Impact of hydrogen on the high cycle fatigue behaviour of Inconel 718 in asymmetric push–pull mode at room temperature

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Introduction
Gas phase embrittlement of materials caused by the presence of damaging species such as oxygen, hydrogen, sulphur or chlorine has been an important issue for a number of industries over the years. At least since the end of the 1950s, hydrogen is known to have a deleterious effect on the mechanical properties of many materials [1][2][3][4]. Among these materials, Ni-based superalloys, which are widely used in stationary gas turbines and liquid rocket engines because of their high strength and good corrosion resistance, are sensitive to hydrogen embrittlement [5,6]. The presence of hydrogen inside the material can originate from the material's processing or from a hydrogen-rich environment through diffusion. Due to its small size, the hydrogen atom diffuses more rapidly than larger atoms. Considering that diffusion is a thermally activated process, the temperature at which the tests are done and also the time, i.e. number of cycles, to failure are decisive. Moreover, hydrogen tends to be attracted to regions of triaxial tensile stress where the crystalline lattice is dilated and thus, it is drawn to regions ahead of cracks under stress [7,8]. For this reason, the diffusion of hydrogen is facilitated by the formation of cracks during fatigue tests.
Increasing lifetime of many engineering components has led to a growing need for materials data and in particular for fatigue data at high number of cycles. To satisfy this demand, fatigue testing by ultrasonic excitation has been pioneered in the second half of the 20th century [9] and has since been established as a means for testing to 10 9 cycles and beyond. Since the technique probes only a small volume it is also well suited for testing welds [10]. An extensive description of ultrasonic high cycle fatigue (HCF) test techniques can be found in the literature [11][12][13]. However, open data on the effect of hydrogen and the stress conditions on the fatigue behaviour of Inconel 718 is incomplete. In this paper the dependence of the fatigue life of Inconel 718 on the environment and stress conditions is studied with the aim of characterising the impact of a high pressure (30 MPa) gaseous hydrogen (GH2) atmosphere on the HCF behaviour of Inconcel 718 in the range of 10 6 -10 7 cycles.

Material
The nominal chemical composition of Inconel 718 is shown in Table 1. Table 2 lists some basic mechanical properties. The alloy has been solution annealed and precipitation hardened (Table 3) to bring it into high strength state. The heat treatments, which were carried out in air, ensure that the alloying elements first are totally dissolved into the matrix before being precipitated. The resulting oxide layer formed after cooling was removed during the manufacturing of the specimens.

Test rig and specimens
The tests were carried out by means of an ultrasonic HCF test rig. Fig. 1 shows a scheme of the autoclave, the core part of the test setup. The setup has been developed for carrying out HCF tests in gaseous environments in asymmetric push-pull mode, i.e. at stress ratios R > À1, where R is the ratio of minimum and maximum stress r min and r max : The symmetric stress generated by ultrasonic excitation is superposed to a static stress resulting from a pressure difference. Before the test, the specimen is mounted between two acoustic horns. The upper horn is fixed to a piezoelectric transducer that converts an AC signal into mechanical oscillations at the test frequency of 20 kHz. The oscillating components are dimensioned to be in resonance with the test frequency so that a longitudinal standing wave can form. The function of the upper horn is to amplify the mechanical oscillations and to transfer them from the piezoelectric converter to the specimen. The reduction of the horn's diameter leads to an increase of the oscillating stress amplitude r a . The horn also serves as a lid closing the top of the autoclave.
Beneath the specimen, a second horn is mounted dividing the autoclave volume into two separate pressure chambers. The upper chamber contains the specimen in hydrogen or argon gas at a certain pressure, i.e., 30 MPa in the present test series. The lower chamber is filled with the same gas at a different (generally lower) pressure. The lower horn is fixed to the specimen and although a gasket is placed between the lower horn and the autoclave walls, the horn can move freely with regard to the autoclave wall. The lower horn is dimensioned to be in resonance with the excitation frequency of 20 kHz so it does not affect the standing wave in the load train. The gasket is positioned at a node of displacement of the lower horn to avoid damping of the oscillation as well as wear of the gasket by friction between the gasket and the autoclave wall. The pressure difference between the two chambers leads to a static force on all components of the load train, and in particular on the specimen. This force results in a static mean stress r m in the waist section of the specimen. A drawing of the specimen is shown in Fig. 2. The hourglass form leads to a maximisation of the mean and oscillating stresses at the specimen centre thus leading to failure at a position where the stress levels are known.
By adjusting the excitation voltage of the piezoelectric element and the pressure difference between the two chambers, the oscillating stress amplitude r a and the static stress r m can be controlled independently.
The specimens were not charged with hydrogen before testing. After installation of the specimens the test chamber was several times filled with the test gas at 1 MPa and purged. To avoid putting an undesired stress onto the specimen before the actual test, both pressure chambers were first brought synchronously to the lower of the two pressures, i.e. the pressure of the bottom chamber. Then the pressure in the upper chamber was increased to establish the environmental conditions for the test (30 MPa of GH2 or Ar). Once stable pressure conditions had been reached, the oscillating part of the stress was applied by manually starting the piezoelectric converter.
It has been shown experimentally that the specimen remains at room temperature without additional cooling. Monitoring the res-

Micro-structural characterisation
The microstructure and fracture surface of the samples were observed with a scanning electron microscope (SEM) (Zeiss Supra 50) equipped with energy dispersive X-ray (EDX) analysis. The samples of the bulk material were prepard for the SEM analysis by polishing followed by etching with glyceregia. Their structure was studied by X-ray diffraction (XRD) in a Panalytical Empyrean X-ray diffractometer using monochromated Cu K radiation and operated at a high voltage of 45 kV and anode current of 40 mA. The diffractograms were recorded from 40°to 100°, with a step size of 0.04°and time-per-step of 125 s.  Tables 6 and 7 in the appendix. In one case the test was stopped before specimen failure (dashed line). It has to be noted that three tests were carried out at somewhat higher gas pressures. These The lifetime decreases as the mean stress or stress amplitude increase. For example, the lifetime in Ar at r m ¼ 500 MPa is 7:79 Á 10 7 cycles when tested at r a ¼ 164 MPa but 4:10 Á 10 6 cycles at r a ¼ 218 MPa. Regarding environmental factors, it is observed that the lifetime of the samples tested in GH2 is in general shorter than in Ar under the same stress conditions. For example, for r m ¼ 300 MPa and r a ¼ 218 MPa the lifetime in Ar is 4:15 Á 10 7 cycles but only 4:66 Á 10 6 cycles in GH2. In Fig. 4 the data points have been plotted in the mean stress vs. stress amplitude plane. The stress region of the investigation was chosen as to accommodate lifetimes of 10 6 to 10 7 cycles and the operation limits of the available generator (Branson PGB 220 A) at low amplitudes [13].

HCF lifetimes
On the convex hull of the test area, a two-dimensional fit of N f as a function of r a and r m has been carried out. The interrupted test in Ar was not taken into account nor were the two tests at in an unrealistic bending of the isolines for low r m because of the insufficient number of data points in that area. Ar; test data GH2; test data GH2; 1e6 cycles GH2; 1e7 cycles Ar; 1e6 cycles Ar; 1e7 cycles Based on this interpolation two isolines for N f ¼ 10 6 and N f ¼ 10 7 cycles have been obtained. The kinks in the isolines (especially for the 10 6 cycles line in Ar) are artefacts of the fitting caused by the irregular spacing of the data points. Nevertheless, it is clear from the plot that the isolines for the tests in GH2 are shifted towards lower stresses compared to the corresponding lines in Ar environment.
For a closer look on the influence of hydrogen on the mechanical performance, the mean stress has been plotted vs. lifetime for a stress amplitude of r a ¼ 218 MPa (Fig. 5) and and the constant stress vs. lifetime for a mean stress of r m ¼ 500 MPa (Fig. 6). The dashed lines are power law fits according to a Basquin type relationship: where r f is either the mean stress or the stress amplitude at which failure occurs after N f cycles. A and B are fitting parameters as compiled in Table 4. The coefficients of determination R 2 were calculated from the logarithmic form of Eq. (2). The deleterious impact of GH2 on the lifetime is clearly visible in both cases. Similar observations have already been reported for other Ni alloys and Ni containing steels [16,17]. Fig. 7 shows the ratio of the lifetimes N f in GH2 and in Ar from the power law fits in Figs. 5 and 6.
At high stress levels the lifetime in GH2 is approximately 80% of the lifetime in Ar. However, the ratio of the lifetimes in GH2 and in Ar decreases as the stress decreases and total lifetime increases. At low stress levels and correspondingly long lifetimes, the lifetime in GH2 is approxmately only 20% of the lifetime in Ar. At least for the situation studied here, the influences of the mean stress and the stress amplitude on the fatigue life are comparable. The reduced impact of hydrogen at higher alternating stress levels for Ni-base alloys has already been mentioned before [16].
That behaviour relates to the hydrogen diffusion through the sample during the test. When the samples are tested at large mean stresses failure occurs after a relatively low number of cycles. The time hydrogen has to diffuse through the sample is therefore smaller than when tested at lower stresses. On the other hand, hydrogen diffusion is accelerated by high stress levels and strong gradients which would speak for a stronger impact of hydrogen at higher stresses. The curves in Fig. 7 show that in the case studied here, the longer exposure to hydrogen is the dominant effect which is consistent with the results reported in [16].
In [17], the impact of GH2 on the fatigue behaviour of two stainless steels with different Ni content at room temperature has been studied. The tests in [17] were carried out on notched specimens at a frequency of 1 Hz. In contrast to what was observed in the present work, the authors there conclude that the negative effect of GH2 at room temperature diminishes with decreasing stress amplitudes.
Although Eq. (2)     In the Goodman equation the stress amplitude r a is normalised by r N f , the stress amplitude leading to failure after a certain number of cycles at fully reversed conditions (i.e. R ¼ À1; r m ¼ 0). Correspondingly, the mean stress r m is normalised by the failure stress at constant load conditions ðR ¼ 1; r a ¼ 0Þ i.e. to the ultimate tensile stress r UTS .
In order to establish a generalised formulation of Eq. (2), the Goodman equation has been modified: r N f has been replaced by the stress amplitude r f at which the specimen fails after N f cycles at a given mean stress level r m -0 and r UTS is replaced by a parameter C 0 . This leads to a set of two equations with three fitting parameters A 0 ; B 0 and C 0 : Combining these equations allows experessing N f as: For fitting the parameters A 0 ; B 0 and C 0 the logarithmic form of Eq. (6) has been used where lg refers to log 10 : Figs. 8 and 9 respectively compare the experimentally observed numbers of cycles to failure N f;obs to the value N f;pred predicted by the fits in Ar and in GH2. The values for the parameters of the fits are listed in Table 5.
The fits describe the data reasonably well although the scatter is significant as confirmed by the R 2 values in Table 5. In the plots for both environments there is one outlier which is highlighted by a circle. The outliers correspond to tests performed at R ¼ À1. Omitting them in the fit considerably improves the quality of the fit as characterised by the increase of R 2 : 0:5418 ! 0:8290 in Ar and 0:6786 ! 0:8178 in GH2. Apparently the function defined by Eq.
(6) describes the data only in a limited section of the r m -r a -plain.
Since only a single test point at R ¼ À1 was available for every environment these tests had little impact on the values of the fitting parameters and are not well described by the resulting function.
The observed fatigue life for R ¼ À1 in Figs. 8 and 9 is much higher than predicted. A possible explanation for the particular location of these tests in the plots might come from a fracture mechanics apporoach. Fatigue life has an initiation part and propagation part. Fatigue crack propagation depends on the stress intensity [11]. In the Paris law for calculating the fatigue crack propagation rate only the stress intensity when a crack is open is accounted for, i.e. the periods of positive stresses. Thus for a given stress amplitude the effective stress intensity range is only half the value for R ¼ À1 compared to R > 0. Alternatively one can invoke crack closure considerations to assess the influence of a compression phase on fatigue crack propagation [11]. This leads to significantly reduced crack propagation rates and a longer propagation life for R ¼ À1. This effect should also be seen for all cases with R < 0. For R ¼ À0:55 and À0:29 the observations lie slightly above the predictions but the effect is very small and these data points lie in the scatter band.
Also a purely experimental reason cannot be excluded with certainty. During the tests at R ¼ À1 a bypass directly connecting the two pressure chambers was opened to guarantee the same pressure in both chambers. During the tests with R > À1 this bypass was closed. Opening this bypass may have led to an unexpected change of the experimental conditions. Further tests at R % À1 are needed to clarify this point.
The tests carried out at higher pressures are highlighted by triangles. But for the test in Ar at R ¼ À1 they are well inline with the other data, thus confirming the insignificant influence of the variation in pressure on the fatigue life.

Table 5
Values for the parameters in Eq. (6) in Ar and in GH2. The tests at R ¼ À1 are outliers in both environments and have been discarded during the fit. both in Ar and GH2. Fig. 10 shows the XRD diffractograms of the four tested specimens. All analysed samples exhibit XRD peaks associated with the c phase as described in [18]. No additional peaks at lower angles from the c diffractions, characteristic of the b hydride phase [19], were observed. It is important to notice that the spectra were acquired after storing the samples for 3 months in air. By this time, the hydride phase has decomposed and could not be detected by XRD [19]. However, the XRD peaks after hydrogen charging at both stress conditions are slightly shifted towards smaller angles as compared to the specimens tested at the same conditions in Ar. This shift which is comparable in size to the angular resolution of the instrument suggests that some hydrogen might still be present in solid solution inside the crystalline lattice of the c phase. This hypothesis however cannot be confirmed by EDX because of the low atomic weight of hydrogen. Effects of the hydride decomposition could nevertheless be deduced from SEM observations in the bulk materials and in the fracture surfaces. Fig. 11 shows SEM images of Inconel 718 tested in Ar (a, c) and in GH2 (b, d). Fig. 12 shows a magnified section of Fig. 11(d). The samples were cut from tested specimens just behind the waist, so they were exposed to almost the same stress conditions as the centre plane where failure occurred. The investigated surfaces are perpendicular to the specimen's tensile axis i.e. parallel to the fracture surfaces.
The microstructure consists of c grains with g precipitates along the grain boundaries and the matrix as indicated by arrows in Fig. 11(c). The g precipitates formed inside each grain follow a Widmanstätten pattern with an orientation generally differing between neighbouring grains (see inset in Fig. 11(d)). These precipitates are formed during annealing to bring the alloy in high strength condition [20].
After testing in hydrogen some parallel cracks are formed inside the grains (white arrows in Fig. 12). No comparably evident cracks were found on the samples tested in Ar. Similar, albeit more obvious cracks have been observed previously in different Ni containing steels and Ni basis alloys [19]. Those cracks were caused by the decomposition of hydrides during the desorption process of Fig. 11. SEM images of the transverse section after testing at ra ¼ 218 MPa with rm ¼ 600 MPa in Ar (a) and GH2 (b), and with rm ¼ 300 MPa in Ar (c) and GH2 (d). The arrows point ot the g plates in the grain boundaries and the matrix.  hydrogen [19]; they were not fatigue related. It seems therefore likely that the cracks shown in Fig. 12 are also caused by hydride decomposition rather than fatigue.

Fracture surfaces
To better understand the influence of hydrogen on the fatigue behaviour, the fracture surfaces of selected specimens have been investigated by SEM after the fatigue tests. Figs. 13 and 14 respectively compare the fracture surfaces of specimens tested at r m ¼ 600 MPa and r m ¼ 300 MPa for a fixed stress amplitude of r a ¼ 218 MPa. In both figures, the images on the left are from specimens tested in Ar, whereas the images on the right show specimens tested in GH2. The images in the top line (a, b) give a global view of the area of crack initiation. The insets in these images are taken at a distance from the actual initiation sites. Images (c) and (d), in the bottom row focus on the initiation sites.  Comparing the specimens tested at the higher mean stress level ðr m ¼ 600 MPaÞ in Fig. 13 for Ar and GH2, several differences can be observed. The fracture surface of the specimen tested in Ar (a, c) clearly shows areas with a dimple structure (inset in (c)) typical for ductile fracture. In the direct vicinity of the crack nucleation site this dimpled surface morphology dominates (a) whereas further away from the nucleation site also areas with more intergranular fracture can be found (inset in (a)). This change of fracture mode with the extension of the crack for Inconel 718 has already been observed previously [21]. Such dimpled areas are not found on the specimen tested in GH2 indicating a more brittle fracture.
In the case of the test in Ar there is no well defined nucleation point whereas the crack nucleation site for the specimen tested in GH2 can be clearly identified. In GH2 a cubic particle with a size of about 10 lm was found at the nucleation site (inset in (d)). The particle was cracked due to the large stresses during fatigue testing. According to EDX analysis, this intermetallic particle is rich in Ti (43 wt.%) and Mn (10 wt.%) and could correspond to Ti 2 Mn. The area in the immediate vicinity of the particle has a very ragged surface. An elongated hole of comparable dimensions above and to the right of the particle may have held another particle that has been removed from the specimen.
Looking at the fracture surfaces from the specimens tested at lower mean stress level ðr m ¼ 300 MPaÞ in Fig. 14 one can also see differences between the samples tested in Ar (a, c) and GH2 (b, d). The specimen tested in Ar shows typical facets indicative for transgranular fracture. The situation for the fracture mode of the specimen tested in GH2 is less clear; although some areas in (b) show facets, the fracture in its integrality can neither be described as clearly transgranular nor intergranular. Hydrogen seems to lead to an embrittlement of the grain boundaries resulting in a transition from essentially transgranular fracture in neutral atmosphere to a more intergranular fracture in GH2. As in the case of the higher mean stress, the specimen tested in Ar does not show a well defined crack nucleation site whereas the fracture of the specimen tested in GH2 can be traced down to a well localised spot. At the site where crack initiation occured, some deep cracks where found (highlighted by arrows in inset in Fig. 14(d)). These cracks outline a cubic geometry which suggests they may be caused by an intermetallic particle acting as stress concentrator similar to the situation found for the test at higher means stress in GH2 (Fig. 13(d)).

Conclusions
I. The presence of gaseous hydrogen at high pressure leads to a significant reduction of the lifetime of Inconel 718 specimens in fatigue tests. II. The deleterious effect of hydrogen on the fatigue life of Inconel 718 specimens increases with decreasing levels of both, the mean stress and the stress amplitude. III. A formulation using a variation of the Goodman relation for describing the number of cycles to failure N f as a function of mean stress r m and stress amplitude r a has been found to cover most of the data well. The two tests carried out at R ¼ À1, however, were not well described by this function. Further investigations are needed to clarify whether this discreapancy between the tests at R ¼ À1 and the other tests can be explained by fracture mechanics or whether there is an experimental reason. IV. The XRD scans of the specimens tested in hydrogen do not show additional peaks characteristic to hydride b phase, but the peaks associated to the c phase are slightly shifted to smaller angles compared to the specimens tested in Ar.
These results suggest that although b-hydrides decompose rapidly once the tested samples are stored, some hydrogen atoms might still remain in solid solution inside the grains. V. SEM analyses of specimens tested at different mean stress levels have revealed signs of hydrogen embrittlement on their fracture surfaces.

Acknowledgment
Funding from the European Union Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 218849 is gratefully acknowledged.

Appendix A
See Tables 6 and 7.