These two factors may reduce the service life of the working components significantly. Therefore, the LCF behavior and CFI of the nickel-base superalloy are of major concern considering the safety and reliability of gas turbine engines. As far as LCF performance of the nickel-base superalloy was concerned, lots of efforts have been devoted to investigate the influential factors on LCF, such as loading waveforms [5], γ″ precipitates [6–9], micro-twinning [10], content of Boron [11,12], loading path [13], ion implantation [14] etc. Prasad et al. [5] investigated the LCF deformation behavior of different sections (rim, hub and bore) in a forged turbine disc of IN718 under slow-fast and fast-slow waveforms at 650 °C. They found that the superalloy showed marginally n
Corresponding author. E-mail address: [email protected] (G. Chen).
http://dx.doi.org/10.1016/j.msea.2015.12.096 0921-5093/& 2015 Elsevier B.V. All rights reserved.
life reduction under slow-fast waveform as compared to fast-slow waveform. They attributed this to the more accumulated damage during slow-fast waveform according to different spaces of planar slip band. Xiao et al. [6] observed planar deformation bands in IN718 at both room temperature and 650 °C. They found that the γ″ precipitates were sheared by dislocations moving on slip planes. Earlier, Fournier and Pineau [7] reported the shearing of γ″ precipitates by dislocations movement during LCF deformation at ambient temperature and 550 °C. Sundararaman et al. [8], however, originally proposed the geometrical aspects of deformation of γ″ precipitates at ambient temperature during tensile deformation. Recently, Zhang et al. [9] investigated the influence of strain amplitude on LCF behavior of a similar nickel-base superalloy GH4698 at 650 °C. They found that fatigue life decreased significantly with the increase of total strain amplitude and the combined effects of brittle fracture and ductile fracture were the main failure mechanism of GH4698. Ye et al. [15] studied the LCF behavior of nickel-base superalloy GH4145/ SQ under 538 °C. They reported the alloy exhibited a pronounced initial hardening followed by continuous softening to failure at high strain amplitudes, while the initial hardening was followed by a saturation stage at low strain amplitudes. They attributed this phenomenon to the microstructure change of slip band density and the variation of precipitates size under varied strain amplitudes. Though quantities of research on the LCF behavior of nickel-base superalloy was carried out in the past years, only very limited data of LCF has been generated for GH4169 superalloy, especially about the alloy's CFI behavior.
176
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
The interaction between LCF and creep, i.e., CFI behavior, is also an important aspect of material behaviors. Various types of tests simulating the condition of CFI such as prior creep followed by fatigue, prior fatigue followed by creep load and asymmetric cycling (with or without hold period at peak strain level) had been practiced in laboratories to study the CFI of other nickel-base superalloys [16–20]. Lord et al. [16] found that tensile strain hold tests gave longer fatigue lives than predicted, while fatigue life of compressive strain hold period tests were shorter than predicted for René 80. However, Meurer et al. [17] reported that hold periods at peak tensile strain impaired LCF resistance of nickel-base superalloy such as Inconel 617, especially at low strain amplitudes. In addition, Hu et al. [18] performed stress-controlled creep-fatigue experiments on superalloy GH4133B at three loading levels, i.e. continuous cyclic creep (CF), prior creep followed by fatigue (CþF) and prior fatigue followed by creep load (FþC), to investigate the interaction between creep damage and fatigue damage. They found that the creep-fatigue damages were larger than unity (indicating the creep-fatigue interaction is negative) in the cases of CF and FþC loading, but it was smaller than unity in CþF loading (indicating the creep-fatigue interaction is positive). Unfortunately, CFI tests of Table 1 Chemical compositions of GH4169 nickel-base superalloy (wt%). Ni
Cr
Nb
Mo
Ti
Al
C
Co
Fe
52.82
18.96
5.23
3.01
1.00
0.59
0.03
0.03
Bal.
2. Materials and methods The material used in this study is a commercial GH4169 nickelbase superalloy. Its composition (wt%) is given in Table 1. The superalloy was first casted by vacuum induction melting and vacuum consumable remelting methods. Then, 3150 t hydraulic press machine was used to forge the casted superalloy. Finally, the superalloy was received as bar stock cut from a forged part along its axis. Fig. 1 shows the initial microstructure of the investigated superalloy. The sample was electrolytically etched with oxalic acid after being polished. The average diameter of initial grains is about 20 μm by linear intercept method. Cylindrical specimens with 18 mm in gauge length and 6.5 mm in diameter were used. Fatigue tests were performed on a closed-loop servo hydraulic testing machine with a load capability of 100 kN. All the tests were conducted at 650 °C in air. Uniform heating of the specimen gauge length was accomplished using an induction coil. Temperature was measured by K-type thermocouples, which were welded onto the gage section of tested specimen located within the gage section. Temperature was stabilized for 30 min to ensure that a uniform temperature field had been reached before tests and the temperature gradient within the gage section of specimen was within two degrees during the tests. LCF tests were performed under fully reversed total strain-controlled mode with strain amplitude varying from 0.3% to 0.9%. The symmetrical triangular wave was implemented in LCF tests. CFI tests were carried out by introducing a holding period of 30 s, 120 s and 300 s at the peak strain of 0.5%. The loading waveforms are described in Fig. 2. The strain rate for all tests was maintained as 5E 3 s 1. The axial strain was measured with a high temperature extensometer, mounted on the gage section of the specimen. The cyclic number, corresponding to the peak tensile load decreased by 50% or the ultimate fracture, was defined as fatigue life. In addition, the surface and fracture morphology of the failed samples were examined by SEM to determine the failure mechanism.
Strain
Strain
Fig. 1. Initial microstructure of the investigated superalloy.
the superalloy GH4169 are still rare. Therefore, a series of LCF tests under different strain amplitudes were carried out at 650 °C and the test temperature was set as equal to the actual working temperature of turbine disc. Meanwhile, CFI tests with hold period at peak tensile strain were conducted under the same temperature. Cyclic deformation behavior and creep-fatigue behavior of GH4169 were analyzed according to the test data. Observation of the surface and fracture morphology of the test specimens were performed by SEM.
Δt
Time
Time
(a)
(b) Fig. 2. Loading waveforms of (a) LCF and (b) CFI tests.
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
177
Fig. 4. Stress relaxation curves under varied holding conditions at half-life.
As for CFI test results shown in Fig. 3(b), the shape of hysteresis loops with different holding periods are similar to those in LCF tests. However, the hysteresis loops shift and a compressive mean stress is generated as the introduction of tensile strain holding. The phenomenon is in accordance with the observation of nickelbase alloy MAR MOO2 [21]. Moreover, the compressive mean stress grew with the elongation of holding period before it was saturated. Another important feature of the hysteresis loop in CFI tests is stress relaxation. Fig. 4 compares the stress relaxation behavior under different holding conditions at half-life under the strain amplitude of 0.5%. A rapid relaxation down to half of the maximum stress occurs in early part of the holding period. During the remaining period, a comparatively additional relaxation occurs. In the meantime, the stress relaxation response with a holding period of 120 s is similar to that of 300 s. 3.2. Cyclic stress response
Fig. 3. Cyclic stress–strain response under (a) LCF and (b) CFI tests at half-life at the strain amplitude of 0.5% (TH: Tensile Holding).
3. Results 3.1. Hysteresis loops The cyclic stress–strain response of the alloy in LCF and CFI tests at half-life were depicted in Fig. 3. The width of hysteresis loop grows with increasing strain amplitude as shown in Fig. 3(a), which indicates more plastic strain produces at larger strain amplitude. It is commonly known that plastic strain exerts important influence on the fatigue performance. Therefore the increase of the plastic strain leads to a significant reduction of fatigue life. In comparison with test result under lower strain rate of 6.67E 5 s 1 [5], the trail of serration flow manifesting dynamic strain aging (DSA) was not observed under the strain amplitude investigated due to the higher strain rate of 5E3 s 1.
The cyclic stress response curves for different strain amplitudes and holding periods are shown in Fig. 5. As shown in Fig. 5(a), the cyclic stress response strongly depends on the total strain amplitude. The initial cyclic stress response value increases as the cyclic strain amplitude grows. Under higher strain amplitudes (Δεt/ 2Z0.4%), the superalloy exhibits continuous cyclic softening throughout the whole life. The phenomenon is in accordance with the observation of Inconel 718 at elevated temperature by Prasad et al. [5,22], Xiao et al. [6] and Fournier et al. [7]. It was mainly attributed to many factors, such as the inhomogeneous plastic deformation, shearing of γ″ precipitates and dissolution of precipitates, etc. [5–7] A nearly stable stress amplitude is, however, achieved from the beginning under lower strain amplitude (Δεt/ 2¼0.3%). This indicates that cyclic saturation is reached at the beginning. A cyclic softening ratio is introduced to further characterize the softening phenomenon, as defined by the following equation,
r=
σH − σ1 σ1
(1)
where s1 and sH represent the stress amplitude at first cycle and half-life, respectively. The relationship between softening ratio and cyclic strain amplitude is plotted in Fig. 6, which indicates that the
178
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
Fig. 6. Relationship between strain amplitude and softening ratio.
Fig. 7. Relationship between strain amplitudes and reversals to failure. Fig. 5. Evolution of the stress amplitude with the number of cycles for (a) different strain amplitudes and (b) different holding periods at strain amplitude of 0.5%.
level of softening rises significantly with the increase of strain amplitude. Generally, stress amplitude drops rapidly before final failure. In the case of tensile holding tests, Fig. 5(b) shows the stress response under different holding periods at peak strain. The alloy still undergoes softening during the course of holding tests. It should be noted that the influence of holding period on softening was unchanged when holding period elongated from 120 s to 300 s, indicating that the fatigue life under holding period of 120 s is similar to that of 300 s. 3.3. Fatigue behavior By combining the Coffin-Manson equation [23] with Basquin equation [24], the variation of fatigue life expressed by reversals to failure (2Nf) with strain amplitudes can be expressed as follows,
Table 2 Fatigue parameter for GH4169.
σ′f /MPa
b
ε′f
c
1570.53
0.1017
0.83332
0.9123
Δϵ p σ f′ Δϵt Δϵe = + = (2Nf )b + ϵ′f (2Nf )c 2 2 2 E
(2)
where Δεt/2, Δεe/2 and Δεp/2 are the total strain amplitude, elastic strain amplitude and plastic strain amplitude, respectively. sf′ is the fatigue strength coefficient, b is the fatigue strength exponent, εf′ is fatigue ductility coefficient, c is the fatigue ductility exponent and E is Young's modulus. Accordingly, liner relationship between elastic strain amplitude and reversals to failure as well as plastic strain amplitude and the
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
179
holding period at peak tensile strain further reduces its creep-fatigue life. However, a saturation effect of holding period at peak tensile strain on the reduction of fatigue life was observed in Fig. 8(b). Similar results were also found for nickel-based alloy 617 [17] and DZ125 [25]. The influence of holding period on fatigue life can be represented by the relaxation behavior during the holding period (seen in Fig. 4). The elastic strain was partially converted into inelastic strain during the process of stress relaxation and the inelastic strain reduced the fatigue resistance of the alloy. 3.4. Fracture behavior
Fig. 8. (a) Fatigue life in LCF and CFI tests of GH4169 at different strain amplitudes with various holding periods at peak tensile strain; (b) relationship between fatigue life and holding period.
reversals to failure can be founded on bi-logarithmic coordinates, as shown in Fig. 7. The corresponding parameters in Eq. (2) are summarized in Table 2 and the relationship between total stain amplitude and reversals to failure is expressed as,
Δϵt = 0.0098776(2Nf )−0.1017 + 0.83332(2Nf )−0.9123 2 This relationship can be used to predict the low cycle fatigue life of the alloy at 650 °C. Fig. 8(a) shows the cyclic fatigue life of GH4169 in LCF and CFI tests. The fatigue life of the alloy decreases sharply with the increase of strain amplitude in LCF tests. Compared to the fatigue life at the same strain amplitude in LCF tests, the creep-fatigue life decreased when tensile holding periods were introduced. In addition, longer
Fig. 9(a) presents the track of fatigue crack on the specimen surface for varied holding periods. The left specimen with holding period of 30 s shows a relative flat appearance of the crack, which is similar to the specimen failed in LCF tests. In contrast, the specimen with a longer holding period of 300 s shows a winding path. SEM observation was performed to further examine the specimen surface near the fracture. The surface of virgin specimen was also included to facilitate the comparison. According to EDS (Energy Dispersive Spectrometer) analysis, two kinds of intermetallic compound with common elements (Nb and Ti) but different contents are found in Fig. 9(b). Different from steels like annealed 2.25Cr1Mo [26], 9Cr1Mo [27] and Inconel 617 [28], no obvious oxide layer is observed on the specimen surface for both tests shown in Fig. 9(c) and (d). Fig. 9(c) and (d) show that oxidation prefers to occur at the sites of intermetallic compound under high temperature and oxide scales may flake off during the fatigue process. Therefore, pits resulted from spalling of oxide lead to stress concentration and crack initiation. However, the specimen surface of specimens tested under CFI loading is heavily oxidized as compared with those tested under LCF loading. The fracture surfaces were also examined by SEM to gain insight into the fatigue failure mechanism in LCF and CFI tests. Fig. 10 shows typical fractographs of the superalloy failed under different cyclic strain amplitudes in LCF tests. Fig. 10 (a) and (c) present the fatigue crack initiation sites, which can be clearly identified on the specimens' surface (indicated by arrows). Only single crack initiation source is observed and it is initiated from the specimen surface under the strain amplitudes investigated. The typical fractographs in the region of stable crack propagation enclosed in boxed ‘b’ and ‘d’ are magnified in Fig. 10(b) and (d). Under the strain amplitude of 0.3%, a large number of fatigue striations (indicated by arrow B) appear on the fracture surface. Moreover, several secondary cracks (indicated by arrow A) are also found. As for the higher strain amplitude of 0.9%, fatigue striation is not well-defined. However, a larger number of secondary cracks form, which are deeper and longer than that in specimen cycled under strain amplitude of 0.3%. In the case of CFI tests, Fig. 11(a) displays the typical fractograph of the crack initiation sites. Apparently different from the LCF tests, the fracture surface is rough and multiple crack initiation sites can be found on the fracture surface. For the crack propagation region of specimen in CFI test shown in Fig. 11(b), secondary cracks can be seen clearly along grain boundaries on fracture surface, as pointed by arrows. In addition, fatigue striation is not well-developed here and character of oxidation is more obvious in comparison with that in LCF tests.
4. Discussion 4.1. Cyclic softening Irrespective of the loading waveform, GH4169 superalloy exhibited cyclic softening during tests at temperature of 650 °C as shown in Fig. 5. The superalloy GH4169 belongs to precipitationhardened alloy, where finely dispersed second-phase particles are
180
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
Fig. 9. (a) Whole surface appearance of CFI specimens; SEM images of the specimen surface (b) before test and (c) conducted at LCF test with strain amplitude of 0.5% and (d) CFI tests with holding period of 300 s.
Fig. 10. Typical fractographs showing the crack initiation sites and propagation character under varied strain amplitudes in LCF tests: (a, b) Δεt/2 ¼0.3% and (c, d) Δεt/2 ¼0.9%.
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
181
for. The mean stress diminishes with the increase of the inelastic strain range [21]. The capacity of the material to withstand the mean stress depends on the ratio of inelastic strain to elastic strain in a cycle. If the inelastic strain is relatively small to the elastic strain, as in the case of the present tests, the developed mean stress is large and significantly influences fatigue life. A high compressive mean stress retards crack opening and thus lowers the growth rate of a crack [16]. Each cycle in fatigue test caused some damages to the material. The evolution of damage can be well described by characterizing the stress relaxation behavior as a function of time described in Fig. 4. The peak stress drops rapidly in the initial several seconds. However, only about twenty percent of the stress relaxation occurs for the rest holding period. During the strain holding, the stress decreased while the total strain amplitude was maintained as constant by the conversion of elastic strain to inelastic strain, which caused creep damage [30].The interaction between cyclic strain and creep strain accounted for the shorted fatigue life in CFI tests. In addition, the reduction of fatigue life reached saturation when the holding period was increased from 120 s to 300 s, corresponding to the stress relaxation saturation phenomenon. 4.3. Damage mechanism
Fig. 11. Typical fractographs showing (a) the crack initiation sites and (b) propagation character in CFI test with holding period of 300 s.
predominantly responsible for its high strength. These precipitates have an ordered crystal structure and the superalloy exhibits planar slip character [6], which indicates that planar slip bands are formed in the γ′ and γ″ strengthened nickel-base superalloy. It leads to shearing of these precipitates and promoting strain localization in the slip bands, where the strain is extremely inhomogeneous. Shearing of γ″ precipitates by dislocations movement was reported by Fournier and Pineau [7] at ambient temperature and 550 °C and Xiao et al. [29] at 650 °C in LCF deformation. In this process, during initial cyclic softening, shearing of γ″ precipitates by mobile dislocations occurs and reduces the size of precipitates. When the cumulative shearing force is high, the precipitates can be sheared into two separate halves. Consequently, dislocations can move easily in these slip bands to an extent that the precipitates offer little or even no resistance to the movement of dislocations. The stress required to shear the smaller particles decreases as a result of successive shearing of precipitates, which eventually leads to cyclic softening [6]. 4.2. Holding period effect It can be observed from Fig. 5(b) that the introduction of tensile holding period causes compressive mean stress in the hysteresis loop. The development of significant mean stress has been reported previously [16,21] in other nickel-base alloys during asymmetric straincontrolled cycling and the low level of plasticity involved was account
Fractographs of the superalloy GH4169 in LCF and CFI tests showed that brittle fracture occurred without evident plastic deformation from macroscopic view. The fatigue cracks were all initiated from specimen surfaces. Single crack initiation site was observed in LCF tests while multiple crack initiation site in CFI tests. This difference can be interpreted by the different surface characters of the specimen in LCF and CFI tests. The surface of specimen was inevitably oxidized once exposed at the 650 °C in both LCF and CFI tests. As stated previously, oxidation preferred to occur around the site of intermetallic compound and continuous oxide layer was not observed. In the course of cyclic loading, oxide cracked and flaked off, which caused the generation of pits where the oxide flaked off. Hence, stress concentration or strain localization would occur near the pits that served as defects on the surface. Then crack initiated and propagated from the pits, as shown in Fig. 9(c) and (d). However, oxidations of the specimen in CFI test were much heavier than those of the specimen in LCF test. Therefore, multiple crack initiation sites were activated for CFI test. Creep and environmental oxidation occur during holding period in CFI tests. Comparing with LCF tests, quantities of intergranular crack was observed on the fracture surface and damage due to considerable oxidation (Fig. 11). It can be concluded that creep and oxidation had great influence on fatigue life in CFI tests, especially for the long holding period. However, creep is negligible in pure LCF tests and the effect of oxidation is limited. Thus fractograph from the LCF tests was characterized by ductile fatigue striations and secondary crack, which shows more transgranular appearance.
5. Conclusions A series of LCF and CFI tests were performed on nickel-base superalloy GH4169 at 650 °C to study the creep-fatigue interaction mechanism. The following conclusions can be drawn. 1. Irrespective of the loading waveform, GH4169 nickel-base superalloy exhibited cyclic softening during the whole life except for the low strain amplitude of 0.3%. 2. The fatigue life of GH4169 decreased with the increase of strain amplitude and tensile holding period. The fatigue life was almost unchanged when the holding period exceeds 120 s. 3. Single crack initiation site was observed in LCF tests while multiple crack initiation sites in CFI tests. The fracture modes of
182
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
GH4169 superalloy under LCF tests and CFI tests were transgranular and intergranular, respectively.
Acknowledgment The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. 51471116), the Program for New Century Excellent Talents in University (NCET-13-0400) of China and Tianjin University Independent Innovation Foundation (No. 2013E3-0003).
References [1] A. Diboine, A. Pineau, Fatigue Fract. Eng. Mater. Struct. 10 (1987) 11. [2] L. Fournier, D. Delafosse, T. Magnin, Mater. Sci. Eng. 269 (1999) 9. [3] L. Cheng, X. Xue, B. Tang, D. Liu, J. Li, H. Kou, J. Li, Mater. Sci. Eng.: A 606 (2014) 24–30. [4] K. Prasad, R. Sarkar, P. Ghosal, V. Kumar, Mater. Sci. Eng.: A 572 (2013) 1–7. [5] K. Prasad, R. Sarkar, P. Ghosal, V. Kumar, M. Sundararaman, Mater. Sci. Eng.: A 568 (2013) 239–245. [6] L. Xiao, D.L. Chen, M.C. Chaturvedi, Mater. Sci. Eng.: A 483–484 (2008) 369–372. [7] D. Fournier, A. Pineau, Metall. Trans. A 8A (1977) 1095–1105. [8] M. Sundararaman, P. Mukhopadhyay, S. Banerjee, Acta Mater. 36 (1988) 18.
[9] P. Zhang, Q. Zhu, C. Hu, C.J. Wang, G. Chen, H.Y. Qin, Mater. Des. 69 (2015) 12–21. [10] A. Bhattacharyya, G.V.S. Sastry, V.V. Kutumbarao, J. Mater. Sci. 34 (1999). [11] L. Xiao, D.L. Chen, M.C. Chaturvedi, Metall. Mater. Trans. A 35A (2004) 11. [12] T.J. Garosshen, T.D. Tillman, G.P. Mccrathy, Metall. Trans. A 18A (1987) 9. [13] G.Q. Sun, D.G. Shang, J. Deng, W. JG, Reseach Explor. Lab. 26 (2007) 3. [14] H.J. Han, M. Su, C.S. Wang, Aerosp. Mater. Technol. 2 (2008) 65–68. [15] D. Ye, D. Ping, Z. Wang, H. Xu, X. Mei, C. Xu, X. Chen, Mater. Sci. Eng.: A 373 (2004) 54–64. [16] D.C. Lord, L.F. Coffin, Metall. Trans. A 4 (1973) 8. [17] Hans-Peter Meurer, Gunter K.H. Gnirss, Wolfgang Mergler, Gerhard Raule, Hans Schuster, G. Ullrich, Nucl. Technol. 66 (1984) 9. [18] D. Hu, R. Wang, Mater. Sci. Eng.: A 515 (2009) 183–189. [19] Y.L. Lu, P.K. Liaw, L.J. Chen, G.Y. Wang, M.L. Benson, S.A. Thompson, J.W. Blust, P.F. Browning, A.K. Bhattacharya, J.M. Aurrecoechea, D.L. Klarstrom, Mater. Sci. Eng.: A 433 (2006) 114–120. [20] W.O. Ngala, H.J. Maier, Mater. Sci. Eng.: A 510–511 (2009) 429–433. [21] W.J. Plumbridge, E.G. Ellison, Fatigue Fract. Eng. Mater. Struct. 14 (1991) 17. [22] E. Hari Krishna, Kartik Prasad, Vikas Kumar, V. Singh, Trans. Indian Inst. Met. 63 (2010) 4. [23] L.F. Coffin, Trans. Am. Soc. Mech. Eng. 76 (1954) 20. [24] O.H. Basquin, Proc. Am. Soc. Mech. Eng. 10 (1910) 6. [25] D. Shi, J. Liu, X. Yang, H. Qi, J. Wang, Mater. Sci. Eng.: A 528 (2010) 233–238. [26] R.L. Hecht, J.R. Weertman, Metall. Mater. Trans. A 29A (1998) 9. [27] B. Fournier, M. Sauzay, Int. J. Fatigue 30 (2008) 14. [28] K.B.S. Rao, Mater. Sci. Eng. A 104 (1988) 15. [29] L. Xiao, D.L. Chen, M.C. Chaturvedi, Scr. Mater. 52 (2005) 603–607. [30] J. Zrnık, J. Semenak, V. Vrchovinsky, P. Wangyao, Mater. Sci. Eng. A 319 (2001) 6.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Low cycle fatigue and creep-fatigue interaction behavior of nickel-base superalloy GH4169 at elevated temperature of 650 °C G. Chen a,n, Y. Zhang a, D.K. Xu b, Y.C. Lin c, X. Chen a a
School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Environmental Corrosion Center, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China c School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 September 2015 Received in revised form 27 December 2015 Accepted 30 December 2015 Available online 31 December 2015
Total strain-controlled low cycle fatigue (LCF) tests of a nickel based superalloy were performed at 650 °C. Various hold times were introduced at the peak tensile strain to investigate the high-temperature creepfatigue interaction (CFI) effects under the same temperature. A substantial decrease in fatigue life occurred as the total strain amplitude increased. Moreover, tensile strain holding further reduced fatigue life. The saturation phenomenon of holding effect was found when the holding period reached 120 s. Cyclic softening occurred during the LCF and CFI process and it was related to the total strain amplitude and the holding period. The relationship between life-time and total strain amplitude was obtained by combining Basquin equation and Coffin-Manson equation. The surface and fracture section of the fatigued specimens were observed via scanning electronic microscope (SEM) to determine the failure mechanism. & 2015 Elsevier B.V. All rights reserved.
Keywords: Low cycle fatigue Creep-fatigue interaction Nickel based superalloys GH4169
1. Introduction GH4169 is a nickel-base superalloy and possesses attractive high temperature mechanical properties such as exceptionally high temperature strength and good resistance to oxidation and creep. The alloy has been extensively used in aircraft engines like the fabrication of turbine discs because of these overall properties. Its working temperature ranges from 600 °C to 700 °C [1–3] as a key hot-end component in the aero-engines. High pressure turbine disc inevitably withstands hostile environment with respect to load and temperature during its service. Therefore, the material is inclined to suffer strain-controlled high temperature LCF and CFI effects [4]. These two factors may reduce the service life of the working components significantly. Therefore, the LCF behavior and CFI of the nickel-base superalloy are of major concern considering the safety and reliability of gas turbine engines. As far as LCF performance of the nickel-base superalloy was concerned, lots of efforts have been devoted to investigate the influential factors on LCF, such as loading waveforms [5], γ″ precipitates [6–9], micro-twinning [10], content of Boron [11,12], loading path [13], ion implantation [14] etc. Prasad et al. [5] investigated the LCF deformation behavior of different sections (rim, hub and bore) in a forged turbine disc of IN718 under slow-fast and fast-slow waveforms at 650 °C. They found that the superalloy showed marginally n
Corresponding author. E-mail address: [email protected] (G. Chen).
http://dx.doi.org/10.1016/j.msea.2015.12.096 0921-5093/& 2015 Elsevier B.V. All rights reserved.
life reduction under slow-fast waveform as compared to fast-slow waveform. They attributed this to the more accumulated damage during slow-fast waveform according to different spaces of planar slip band. Xiao et al. [6] observed planar deformation bands in IN718 at both room temperature and 650 °C. They found that the γ″ precipitates were sheared by dislocations moving on slip planes. Earlier, Fournier and Pineau [7] reported the shearing of γ″ precipitates by dislocations movement during LCF deformation at ambient temperature and 550 °C. Sundararaman et al. [8], however, originally proposed the geometrical aspects of deformation of γ″ precipitates at ambient temperature during tensile deformation. Recently, Zhang et al. [9] investigated the influence of strain amplitude on LCF behavior of a similar nickel-base superalloy GH4698 at 650 °C. They found that fatigue life decreased significantly with the increase of total strain amplitude and the combined effects of brittle fracture and ductile fracture were the main failure mechanism of GH4698. Ye et al. [15] studied the LCF behavior of nickel-base superalloy GH4145/ SQ under 538 °C. They reported the alloy exhibited a pronounced initial hardening followed by continuous softening to failure at high strain amplitudes, while the initial hardening was followed by a saturation stage at low strain amplitudes. They attributed this phenomenon to the microstructure change of slip band density and the variation of precipitates size under varied strain amplitudes. Though quantities of research on the LCF behavior of nickel-base superalloy was carried out in the past years, only very limited data of LCF has been generated for GH4169 superalloy, especially about the alloy's CFI behavior.
176
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
The interaction between LCF and creep, i.e., CFI behavior, is also an important aspect of material behaviors. Various types of tests simulating the condition of CFI such as prior creep followed by fatigue, prior fatigue followed by creep load and asymmetric cycling (with or without hold period at peak strain level) had been practiced in laboratories to study the CFI of other nickel-base superalloys [16–20]. Lord et al. [16] found that tensile strain hold tests gave longer fatigue lives than predicted, while fatigue life of compressive strain hold period tests were shorter than predicted for René 80. However, Meurer et al. [17] reported that hold periods at peak tensile strain impaired LCF resistance of nickel-base superalloy such as Inconel 617, especially at low strain amplitudes. In addition, Hu et al. [18] performed stress-controlled creep-fatigue experiments on superalloy GH4133B at three loading levels, i.e. continuous cyclic creep (CF), prior creep followed by fatigue (CþF) and prior fatigue followed by creep load (FþC), to investigate the interaction between creep damage and fatigue damage. They found that the creep-fatigue damages were larger than unity (indicating the creep-fatigue interaction is negative) in the cases of CF and FþC loading, but it was smaller than unity in CþF loading (indicating the creep-fatigue interaction is positive). Unfortunately, CFI tests of Table 1 Chemical compositions of GH4169 nickel-base superalloy (wt%). Ni
Cr
Nb
Mo
Ti
Al
C
Co
Fe
52.82
18.96
5.23
3.01
1.00
0.59
0.03
0.03
Bal.
2. Materials and methods The material used in this study is a commercial GH4169 nickelbase superalloy. Its composition (wt%) is given in Table 1. The superalloy was first casted by vacuum induction melting and vacuum consumable remelting methods. Then, 3150 t hydraulic press machine was used to forge the casted superalloy. Finally, the superalloy was received as bar stock cut from a forged part along its axis. Fig. 1 shows the initial microstructure of the investigated superalloy. The sample was electrolytically etched with oxalic acid after being polished. The average diameter of initial grains is about 20 μm by linear intercept method. Cylindrical specimens with 18 mm in gauge length and 6.5 mm in diameter were used. Fatigue tests were performed on a closed-loop servo hydraulic testing machine with a load capability of 100 kN. All the tests were conducted at 650 °C in air. Uniform heating of the specimen gauge length was accomplished using an induction coil. Temperature was measured by K-type thermocouples, which were welded onto the gage section of tested specimen located within the gage section. Temperature was stabilized for 30 min to ensure that a uniform temperature field had been reached before tests and the temperature gradient within the gage section of specimen was within two degrees during the tests. LCF tests were performed under fully reversed total strain-controlled mode with strain amplitude varying from 0.3% to 0.9%. The symmetrical triangular wave was implemented in LCF tests. CFI tests were carried out by introducing a holding period of 30 s, 120 s and 300 s at the peak strain of 0.5%. The loading waveforms are described in Fig. 2. The strain rate for all tests was maintained as 5E 3 s 1. The axial strain was measured with a high temperature extensometer, mounted on the gage section of the specimen. The cyclic number, corresponding to the peak tensile load decreased by 50% or the ultimate fracture, was defined as fatigue life. In addition, the surface and fracture morphology of the failed samples were examined by SEM to determine the failure mechanism.
Strain
Strain
Fig. 1. Initial microstructure of the investigated superalloy.
the superalloy GH4169 are still rare. Therefore, a series of LCF tests under different strain amplitudes were carried out at 650 °C and the test temperature was set as equal to the actual working temperature of turbine disc. Meanwhile, CFI tests with hold period at peak tensile strain were conducted under the same temperature. Cyclic deformation behavior and creep-fatigue behavior of GH4169 were analyzed according to the test data. Observation of the surface and fracture morphology of the test specimens were performed by SEM.
Δt
Time
Time
(a)
(b) Fig. 2. Loading waveforms of (a) LCF and (b) CFI tests.
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
177
Fig. 4. Stress relaxation curves under varied holding conditions at half-life.
As for CFI test results shown in Fig. 3(b), the shape of hysteresis loops with different holding periods are similar to those in LCF tests. However, the hysteresis loops shift and a compressive mean stress is generated as the introduction of tensile strain holding. The phenomenon is in accordance with the observation of nickelbase alloy MAR MOO2 [21]. Moreover, the compressive mean stress grew with the elongation of holding period before it was saturated. Another important feature of the hysteresis loop in CFI tests is stress relaxation. Fig. 4 compares the stress relaxation behavior under different holding conditions at half-life under the strain amplitude of 0.5%. A rapid relaxation down to half of the maximum stress occurs in early part of the holding period. During the remaining period, a comparatively additional relaxation occurs. In the meantime, the stress relaxation response with a holding period of 120 s is similar to that of 300 s. 3.2. Cyclic stress response
Fig. 3. Cyclic stress–strain response under (a) LCF and (b) CFI tests at half-life at the strain amplitude of 0.5% (TH: Tensile Holding).
3. Results 3.1. Hysteresis loops The cyclic stress–strain response of the alloy in LCF and CFI tests at half-life were depicted in Fig. 3. The width of hysteresis loop grows with increasing strain amplitude as shown in Fig. 3(a), which indicates more plastic strain produces at larger strain amplitude. It is commonly known that plastic strain exerts important influence on the fatigue performance. Therefore the increase of the plastic strain leads to a significant reduction of fatigue life. In comparison with test result under lower strain rate of 6.67E 5 s 1 [5], the trail of serration flow manifesting dynamic strain aging (DSA) was not observed under the strain amplitude investigated due to the higher strain rate of 5E3 s 1.
The cyclic stress response curves for different strain amplitudes and holding periods are shown in Fig. 5. As shown in Fig. 5(a), the cyclic stress response strongly depends on the total strain amplitude. The initial cyclic stress response value increases as the cyclic strain amplitude grows. Under higher strain amplitudes (Δεt/ 2Z0.4%), the superalloy exhibits continuous cyclic softening throughout the whole life. The phenomenon is in accordance with the observation of Inconel 718 at elevated temperature by Prasad et al. [5,22], Xiao et al. [6] and Fournier et al. [7]. It was mainly attributed to many factors, such as the inhomogeneous plastic deformation, shearing of γ″ precipitates and dissolution of precipitates, etc. [5–7] A nearly stable stress amplitude is, however, achieved from the beginning under lower strain amplitude (Δεt/ 2¼0.3%). This indicates that cyclic saturation is reached at the beginning. A cyclic softening ratio is introduced to further characterize the softening phenomenon, as defined by the following equation,
r=
σH − σ1 σ1
(1)
where s1 and sH represent the stress amplitude at first cycle and half-life, respectively. The relationship between softening ratio and cyclic strain amplitude is plotted in Fig. 6, which indicates that the
178
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
Fig. 6. Relationship between strain amplitude and softening ratio.
Fig. 7. Relationship between strain amplitudes and reversals to failure. Fig. 5. Evolution of the stress amplitude with the number of cycles for (a) different strain amplitudes and (b) different holding periods at strain amplitude of 0.5%.
level of softening rises significantly with the increase of strain amplitude. Generally, stress amplitude drops rapidly before final failure. In the case of tensile holding tests, Fig. 5(b) shows the stress response under different holding periods at peak strain. The alloy still undergoes softening during the course of holding tests. It should be noted that the influence of holding period on softening was unchanged when holding period elongated from 120 s to 300 s, indicating that the fatigue life under holding period of 120 s is similar to that of 300 s. 3.3. Fatigue behavior By combining the Coffin-Manson equation [23] with Basquin equation [24], the variation of fatigue life expressed by reversals to failure (2Nf) with strain amplitudes can be expressed as follows,
Table 2 Fatigue parameter for GH4169.
σ′f /MPa
b
ε′f
c
1570.53
0.1017
0.83332
0.9123
Δϵ p σ f′ Δϵt Δϵe = + = (2Nf )b + ϵ′f (2Nf )c 2 2 2 E
(2)
where Δεt/2, Δεe/2 and Δεp/2 are the total strain amplitude, elastic strain amplitude and plastic strain amplitude, respectively. sf′ is the fatigue strength coefficient, b is the fatigue strength exponent, εf′ is fatigue ductility coefficient, c is the fatigue ductility exponent and E is Young's modulus. Accordingly, liner relationship between elastic strain amplitude and reversals to failure as well as plastic strain amplitude and the
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
179
holding period at peak tensile strain further reduces its creep-fatigue life. However, a saturation effect of holding period at peak tensile strain on the reduction of fatigue life was observed in Fig. 8(b). Similar results were also found for nickel-based alloy 617 [17] and DZ125 [25]. The influence of holding period on fatigue life can be represented by the relaxation behavior during the holding period (seen in Fig. 4). The elastic strain was partially converted into inelastic strain during the process of stress relaxation and the inelastic strain reduced the fatigue resistance of the alloy. 3.4. Fracture behavior
Fig. 8. (a) Fatigue life in LCF and CFI tests of GH4169 at different strain amplitudes with various holding periods at peak tensile strain; (b) relationship between fatigue life and holding period.
reversals to failure can be founded on bi-logarithmic coordinates, as shown in Fig. 7. The corresponding parameters in Eq. (2) are summarized in Table 2 and the relationship between total stain amplitude and reversals to failure is expressed as,
Δϵt = 0.0098776(2Nf )−0.1017 + 0.83332(2Nf )−0.9123 2 This relationship can be used to predict the low cycle fatigue life of the alloy at 650 °C. Fig. 8(a) shows the cyclic fatigue life of GH4169 in LCF and CFI tests. The fatigue life of the alloy decreases sharply with the increase of strain amplitude in LCF tests. Compared to the fatigue life at the same strain amplitude in LCF tests, the creep-fatigue life decreased when tensile holding periods were introduced. In addition, longer
Fig. 9(a) presents the track of fatigue crack on the specimen surface for varied holding periods. The left specimen with holding period of 30 s shows a relative flat appearance of the crack, which is similar to the specimen failed in LCF tests. In contrast, the specimen with a longer holding period of 300 s shows a winding path. SEM observation was performed to further examine the specimen surface near the fracture. The surface of virgin specimen was also included to facilitate the comparison. According to EDS (Energy Dispersive Spectrometer) analysis, two kinds of intermetallic compound with common elements (Nb and Ti) but different contents are found in Fig. 9(b). Different from steels like annealed 2.25Cr1Mo [26], 9Cr1Mo [27] and Inconel 617 [28], no obvious oxide layer is observed on the specimen surface for both tests shown in Fig. 9(c) and (d). Fig. 9(c) and (d) show that oxidation prefers to occur at the sites of intermetallic compound under high temperature and oxide scales may flake off during the fatigue process. Therefore, pits resulted from spalling of oxide lead to stress concentration and crack initiation. However, the specimen surface of specimens tested under CFI loading is heavily oxidized as compared with those tested under LCF loading. The fracture surfaces were also examined by SEM to gain insight into the fatigue failure mechanism in LCF and CFI tests. Fig. 10 shows typical fractographs of the superalloy failed under different cyclic strain amplitudes in LCF tests. Fig. 10 (a) and (c) present the fatigue crack initiation sites, which can be clearly identified on the specimens' surface (indicated by arrows). Only single crack initiation source is observed and it is initiated from the specimen surface under the strain amplitudes investigated. The typical fractographs in the region of stable crack propagation enclosed in boxed ‘b’ and ‘d’ are magnified in Fig. 10(b) and (d). Under the strain amplitude of 0.3%, a large number of fatigue striations (indicated by arrow B) appear on the fracture surface. Moreover, several secondary cracks (indicated by arrow A) are also found. As for the higher strain amplitude of 0.9%, fatigue striation is not well-defined. However, a larger number of secondary cracks form, which are deeper and longer than that in specimen cycled under strain amplitude of 0.3%. In the case of CFI tests, Fig. 11(a) displays the typical fractograph of the crack initiation sites. Apparently different from the LCF tests, the fracture surface is rough and multiple crack initiation sites can be found on the fracture surface. For the crack propagation region of specimen in CFI test shown in Fig. 11(b), secondary cracks can be seen clearly along grain boundaries on fracture surface, as pointed by arrows. In addition, fatigue striation is not well-developed here and character of oxidation is more obvious in comparison with that in LCF tests.
4. Discussion 4.1. Cyclic softening Irrespective of the loading waveform, GH4169 superalloy exhibited cyclic softening during tests at temperature of 650 °C as shown in Fig. 5. The superalloy GH4169 belongs to precipitationhardened alloy, where finely dispersed second-phase particles are
180
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
Fig. 9. (a) Whole surface appearance of CFI specimens; SEM images of the specimen surface (b) before test and (c) conducted at LCF test with strain amplitude of 0.5% and (d) CFI tests with holding period of 300 s.
Fig. 10. Typical fractographs showing the crack initiation sites and propagation character under varied strain amplitudes in LCF tests: (a, b) Δεt/2 ¼0.3% and (c, d) Δεt/2 ¼0.9%.
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
181
for. The mean stress diminishes with the increase of the inelastic strain range [21]. The capacity of the material to withstand the mean stress depends on the ratio of inelastic strain to elastic strain in a cycle. If the inelastic strain is relatively small to the elastic strain, as in the case of the present tests, the developed mean stress is large and significantly influences fatigue life. A high compressive mean stress retards crack opening and thus lowers the growth rate of a crack [16]. Each cycle in fatigue test caused some damages to the material. The evolution of damage can be well described by characterizing the stress relaxation behavior as a function of time described in Fig. 4. The peak stress drops rapidly in the initial several seconds. However, only about twenty percent of the stress relaxation occurs for the rest holding period. During the strain holding, the stress decreased while the total strain amplitude was maintained as constant by the conversion of elastic strain to inelastic strain, which caused creep damage [30].The interaction between cyclic strain and creep strain accounted for the shorted fatigue life in CFI tests. In addition, the reduction of fatigue life reached saturation when the holding period was increased from 120 s to 300 s, corresponding to the stress relaxation saturation phenomenon. 4.3. Damage mechanism
Fig. 11. Typical fractographs showing (a) the crack initiation sites and (b) propagation character in CFI test with holding period of 300 s.
predominantly responsible for its high strength. These precipitates have an ordered crystal structure and the superalloy exhibits planar slip character [6], which indicates that planar slip bands are formed in the γ′ and γ″ strengthened nickel-base superalloy. It leads to shearing of these precipitates and promoting strain localization in the slip bands, where the strain is extremely inhomogeneous. Shearing of γ″ precipitates by dislocations movement was reported by Fournier and Pineau [7] at ambient temperature and 550 °C and Xiao et al. [29] at 650 °C in LCF deformation. In this process, during initial cyclic softening, shearing of γ″ precipitates by mobile dislocations occurs and reduces the size of precipitates. When the cumulative shearing force is high, the precipitates can be sheared into two separate halves. Consequently, dislocations can move easily in these slip bands to an extent that the precipitates offer little or even no resistance to the movement of dislocations. The stress required to shear the smaller particles decreases as a result of successive shearing of precipitates, which eventually leads to cyclic softening [6]. 4.2. Holding period effect It can be observed from Fig. 5(b) that the introduction of tensile holding period causes compressive mean stress in the hysteresis loop. The development of significant mean stress has been reported previously [16,21] in other nickel-base alloys during asymmetric straincontrolled cycling and the low level of plasticity involved was account
Fractographs of the superalloy GH4169 in LCF and CFI tests showed that brittle fracture occurred without evident plastic deformation from macroscopic view. The fatigue cracks were all initiated from specimen surfaces. Single crack initiation site was observed in LCF tests while multiple crack initiation site in CFI tests. This difference can be interpreted by the different surface characters of the specimen in LCF and CFI tests. The surface of specimen was inevitably oxidized once exposed at the 650 °C in both LCF and CFI tests. As stated previously, oxidation preferred to occur around the site of intermetallic compound and continuous oxide layer was not observed. In the course of cyclic loading, oxide cracked and flaked off, which caused the generation of pits where the oxide flaked off. Hence, stress concentration or strain localization would occur near the pits that served as defects on the surface. Then crack initiated and propagated from the pits, as shown in Fig. 9(c) and (d). However, oxidations of the specimen in CFI test were much heavier than those of the specimen in LCF test. Therefore, multiple crack initiation sites were activated for CFI test. Creep and environmental oxidation occur during holding period in CFI tests. Comparing with LCF tests, quantities of intergranular crack was observed on the fracture surface and damage due to considerable oxidation (Fig. 11). It can be concluded that creep and oxidation had great influence on fatigue life in CFI tests, especially for the long holding period. However, creep is negligible in pure LCF tests and the effect of oxidation is limited. Thus fractograph from the LCF tests was characterized by ductile fatigue striations and secondary crack, which shows more transgranular appearance.
5. Conclusions A series of LCF and CFI tests were performed on nickel-base superalloy GH4169 at 650 °C to study the creep-fatigue interaction mechanism. The following conclusions can be drawn. 1. Irrespective of the loading waveform, GH4169 nickel-base superalloy exhibited cyclic softening during the whole life except for the low strain amplitude of 0.3%. 2. The fatigue life of GH4169 decreased with the increase of strain amplitude and tensile holding period. The fatigue life was almost unchanged when the holding period exceeds 120 s. 3. Single crack initiation site was observed in LCF tests while multiple crack initiation sites in CFI tests. The fracture modes of
182
G. Chen et al. / Materials Science & Engineering A 655 (2016) 175–182
GH4169 superalloy under LCF tests and CFI tests were transgranular and intergranular, respectively.
Acknowledgment The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. 51471116), the Program for New Century Excellent Talents in University (NCET-13-0400) of China and Tianjin University Independent Innovation Foundation (No. 2013E3-0003).
References [1] A. Diboine, A. Pineau, Fatigue Fract. Eng. Mater. Struct. 10 (1987) 11. [2] L. Fournier, D. Delafosse, T. Magnin, Mater. Sci. Eng. 269 (1999) 9. [3] L. Cheng, X. Xue, B. Tang, D. Liu, J. Li, H. Kou, J. Li, Mater. Sci. Eng.: A 606 (2014) 24–30. [4] K. Prasad, R. Sarkar, P. Ghosal, V. Kumar, Mater. Sci. Eng.: A 572 (2013) 1–7. [5] K. Prasad, R. Sarkar, P. Ghosal, V. Kumar, M. Sundararaman, Mater. Sci. Eng.: A 568 (2013) 239–245. [6] L. Xiao, D.L. Chen, M.C. Chaturvedi, Mater. Sci. Eng.: A 483–484 (2008) 369–372. [7] D. Fournier, A. Pineau, Metall. Trans. A 8A (1977) 1095–1105. [8] M. Sundararaman, P. Mukhopadhyay, S. Banerjee, Acta Mater. 36 (1988) 18.
[9] P. Zhang, Q. Zhu, C. Hu, C.J. Wang, G. Chen, H.Y. Qin, Mater. Des. 69 (2015) 12–21. [10] A. Bhattacharyya, G.V.S. Sastry, V.V. Kutumbarao, J. Mater. Sci. 34 (1999). [11] L. Xiao, D.L. Chen, M.C. Chaturvedi, Metall. Mater. Trans. A 35A (2004) 11. [12] T.J. Garosshen, T.D. Tillman, G.P. Mccrathy, Metall. Trans. A 18A (1987) 9. [13] G.Q. Sun, D.G. Shang, J. Deng, W. JG, Reseach Explor. Lab. 26 (2007) 3. [14] H.J. Han, M. Su, C.S. Wang, Aerosp. Mater. Technol. 2 (2008) 65–68. [15] D. Ye, D. Ping, Z. Wang, H. Xu, X. Mei, C. Xu, X. Chen, Mater. Sci. Eng.: A 373 (2004) 54–64. [16] D.C. Lord, L.F. Coffin, Metall. Trans. A 4 (1973) 8. [17] Hans-Peter Meurer, Gunter K.H. Gnirss, Wolfgang Mergler, Gerhard Raule, Hans Schuster, G. Ullrich, Nucl. Technol. 66 (1984) 9. [18] D. Hu, R. Wang, Mater. Sci. Eng.: A 515 (2009) 183–189. [19] Y.L. Lu, P.K. Liaw, L.J. Chen, G.Y. Wang, M.L. Benson, S.A. Thompson, J.W. Blust, P.F. Browning, A.K. Bhattacharya, J.M. Aurrecoechea, D.L. Klarstrom, Mater. Sci. Eng.: A 433 (2006) 114–120. [20] W.O. Ngala, H.J. Maier, Mater. Sci. Eng.: A 510–511 (2009) 429–433. [21] W.J. Plumbridge, E.G. Ellison, Fatigue Fract. Eng. Mater. Struct. 14 (1991) 17. [22] E. Hari Krishna, Kartik Prasad, Vikas Kumar, V. Singh, Trans. Indian Inst. Met. 63 (2010) 4. [23] L.F. Coffin, Trans. Am. Soc. Mech. Eng. 76 (1954) 20. [24] O.H. Basquin, Proc. Am. Soc. Mech. Eng. 10 (1910) 6. [25] D. Shi, J. Liu, X. Yang, H. Qi, J. Wang, Mater. Sci. Eng.: A 528 (2010) 233–238. [26] R.L. Hecht, J.R. Weertman, Metall. Mater. Trans. A 29A (1998) 9. [27] B. Fournier, M. Sauzay, Int. J. Fatigue 30 (2008) 14. [28] K.B.S. Rao, Mater. Sci. Eng. A 104 (1988) 15. [29] L. Xiao, D.L. Chen, M.C. Chaturvedi, Scr. Mater. 52 (2005) 603–607. [30] J. Zrnık, J. Semenak, V. Vrchovinsky, P. Wangyao, Mater. Sci. Eng. A 319 (2001) 6.