High-cycle fatigue behavior of Co-based superalloy 9CrCo at elevated temperatures

Wan Aoshuang,Xiong Junjiang,Lyu Zhiyang,Li Kuang,Du Yisen,Chen Kejiao,Man Ziyu

School of Transportation Science and Engineering,Beihang University,Beijing 100083,China

High-cycle fatigue behavior of Co-based superalloy 9CrCo at elevated temperatures

Wan Aoshuang,Xiong Junjiang*,Lyu Zhiyang,Li Kuang,Du Yisen,Chen Kejiao,Man Ziyu

School of Transportation Science and Engineering,Beihang University,Beijing 100083,China

A modified model is developed to characterize and evaluate high-cycle fatigue behavior of Co-based superalloy 9CrCo at elevated temperatures by considering the stress ratio effect.The model is informed by the relationship surface between maximum nominal stress,stress ratio and fatigue life.New formulae are derived to deal with the test data for estimating the parameters of the proposed model.Fatigue tests are performed on Co-based superalloy 9CrCo subjected to constant amplitude loading at four stress ratios of-1,-0.3,0.5 and 0.9 in three environments of room temperature(i.e.,about 25 °C)and elevated temperatures of 530 °C and 620 °C,and the interaction mechanisms between the elevated temperature and stress ratio are deduced and compared with each other from fractographic studies.Finally,the model is applied to experimental data,demonstrating the practical and effective use of the proposed model.It is shown that new model has good correlation with experimental results.

1.Introduction

Due to the superior stiffness and strength,excellent resistance to creep,oxidation and corrosion as well as good fracture toughness at elevated temperature,Ti-,Co-and Ni-based single crystals or polycrystalline superalloys are undergoing a wide application as gas turbine blade materials in advanced aircraft engine engineering and are commonly confronted witha wide range of high temperatures(25 °C to 1000 °C).High temperatures can heavily affect fracture and fatigue characteristics and damage mechanism and it is possible for some superalloy materials to experience fatigue transition from cleavage mode at lower temperatures to ductile fracture at higher temperatures.1–9In addition,it is proved that static strength and fatigue characteristics of superalloys at elevated temperatures are fundamentally dependent on a number offactors such as constituent content,10microstructure type(e.g.,grain size,boundary,etc.)11,12and sampling orientation13of material,specimen configuration(e.g.,smooth,notched,etc.)14–16and geometric dimensions17,surface condition(e.g.,surface finish,initial-flaw,etc.),18,19processing technique,20,21mean stress of cyclic loading,22,23etc.As a result,it is becoming important to study the effect of these factors on fatigue characteristics and damage mechanism at elevated temperatures during the design prediction stage for failure limits and reliability assessments of aircraft engines.

In reality,during engine operation,some aircraft engine components usually undergo small vibrational loading at high stress ratio and high frequency in elevated temperature environments,causing the cracking initiation from small defects.Therefore,the temperature-dependent high-cycle fatigue(HCF)failure at high stress ratio and high frequency loading is becoming the single largest cause of aircraft enginefailures,and temperature-dependent HCF property at high stress ratio and high frequency loading is one of the most critical mechanical properties of superalloy.Although large amount of investigations were performed on temperature-dependent HCF properties of superalloys,the effects of high stress ratios on the temperature-dependent HCF property of superalloy are scarcely reported and the related mechanism is not systematically studied.Hence,it is important and crucial in engineering design of superalloys to fully understand the effects of fatigue loading at high stress ratio on the temperature-dependent HCF property.It is desirable to have a technique to assess the above effects on the high temperature fatigue lifetimes of the superalloy components in aircraft engines.

This paper seeks to develop an appropriate model to characterize and assess the effects of fatigue loading at high stress ratio on the temperature-dependent HCF property of the superalloy components in aircraft engines.The underpinning work comprises five features:(1)a modified model is developed to characterize the temperature-dependent HCF property of the superalloy by considering the effects of stress ratio;(2)novel formulae are derived to deal with the test data for estimating the parameters for the proposed model;(3)HCF property tests are performed on Co-based superalloy 9CrCo subjected to constant amplitude loading at four stress ratios of-1,-0.3,0.5 and 0.9 in three environments of room temperature(i.e.,about 25°C)and elevated temperatures of 530 °C and 620 °C;(4)the interaction mechanisms between the elevated temperature and stress ratio are deduced from fractographic studies;(5)applications of the modified model show good correlation with experimental results.

2.Modified model for high-cycle fatigue behavior by considering stress ratio effect

Generally,the S–N curve expressed by empirical power function formula with three-parameter is used to characterize the material fatigue performance.24Fatigue performances of materials pertinent to symmetrically cyclic loading(or at a specific stress ratio of-1)can be described as

where S-1is the maximum nominal stress pertinent to symmetrically cyclic loading in fatigue tests,S0is the fatigue endurance limit fitted from experimental dataset,C and m are the material constants,and N is the number of stress cycle before fatigue failure.

It is worth pointing out that fatigue tests are usually conducted only at a specific load ratio of-1 to determine fatigue performances of materials.Conversely,there are a large number of stress cycles with different stress ratios in an actual load history.Therefore,it is essential to correct the S–N curve to be suited for the stress cycles with different stress ratios in an actual load history using the empirical constant life diagram.

The empirical Goodman diagram25is applied to correcting the S–N curve as

where Saand Smrepresent the nominal stress amplitude and mean nominal stress,respectively,and σbis the ultimate strength of material.

From the definition of stress ratio,it can be shown as

where Smaxand Sminrepresent the maximum and minimum nominal stresses,respectively.

Taking transformation of Eqs.(2)and(3)gives

Substituting Eq.(4)into Eq.(1)leads to a fatigue S–N curve for materials suited for different stress ratios as

It is seen that Eq.(5)describes the relationship between maximum nominal stress Smax,stress ratio R and fatigue life N,displaying an S–N–R surface in three-dimensional coordinate system.The unknown material constants m,C and S0of Eq.(5)can be determined from experimental dataset.

Taking the logarithm form of Eq.(5)yields

where

From the above equations,it can be seen that¯y,Lyyand Lyxare associated with the undetermined constant S0.Alternatively,¯y,Lyyand Lyxare functions with respect to S0.So the undetermined parameters a,b and r(S0)are also the functions with regard to S0.By optimizing the absolute value of the linearly dependent coefficient r(S0),it is possible to numerically solve S0from Eq.(9).The unknown constants m and C are the n determined.

Table 1 Nominal chemical composition of 9CrCo alloy.

Table 2 Mechanical properties of superalloy 9CrCo.

Fig.1 Diagram of specimens for HCF tests.

From Eq.(5),it can be allowed that the S–N curve corresponds to a given stress ratio of R0,namely,

3.Fatigue tests at room temperature and at elevated temperatures

Fig.2 Fatigue experiments of superalloy 9CrCo at the same stress ratio but different temperatures.

All specimens manufactured for high-cycle fatigue experiments were smooth and made of Co-based superalloy 9CrCo.The nominal chemical composition(wt%)and mechanical properties of Co-based superalloy 9CrCo are listed in Table 1 and Table 2,respectively.The geometry and dimensions of the specimen are shown in Fig.1.High-cycle fatigue experiments were performed on QBG-50kN high-frequency tester under tension–tension(T–T)or tension–compression(T–C)cycle loadings with a constant stress amplitude and sinusoidal waveform at four stress ratios of-1,-0.3,0.5 and 0.9 in three environments of about 25 °C and elevated temperatures of 530 °C and 620°C.The loading frequency ranges from 80 Hz to 120 Hz and the experimental temperature was controlled through QBT-1200K split and drum-type high-temperature furnace with a temperature fluctuation within ±2 °C.Note that previous research26–28shows the effect of load frequency below 250 Hz on fatigue life is negligibly small(i.e.,less than 3%),so the loading frequency ranging from 80 Hz to 120 Hz is argued to be valid and appropriate for fatigue tests in this work.

According to the ASTM E468-9029and E739-91,30in order to determine fatigue S–N curves of the specimens,three sets of fatigue life tests were conducted with three different levels of constant stress amplitudes,and at least three specimens were employed for each set of fatigue life tests.After this,fatigue up-down tests were carried out to determine fatigue endurance limit at N=107and at least three matched pairs were obtained in the fatigue up-down tests.The fatigue endurance limit has to be estimated and the n a fatigue life test is conducted at this stress level.If the specimen fails prior to infinite life(i.e.,107cycles),the next specimen has to be tested at a lower stress level.If the specimen does not fail within this life of interest,the new test is run at a higher stress level.Therefore,each test is dependent on the previous test results,and the tests continue in this manner in sequence with the stress level being increased or decreased by selected stress increments.If a specimen fails before 107cycles at the ith stress level of the maximum stress Si,while another specimen does not fail at this life at a lower(i+1)th stress level of the maximum stress Si+1,it is deduced that the maximum stress pertinent to 107cycles is between Siand Si+1.If the stress difference Si-Si+1is very small and less than 5%of Si+1,the mean of Siand Si+1can be thought as the fatigue endurance limit given by

As mentioned above,the two experimental data of Siand Si+1with the reverse results(failed and unfailed)form an individual Srisampled randomly.Using these data of Sriand statistical principles,the mean and standard deviation of the fatigue endurance limit at a given life can be estimated as

Fig.3 Fatigue experiments of superalloy 9CrCo at the same temperature but different stress ratios.

The experimental results are shown in Figs.2 and 3 and Tables 3 and 4(here T is the temperature in fatigue tests).It is worth pointing out that the experimental data points labeled with the arrows and attendant numbers in Figs.2 and 3 represent the mean value and the number of matched pairs from the up-down tests.From Figs.2 and 3 and Tables 3 and 4,it can be seen that(i)in the same stress ratio case,fatigue strengths and fatigue endurance limits are lower at two elevated temperatures of 530 °C and 620 °C than at about 25 °C,which means that simultaneous interaction of elevated temperature and fatigue load substantially weakens high-temperature fatigue properties as against pure fatigue(about 25°C)condition,and hereby,it is argued that elevated temperature has significant adverse effects on high-cycle fatigue property for superalloy 9CrCo;(ii)the difference between experimental results of fatigue properties for the elevated temperature(i.e.,530°C or 620 °C)and about 25 °C increases with the increasing stress ratio,which implies that the elevated temperature-loading interaction is enhanced with the increasing stress ratio,causing a greater decrease of fatigue strength.

From the experimental observation(Fig.4),it is apparent that in three environments of about 25°C and elevated temperatures of 530 °C and 620 °C,tested specimens exhibit the similar fatigue failure modes.In other words,under T–C cycle loadings at two stress ratios of-1 and-0.3 in three temperature environments,fatigue failure modes of tested specimens can be reckoned to be characteristic of fatigue crack initiation and propagation until rupture.In contrast,as distinct from tested specimens subjected to T–C cycle loadings at two stress ratios of-1 and-0.3,under T–T cycle loadings at two stress ratios of 0.5 and 0.9 in three temperature environments,tested specimens experience distinct plastic deformation until ductile fracture and display clear necking phenomenon.Moreover,in the same stress ratio case,necking increases with the increasing temperature and more appreciable necking appears on failed specimen at stress ratio of 0.9 than at stress ratio of 0.5.

Table 3 Matched pairs of superalloy 9CrCo.

Table 4 Mean values of fatigue limits from matched pairs of superalloy 9CrCo.

Fig.4 Failure pictures at about 25°C.

4.Result analysis and discussion

In order to compare fatigue endurance limits of superalloy 9CrCo at four stress ratios of-1,-0.3,0.5 and 0.9 in three environments of about 25°C and elevated temperatures of 530 °C and 620 °C,the reduction rate is introduced to define the nondimensional fatigue endurance limit as

where Smax,rtand Smax,Tare the fatigue endurance limits responding to about 25°C and elevated temperature(e.g.,530 °C or 620 °C),respectively.

From Eq.(16)and the experimental data in Table 4,the reduction rate curves of fatigue endurance limits of superalloy 9CrCo at elevated temperatures of 530 °C and 620 °C relative to those at about 25°C can be determined respectively(Fig.5).From Fig.5,it is obvious that(i)the reduction rates of fatigue endurance limits of superalloy 9CrCo at four stress ratios of-1,-0.3,0.5 and 0.9 are less in elevated temperature environment of 530°C than in elevated temperature environment of 620°C,which reveals that fatigue endurance limit of superalloy 9CrCo decreases with the increasing temperature.In reality,the heat stress at elevated temperature enhances the actual stress level at the same nominal stress level.The higher the temperature is,the greater the actual stress level at the same nominal stress level becomes;(ii)the reduction rates of fatigue endurance limits of superalloy 9CrCo in elevated temperature environments of 530 °C and 620 °C are greater at stress ratios of 0.5 and 0.9 than at stress ratios of-1 and-0.3,which reveals that the elevated temperature-loading interaction is more significant at positive stress ratio than at negative stress ratio,causing a greater decreasing of fatigue strength.It is worth pointing out that in elevated temperature environment of 530°C,the reduction rate of fatigue endurance limits at a stress ratio of 0.5 is conversely less than at two stress ratios of-1 and-0.3.This is possibly because the experimental data is the small sample size of the test data.It is well known that fatigue endurance limit is often very scattered.For this reason,generally,many sets of large sample experiments are conducted to obtain the population law and the analysis results at high reliability levels.In this case,resource constraints limited the numbers of experiments.If more specimens are used for fatigue tests,more exact fatigue endurance limit can be determined and more appropriate experimental results can be obtained.

Fig.5 Reduction rate curves for fatigue endurance limit of superalloy 9CrCo.

From Eq.(5)and the experimental data in Figs.2 and 3,fatigue S–N–R surfaces of superalloy 9CrCo in three environments of about 25 °C and elevated temperatures of 530 °C and 620°C can be determined respectively.

From Eqs.(17)–(19),it can be seen that the coefficients of m and C obtained by best fitting of the surface model increase with the increasing temperature,and in contrast,the fitted value of S0decreases with the increasing temperature.This implies that fatigue life at the same stress level or fatigue strength at the same fatigue life decreases with the increasing temperature.One reason for the decrease of fatigue strength or fatigue life is the increasing actual stress level resulted from the heat stress at high temperature.The higher the temperature is,the greater the actual stress level at the same nominal stress level becomes.

Fig.6 Fatigue S–N–R surfaces for superalloy 9CrCo at different temperatures.

Fig.7 Fractographic pictures at stress ratio of-1 but different temperatures.

From Eqs.(17)–(19),it is possible to have the S–N curves corresponding to the stress ratios of-1,-0.3,0.5 and 0.9 in three environments of about 25°C and elevated temperatures of 530 °C and 620 °C.Eqs.(17)–(19)are plotted in Fig.6 respectively and the S–N curves corresponding to the stress ratios of-1,-0.3,0.5 and 0.9 in three environments of about 25 °C and elevated temperatures of 530 °C and 620 °C are separately plotted in Fig.2 and 3.From Figs.2,3 and 6,it is clear that(i)there is good agreement between the experimental data and the predicted curves or surfaces;(ii)the S–N–R surface decreases with the increasing temperature,i.e.,fatigue property decreases with the increasing temperature;(iii)fatigue life on the S–N–R surface decreases with the increasing stress level,but increases with the increasing stress ratio;(iv)the difference between S–N–R surfaces for the elevated temperature(i.e.,530 °C or 620 °C)and the room temperature decreases with the increasing stress level(Fig.6(a)),but increases with the increasing stress ratio(Fig.6(b)).Thus it is argued that the S–N–R surface model of Eq.(5)has adequately and logically characterized the physical characteristics and the phenomenological quantitative laws.Importantly,the parameters of this model can be determined expediently and easily.

Fig.8 Fractographic pictures at stress ratio of-0.3 but different temperatures.

Fig.9 Fractographic pictures at stress ratio of 0.5 but different temperatures.

Fig.10 Fractographic pictures at stress ratio of 0.9 but different temperatures.

In order to understand high-cycle fatigue damage mechanism and to reveal the influence of temperature and stress ratio on fatigue behavior of superalloy 9CrCo,the fractography for representative fracture appearances from failed specimens was undertaken using the scanning electron microscope(SEM)to provide direct evidence of crack nucleation and growth in a region that was not observable during fatigue process.The fracture surfaces for four stress ratio cases of-1,-0.3,0.5 and 0.9 are shown in Figs.7–10.Figs.7 and 8 show the evident fatigue origins,smooth crack propagation and coarse rupture zones.Fatigue origins firstly occurred at the initial flaws on the surfaces of tested specimens,which was followed by fatigue crack propagating radially outward from fatigue origins.So it can be concluded that fatigue crack initiation and propagation at initial flaws on the surfaces of tested specimens are the primary reasons for the failure of tested specimens at two stress ratios of-1 and-0.3.In contrast,as distinct from Figs.7 and 8,Figs.9 and 10 show the insignificant fatigue crack nucleation and crack propagation.Fatigue origins firstly occurred at the initial flaws(including second-phase particle,inclusion,casting defect,etc.)inside tested specimens,which was followed by instantaneous and extensive equal-axis dimple and cavity generation outward from fatigue origins due to the plastic deformation.Thus,fatigue failure modes of tested specimens at two stress ratios of 0.5 and 0.9 can be reckoned to be characteristic of fatigue crack nucleation,equal-axis dimples and cavity propagation from the inside initial flaws until ductile fracture.

From Figs.7–10,it can be seen that more and greater secondary cracks,equal-axis dimples and cavities are found on fracture surfaces with the increasing temperature.Hence,fracture surfaces are coarser with the increasing temperature.This implies that the ductility of superalloy 9CrCo increased with the increasing temperature,causing more rapid crack propagation or greater and more dimples and cavities.Again,from Figs.7–10,it is also observed that the secondary cracks,equal-axis dimples or cavities on fracture surfaces increase with the increasing stress ratio.This reveals that the ductile fracture is enhanced owing to the ductile intergranular cracking or the irrecoverable plastic deformation that results from higher stress ratio.Fatigue failure features can be concluded as shown in Table 5.

Table 5 Comparison of fractographic pictures for fracture surfaces at different stress ratios and temperatures.

5.Conclusions

The focus of this paper has been to develop a modified model to characterize and evaluate high-cycle fatigue behavior of superalloys at elevated temperature.New formulae are derived to deal with the test data for estimating the parameters of the proposed model.Fatigue tests were performed on superalloy 9CrCo subjected to constant amplitude at four stress ratios of-1,-0.3,0.5 and 0.9 in three environments of room temperature and elevated temperatures of 530 °C and 620 °C.The interaction mechanisms between the elevated temperature and stress ratio are deduced from fractographic studies.A reasonable correlation is achieved between predictions and experiments,demonstrating the practical and effective use of the proposed model.

Acknowledgment

This project was supported by the National Natural Science Foundation of China(Nos.51375033 and 51405006).

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Wan Aoshuangis an M.S.student at School of Transportation Science and Engineering,Beihang University.She received her B.S.degree from Beihang University in 2015.Her area of research is fatigue and fracture reliability.

Xiong Junjiangis a professor and Ph.D.supervisor at School of Transportation Science and Engineering,Beihang University.He received the Ph.D.degree from the same university in 1995.His current research interests are fatigue and fracture reliability engineering,and aircraft structural airworthiness.

9 October 2015;revised 20 November 2015;accepted 22 December 2015

Available online 23 February 2016

Elevated temperature;

Fatigue;

Met als and alloys;

SEM;

Stress ratio

©2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.Tel.:+86 10 82316203.

E-mail address:jjxiong@buaa.edu.cn(J.Xiong).

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