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Nickel-base alloys are now used extensively in gas turbine engines as turbines and discs. Differ from the compressors, turbines and turbine discs are certainly suffered from high temperatures and high stress cycles . Due to the low creep rate and good high temperature strength, nickel-base alloys are developed to fabricate the blades and discs. It is obviously that the operating environment of turbine blade and disc are severe, so the importance of understanding and predicting the life time of these components is considerable.
Common failures which may occur in the gas turbine blades and discs are classified as FOD (Foreign Object Damage), high temperature failure, fatigue, creep and corrosion . Although, gas turbine engines are considered to having high reliability, in reality, this high reliability is achieved by components replacement. In operation, one critical failure is fatigue crack which involves to the initial defects which result from the fabrication or FOD of Ni-base alloy. The crack will grow from the defects during the high stress cycles .
There are two situations in operating gas turbine engines which may lead to the fatigue crack. They are defined as the low cycle fatigue (LCF) and the high cycle fatigue (HCF). LCF involves to the starting and stopping of the turbine and the HCF is related to the vibrational stress during the operating time [2, 3]. The criteria of operating the turbine under a safe condition is that when the engine has been started, the blades and discs should be strong enough to support the accumulate stress which comes from the high rotation vibrational load . In HCF situation, due to the high rotation speed of the rotors, the stress cycle that result from the vibration can easily go up to cycles per hour, this is sufficient to get cycles in less than 500 hours . So, the high temperature strength of the blades and discs should be carefully designed. Under LCF condition, the stress is much larger than the stress that generated by the vibration. The gas turbine engines are usually big so the self-weights of turbine blades and discs will lead to a large stress at low temperature when the engine is switched to start and stop. In addition, the thermal cycle will also occur during the starting and stopping. These are seen as the life time limit for the blades and discs. A typical life time of a turbine disc is only 10000 cycles or less . So, the balance is that the engines are designed to reach the fatigue life limit of the airplane body before they reach the limit of LCF.
According to the studies of others, Ni-base superalloys can retain their high strength at relatively high temperatures are as a result of precipitation strengthening. The main alloying elements of Ni-base superalloys are Ti and Al and they can form precipitations in the form of, which is so called prime () . Turbine blades and discs usually work at 540 or even higher, can remain at this high temperature and offer strengthening to make Ni-base superalloy good performance. It was also found that the Nb and V could form precipitations like and so called. It is based on a body-centred tetragonal lattice and can offer great strength at lower temperatures .
In industrial processing, the turbine discs are made from casted polycrystalline crystal Ni-base superalloys to against the cycle fatigue limitation. And casted single crystal Ni-base superalloys are used to produce the blades which are the hottest parts in the gas turbine engines . Some investigations have been carried out to research the fatigue behaviours of these two components. In this report, typical Ni-base superalloys for both turbine blades and discs were studied according to the Studies of Xiao-Feng Ma and Karel Obrtlík [6, 7].
Fig.1 Typical fatigue crack occurs at the trailing edge of blade .
2.0 Experiment Procedure
Two typical Ni-base superalloys were test in the experiment are Inconel 718 and Inconel 738LC. Inconel 718 is generally used to make turbine discs and Inconel 738LC is used to fabricate the turbine blades which are the hottest parts in gas turbine engine. The experiments are processed to investigate the very high cycle fatigue (VHCF) behaviour of Inconel 718 at room temperature and the low cycle fatigue crack growth of Inconel 738LC at high temperature.
2.1 Procedure to Investigate VHCF of Inconel 718
The composition of investigated Inconel 718 is: 18.67 Fe, 18.67 Cr, 5.12 Nb, 5.12 Ta, 3.09 Mo, 0.9 Ti, 0.66 Al, 0.12 Mn, 0.11 Si, 0.09 Co, 0.02 C, 0.009 P, 0.004 B, 0.001 S, and balanced Ni. The alloy was solution heat treated at 970 for 1h and water quenched. Then it was aged at 720 for 8 hours before it cool to 620 with the furnace. After aging for 8h at 620, the alloy was air cooled to room temperature .
The test is carried out on a four-axis cantilever-type rotation bending fatigue machine which is developed by the Research Group for Statistical Aspects of Material Strength in Japan. The specimens were processed to the shape which is show blow. The frequency is set to 52.5 Hz and load ratio R=. All the tests were taken under ambient atmosphere and at room temperature. The stress concentration factor was given by 1.024 which was processed by finite element method .
Fig. 2 Parameters of Test Specimens .
2.2 Procedure to investigate LCF of Inconel 738LC
As mentioned above, the LCF usually occur when the component receive high stress cycle. The stress is usually above the material's yielding stress. According to the lectures, this kind of fatigue is controlled by strain which involves to open/close route, thermal cycle and some severe notches . The experiment which taken by Karel in order to reveal the low cycle fatigue of Inconel 738LC at high temperature (800) .
The chemical composition of tested material is: 0.008 B, 0.04 Zr, 0.1 C, 0.84 Nb, 0.2 Fe, 1.71 Mo, 2.63 W, 3.35 Al, 3.37 Ti, 8.78 Co, 16.22 Cr and balanced Ni. The Inconel 738LC samples were heat treated and reveal coarse dendritic grains. Average grain size which measured was 1.3mm and the microstructure told the volume fraction of precipitation was about 61% with average 670nm in size. The specimens were shaped to button-end form and the gauge length was 15mm with 6mm in cross section. The gauge part was parallel to the longitudinal axis and electrolytically polished for SEM observation .
The fatigue test was carried out on a computer controlled electrohydraulic push/pull machine. It is mentioned that the LCF is controlled by strain, so all the specimens were tested under strain cycles with constant strain rate /s . The experiments were taken under room temperature and 800, in order to reveal the specific features of LCF at high temperatures.
Fig. 3 TEM image shows the microstructure of Inconel 738LC 
3.0 Results and Discussion
3.1 Results of High Cycle Fatigue Test of Inconel 718
The S-N curve (Fig. 4) showed that fatigue of Inconel 718 at room temperature can still occur after cycles. The experiment longest fatigue life time is cycles . And then, all the specimens were taken to SEM observations to exam the fracture surface. The crack initiation sites showed differently in different fatigue life conditions. Fig. 5 gave the images of four specimens which showed that with longer fatigue life time, the crack initiation sites turned to be reduced. There was only one crack initiation site for the specimen which has a magnitude larger than cycles fatigue life compared to that about 6 initiation sites for a magnitude of cycles fatigue life time.
Fig. 3 S-N curve of Inconel 718 at room temperature .
Fig. 4 SEM images of different specimens' fracture surfaces. (a) 1.481Ã- cycles, 6 crack initiation sites. (b) 4.91Ã- cycles, 3 crack initiation sites. (c) 9.912Ã- cycles, 2 crack initiation sites. (d) 3.3894Ã- cycles, 1 crack initiation sties .
Typical fatigue features were disclosed through SEM images. Four zones were discovered at the fracture surface. For zone I, it was the initial area, often had a flat surface. It was seen as the crack initiation zone. Zone II showed the propagation of cracks. For zone III, there were radial steaks formed in a relatively large area compared to zone I and zone II. The last zone IV revealed that some dimples occurred . Fig. 5 presented below showed the macrostructure of the fracture surface.
Fig. 5 Fatigue regions found in fracture surface.
It was also found that when the stress amplitude came up to 520MPa, the fatigue life would sensitive to the stress level. One typical sample which had up to cycles fatigue life was taken as an example of general fatigue regions (Shown in Fig. 6). In zone I, crack initiation occurred at the surface grains and then a cleavage like crack was found just near the crack initiation site and this kind of crack dominant in the zone II (Fig. 7c). In low regime of zone III, the striation could be seen together with the cleavage like crack (Fig. 7d). And at the high regime of zone III, a ductile dimpled fracture could be found (Fig. 7e). In zone IV, the typical ductile failure features is visible (Fig. 7f). At last, secondary crack initiation was found in the later stage of zone III and early stage of zone IV (Fig. 7e) .
Fig. 6 Crack initiation site in zone I .
Fig.7 (c) Cleavage like fracture. (d) Striations in early stage of zone III. (e) Secondary crack initiation in zone III. (f) Ductile dimpled fracture in zone IV .
Another observation was that when the samples with longer life time up to cycles showed that the crack initiation sites became to form at subsurface grains. And some tyre patterns were found near the crack initiation site which was unusual. The other features were similar to those of cycle samples .
22.214.171.124 Crack initiation
Based on the experiment, no inclusions were found in the microstructure. The fatigue crack usually occurs at slip bands. The cyclic plastic strain makes slip bands oriented to their favourite grains and form persistent slip band. The crack will then initiate at this kind of slip band . Based on the results of the experiment, the crack initiation sites were differ from different fatigue life times which means the crack initiation sites were changed with different stress amplitude. Basically, the crack initiation involves to the energy which is offered to form a crack and the surface is a more favourable place than the transgranular boundaries for crack formation and growth.
In high stress amplitude situation, the energy is sufficient to active more than one slip band, and then the crack initiation sites will more than 1. And under lower stress amplitude condition which usually leads to a longer fatigue life time, only the favourite slip band will be activated. Ni has a FCC crystal, the most easily slip plane is, that why the facet is usually 45 to the rod axis. It is proved that those with more than 1 crack initiation sites samples have shorter fatigue life time than those with only 1 crack initiation site.
126.96.36.199 Crack propagation
Ideally, the crack will propagate after the initiation means the crack propagation will occur follow the formation of crack initiation zone which is usually several grains size area. According to the Paris Regime, the crack growth rate has special relationship with the stress intensity range (). At the first stage, the stress intensity factors (K) of different fatigue zones were calculated carefully by using the equations which were summarised by Anderson .
Equation (1) gives the method to calculate stress intensity factor (K) at crack initiation site. In addition, this equation can also be used to calculate the K of the other fatigue regions, such like zone II, zone III. The represent the applied normal stress amplitude, is the shape factor, E(k) is the second integral of ellipse and b is the length of semi-minor axis of the ellipse .
Also, for the condition of initiation at subsurface, the equation is modified to equation (2) which is shown below. The is the subsurface crack initiation size.
Then, the stress intensity ranges for zone I, II and III were calculated and plotted in a stress intensity range vs. fatigue life cycle figure (Fig. 8). It is visible from the plot that the stress intensity ranges at crack initiation site decrease slightly with the increasing fatigue life. This was found that those cracks which initiate at lower stress amplitude can propagate at smaller stress intensity factor. The ranges change from 9 to 15 . According to the Paris regime, this range can be seen close to the Threshold range of Inconel 718 . At the threshold point, the crack growth rate becomes sensitive to the meal stress, means the cracks will begin to propagate.
Fig. 8 Stress intensity range () vs. Fatigue life cycles. is the range for zone I, is the range for zone II and the range at zone III is shown as .
A typical Paris Regime curve is shown in Appendix. For the stress intensity range of zone II, it is ranged from 19 to 29 . It can be seen as the near threshold region and the lower Paris regime. It was also found by Xiao-Feng Ma that at the later zone II, when the striations occurred in large area, the stress intensity range is about 37-55 . This proved that a typical striation became to dominant when stress intensity range larger than 35 which was summarized by Mercer .
In zone III, stress intensity ranges were distribute from 70 to 80 . This is regard as the effect of fracture toughness of Inconel 718 . From Paris Regime curve, zone III was define as a rapidly crack propagation area. This can be close to the higher Paris Regime. And then, as shown on the Paris Regime curve, the material will fracture under a tensile overload condition.
188.8.131.52 Prediction of Fatigue Life Time
The method which is widely used to predict fatigue life time is to sum the crack initiation time and the time that crack propagate to the final fracture together. For Inconel 718 superalloy at HCF condition, the crack initiation time model was assumed by Chan .
Where is the stress range, M represents the Taylor factor for the favorable oriented grain. is the friction stress of dislocations. is the crack initiation time, c is regarded as the depth of initiation sites, Î¼ is the shear modulus, h is the width of slip band, is the Poisson's ratio and d is the grain size .
It can be seen from equation (3) that generally, a smaller grain size will give a longer crack initiation time which can longer the fatigue life partly. And also, with a deeper initiation site, crack initiation will need more cycle time. That is proved in the observation in VHCF samples that the crack initiation sites are turning to go inwards to the subsurface.
The crack propagation time is assumed by Fournier which is shown below in equation (4) .
Where is the crack initial length, is the final length of the crack at fracture which can be seen as the same as sample radius, is the geometry factor which is constant equal to 0.5. C and n can get from the Paris Law: .
A typical fatigue life time prediction model is summarized by Alexandre in his study of Inconel 718 .
The values of C and n can be gotten from the curve fit to Paris Regime curve. It is proved to have a good fitting to the experiment datas.
One critical issue in predicting the life time of HCF is that in most HCF cases, the crack initiation time takes over the fatigue life up to 90%. It is different from LCF where the crack initiation time is only 40% of fatigue life. This is due to the low stress amplitude in HCF which leads to crack initiation .
3.2 Results of Low Cycle Fatigue Test of Inconel 738LC
The stress amplitude vs. cycle numbers curves for room temperature and 800 are shown below (Fig. 9). Hardening was obviously under both high and low strain amplitude at room temperature. And softening was observed at the end of life cycles. Stress saturation only occurred at lower strain amplitude. In medium strain amplitude, softening occurred after the primary hardening and then slightly hardened before the final softening. Differently, at 800 hardening was not obviously at medium and low strain amplitude. And stress saturation could be found at medium and low strain amplitude.
Fig. 9 Stress amplitude vs. cycle numbers curves for (a) room temperature, (b) 800 .
Image of surface topography is shown in Fig. 10. Slip marking were observed at the surface and at the right up corner of the image showed the extrusion and intrusion of material at slip band. The experiment data showed that the slip bands decreased at 800 than at room temperature .
Fig. 10 Surface relief of samples tested at 800 (Failure strain=0.5%).
As mentioned before, the LCF is a strain controlled fatigue. Hardening and softening is normal at LCF experiments. It is agreed that at the first few cycles, this kind of kind of superalloy turned to be hardened. This may results from the movement of dislocations. As the stress were applied, dislocations likely to move and would interaction with each other. Normally, dislocations would be arrested at grain boundaries, and the stack of dislocations would inhibit the movement of other dislocations. This can cause hardening. Also, the precipitations in Inconel 738LC would also act as barriers to inhibit the movement of dislocations. Softening is cause by the increased stress which can make dislocations come across the grain boundaries. Once the dislocations cross the boundary, the stress will decrease because of no other stack of dislocations to inhibit the movement. The final softening maybe usually cause by tensile overload which cause the final fracture. Lower stress would be needed to get to the final failure strain.
At room temperature and high strain amplitude, the applied stress is high, so the softening is not obviously after visible hardening. The stress is too high and the material fracture easily. At medium strain amplitude, the second hardening may be caused by the secondary stack of dislocations. And at low strain amplitude, the stress saturation occurred due to the steady state that one dislocation stack at grain boundary and another new dislocation formed at the other side of the boundary.
At 800, due to the effect of temperature, it's likely that the precipitations will dissolve and the grains will grow. It is not easy to form the stack of dislocations. Only at high strain amplitude, the stress is high and then more dislocations will occur and form stack of dislocations at boundaries. Another observation is that the stress is lower at 800 than that at room temperature for same strain amplitude. This can used to explain that the slip bands decreased with increased temperatures. Fewer dislocations would be generated at lower applied stress and the dissolving of precipitations would make dislocations more easily to move.
To predict the fatigue life time, plastic strain amplitude at half-life can be used. Fig. 11 is the plastic strain amplitude vs. number of fracture cycles curve. This was mentioned to obey the Manson-Coffin law .
Stress amplitude applied at half-life vs. numbers of life cycles curve is plotted in Fig. 12. The data of the experiment obeys the Basquin law .
and are the ductility coefficient and strength coefficient of fatigue, and the fatigue ductility exponent c, strength exponent b as well as the two components in former can be calculated by using regression analysis technology. The calculated numbers is shown in Table. 1.
Fig. 11 Plastic strain amplitude vs. number of fracture cycles .
Fig. 12 Stress amplitude applied at half-life vs. numbers of life cycles .
Table. 1 Values for Paris Regime, Manson-Coffin law and Basquin law.
In this study, HCF of Inconel 718 at room temperature and LCF of Inconel 738LC at 800 were investigated. It can be conclude that Inconel 718 which used to build turbine discs has a good HCF property at room temperature. The crack initiation sites decreases as decreased stress amplitude. Only one initiation site occur at HCF situation. Four fatigue zones were classified for evidence of fatigue failure stage I and stage II based on Paris Regime. And for Inconel 738LC which is used to fabricate turbine blades, LCF should be a problem in real operation. Due to their large grain size, the resistance of fatigue is poor. However, large grain size is designed to prevent high temperature creep failure. In reality, the fatigue of turbine discs and turbine blades are rarely to seen. The turbine blades will be replaced if critical defects occur. The turbine engines usually have a longer life than the airframe. But, the LCF can be still a problem in those airplanes which were used in short distance fly .
What's more, the modern fatigue test cannot reflect the real fatigue process. The results vary with stress ratio, frequency and test environment . Further work should be focus on the initial microstructure evolution of materials and advanced testing technology and modelling.
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