Jack Telesman, Timothy P. Gabb, Louis J. Ghosn, and John Gayda, Jr.

Glenn Research Center, Cleveland, Ohio

Effect of Notches on Creep-Fatigue Behavior

of a P/M Nickel-Based Superalloy

NASA/TM—2015-218887

November 2015
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Jack Telesman, Timothy P. Gabb, Louis J. Ghosn, and John Gayda, Jr.

Glenn Research Center, Cleveland, Ohio

Effect of Notches on Creep-Fatigue Behavior

of a P/M Nickel-Based Superalloy

NASA/TM—2015-218887

November 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
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Acknowledgments

The authors wish to acknowledge the work of Andrew Ring in conducting mechanical testing and Joy Buehler in 

performing the metallography. The work was funded by NASA’s Aviation Safety program.
NASA/TM—2015-218887 1 

Effect of Notches on Creep-Fatigue Behavior of a 

P/M Nickel-Based Superalloy 

Jack Telesman, Timothy P. Gabb, Louis J. Ghosn, and John Gayda, Jr.*

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

A study was performed to determine and model the effect of high temperature dwells on notched low 

cycle fatigue (NLCF) and notch stress rupture behavior of a fine grain LSHR powder metallurgy (P/M) 

nickel-based superalloy. It was shown that a 90 sec dwell applied at the minimum stress (“min dwell”) 

was considerably more detrimental to the NLCF lives than similar dwell applied at the maximum stress 

(“max dwell”). The short min dwell NLCF lives were shown to be caused by growth of small oxide 

blisters which caused preferential cracking when coupled with high concentrated notch root stresses. The 

cyclic max dwell notch tests failed mostly by a creep accumulation, not by fatigue, with the crack origin 

shifting internally to a substantial distance away from the notch root. The classical von Mises plastic flow 

model was unable to match the experimental results while the hydrostatic stress profile generated using 

the Drucker-Prager plasticity flow model was consistent with the experimental findings. The max dwell 

NLCF and notch stress rupture tests exhibited substantial creep notch strengthening. The triaxial 

Bridgman effective stress parameter was able to account for the notch strengthening by collapsing the 

notched and uniform gage geometry test data into a singular grouping. 

Introduction 

A new generation of powder metallurgy (P/M) disk superalloys has been designed for higher engine 

operating temperatures by improvement of their strength and creep resistance. This increase in the engine 

operating temperatures has resulted in additional emphasis being placed on high temperature environmental resistance and dwell behavior of these alloys to determine their long term high temperature durability. 

The increased strength and creep resistance of these alloys may also increase their notch sensitivity to 

fatigue loading and thus have a profound effect on the notched low cycle fatigue life. NLCF is a key 

mechanical property of the highly stressed gas turbine rotating components since it simulates behavior at 

notches and bolt holes which are the regions from where the majority of failures of rotating components 

tend to originate (Ref. 1). 

With the increase in the disk operating temperatures, sustained dwells applied at the maximum stress 

have been shown to significantly degrade both smooth and notched LCF fatigue life (Refs. 2 to 4). More 

surprising has been a finding by Bache et al. (Ref. 5) that an imposition of a 90 sec dwell at the minimum 

stress produced an even greater reduction in NLCF life. This was also confirmed in our study of the ME3 

disk alloy (Ref. 6). The differences in the notch fatigue life response to max dwell and min dwells are 

thought to be influenced by both notch stress relaxation and environmental degradation (Refs. 5 and 6), but 

more work remains to be performed to further understand the mechanisms by which these interactions occur. 

The presence of notches adds another level of complexity to the already complex world of 

environment-load history interactions. The resulting multiaxial stress state at the notch root, combined 

with visco-plastic high temperature material response, can produce significant redistributions of stresses 

and strains in the notch region which in turn affect the life and the overall durability of the disk alloys. 

The role that axial stress, hydrostatic stress and the effective stress play in determining the durability 

needs to be sorted out. Due to these complexities, currently available life prediction models are not able to 

 

*

 Retired. 
NASA/TM—2015-218887 2 

accurately predict dwell notched low cycle fatigue life. Formulation of more accurate life prediction 

models requires an improved understanding of the damage mechanisms responsible for material 

degradation and accumulation of fatigue damage. The key to gaining this understanding is the 

identification of the active material damage mechanisms for a given set of test conditions and their 

relationship to the redistribution of the notch root stresses and strains which takes place during the 

prolonged dwells. 

The approach of the current study was to isolate as much as possible the major variables which affect 

the dwell NLCF behavior so that their individual mechanistic contributions to material durability could be 

studied, quantified and modeled. The work was performed by testing the NASA developed LSHR P/M 

disk alloy. A variety of test types were conducted to characterize the material behavior. Cyclic, cyclicdwells, stress-rupture and creep testing was performed using both notch and uniform section specimen 

geometries to characterize material response under varied loading conditions. Baseline cyclic tests were 

performed as well as notch dwell fatigue tests with 90 sec holds at either maximum or minimum stress. 

The application of 90 sec dwells at the min stress was utilized so that the role of the environment can be 

studied without the complication of visco-plastic stress redistribution. Notch and smooth stress-rupture 

testing was used to quantify the creep contribution to the damage process. While most of the testing was 

performed in lab air, selected specimens were tested in vacuum to isolate and quantify the environmental 

contribution to the damage evolution. 

This paper will compare the pronounced effect that both environmental damage and the visco-plastic 

stress redistribution have on the lives of LSHR specimens. The aim of the study is to identify the key 

parameters which account for these differences in behavior and to present a methodology which can 

explain and predict these results. 

Materials and Procedure 

The LSHR P/M alloy with a composition consisting in weight percent of 20.7 Co, 4.3 W, 3.5 Al, 

3.5 Ti, 2.7 Mo, 1.6 Ta, 1.5 Nb, 0.05 Zr, 0.03C, 0.03 B with balance Ni was used in the study. Small 

pancake forgings approximately 15 cm in diameter and 3.7 cm thick of this composition were heat treated 

as follows to produce a fine grain subsolvus microstructure: solution at 1135 °C, fan cooled and aged at 

855 °C/4 hr + 775 °C/8 hr. The heat treatment produced a fine grain microstructure approximately 

5 to 10 m in diameter (ASTM 11-12). Specimens were machined from heat treated forgings. 

Approximate cooling rate from the solutioning temperature was designated for the location of each blank 

removed from the pancake forgings. 

Testing consisted of cyclic notch fatigue, cyclic notch dwell fatigue, creep notch rupture, combo-bar 

creep and uniform gage creep tests. The details of all the test conditions are shown for the cyclic and 

cyclic dwell NLCF tests in Table I and for the creep and stress rupture tests in Table II. Specimen 

geometry of the notched bars are shown in Figures 1 and 2. All the notched bars had an elastic stress 

concentration factor (Kt) of 2.0. Combo-bar geometry, shown in Figure 3, consists of a uniform gage 

section and a notched region with the notch diameter being equal to that of the smooth section. All testing 

was performed at 704 °C. Three different waveforms were utilized: sinusoidal with frequencies of 10 Hz 

and 0.333 Hz, max dwell (1.5-90-1.5) seconds and min dwell (1.5-1.5-90) seconds with dwell cycles 

shown in Figure 4. As shown in Tables I and II, in addition to lab air, selected tests were performed in 

vacuum. The testing was conducted at various net section stresses ranging from 483 to 896 MPa with the 

majority of the tests being conducted at 793 MPa to determine the data repeatability. 

Stress relaxation testing was conducted at 704 °C to obtain a constitutive creep relationship for the 

alloy for use in the visco-plastic modeling. Stress relaxation was measured after a 1 percent total strain 

was achieved in a standard tensile test. The specimen was then held at 1 percent strain for 100 hr while 

the change in stress was monitored by an automated data acquisition system. Visco-plastic axi-symmetric 

finite element analysis was performed on the notch specimen geometry to determine the redistribution of 

notch root stresses. Both von Mises and Drucker-Prager plasticity flow models embedded in the 

ABAQUS finite element code (Ref. 7) were used for the analysis. 
NASA/TM—2015-218887 3 

Results and Discussion 

Nonunified Visco-Plastic FEM Analysis of Notch Root Stresses 

The evolution of the notch root stresses was modeled using finite element modeling (FEM) as a 

function of the number of applied cycles for both max dwell and min dwell loading profiles. The notched 

specimen geometry was modeled with two-dimensional axi-symmetric nonlinear elements and the 

material modeled using a nonunified viscoplastic analysis wherein the strain is decomposed into separate 

elastic, plastic, creep, and thermal components. 

The inelastic strain was computed using both classical von Mises and Drucker-Prager plasticity flow 

models within ABAQUS, the required material parameters being obtained from the tensile and stress 

relaxation data. The stress relaxation material response was correlated using the following creep law: 

n m p   A t  B (1) 

where εሶ is the strain rate, σ is the equivalent creep stress defined as either von Mises stress for the von 

Mises flow model or the effective creep stress for the Drucker-Prager model function of the von Mises 

stress and the hydrostatic stress, t is time and A, B, n, m and p are fitting constants. The creep coefficients 

which fit this equation were determined and are shown in Figure 5 together with the comparison to the 

experimentally obtained stress relaxation results. The notch stress distribution profiles for various types of 

stress components were calculated for both max and min dwell loading histories. The results of the FEM 

analysis will be discussed later to help explain experimental results for each type of the loading history 

investigated. 

Notch Cyclic and Dwell Fatigue Behavior 

Comparison of notch low cycle fatigue results for the three waveforms used in the study is shown in 

Figure 6 and Table I. All the tests shown in the figure were performed in lab air with a maximum applied 

net section stress of 793 MPa. As shown, the fatigue lives were highly dependent on the applied 

waveform. The high frequency cyclic notch fatigue tests exhibited fatigue lives in the order of 250,000 

cycles. Reduction of frequency from 10 to 0.333 Hz resulted in notch LCF lives of approximately 

150,000 cycles. Imposition of a 90 sec hold at the maximum stress had a very significant effect on NLCF 

with the specimens failing in the range of 15,000 to 35,000 cycles. Further significant reduction in fatigue 

lives occurred when the 90 sec dwell was applied at the minimum stress. As shown in Figure 6, the dwell 

notch fatigue lives for the min dwells were approximately an order of magnitude lower in comparison to 

the max dwell tests. While these results are somewhat counter-intuitive, they are in agreement with the 

trends observed by Bache et al. for RR1000 (Ref. 5) as well as in our study of the ME3 alloy (Ref. 6). 

Fractographic examination of specimens tested utilizing the three waveforms revealed that the failure 

mode differed substantially for each type of test as shown in Figure 7. For the high frequency cyclic 

baseline tests only a single initiation site located near the notch surface was observed (Fig. 7(a)) from 

which the crack propagated internally until failure occurred. Higher magnification images of the initiation 

site (Fig. 8) revealed that the crack initiated from a near surface inclusion which was present in this high 

stress concentration region. This is a well-known failure mode in P/M disk superalloys and is not 

significantly influenced by the environment since the initiations often occur in the subsurface region. 

In contrast to the single fatigue crack initiation site for specimens tested using high frequency 

waveform, the 90 sec min dwell tests produced multiple fatigue crack surface initiation sites around the 

notch root perimeter as shown Figure 7(b). These multiple cracks coalesced and caused the specimen to 

fail. A more detailed discussion of this environmentally influenced failure mode will be presented in the 

next section. The 90 sec max dwell tests failure mode was radically different from the two already 

described. As shown in Figure 7(c), the primary initiation site was internal at a substantial distance away 

from the notch root. In addition to the primary internal initiation site, a single small secondary surface 
NASA/TM—2015-218887 4 

initiation region was also present as also marked in Figure 7(c). The shift in the location of the primary 

failure away from the notch root points to the crucial role that visco-plastic stress redistribution can play 

in controlling the damage evolution process. This topic will be discussed extensively in this paper. 

Cyclic Minimum Dwell Notch Fatigue 

As was shown in Figure 7(b), the min dwell notch LCF testing resulted in multiple surface initiations 

which produced short fatigue lives in the order of 2000 to 5000 cycles when tested in air at maximum net 

section stress of 793 MPa. A more detailed fractographic initiation examination revealed the presence of a 

multitude of cracks at the notch root surface. As shown in Figure 9, these cracks typically initiated at 

oxide blisters which formed at the notch root surfaces during testing. The cause of the formation of these 

localized oxide blisters has not been established in this study but in our previous study of ME3 (Ref. 6) 

similar blisters originated either from the oxidation of MC-type carbides (M = Ti, Nb, W, Ta) or were due 

to local heterogeneities in the microstructure. Recently, O’Hanlon et al. (Ref. 8) also documented these 

type of features causing early crack initiation during min dwell tests. As shown in Figure 9, these 

oxidized areas are only few microns in width, yet due to the high stresses at the notch root these brittle 

particles fracture and initiate cracks. In essence, the growth of the brittle oxidized particles can be 

considered to be analogous to the presence of ceramic inclusions which are also known to initiate cracks 

when exposed to high enough cyclic stresses. The difference being that the oxidized blisters form and 

grow during the test itself while ceramic inclusions are present from the outset. 

To confirm that the environment is indeed the culprit in reducing the notch dwell fatigue lives for min 

dwell testing, a test was conducted in a vacuum test chamber under the same loading conditions. As 

shown in Figure 10, the min dwell notch fatigue life of the specimen was approximately 39,000 cycles 

and thus an order of magnitude longer than the tests performed in air. It should be noted that the life of the 

vacuum specimen would likely have been even longer, since an improper bake out of a new heating 

element installed at approximately 28,600 cycles coated the specimen with a thin layer of a brittle ceramic 

phase. An array of cracks formed in this layer upon the restart of the test, with these cracks growing into 

the substrate and shortening the specimen’s life. The specimen notch surface which was examined in the 

SEM at 28,600 cycles prior to the installation of the new heating element shows the notch in almost 

pristine condition with no apparent cracks (Fig. 11(a)). As shown, after 28,600 cycles no oxide blisters or 

cracks were present on the notch root surface. This is in stark contrast to the min dwell notch specimens 

tested in air where a multitude of cracks were present after only few thousand cycles. Thus the 

relationship between oxidation damage and min dwell notch fatigue life is quite evident. The same 

vacuum specimen examined after failure at approximately 39,000 cycles shows an array of cracks 

originating from the inadvertently deposited brittle coating (Fig. 11(b)). The vacuum test has not as yet 

been repeated due to the unavailability of the test rig. 

In addition to the presence of brittle oxide blisters, surface stresses high enough to fracture these 

brittle particles are required for crack initiation to occur. The evolution of notch root stresses was 

modeled for the min dwell tests through FEM analysis. Figure 12, shows the stress distribution profiles 

for the first forty min dwell cycles as a function of the distance from the notch root in terms of axial, von 

Mises and hydrostatic stresses. While there is a small change in stresses after the first cycle, all the 

subsequent cycle stress distributions lie directly on top of each other. The figure shows that for all three 

stress types, stresses are highest in the near notch root region and drop off significantly as a function of 

distance away from the notch. The calculated notch root axial maximum stresses are approximately 

1300 MPa while the von Mises stresses approach 1100 MPa and thus both are still considerably higher 

than the 793 MPa applied net section stress. This is not surprising since the 90 sec min dwells occur at 

stresses where compressive creep is minimal and has no significant effect on the visco-plastic evolution 

of maximum notch root stresses. 

To better understand the inter-relationship between oxidation damage and the surface stresses, a 

90 sec min dwell test was performed in air using a uniform gage specimen geometry. This test was 

performed at the same 793 MPa net section stress as was done for the notch specimens. After no failure 
NASA/TM—2015-218887 5 

occurred during the first 50,000 cycles, the test was stopped and the specimen surface was examined in 

the SEM. As shown in Figure 13, while the specimen surface is covered with oxide particles, no surface 

cracking was detected on the oxide covered surface. Thus, for the uniform gage specimen, the 793 MPa 

applied max stress was too low to crack the thin, brittle oxide layer. Without the onset of early cracking 

from oxide blisters, the min dwell fatigue life is considerably longer for the uniform gage specimens than 

for notched min dwell tests performed at the same net section stress. 

Cyclic Maximum Dwell Notch Fatigue and Notch Rupture Testing 

As shown earlier, the life of the cyclic max dwell notch tests performed at the 793 MPa net section 

stress was considerably higher than for the min dwell tests performed at the same maximum stress 

(Fig. 6). It was also shown (Fig. 7(c)) that in contrast to the cyclic and the min dwell cyclic tests tested 

conducted at the same stress, the primary crack initiation shifted internally at a considerable distance 

away from the notch root. Fractography of some the other cyclic max dwell notch tests showed similar 

behavior (Fig. 14(a)). The measured distances from the notch root to the internal initiation locations for 

the various specimens is shown in Table III. As shown, while there is a considerable scatter, most of the 

internal initiations occurred at distances ranging from 1 to 2.5 mm away from the notch root. A 

companion test performed in vacuum not only revealed a similar internal initiation mechanism 

(Fig. 14(b)), but also had a fatigue life similar to the other cyclic max dwell notch specimens tested in air 

(Fig. 14(c)). The comparable fatigue life for both air and vacuum tests is due to the environment not being 

a major factor in influencing the life of the specimen due to its internal initiation. 

Further fractographic examination of the internal initiation locations revealed extensive plastic 

deformation near the crack origins. These features were consistent with failure by a creep deformation 

process (Fig. 15) and not by a fatigue process. For all the internal initiations examined, no fractographic 

evidence of fatigue failure mechanisms were observed near the internal initiation regions. It should be 

noted that while most of the cyclic max dwell notch test specimens tested at 793 MPa net section stress 

exhibited a primary internal initiation, many also exhibited a secondary near surface initiations which 

likely are a result of fatigue (Fig. 16). 

If creep damage accumulation, and not fatigue, was the primary failure mechanism for these cyclic 

notch max dwell tests, then the notch creep rupture tests conducted at the same temperature and net 

section stress should also result in similar time to failure and exhibit the same failure mechanisms. The 

comparison of test results in terms of time to failure between the max dwell tests and notch rupture tests is 

shown in Figure 17. As shown, the time to failure is similar for both types of tests even though significant 

scatter is also present. Further evidence for the creep deformation being the dominant damage 

accumulation mechanism is obtained through the comparison of the fractographic and metallographic 

analyses of the two test types. As shown in Figure 18, the crack initiation location for the creep notch 

rupture tests is also internal and has very similar appearance to the cyclic notch max dwell tests (Figs. 7 

and 14). A comparison of metallographic cross sections of the cyclic notch max dwell tests and the creep 

notch rupture tests obtained slightly below the fracture plane is shown in Figure 19. Both types of tests 

exhibited the classical creep damage accumulation through formation and coalescence of voids at grain 

boundaries thus confirming the dominant role that creep deformation played in these two test types. Our 

findings are in agreement with previous work performed by Pandey et al. (Ref. 9) on Inconel alloy X-750. 

In their work, they also found that crack initiations in notch creep rupture specimens occurred at a 

substantial distance away from the notch root. 

One difference not discussed as yet between the fractography of the cyclic notch max dwell tests and 

creep notch rupture tests was the presence of the secondary notch root surface crack initiation regions. 

While these surface secondary initiation sites were present in most of the 793 MPa cyclic max dwell tests 

(Figs. 7 and 14), they were completely absent in the creep notch rupture tests (Fig. 18). Even though 

extensive visco-plastic stress redistribution occurs during max dwells, if the remaining notch root cyclic 

stress range is high enough, fatigue cracks can still initiate. Creep notch rupture tests do not exhibit these 

surface initiations since they are not exposed to cyclic loading. It is interesting to note that cyclic notch 
NASA/TM—2015-218887 6 

max dwell tests which were performed at higher next section stress of 896 MPa exhibited only notch root 

surface initiations (Fig. 20). It is thought that at this higher applied net section stress, the notch root cyclic 

stress range was high enough to cause earlier fatigue crack initiation which dominated the failure process. 

Creep and Combo Creep Test Results 

The results of the uniform gage creep tests performed in air and vacuum are shown in Figure 21 and 

also in Table II. The testing was conducted at the maximum net section stresses ranging from 483 to 

896 MPa. At the highest applied stress, the four tests performed in air failed between 25 to 35 hr, while 

the two tests performed in vacuum failed after 55 and 90 hr, respectively. This difference in creep life 

between air and vacuum tests disappeared at lower stresses as shown in Figure 21 with both air and 

vacuum uniform gage specimens exhibiting similar time to failure. 

In addition to the smooth specimens, creep rupture tests were performed on six combo-bar specimens 

of the geometry shown in Figure 3. All the combo-bar tests were done at 793 MPa. All six combo-bar 

failures occurred strictly in the uniform gage region. The lives of the combo-bar specimens were very 

similar to the uniform gage creep specimens as shown in Figure 22. For comparison, the much longer 

notch creep rupture and cyclic dwell NLCF lives are also shown in this figure. 

It is interesting to note the differences in the failure mechanisms of the uniform gage creep tests 

performed in air and in vacuum. As shown in Figure 23(a), the creep test conducted in air exhibited a 

multitude of surface cracks which initiated at the oxidized blisters formed during the test. These oxide 

cracks are perpendicular to the loading direction. Also as shown, the main crack initiation region in this 

specimen occurred on the specimen surface. The surface cracking from environmentally created brittle 

oxide regions is reminiscent of the oxide induced early crack initiation and surface failure of the cyclic 

min dwell tests discussed previously. 

In contrast, the vacuum tested uniform gage creep specimen exhibited a markedly different 

appearance. As shown in Figure 23(b), on the machined surface of the specimen only shear plastic 

deformation bands are present resulting in cracks angular to the loading direction. The specimen surface 

appearance is that of a material which has experienced extensive plastic deformation. Examination of the 

fracture surface revealed that the crack initiation occurred internally in the mid-thickness region of the 

specimen (Fig. 23(b)). Thus the presence of a brittle, oxidized phases on the surface can significantly alter 

the damage accumulation process. 

Modeling of the Visco-Plastic Notch Root Stress Redistribution 

The shift in the failure initiation location away from the root of the notch towards interior regions of 

the specimens, as was experienced in both cyclic notch max dwell tests and creep notch rupture tests, 

must be fully understood so that accurate life prediction models can be developed. Stress redistribution 

due to the presence of the notch was modeled using a number of different approaches to determine the 

applicable methodology which can best predict the observed behavior. The resulting stress distribution 

profiles were compared to the observations in terms of the location of the maximum stress which is 

assumed to control the initiation process. 

An axi-symmetric visco-plastic FEM analysis was performed using the constitutive creep model 

previously derived (Fig. 5). The creep analyses were performed using both the von Mises and DruckerPrager inelastic flow models embedded in ABAQUS to determine their ability to predict material 

behavior. The von Mises flow model is most commonly used for ductile metals. One of its theoretical 

assumptions is that the yield strength is independent of hydrostatic stresses. The resulting yield surface of 

the von Mises flow model is a circular cylinder. The Drucker-Prager yield criterion is rarely used to 

model metal inelastic behavior, however for high hydrostatic stresses, the model may be preferable to 

von Mises (Ref. 10). It differs in that in the model formulation, the effective inelastic stress is a function 

of the hydrostatic stress as the deviatoric stress. In terms of the yield surface, Drucker-Prager yield 

function results in a conical yield surface. 
NASA/TM—2015-218887 7 

The results of the visco-plastic analysis using the von Mises plasticity flow model are shown in 

Figure 24 in terms of the stress distribution profiles for the axial, von Mises and hydrostatic stresses. The 

figure shows these stress profiles at the beginning of the test as well as after 1000 hr at the sustained max 

dwell. As shown, a significant redistribution of all three stress types occurs after the 1000 hr dwell. After 

the dwell, the von Mises stresses are still considerably higher at the notch root than in the interior regions 

and thus they do not predict the observed behavior. Both the axial and hydrostatic stresses after 1000 hr of 

creep calculated using the von Mises flow model are still the highest near the notch root with the peak 

stress being approximately 0.4 mm below the surface. The measured location of failure initiation sites for 

the tested specimens is shown both in Table III and graphically superimposed onto Figure 24. As shown, 

the actual initiation locations are considerably deeper and do not correspond to either the axial or 

hydrostatic stress distributions shown in the figure. Thus none of the three creep redistributed stress 

profiles generated by the von Mises plastic flow model are in agreement with the observed behavior. 

The results for the Drucker-Prager flow model are shown in Figure 25. Again the stress profile 

distributions are shown for both the initial as well as 1000 hr max dwell conditions. As shown, after the 

dwell, neither the redistributed axial or von Mises stresses are in good agreement with the experimental 

results. The peak von Mises stresses are still at the notch root while the redistributed axial stresses are 

highest in the vicinity of the notch and are considerably higher in that region than at the depths at which 

the majority of the specimens’ crack initiations occurred. 

The hydrostatic stress profile after the application of 1000 hr dwell, shown in Figure 25, is 

considerably different than the other profiles already described. As shown, the lowest hydrostatic stresses 

are at the notch and rise gradually as a function of the distance from the notch root. They peak 

approximately 1 mm away from the notch and remain fairly uniform and close to the peak level over the 

entire distance to the center of the specimen. Thus the triaxial hydrostatic stress profile is in the agreement 

with the experimental observations of the location of the failure initiation sites for the cyclic max dwell 

and notch stress rupture tests performed at max stress of 793 MPa. 

As described earlier and shown in Table III and Figure 25, the initiation locations are spread out in a 

region away from the notch. The lack of one distinct location for the initiations to occur can be explained 

by a relatively flat distribution of the hydrostatic stresses which allows for initiations to occur at the 

weakest point in the material over the region subjected to the high stresses. 

Bridgman Effective Stress Analysis 

Hydrostatic stress is the mean of the sum of the three principal stresses and thus its ability to explain 

the creep dominated failures in the tested notched specimens emphasizes the importance of stress 

triaxiality under highly plastically deformed notch conditions. One of the earliest studies of the effect of 

stress multiaxiality on plastic deformation was performed by Bridgman (Ref. 11). Based on his analysis, 

he formulated an effective triaxial stress parameter, σe, to be as follows: 

1

net 2

ln 1 2 1







 



 



 



    





   

R

a

a

R e (2) 

where σnet is the net section stress, a is the distance from the center of the specimen to the notch root and 

R as originally defined was the radius of curvature of the neck down profile for a smooth specimen but 

being extended here to be the notch root radius. 

The test data generated in the program for the notch and smooth specimen geometries was used to 

evaluate the ability of the Bridgman effective stress to correlate the cyclic max dwell and creep rupture 

behavior. For uniform gage specimens, the effective stress is equal to the net section stress while for the 

notch geometry used in the study the effective stresses were calculated per Equation (2). Both the notched 

and smooth test data is first plotted in terms of the applied net section stress and shown in 

Figure 26. As shown, the data can be grouped separately with the notched specimens exhibiting 
NASA/TM—2015-218887 8 

considerably longer lives to failure in terms of the net section stresses than the uniform gage specimens. 

However when the same data set is plotted in terms of the Bridgman effective stress (Fig. 27), most of the 

data converges into a singular grouping. It should be noted that much of the scatter still present in the 

Bridgman effective stress plot shown in Figure 27 is due to the inherent variations in lives of specimens 

tested under “identical” conditions. No mechanistically derived parameter can account for that type of 

scatter. Thus, this methodology, which was developed many years ago, is still very useful in modeling 

notch-induced plastic deformation. 

Finally, it should be noted that in our test program both “notch strengthening” and “notch weakening” 

was induced in the same material. As shown in Figure 26, substantial amount of notch strengthening 

occurred for the cyclic max dwell and creep notch rupture specimens. The notch strengthening was 

created by the extensive notch stress redistribution which occurred due to the creep strain accumulation at 

the notch root. In contrast, the cyclic min dwell testing produced a notch weakening effect. In that case, 

the notch region was embrittled by oxidation of the surface which took place during the dwells. Since the 

min dwell notch stress redistribution is rather limited, high concentrated notch stresses remained and 

caused early crack initiation in the oxidized notch region which led to much shorter fatigue lives. For the 

uniform gage specimens tested under the same cyclic min dwell conditions, the surface is also embrittled 

through oxidation, however, the applied net section stress was too low to cause initiation on the 

environmentally embrittled surfaces resulting in much longer fatigue life. 

Summary 

A study was performed to determine and model the effect of high temperature dwells on notched low 

cycle fatigue and notch stress rupture behavior of a fine grain LSHR disk alloy. The dwell cycles 

consisted of either 90 sec hold at the maximum stress or the minimum stress. While both dwell cycles 

significantly reduced the lives of the notched specimens in comparison to the no-dwell baseline NLCF, 

the min dwell tests resulted in the largest reduction in the notched low cycle fatigue lives. The severe 

reduction in the lives of the notched min dwell specimens was shown to be the result of formation of 

small surface oxide blisters during the dwells which cracked due to the high sustained concentrated notch 

root stresses. The FEM analysis of the min dwell NLCF tests showed that the notch root stresses 

remained high during the test duration causing multiple surface crack initiations from the oxidized and 

embrittled particles. 

In contrast, the controlling failure initiation for the cyclic notch max dwell and notch rupture tests at 

comparable applied stresses typically occurred internally at a substantial distance away from the notch 

root. It was shown that the controlling damage accumulation mechanism for max dwell cyclic tests was 

creep and not fatigue. Stress redistribution due to the presence of the notch was modeled using a number 

of different approaches to determine the applicable methodology which can best predict the observed 

behavior. Both von Mises and Drucker-Prager flow models were examined and the axial, von Mises and 

hydrostatic stress profiles were generated for both flow models. None of the stress profiles generated 

using von Mises flow model was consistent with the experimental observations. Only the hydrostatic 

stress profile generated through the use of the Drucker-Prager flow model was consistent with the 

experimental results pointing to the controlling effect of stress triaxiality on the creep notch stress 

redistribution. 

A Bridgman net section effective stress formulation which takes into account the triaxiality of state of 

stress along the notch plane was used to correlate the notched cyclic max dwell, notch stress rupture and 

uniform gage creep tests. While the data sets showed a pronounced notch strengthening effect when 

correlated using the net section stress parameter, the Bridgman effective stress parameter was able to 

more reasonably collapse the data into a singular grouping. 

 
NASA/TM—2015-218887 9 

References 

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Engines,” Key Engineering Materials, v. 380, 2008. 

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in Notches of Powder Metallurgy Nickel Disk Alloy; Int. J. of Fatigue 48, 2013, 55–67. 

3. Goswain T., Hanninen H., “Dwell Effects on High Temperature Fatigue Behavior – Part I,” Matl 

and Design vol. 22, 2001. 

4. Greving D., Kantzos P., Neumann J., Rice D., Kington H.; “Dwell Notch Low-Cycle Fatigue 

Performance of Powder Metallurgy Alloy 10,” 12th Int. Symposium on Superalloys, Superalloys 

2012. 

5. Bache M.R., Jones J.P., Drew G., Hardy M., Fox N., “Environment and Time Dependent Effects on 

the Fatigue Response of an Advanced Nickel Based Superalloy,” Int. J. of Fatigue 31, 2009, 1719–

1723. 

6. Telesman J., Gabb T., Ghosn L., Yamada Y., Jayaraman N., “Dwell Notch Low Cycle Fatigue 

Behavior of A Powder Metallurgy Nickel Disk Alloy,” 12th Int. Symposium on Superalloys, 

Superalloys 2012. 

7. ABAQUS Version 6.13-1, Dassault Systèmes Simulia Corp., Providence, RI, © Dassault Systèmes, 

2013. 

8. O’Hanlon J., Hardy M., Child D., Foss B., Withers P., Bache M.; “The effect of Minimum Dwell 

Cycles on the Environment and Fatigue Response of RR1000,” MATEC Web of Conferences 14, 

04003, 2014. 

9. Pandey M., Mukherjee A., “Effect of Triaxial Stress-State on Creep Fracture in Inconel Alloy 

X-750,” J. of Matl Science, vol. 20, 1985, 1201–1206. 

10. Wilson C.; “A Critical Reexamination of Classical Metal Plasticity,” – J. of Applied Mechanics, 

vol. 69, Jan 2002. 

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Hydrostatic Pressure, McGraw-Hill, NY, 1952. 
TABLE I.—DWELL AND CYCLIC NOTCH LCF TEST RESULTS 

Specimen 

ID 

Test type Cooling rate 

from 

solutioning 

to 871 °C, 

°C/min 

Test 

temp.,

°C 

Max 

stress, 

MPa 

Min 

stress, 

MPa 

Hold 

timeseconds 

Max/Min 

dwell; 

cyclic 

Frequency, 

Hz 

Cycles to 

failure 

E2-N1 DNLCF-Kt=2 Air 64 704 793 40 90 Max N/A 37361 E2-N2 DNLCF-Kt=2 Air 73 704 793 40 90 Max N/A 38280 E2-N3 DNLCF-Kt=2 Air 73 704 793 40 90 Max N/A 24452 E2-N4 DNLCF-Kt=2 Air 73 704 793 40 90 Max N/A 42361 E2-N5 DNLCF-Kt=2 Air 73 704 793 40 90 Max N/A 14991 E2-N6 DNLCF-Kt=2 Air 73 704 793 40 90 Max N/A 23897 C-N8 DNLCF-Kt=2 Air 71 704 793 40 90 Max N/A 14248 C-N10 DNLCF-Kt=2 Air 71 704 827 41 90 Max N/A 13443 C-N11 DNLCF-Kt=2 Air 71 704 793 40 90 Max N/A 32104 C-N13 DNLCF-Kt=2 Air 68 704 793 40 90 Max N/A 30541 C-N15 DNLCF-Kt=2 Air 68 704 896 45 90 Max N/A 2123 C-N18 DNLCF-Kt=2 Air 76 704 827 41 90 Max N/A 18793 9D-L1 DNLCF-Kt=2 Air 67 704 896 45 90 Max N/A 5541 0A-L5 DNLCF-Kt=2 Air 71 704 793 40 90 Max N/A 26128 9D-L3 DNLCF-Kt=2 Air 71 704 690 34 90 Max N/A 66249 9C-L5 DNLCF-Kt=2 Air 71 704 690 34 90 Max N/A 55396 9D-L5 DNLCF-Kt=2; Vacuum 71 704 793 34 90 Max N/A 44709 9D-L2 DNLCF-Kt=2; Vacuum 71 704 896 45 90 Max N/A 14156 C-N9 DNLCF-Kt=2 Air 71 704 793 40 90 Min N/A 3500 C-N17 DNLCF-Kt=2 Air 76 704 793 40 90 Min N/A 4778 0F-L4 DNLCF-Kt=2 Air 71 704 793 40 90 Min N/A 2200 0A-L2 DNLCF-Kt=2 Vacuum 71 704 793 40 90 Min N/A 39106 C-N1 NLCF Kt=2 Air 79 704 793 40 N/A Cyclic 10 245105 C-N5 NLCF Kt=2 Air 66 704 793 40 N/A Cyclic 10 297795 0A-L4 NLCF Kt=2 Air 71 704 793 40 N/A Cyclic 0.333 173659 0A-L1 NLCF Kt=2 Air 67 704 793 40 N/A Cyclic 0.333 153546 

NASA/TM—2015-218887 10
NASA/TM—2015-218887 11 

TABLE II.—UNIFORM GAGE CREEP, COMBO-BAR AND NOTCH RUPTURE TEST RESULTS 

Spec ID Test type Cooling rate 

from 

Solutioning to 

871 °C (°C/min) 

Test temp, 

°C 

Stress, 

MPa 

Rupture life, 

hr 

E2-T1 Creep -Air 70 704 896 35.4 

E2-C1 Creep -Air 68 704 690 261.9 

E2-C2 Creep -Air 68 704 483 1531.7 

C-T1 Creep -Air 69 704 793 146 

C-T7 Creep -Air 71 704 690 457.4 

C-T11 Creep -Air 71 704 896 33.9 

50C-T2 Creep -Air 67 704 793 128.3 

9C-T1 Creep -Air 68 704 793 117.8 

9C-T7 Creep -Air 79 704 793 127 

0A-T1 Creep -Air 68 704 690 349.9 

0A-T7 Creep -Air 79 704 793 133.6 

0F-T1 Creep -Air 68 704 896 28.3 

0A-T3 Creep -Air 68 704 690 284.3 

50C-TM1 Creep - Vacuum 77 704 896 90 

50C-TM6 Creep - Vacuum 77 704 896 56.5 

0F-T6 Creep - Vacuum 70 704 793 123 

9C-T4 Creep - Vacuum 67 704 793 203 

9D-T3 Creep - Vacuum 68 704 586 1255 

0A-T4 Creep - Vacuum 67 704 690 271 

E2-NC1 ComboCreep-Kt=2 68 704 793 141.7 

E2-NC2 ComboCreep-Kt=2 66 704 793 132.15 

E2-NC3 ComboCreep-Kt=2 68 704 793 127.2 

E2-NC4 ComboCreep-Kt=2 71 704 793 110.3 

E2-NC5 ComboCreep-Kt=2 67 704 793 123.6 

E2-NC6 ComboCreep-Kt=2 71 704 793 128.2 

C-R2 Notch Rupture Kt=2 72 704 690 1105 

C-R3 Notch Rupture Kt=2 77 704 793 620 

C-R4 Notch Rupture Kt=2 77 704 793 1590 

C-R7 Notch Rupture Kt=2 69 704 896 313 

50C-R1 Notch Rupture Kt=2 77 704 690 809 

50C-R2 Notch Rupture Kt=2 78 704 793 506 

 
NASA/TM—2015-218887 12 

TABLE III.—DISTANCE FROM THE NOTCH ROOT TO THE 

CRACK ORIGIN FOR CYCLIC MAX DWELL NLCF TESTS 

Specimen Life, 

hr 

Distance from notch, 

mm 

E2-N1 955 2.4 

E2-N2 978 2.6 

E2-N3 625 1.6 

E2-N6 610 1.5 

E2-CN11 820 2.4 

E2-CN13 780 2.6 

9D-L5 Vac 1180 1 

Figure 1.—Notched LCF specimen. 

Figure 2.—Stress rupture specimen geometry.

Figure 3.—Combo-bar specimen geometry. (a) Notch detail; (b) Specimen geometry.

Figure 4.—The two dwell cycles utilized for the NLCF testing. (a) Max dwell: 1.5-90-1.5s. 

(b) Min dwell: 1.5-1.5-90s.
NASA/TM—2015-218887 13 

Figure 5.—Stress relaxation experiment and model fit.

Figure 6.—Notched LCF results for cyclic and dwell tests performed in air at a maximum stress of 793 MPa. 
NASA/TM—2015-218887 14 

Figure 7.—Failure modes were drastically different for the cyclic and dwell NLCF tests performed at a max stress of 

793 MPa. (a) Cyclic NLCF: 10 Hz. (b) Min dwell NLCF. (c) Max dwell NLCF. 

Figure 8.—Initiations in the cyclic NLCF tests originated at near 

surface ceramic inclusions. 
NASA/TM—2015-218887 15 

Figure 9.—Min dwell NLCF initiations occurred from microscopic oxide blisters. 

Figure 10.—Min dwell NLCF test results in air versus vacuum at a max stress 

of 793 MPa. 
NASA/TM—2015-218887 16 

Figure 11.—Surface cracking in a vacuum notch min dwell test only occurred when an improper bake-out of a 

replacement heating element deposited a brittle coating on the surface of specimen. (a) Vacuum min dwell: 

28,600 cycles. (b) Vacuum min dwell: 39,106 cycles. 

Figure 12.—Axial, von Mises and hydrostatic stress profiles remain almost unchanged after the first 

40 min dwell NLCF cycles. 
NASA/TM—2015-218887 17 

Figure 13.—Uniform gage specimen tested for 50,000 min dwell cycles at a max stress 793 MPa. Surface covered 

with oxide particles yet no surface cracking was detected. (a) Lower magnification. (b) Higher magnification. 
NASA/TM—2015-218887 18 

Figure 15.—Creep process deformation mechanisms observed at the internal initiation sites. (a) Lower magnification. 

(b) Higher magnification. 

Figure 16.—Secondary initiations in the cyclic max dwell NLCF specimens typically occurred from near surface 

inclusions and are thought to be caused by a fatigue process. (a) Secondary initiation-near surface inclusion. 

(b) Near surface fatigue initiation. 
NASA/TM—2015-218887 19 

Figure 17.—Notch creep rupture lives were similar to the cyclic max dwell NLCF lives in 

terms of hours to rupture. 

Figure 18.—Failure of notch rupture specimens tested at 793 MPa resulted from internal initiations similar 

to cyclic max dwell NLCF specimens. (a) Specimen A. (b) Specimen B. 
NASA/TM—2015-218887 20 

Figure 19.—Metallographic cross sections of notch rupture and cyclic max dwell NLCF specimens tested at 793 MPa, 

obtained from regions slightly below the internal crack initiation locations. Both types of specimens show creep 

rupture through grain boundary void coalescence. (a) Notch rupture. (b) Cyclic max dwell NLCF. (c) Cyclic max 

dwell NLCF at a higher magnification. 

Figure 20.—Crack initiation for cyclic max dwell NLCF tested at 896 MPa occurred near the 

notch root both in air and vacuum. (a) Cyclic max dwell NLCF in air. (b) Cyclic max dwell NLCF 

in a vacuum. 
NASA/TM—2015-218887 21 

Figure 21.—Comparison of uniform gage creep behavior in air versus vacuum at 704 °C. 

Figure 22.—Comparison of combo-bar rupture lives versus smooth creep and notched specimens. 

All combo-bar specimens failed in the smooth section. 
NASA/TM—2015-218887 22 

Figure 23.—Differences in surface deformation mode between uniform gage creep tests. (a) In air. (b) In 

a vacuum. 
NASA/TM—2015-218887 23 

Figure 24.—Distribution profile of axial, von Mises and hydrostatic stresses based on von Mises 

plasticity flow model at 0 and 1000 hr of applied dwell at 793 MPa. Dotted box represents the 

distribution of the observed crack initiation sites in cyclic max dwell NLCF tests. 

Figure 25.—Distribution profile of axial, von Mises and hydrostatic stresses based on 

Drucker-Prager plastic flow model at 0 and 1000 hr of dwell at 793 MPa. Dotted box 

represents the distribution of the observed crack initiation sites in cyclic max dwell 

NLCF tests. 
NASA/TM—2015-218887 24 

Figure 26.—Notch cyclic max dwell and creep notch rupture test exhibited longer life than 

uniform gage creep and combo-bar tests in terms of net section stress. Notch creep 

strengthening observed. 

Figure 27.—Notch and uniform gage test data plotted in terms of the Bridgman effective stress. 

Methodology adequately accounts for visco-plastic notch strengthening.