Irebert R. Delgado

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Grainex Mar-M 247 Turbine Disk Life Study for

NASA's High Temperature High Speed Turbine

Seal Test Facility

NASA/TM—2005-213873

October 2005

ARL–TR–3528

U.S. ARMY

RESEARCH LABORATORY
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Irebert R. Delgado

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Grainex Mar-M 247 Turbine Disk Life Study for

NASA's High Temperature High Speed Turbine

Seal Test Facility

NASA/TM—2005-213873

October 2005

National Aeronautics and

Space Administration

Glenn Research Center

ARL–TR–3528

U.S. ARMY

RESEARCH LABORATORY
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Trade names or manufacturers’ names are used in this report for

identification only. This usage does not constitute an official

endorsement, either expressed or implied, by the National

Aeronautics and Space Administration.

This report contains preliminary

findings, subject to revision as

analysis proceeds.

Available electronically at http://gltrs.grc.nasa.gov

Acknowledgments

The author wishes to acknowledge the invaluable help of the following individuals:

Andrew Diez, Rolls-Royce Corporation

Tim Gabb and Gary R. Halford, NASA Glenn Research Center

Ramesh Kalluri and Pete Kantzos, Ohio Aerospace Institute

Dennis Keller, Real World Quality Systems

Mar-Test, Inc., Cincinnati, Ohio

Clare Rimnac, Case Western Reserve University

Bruce Steinetz and Jack Telesman, NASA Glenn Research Center

Brian Shannon, Ohio Aerospace Institute.
NASA/TM—2005-213873 iii 

 

Contents 

1. Introduction, Background, Objective................................................................1

1.1 Introduction.............................................................................................1

1.2 Objectives...............................................................................................6

1.3 Benefits of Study ....................................................................................6

2. Background on Grainex Mar-M 247.................................................................8

2.1 Grainex Mar-M 247 Material...................................................................8

2.2 Material Processing and Microstructure..................................................8

2.3 Material Properties ...............................................................................11

3. Material Sectioning Plan and Material Characterization ................................18

3.1 Sectioning Plan for the NASA Disk.......................................................18

3.2 Material Characterization......................................................................20

4. Fatigue Strain-Life Behavior of Grainex Mar-M 247 ......................................28

4.1 Introduction...........................................................................................28

4.2 Materials and Methods: Tensile Behavior............................................28

4.3 Materials and Methods: Fatigue Strain-Life Behavior ..........................32

4.4 Results and Discussion: Tensile Behavior...........................................38

4.5 Results and Discussion: Fatigue Strain-Life Behavior .........................41

5. Fatigue Crack Growth Behavior of Grainex Mar-M 247.................................65

5.1 Introduction...........................................................................................65

5.2 Materials and Methods .........................................................................65

5.3 Results and Discussion ........................................................................78

6. Determination of the NASA Disk Inspection Interval......................................91

6.1 Introduction...........................................................................................91

6.2 Methods................................................................................................91

6.3 Results and Discussion ........................................................................92

7. Future Work...................................................................................................95

7.1 Effect of Material limitations..................................................................95

7.2 Effect of Test Parameter Limitations.....................................................95

7.3 Eddy-Current Limitations ......................................................................96

7.4 Recommendations for further research or improvements.....................96

Bibliography ........................................................................................................97

NASA/TM—2005-213873 v 

List of Abbreviations 

Symbol Description Units

2Lpctr center potential probe spacing [mm] 

2Lpmax maximum potential probe spacing [mm] 

2Lpmin minimum potential probe spacing [mm] 

2Nf reversals to failure 

2r0ε plastic zone size diameter under plane strain conditions [mm] 

2r0σ plastic zone size diameter under plane stress conditions [mm] 

A649°C gage section area at 649°C [m2

] 

Af final gage section area [m2] 

Ai initial gage section area [m2] 

a desired percentile level 

ac crack depth [mm] 

acrit critical crack depth [mm] 

ai lowest detectable crack depth [mm] 

an initial EDM crack depth [mm] 

b fatigue strength exponent 

bc crack half-height [mm] 

bn initial crack half-height [mm] 

C constant coefficient for Paris model ( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

m

MPa m

mm cycle

C1 constant coefficient for elastic term of Method of 

Universal Slopes model 

C2 constant coefficient for plastic term of Method of 

Universal Slopes model 

c fatigue ductility exponent 

cc crack surface half-width [mm] 

cn initial crack surface half-width [mm] 

D21 °C gage section diameter at 21°C [mm] 

D649 °C gage section diameter at 649°C [mm] 

E Young’s Modulus [GPa] 

F F-table value 

Fs boundary correction factor 

F* test statistic 

Fˆ dimensionless geometry factor 

h half-height of Kb specimen gage section from EDM notch [mm] 

K stress-intensity factor [MPa m ] 

k transfer function 

KI stress-intensity factor (Mode I) [MPa m ] 

Kb surface flawed fatigue crack growth specimen 

Kc critical fracture toughness [MPa m ] 

KIC critical fracture toughness (Mode I) [MPa m ] 
NASA/TM—2005-213873 vi 

Kmax maximum stress-intensity factor [MPa m ] 

Lf final gage section length [mm] 

Li initial gage section length [mm] 

Lp potential probe spacing half-width [mm] 

m constant exponent for Paris model 

N cycle 

Nf cycles to failure [cycles] 

Nfm cycles to failure in presence of mean stress [cycles] 

Nf0 cycles to failure under zero mean stress [cycles] 

Ni cycles to crack initiation [cycles] 

Nt transition life 

n1 number of data points for data set 1 

n2 number of data points for data set 2 

P load [N] 

Pmax maximum load [N] 

Pε=0.2 percent load at 0.2 percent strain [N] 

Q shape factor 

R load ratio 

Rε strain ratio = ( min max ε ε ) 

Rσ stress ratio = (σ min σ max ) 

R2

 coefficient of determination 

SSE(F) sum of the squares of the errors of the full model 

SSE(R) sum of the squares of the errors of the reduced model 

s remote uniform tensile stress [MPa] 

t through thickness of fatigue crack growth specimen [mm] 

V crack length voltage [volts] 

Veff effective ratio of mean stress to stress amplitude 

VN reference voltage for fatigue crack growth tests [volts] 

Vσ ratio of mean stress to stress amplitude 

w width of fatigue crack growth specimen gage section [mm] 

Xij independent variable of the reduced statistical model 

Yij predicted value of the reduced statistical model 

Z constant coefficient 

dN

dac fatigue crack growth rate [mm/cycle] 

∆a incremental striation spacing [mm] 

∆K stress intensity range [MPa m ]

∆Kc critical fracture toughness range [MPa m ] 

∆Kth fatigue threshold stress intensity range [MPa m ] 

∆T temperature differential from 21°C to 649°C [°C] 

∆ε total strain range 

2

∆ε strain amplitude
NASA/TM—2005-213873 vii 

el ∆ε elastic strain range 

2

el ∆ε elastic strain amplitude

in ∆ε inelastic strain range 

2

in ∆ε inelastic strain amplitude 

∆σ stress range [MPa] 

α649 °C thermal expansion coefficient at 649°C [m/m/°C] 

β0 intercept of the reduced statistical model 

β1 slope of the reduced statistical model 

δ crack tip opening displacement [mm] 

ε strain [m/m] 

εij error term of the reduced statistical model 

εmin minimum strain 

εmax maximum strain 

εa strain amplitude 

εf true fracture ductility 

'

f ε fatigue ductility coefficient 

f

~

ε true fracture strain 

φ ellipse parametric angle [radians] 

π pi 

σ stress [MPa] 

σa stress amplitude [MPa] 

σf engineering fracture stress [MPa] 

' σ f fatigue strength coefficient [MPa] 

f

~

σ true fracture strength [MPa]

σm mean stress [MPa] 

σmax maximum stress during cycling [MPa] 

σmin minimum stress during cycling [MPa]

σUTS ultimate tensile strength [MPa] 

σy(0.2 percent) 0.2 percent offset yield strength [MPa] 

ζ constant exponent 

%EL percent elongation 

%RA percent reduction in area 

%∆ε percent total strain 
NASA/TM—2005-213873 1 

Grainex Mar-M 247 Turbine Disk Life Study 

for NASA’s High Temperature High Speed 

Turbine Seal Test Facility 

Irebert R. Delgado 

U.S. Army Research Laboratory 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract

 An experimental and analytical fatigue life study was performed on the 

Grainex Mar-M 247 disk used in NASA’s Turbine Seal test facility. To preclude 

fatigue cracks from growing to critical size in the NASA disk bolt holes due to 

cyclic loading at severe test conditions, a retirement-for-cause methodology was 

adopted to detect and monitor cracks within the bolt holes using eddy-current 

inspection. 

 For the NASA disk material that was tested, the fatigue strain-life to crack 

initiation at a total strain of 0.5%, a minimum to maximum strain ratio of 0, and a 

bolt hole temperature of 649°C was calculated to be 665 cycles using -99.95% 

prediction intervals. The fatigue crack propagation life was calculated to be 367 

cycles after implementing a safety factor of 2 on life. Thus, the NASA disk bolt 

hole total life or retirement life was determined to be 1032 cycles at a crack 

depth of 0.501 mm. An initial NASA disk bolt hole inspection at 665 cycles is 

suggested with 50 cycle inspection intervals thereafter to monitor fatigue crack 

growth. 

1. Introduction, Background, Objective 

1.1 Introduction 

 The High Temperature High Speed Turbine Seal test facility, located at NASA 

Glenn Research Center (NASA GRC) in Cleveland, Ohio provides a critical 

research capability in testing gas path air seals, such as labyrinth, brush, or 

finger seals, for next generation aircraft engines. Engine seals are located in the 

compressor and turbine engine sections as well as in the secondary flow areas 

and serve to minimize unwanted air leakage across blades tips and rims as well 

as main shafts. By maintaining a close clearance, they help to reduce specific 

fuel consumption and thereby aid in reducing direct operating costs.1

 The turbine 

seal test stand (Figure 1.1) can test candidate seal designs at high temperatures, 

high seal pressures, and surface speeds greater than 300 m/s. 
NASA/TM—2005-213873 2 

Figure 1.1 NASA’s turbine seal test facility. 

The test facility uses a disk made of Grainex Mar-M 247 (hereafter called 

the NASA disk). It is a cast nickel based superalloy whose outer diameter is 

in contact with or is within close proximity of the test seal inner diameter. 

The Grainex Mar-M 247 material’s high strength and creep resistance at 

temperatures between 150 to 1500°C make it an excellent material for turbine 

blades, vanes, and disks.2

 Because the NASA disk experiences a severe test combination of high 

temperature, high pressure, and high speed, the possibility exists that fatigue 

cracks will develop with cycling at the 6 bolt hole locations, which fasten it to the 

main shaft of the turbine seal test stand. If allowed to grow to a critical size, the 

cracks could cause the NASA disk to catastrophically burst during use. 

 Preliminary analyses by Tong and Steinetz3

 have placed a strain-life limit, Lsys, 

of 6000 cycles based upon an equivalent -3σ reduction factor and a probabilistic 

approach4

 accounting for n = 6 bolt holes: 

e

sys

n

L L 1 = Eqn. 1.1 (Ref. 4) 

where Lsys = overall system life 

 L = calculated NASA disk life = 10,000 cycles 

 n = number of bolt holes = 6 

 e = Weibull slope parameter = 3.57 (Gaussian Distribution) 

Eqn. 1.1 is based on the Lundberg-Palmgren4 analysis for rolling element 

bearing system lives. L is the predicted life for a disk with a single bolt hole. The 

predicted life, L, and Weibull slope parameter, e, are assumed to be identical for 
NASA/TM—2005-213873 3 

all six disk bolt holes. However, the preliminary analysis does not address the 

existence of a crack at the bolt hole surface which, if allowed to grow to a critical 

size, would lead to a catastrophic NASA disk failure in the turbine seal test rig. 

 The 1996 engine failure of an MD-88 during take-off was a specific example 

of an uncontained disk failure resulting from a pre-existent crack.5

 During takeoff the hub section of the Pratt & Whitney JT8D-219 engine separated from its 

low-pressure compressor section. The hub failure released high energy blade 

and engine fragments (Figure 1.2) which broke through the engine structure and 

penetrated the plane’s main cabin killing 2 of the passengers. Metallurgical 

examination of the origin of the hub failure revealed a 25 mm crack found within 

one of the twenty-four 12.7 mm diameter tierod bolt holes which secure the hub 

to the low-pressure compressor (Figure 1.2). The crack was described by a 

National Transportation and Safety Board senior metallurgist as a “progressive 

crack that increased with time”.5

 Inspection records indicated that the hub had 

accumulated approximately 13,000 cycles of an expected 20,000 cycles to 

replacement, a cycle being defined as a takeoff and touchdown. The hub had 

been visually inspected six months before using a dye penetrant procedure that 

should have indicated the presence of any cracks.5 

The crack may have been missed during inspection or may have developed 

in the following months of engine operation. The consequences of such fatigue 

failures strongly emphasize the need to accurately detect the presence, location, 

and size of a crack within a structure and then to assess the integrity of that 

structure for further operation. Similarly, cracks within the bolt holes of the NASA 

disk of the turbine seal test facility may develop and grow over time with 

increasing number of cycles. NASA disk cycles are defined as a ramp up and 

down in speed at constant test air temperature and pressure. 
NASA/TM—2005-213873 4 

Figure 1.2 Uncontained failure of an engine hub with the crack location at 

the tierod holes of a Pratt & Whitney JT8D-219 engine.5

 

The process of regularly inspecting a critical component to detect the 

presence, location, and size of a crack is usually accomplished through nondestructive inspection methods, such as eddy-current inspection. Using strainlife and fatigue crack growth data, the cycles to crack initiation and failure can be 

determined. From this data, the inspection frequency and an appropriate NASA 

disk retirement criteria (i.e. crack length) can be determined. 

Eddy-current inspection is based on electromagnetic induction principles, and 

is used to detect microscopic cracks at or near a material’s surface. A wire 

coiled probe (Figure 1.3), containing an alternating current, is normally inserted 

into the disk bolt holes. Any surface or subsurface cracks can be sensed by the 

coil. A reference sample of the same material with a mechanically produced 

crack is used for comparison.6

Tierod 
NASA/TM—2005-213873 5 

Figure 1.3 Eddy-Current inspection of disk bolt holes using a Bobbin-Type 

coil.6

 The detection of cracks on aircraft engine components through eddy-current 

inspection is part of a fracture control philosophy in which critical engine parts are 

designed based upon a damage tolerance approach. This requires that a 

fracture critical part is still functional even though microscopic cracks, introduced 

during manufacture or service, are present. The Air Force’s Engine Structural 

Integrity Program is an example of one program that has adopted this damage 

tolerance philosophy.7

 Damage tolerant approaches fit under fail-safe design 

methodologies which hold the view that a crack will not be allowed to grow to 

critical size within a component before it can be inspected and either replaced or 

repaired.7
NASA/TM—2005-213873 6 

1.2 Objectives 

 The Grainex Mar-M 247 NASA disk in the turbine seal test rig can be 

considered as the fracture critical component that may contain a defect that could 

grow to critical size during service. A damage tolerant approach for the NASA 

disk would require an inspection interval to monitor the growth of cracks within 

the bolt holes and would also require a critical crack length criterion from which to 

retire the NASA disk from service. 

 This study proposes a damage tolerant approach to monitoring the presence 

and growth of cracks within the bolt holes of the NASA disk. Fatigue crackinitiation and fatigue crack growth lives would be experimentally determined to 

obtain a total fatigue life for the NASA disk and an appropriate inspection interval. 

 Little has been published on the strain-life and fatigue crack growth of Grainex 

Mar-M 247, particularly at the 649°C operating temperature of interest.8,9,10,11,12,13

The goals of the study were two-fold. 

1. Determine the crack initiation life of the NASA disk, at various strain ratios, 

using experimentally determined strain-life fatigue behavior at its maximum 

operational test temperature. Conduct a statistical analysis of the test data to 

bound the fatigue life within known prediction limits. 

2. Experimentally determine the critical crack size of the NASA disk and use the 

results to determine an eddy-current inspection interval. Perform a statistical 

analysis of the crack-growth data to determine the fit of the data to the Paris14

relation. 

1.3 Benefits of Study 

 The study will primarily benefit the safe operation of the turbine seal test 

facility. Specifically: 

1. The study will result in a damage tolerant approach to monitoring the growth 

 of cracks in the NASA disk bolt holes through scheduled eddy-current 

 inspection. 

2. The total life of the NASA disk, crack initiation and crack growth, will be 

statistically calculated to support the inspection interval placed on the bolt 

holes. 
NASA/TM—2005-213873 7 

 

Chapter 1 Works Cited 

 1. Ludwig, Lawrence P., and Robert C. Bill. “Gas Path Sealing in Turbine 

 Engines.” ASLE Transactions 23.1 (1978):1-5. 

 2. Davis, Joseph R., ed. Heat Resistant Materials. Materials Park: ASM 

 International, 1997. 

 3. Tong, Mike and Bruce Steinetz. “Mar-M 247 Disk Finite Element Thermal 

 and Stress Analysis”, NASA Glenn Research Center, Cleveland. 30 

 January 1997. 

 4. Melis, M.E., E.V. Zaretsky, and R. August. “Probabilistic Analysis of 

Aircraft Gas Turbine Disk Life and Reliability.” Journal of Propulsion and 

Power, 15.5 (1999) 658-666. 

 5. Ott, James. “JT8D Hub Failure Sparks Intense Inquiry.” Aviation Week & 

 Space Technology, 15 July 1996: 29+. 

 6. ASM International Handbook Committee. “Eddy-Current Inspection.” 

 Metals Handbook 9th Edition Volume 17: Nondestructive Evaluation and 

 Quality Control. Metals Park: ASM International, 1989. 164+. 

 7. Cowie, William D. “Fracture Control Philosophy.” Metals Handbook 9th 

 Edition Volume 17: Non-Destructive Evaluation and Quality Control. Metals 

 Park: ASM International, 1989. 666+.

 8. Howmet Turbine Components Corporation. TB 3000: Grainex Cast Mar-M 

 247 Alloy. Greenwich: Howmet Turbine Components Corporation. 

 9. Macha, D.E., G.R. Cole, and J.A. Butzer. “Fine Grain, Investment-Cast 

 Integral Turbine Wheels.” Grain Refinement in Castings and Welds. Ed. 

 G.J. Abbaschian and S.A. David. New York: The Metallurgical Society of 

 AIME, 1983. 197-219. 

10. Kaufman, M. “Properties of Cast Mar-M-247 for Turbine Blisk Applications.” 

 Superalloys 1984. Ed. Maurice Gell et al. Warrendale: Metallurgical 

 Society of AIME, 1984. 43-52. 

11. “Microcast-X Mar-M 247.” Alloy Digest May 1995. 

12. Helmink, R.C. et. al. “Advanced Superalloys and Tailored Microstructures 

 for Integrally Cast Turbine Wheels.” Superalloys 2000. Ed. T.M Pollock et 

 al. Warrendale: TMS, 2000. 171-179. 

13. MacIntyre, Cal A. and P. Neil Agarwal. “Development of Fine Grain Cast 

 Mar-M 247 Axial and Radial Turbine Wheels.” Advanced Aerospace 

 Materials Technology: SP-597. Warrendale: Society of Automotive 

 Engineers, Inc., 1984. 35-45. 

14. Dowling, Norman E. Mechanical Behavior of Materials : engineering 

 methods for deformation, fracture, and fatigue. Upper Saddle River: 

 Prentice-Hall, Inc., 1999. 
NASA/TM—2005-213873 8 

2. Background on Grainex Mar-M 247 

2.1 Grainex Mar-M 247 Material 

Grainex Mar-M 247 is a class of cast nickel-based superalloys (Figure 2.1) 

and is primarily used in gas turbine engine components such as turbine blades, 

turbine disks, burner cans, and vanes.1

 In general 90 percent of superalloys 

produced are used for gas turbine engines and approximately half of the engine 

weight is composed of nickel-based superalloys. 1 Superalloys are well suited for 

jet engine applications where they generally operate from 540°C to over 80% of 

their melting temperature.1 Additionally they retain their strength at these 

temperatures while providing creep and corrosion resistance.1

Figure 2.1 Grainex Mar-M 247 is part of the family of superalloys 

represented by the dashed line. 1

2.2 Material Processing and Microstructure 

 The Mar-M 247 alloy (Table 2.1) was developed in the 1970s by Danesi and 

Thieleman. 2 It is manufactured by melting and investment casting under vacuum 

In contrast to wrought superalloys, cast superalloys exhibit improved creep and 

rupture characteristics due to coarser grain sizes and alloy segregation. 

However, the larger grain sizes reduce ductility and lower cyclic fatigue life.3

 

Also, columnar grains are found in thin sections such as turbine disks (Figure 

2.2) and blades resulting in material properties inconsistent with those found in 

the disk hub. 
NASA/TM—2005-213873 9 

Table 2.1 Nominal chemical composition of Mar-M 247 alloy 4

Element Wt% Element Wt% Element Wt% 

Co 10 Ta 3 C 0.16 

W 10 Hf 1.5 Zr 0.05 

Cr 8.2 Ti 1 B 0.015 

Al 5.5 Mo 0.6 Ni Balance 

Figure 2.2 Conventionally cast Mar-M 247 macrostructure showing coarse, 

columnar oriented grains.4

 The NASA Mar-M 247 test rotor was made through the Grainex investment 

casting process.5

 The Grainex process was developed by Howmet Turbine 

Components Corporation in the early 1980s and uses traditional investment 

casting processes in combination with mold-agitation during solidification to 

produce an equiaxed grain structure that results in more consistent material 

properties throughout the casting (Figure 2.3).4 
NASA/TM—2005-213873 10 

Figure 2.3 Grainex cast Mar-M 247 macrostructure showing fine, equiaxed 

grains.4

Investment casting is preferred over wrought processing for complex turbine 

engine components in that it produces near net shape structures. Following 

solidification, the casting is mechanically separated from its ceramic mold and 

then radiographically or ultrasonically inspected for cracks, pores or tears which 

would negatively affect material properties. Prior to final machining, the casting 

is hot-isostatic pressed (HIP) at 1185°C and 172 MPa for 4 hours, solution 

treated at 1185°C for 2 hours, and aged at 871°C for 20 hours. The HIP process 

reduces the porosity inherent in the investment casting process. Minimizing 

porosity reduces possible crack initiation sites and improves material fatigue life. 

Solution treating the casting homogenizes the microstructure to an austenitic 

FCC γ-phase matrix. Strengthening of the alloy is derived from solid solution 

strengthening constituents including Co, Cr, Mo, W, and Ta.1 The aging process 

precipitates a coherent γ’ phase [Ni3,(Al,Ti)] which gives primary strengthening 

and improves tensile and creep-rupture properties.1

 A number of sub-structures within the Grainex Mar-M 247 material serve 

major roles in strengthening or weakening the material. Metal carbides (MxCy) 

serve to strengthen grain boundaries, strengthen the γ matrix through 

precipitation of fine carbides, and combine with elements to promote phase 

stability.1

 For example, discontinuous M23C6 (M = Cr, Ni-Co, Mo, W) provides 

grain boundary strengthening by inhibiting the movement of grains thereby 

improving rupture strength. Borides serve as grain boundary strengtheners 

particularly under creep rupture loading.6

 Surface oxidation resistance is 

provided by scale build-up of Cr2O3 and Al2O3. However, metal carbide failure 

may occur by fracture of the M23C6 particle or by decohesion.1

 Topologically 
NASA/TM—2005-213873 11 

closed-pack phases are harmful structures that deplete refractory elements 

which ultimately reduces creep rupture strength. Found primarily as grain 

boundary carbides they appear as long plates or needles and contribute to 

premature cracking due to their hard, brittle nature.6 

2.3 Material Properties 

2.3.1 Literature Review 

While much has been written on Mar-M 247, only a small number of 

references have been found on Grainex Mar-M 247 that report tensile, strain-life, 

and fatigue crack growth data. 

2.3.2 Tensile Behavior 

Tensile properties determined from specimens taken from the rim of turbine 

disks show that Grainex Mar-M 247 is equal to if not better than the 

conventionally cast Mar-M 247 through 760°C (Figure 2.4).4 The ultimate tensile 

strength for Grainex Mar-M 247 is 1034 MPa at room temperature and increases 

slightly through 760°C while that for conventionally cast Mar-M 247 is no higher 

than 1000 MPa. Also, the 0.2% offset yield strength for Grainex Mar-M 247 is 

828 MPa from room temperature through 760°C while that for conventionally cast 

Mar-M 247 begins to fall off after 500°C. Finally, reduction in area and 

elongation for both Grainex and conventionally cast Mar-M 247 decrease above 

482°C. Other sources cite comparable tensile properties for Grainex Mar-M 

247.7,8,9 Macha et. al. and Kaufman report Young’s Modulus decreasing with 

increasing temperature (Table 2.2). 
NASA/TM—2005-213873 12 

Figure 2.4 Comparison of tensile properties of Grainex Mar-M 247 and 

conventionally cast Mar-M 247.4

Table 2.2 Comparison of Young's modulus for Grainex 

 Mar-M 247 at various temperatures 

 Source 

Macha et al. 7

 Kaufman8

Temp [°C] E [MPa] E [MPa] 

21 226 n/a 

204 n/a 210 

427 205 203 

760 n/a 175 
NASA/TM—2005-213873 13 

2.3.3 Strain-Life Behavior 

 Strain-life data reported by Macha et al. at 427°C and Rε = -1 (Figure 2.5)7

 for 

Grainex cast Mar-M 247 show a slight increase in cyclic fatigue life at the -3σ

property line at higher strain ranges when compared to conventionally cast 

Mar-M 247. Kaufman reports Grainex Mar-M 247 data for Rε = 0 at 204°C, 

427°C, and 760°C (Figure 2.6).8

 As expected, lower cyclic lives result from 

increasing temperature for a constant strain range. Finally strain-life data 

reported by Helmink et al. for Grainex Mar-M 247 at 538°C (Figure 2.7)10 is 

slightly better in comparison with directionally-solidified Mar-M 247. 

Figure 2.5 Grainex Mar-M 247 strain-life data at 427°C per Macha et al., 

Rε = -1.7
NASA/TM—2005-213873 14 

Figure 2.6 Grainex Mar-M 247 strain-life data per Kaufman at Rε = 1.8 

Figure 2.7 Strain-Life data per Helmink et al. at 538°C.10
NASA/TM—2005-213873 15 

2.3.4 Fatigue crack-growth data 

 Grainex Mar-M 247 shows a lower fatigue crack-growth rate for a constant 

stress intensity range than both conventionally cast Mar-M 247 at 427°C (Figure 

2.8), as reported by Macha et al.7 and for Inco 713LC at 538°C (Figure 2.9) as 

reported by MacIntyre et al.11 Finally, the Grainex Mar-M 247 fatigue crack 

growth rate compares similarly with those of materials CM 681 and CM 681A at 

538°C (Figure 2.10), as reported by Helmink et al.10 However no fatigue crackgrowth data were available at 649°C and greater than 300 m/s operating 

condition which is needed to determine a critical crack length for the NASA 

Grainex Mar-M 247 disk. 

Figure 2.8 Comparison of Grainex Mar-M 247 and conventionally cast 

Mar-M 247 fatigue crack growth data per Macha et al. at 427°C.7
NASA/TM—2005-213873 16 

Figure 2.9 Comparison of Grainex Mar-M 247 and IN713LC fatigue crackgrowth data at 538°C per MacIntyre et al.11

Figure 2.10 Comparison of Grainex Mar-M 247 data with CM681 and 

CM681A fatigue crack-growth data at 538°C per Helmink et al.10
NASA/TM—2005-213873 17 

 

Chapter 2 Works Cited 

 1. Davis, Joseph R., ed. Heat Resistant Materials. Materials Park: ASM 

 International, 1997. 

 2. United States Patent and Trademark Office. U.S. Patent 3720509: Nickel 

 Base Alloy. By Danesi, Wilbert P. and Rudolph H. Thielemann. 1973. 

 3. Freeman, William R., Jr. “Investment Casting.” Superalloys II. Ed. 

 Chester T. Sims et al. New York: John Wiley & Sons, Inc., 1987. 411-

 439. 

 4. Howmet Turbine Components Corporation. TB 3000: Grainex Cast Mar-M 

 247 Alloy. Greenwich: Howmet Turbine Components Corporation. 

 5. United States Patent and Trademark Office. Trademark: Grainex, 

 Registration No. 121275. By Howmet Turbine Components Corporation. 

 1982. 

 6. Ross, Earl W., Chester T. Sims. “Nickel-Base Alloys.” Superalloys II. Ed. 

 Chester T. Sims et al. New York: John Wiley & Sons, Inc., 1987. 97-133. 

 7. Macha, D.E., G.R. Cole, and J.A. Butzer. “Fine Grain, Investment-Cast 

 Integral Turbine Wheels.” Grain Refinement in Castings and Welds. Ed. 

 G.J. Abbaschian and S.A. David. New York: The Metallurgical Society of 

 AIME, 1983. 197-219. 

 8. Kaufman, M. “Properties of Cast Mar-M-247 for Turbine Blisk Applications.” 

 Superalloys 1984. Ed. Maurice Gell et al. Warrendale: Metallurgical 

 Society of AIME, 1984. 43-52. 

 9. “Microcast-X Mar-M 247.” Alloy Digest May 1995. 

10. Helmink, R.C. et. al. “Advanced Superalloys and Tailored Microstructures 

 for Integrally Cast Turbine Wheels.” Superalloys 2000. Ed. T.M Pollock et 

 al. Warrendale: TMS, 2000. 171-179. 

11. MacIntyre, Cal A. and P. Neil Agarwal. “Development of Fine Grain Cast 

 Mar-M 247 Axial and Radial Turbine Wheels.” Advanced Aerospace 

 Materials Technology: SP-597. Warrendale: Society of Automotive 

 Engineers, Inc., 1984. 35-45. 
NASA/TM—2005-213873 18 

3. Material Sectioning Plan and Material Characterization 

3.1 Sectioning Plan for the NASA Disk 

A sacrificial Grainex Mar-M 247 NASA disk was cut-up for tensile, strain-life, 

and fatigue crack growth specimens following general guidelines: 

1. A cross-section of the NASA disk from rim to centerline was used for 

 metallurgical examination. 

2. Tensile and strain-life specimens were taken in a randomized fashion 

 throughout the hub and web sections (Figure 3.1a and Figure 3.1b). 

3. Fatigue crack-growth specimens were taken as close to the bolt holes as 

possible since crack-initiation and growth were a concern within the bolt 

hole surfaces (Figure 3.1a) over repeated cycling at maximum operating 

conditions. 

Figure 3.1a NASA disk specimen identification. Nomenclature: ##T = 

Tensile, ##K = fatigue crack-growth, ##X = extra, ##L = strainlife. 
NASA/TM—2005-213873 19 

Figure 3.1b NASA disk specimen identification. Nomenclature: ##T = 

Tensile, ##K = fatigue crack-growth, ##X = extra, ##L = strainlife. 

A total of four tensile specimens were also taken from the hub and web 

sections of the NASA disk. From statistical experimental design, 15 specimens 

were made for each strain-ratio (Rε = 0 and Rε = -1) with 3 repeats at each of 5 

strain-ranges1. This complied with ASTM E606 suggested use of a minimum of 

10 specimens to generate strain-life curves2

. Minimum suggested strain-life 

specimens and percent replication were also followed per ASTM E739 and 

ASTM STP 588. Specifically, the ‘design allowables’ suggest a minimum of 12 to 

24 strain-life specimens and a 50 to 75% replication. Thus, fifteen specimens 

with 3 repeats at 5 strain levels give a percent replication of 67% (ASTM STP 

588):3,4

 % replication = 100 [1 – (number of strain levels /total number of 

 specimens)] 

 Eqn. 3.1 

Finally, 8 fatigue crack growth (FCG) specimens were electro-discharged 

machined (EDM) near the bolt holes of the NASA disk. 
NASA/TM—2005-213873 20 

3.2 Material Characterization 

3.2.1 Objectives 

 The metallurgical examination addressed the microstructure uniformity from 

the hub center to the rim of the NASA disk. Although the Grainex process gives 

a uniform, equiaxed grain structure resulting in uniform material properties, the 

relative difference in thickness between the hub and rim sections may cause the 

grain structure to vary. This is due to the relative cooling rates, during disk 

processing, from the thickest portion of the disk at the hub (slowest cooling) to its 

thinnest portion at the rim (fastest cooling). This may result in varying material 

properties. In a conventionally cast disk, differences in microstructure have 

resulted in varying tensile, strain-life, and fatigue crack-growth properties. 5 This 

was shown previously in Figure 2.4. Also, Figure 3.2 shows the variability in 

dynamic modulus for test specimens taken from different orientations from a 

conventionally cast disk of Mar-M 247. The data is compared to Grainex Mar-M 

247 which shows minimal orientation effects on dynamic modulus. The effect of 

microstructural differences between Grainex and conventionally cast Mar-M 247 

on fatigue strain life and fatigue crack growth was shown previously in Chapter 2 

(Figure 2.5 and Figure 2.8). 

Figure 3.2 Comparison of the dynamic modulus of Grainex Mar-M 247 and 

conventionally cast Mar-M 247 specimens removed in the axial, 

radial, tangential and 45° off-axis orientation.5 

 
NASA/TM—2005-213873 21 

The metallurgical examination addressed this concern for uniformity in 

microstructure specifically by: 

1. Qualitatively assessing the differences in grain size, structure, and orientation 

from the NASA disk hub to rim. 

2. Determining the extent of porosity in the microstructure from the hub to the 

rim of the NASA disk. 

3.2.2 Procedure 

Chord-Slice Preparation

 A chord slice of the NASA disk was electro-discharge machined for the 

metallurgical examination. This included the two halves of the hub section, and 3 

sections that accounted for the web and rim of the NASA disk (Figure 3.3 and 

Figure 3.4). 

Figure 3.3 Cut-up and orientation of web and rim metallurgical specimens. 

b-b 

c-c 

d-d 

e-e 

f-f 
NASA/TM—2005-213873 22 

Figure 3.4 Cut-up and orientation of hub section metallurgical specimens. 

 The three web/rim pieces were mounted in Bakelite. The hub sections were 

mounted on special fixturing and polished. Polishing was performed following 

standard metallographic methods. The etchant used was a mixture of acetic 

acid, nitric acid, deionized water and hydrofluoric acid (HF). 

Qualitative Assessment of Grain-Size

 A light microscope was used to obtain photomicrographs of the 

microstructure. The photomicrographs were qualitatively compared with respect 

to overall grain size and orientation. 

Qualitative Assessment of Porosity

Porosity, as defined in Mil-Std-1907, is a specific type of indication. Other 

types of indications include microstructural discontinuities such as inclusions, 

cracks, tears, cold shuts, microshrinkage, and phase segregation. Grade A 

requirements were used per section Mil-Std-1907 Section 4.1.1 for a highly 

stressed rotating cast component at high temperature.6 Table 3.1 gives specific 

indications that were used for comparison. 
NASA/TM—2005-213873 23 

Table 3.1 Mil-Std-1907 Grade A specifications for castings6

Indication Criteria (mm) Criteria (inch)

Cracks reject Reject 

hot tears reject Reject 

cold shuts reject Reject 

non-metallic inclusions 

 max dia 0.79 0.031 

 min separation = 3x 2.36 0.093 

Shrinkage 6.35 0.250 

Microshrinkage 

 max dia 1.60 0.063 

 min separation = 3x 4.80 0.189 

phase segregation 

 Surface 3.18 0.125 

 Subsurface 6.35 0.250 

gas holes 

 max dia 0.79 0.031 

 min separation = 3x 2.36 0.093 

 Fluorescent dye penetrant inspection was performed on each chord slice 

following ASTM E1417, Method C, Level 4.7 Any oils, dirt, or dust on the 

specimens were removed with alcohol. After air drying the specimens penetrant 

was applied and allowed to settle for 20 minutes. Excess penetrant was carefully 

removed and a developer applied to highlight any possible indications. 

3.2.3 Results and Discussion of Chord Slice Examinations 

Discussion of Grain Size Results

 The nominal grain size for Grainex Mar-M 247 is reported to range from 

0.18 mm to 1.6 mm depending upon relative material thickness at specific 

locations on cast wheels for engine components (Table 3.2).5

Table 3.2 Grain sizes in various sections of Grainex 

cast integral wheels5

 Hub Rim Airfoil 

Nominal Diameter (mm) 

(range-mm) 

1.2 

1.0 – 1.6 

1.4 

1.2 – 1.6 

0.42 

0.18 – 0.67 

ASTM Macrograin 

Size Number M10 – M9 M10 – M9 M15 – M11.5 
NASA/TM—2005-213873 24 

 Qualitative analysis of the grain size of the chord sections (Figure 3.3 and 

Figure 3.4) showed similar grain size and random orientation between chord 

sections (Figure 3.5 to Figure 3.7). Grain size was estimated from the 

photomicrographs to be 1.3 to 1.9 mm (Figure 3.6). The grain size was also 

comparable to reported data (Table 3.2). 

Figure 3.5 Grainex Mar-M 247 rim chord slice (S4B-1) at 16x. 
NASA/TM—2005-213873 25 

Figure 3.6 Grainex Mar-M 247 web chord slice (S4C-1) at 16x. 

Figure 3.7 Grainex Mar-M 247 hub cross-section (Bore1-2) at 16x. 
NASA/TM—2005-213873 26 

 A major difference in microstructure was observed within the grains where 

secondary dendritic arm spacings (SDAS) became increasingly larger from the 

rim to the hub section. The smallest SDAS were found near the rim while the 

coarsest were found at the hub. An exception was found at the NASA disk boss 

(see Figure 3.1b) where SDAS sizes were very similar to those found at the rim. 

These observations corroborate those observed by Howmet Turbine 

Components Corporation as shown in Table 3.3.5 SDAS was observed to 

become coarser from rim to hub (0.05-0.10 mm). The increase in SDAS from rim 

to hub can be observed by comparing Figure 3.5 with Figure 3.6 and Figure 3.7. 

Table 3.3 Reported SDAS measurements for Grainex 

Mar-M 247 disk/blade sections5

Casting Process Hub Rim Airfoil 

Grainex 0.10 0.05 0.03 

Discussion of Fluorescent Penetrant Inspection Results

Based upon the criteria given in Table 3.1, no major indications were revealed 

by the fluorescent penetrant inspection (Figure 3.8). Of particular importance is 

the fact that no indications were observed along the bolt hole surfaces. 

Figure 3.8 Typical fluorescent penetrant inspection results for hub section 

of Grainex Mar-M 247 NASA disk showing negligible indications. 
NASA/TM—2005-213873 27 

 

Chapter 3 Works Cited

1. Keller, Dennis. “Strain-Life Model with Statistics.” Real World Quality 

 Systems, Fairview Park. 05-09-01. 

2. ASTM Committee E-8 on Fatigue and Fracture. “ASTM E-606 – 92 

 (Reapproved 1998): Standard Practice for Strain-Controlled Fatigue 

 Testing.” Annual Book of ASTM Standards 2001: Section 3 Metals Test 

 Methods and Analytical Procedures: Volume 03.01 Metals—Mechanical 

 Testing; Elevated and Low-Temperature Tests; Metallography. ASTM. 

 West Conshohocken: ASTM, 1998. 543-557. 

3. ASTM Committee E-8 on Fatigue and Fracture. “ASTM E-739 – 91 

 (Reapproved 1998): Standard Practice for Statistical Analysis of Linear or 

 Linearized Stress-Life (S-N) and Strain-Life (ε-N) Fatigue Data.” Annual 

 Book of ASTM Standards 2001: Section 3 Metals Test Methods and 

 Analytical Procedures: Volume 03.01 Metals—Mechanical Testing; 

 Elevated and Low-Temperature Tests; Metallography. ASTM. West 

 Conshohocken: ASTM, 1998. 543-557. 

4. Little, R.E. and E.H. Jebe. ASTM STP 588: Manual on Statistical Planning 

 and Analysis for Fatigue Experiments. ASTM, 1975. 

5. Howmet Turbine Components Corporation. TB 3000: Grainex Cast Mar-M 

 247 Alloy. Greenwich: Howmet Turbine Components Corporation. 

6. Department of Defense. Mil-Std-1907: Inspection, liquid penetrant and 

magnetic particle, soundness requirements for materials, parts and 

weldments. Department of Defense. 7 Sept 1989. 

7. ASTM Committee E-7 on Nondestructive Testing. “ASTM E-1417 – 99: 

Standard Practice for Liquid Penetrant Examination.” Annual Book of ASTM 

Standards 2002: Section 3 Metals Test Methods and Analytical 

Procedures: Volume 03.03 Nondestructive Testing. ASTM. West 

Conshohocken: PA, 2002. 
NASA/TM—2005-213873 28 

4. Fatigue Strain-Life Behavior of Grainex Mar-M 247 

4.1 Introduction 

The presence and growth of cracks inside the bolt holes of the Grainex Mar-M 

247 NASA disk due to cyclic operation can be monitored and the disk removed 

from operation to preclude catastrophic disk failure. Both fatigue strain-life 

behavior and fatigue crack growth behavior will be used to determine a 

maintenance inspection interval for the bolt holes. This section focuses on the 

fatigue strain-life behavior of Grainex Mar-M 247. 

Strain-life tests will be used to determine the cycles to crack initiation and 

cycles to failure of the Grainex Mar-M 247 material at maximum NASA disk 

operating conditions in the turbine seal rig facility. Previous NASA disk analyses 

showed that the region adjacent the disk bolt hole just enters the plastic region of 

the stress-strain curve at its maximum operating temperature, pressure, and 

surface speed (816°C, 1724 KPa, and +300 m/s).1

 Thus, a strain-based 

approach to fatigue is used to address the local yielding in the material. 

 The strain-life tests on the Grainex Mar-M 247 NASA disk will be compared to 

estimates by Tong and Steinetz1, estimates reported in the literature,2,3

predictions using the Method of Universal Slopes and the Halford-Nachtigall 

Method.4 To predict fatigue strain-life using these methods, tensile tests were 

conducted at 649°C which is the local NASA disk bolt hole temperature at 816°C 

test air temperature. 

4.2 Materials and Methods: Tensile Behavior 

Experiment

 Tensile tests were performed at Mar-Test Inc. in Cincinnati, Ohio per ASTM 

E-8 and ASTM E-21 standards. Tensile testing was conducted on a Mar-Test, 

Inc. hydraulic servo controlled test system5, using a box furnace for specimen 

heating (Figure 4.1). Load was recorded using a load cell.5

 Strain was 

recorded using a Mar-Test fused quartz extensometer with a linear variable 

differential (LVDT) for sensing deflection. The resolution of the LVDT was the 

greater of 0.0001 m/m or 0.25% of the measurement (ASTM E83, Class B2).5 
NASA/TM—2005-213873 29 

Figure 4.1 A typical tensile test set-up. 5

Figure 4.2 Tensile test specimen geometry.6

The tensile test specimen geometry was 3.56 mm in diameter by 50.8 mm in 

length per ASTM E-8 (Figure 4.2). The gage diameter was constant and the grip 

region was threaded. The gage section diameter of each specimen was 

measured at 21°C and gage markings were etched at the gage section at a 

spacing of 14.22 mm. This distance is equal to the uniform section length minus 

the gage diameter.5 
NASA/TM—2005-213873 30 

Figure 4.3 A sample tensile test plot. English units are used. 

 A total of four tensile specimens were tested. Thermocouples were 

positioned at the transition region to monitor the temperature. Also, 

extensometer knife edges were positioned at the uniform gage section and held 

in place with springs. Specimens were then heated to 649°C ± 1% for testing. 

Tests were conducted at 649°C at a strain-rate of 2.8x10-4 s-1. 

For each specimen, plots of load versus strain were obtained (Figure 4.3). 

After the 0.2% strain was reached, the load rate was increased to finish the test 

quickly. The final strain was thus not known; this is standard operating 

procedure for Mar-Test, Inc.5 

 Tensile properties were determined by Mar-Test from strip chart recorder data 

(Figure 4.3). This included; Young’s Modulus, E, at 21°C and at 649°C; the 

ultimate tensile strength, σUTS; the 0.2% offset yield strength, σy(0.2%); percent 

reduction in area, %RA; and percent elongation, %EL. To calculate E, σUTS, 

σy(0.2%), and %RA, the thermal expansion coefficient, α, for Grainex Mar-M 247 at 

649°C (3.32 x 10-6 m/m/°C) was used to determine the diameter of the gage 

section: 

D D D T C C C C D = D + D × D × ∆ 649 21 21 649 α Eqn. 4.1 

 where D649°C = gage section diameter at 649°C [mm] 

 D21°C = gage section diameter at 21°C [mm] 

α649°C = thermal expansion coefficient at 649°C [m/m/°C] 

∆T = temperature differential from 21°C to 649°C [°C] 
NASA/TM—2005-213873 31 

E was obtained by manually identifying the slope of the initial load versus 

strain behavior for each specimen (Figure 4.3): 

ε ε

σ P A C E D 649 = = Eqn. 4.2 

 where σ = stress [MPa] 

ε = strain [m/m] 

 P = load [N] 

 A649°C = gage section area at 649°C [m2] 

σUTS was calculated using the ratio of Pmax, and A649°C: 

C

UTS A

P

D 649

max σ = Eqn. 4.3 

 where Pmax = maximum load [N] 

σy(0.2%), was calculated using the ratio of the load at 0.2% offset strain, Pε=0.2%, 

and A649°C: 

( )

C

y A

P

D 649

(0.2%)

= 0.2% = ε

σ Eqn. 4.4

The reduction in area, %RA was calculated using 

% ×100 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − =

i

i f

A

A A

RA Eqn. 4.5

where Ai is the initial gage section area and Af is the final gage section area. 

The percent elongation, %EL, was calculated using 

% ×100 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − =

i

f i

L

L L

EL Eqn. 4.6 

 where Lf = final gage section length [mm] 

 Li = initial gage section length [mm] 

For brittle materials, the engineering fracture stress, σf, can be substituted 

with the ultimate tensile strength, σUTS.

7

 Thus, the true fracture strength, f

~

σ , 

was estimated by : 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = =

f

i

UTS

f

i

f

f

f

f

A

A

A

A

A

P

σ σ σ ~ Eqn. 4.7 (Ref. 7) 

 Similarly, the true fracture strain, f

~

ε , was estimated by: 
NASA/TM—2005-213873 32 

f

i

f

A

A ln ~

ε = Eqn. 4.8 (Ref. 7) 

Fractographic Examination

 Fracture surfaces from each of the four tested tensile specimens were 

examined by light stereomicroscopy and scanning electron microscopy. Prior to 

scanning electron microscopy examination, the specimens were ultrasonically 

cleaned in acetone for 5 minutes, rinsed in alcohol, and then air dried. 

Scanning electron microscopy was performed in both secondary electron 

(SE) and backscattered electron (BE) modes. SE mode was used to identify 

general fractographic features such as evidence of brittle or ductile fracture, 

including necking, and the presence or absence of shear lips while BE mode was 

used to identify the site of fracture initiation. 

4.3 Materials and Methods: Fatigue Strain-Life Behavior 

Experimental

 Fatigue strain-life tests were performed at Mar-Test Inc. in Cincinnati, Ohio 

per ASTM E-606 using Mar-Test, Inc. closed loop, servo-hydraulic test systems 

(Figure 4.4). The extensometer system was identical to that used for the tensile 

tests. Induction heating was utilized for tests at high temperature. 

Figure 4.4 Typical fatigue strain-life test set-up.5

 
NASA/TM—2005-213873 33 

Figure 4.5 Strain-life specimen geometry.8

Table 4.1 Grainex Mar-M 247 strain-life test matrix. 

Specimen identifications refer to the NASA disk 

location where the specimens were obtained 

(Figure 3.1a and Figure 3.1b) 

Specimen Identification % Strain Range Rε 

66L, 86L, CB1L 0.50 -1 

57L, 76L, CA9L 0.58 -1 

47L, CA7L, CB8L 0.67 -1 

27L, CA4L, CB6L 0.78 -1 

15L, CA2L, CB3L 0.90 -1 

67L, 77L, CA8L 0.50 0 

56L, 87L, CB2L 0.58 0 

46L, CA1L, CB5L 0.67 0 

35L, CA3L, CB7L 0.78 0 

26L, CA6L, CB9L 0.90 0 

The specimen geometry for the strain-life tests followed recommended 

specimen geometry per ASTM E-606 (Figure 4.5). 9

A total of 15 fatigue strain-life specimens were obtained from the sacrificial 

NASA disk. The tests were conducted in air at 649°C at a strain ratio of Rε = -1 

and Rε = 0 with a frequency of 0.33 Hz using a triangular waveform. Five strain 

ranges were tested (0.50%, 0.58%, 0.67%, 0.78%, and 0.90%) with three 

repeats at each strain range (Table 4.1). 

Prior to testing the specimen diameter, D21°C for each specimen was 

measured and Ai was calculated. Using α649°C for Grainex Mar-M 247, 

(3.32 x 10-6 /°C), D649°C and A649°C were calculated. Chromel-alumel 

thermocouples were then attached at both ends of the gage section for 
NASA/TM—2005-213873 34 

temperature control with reference thermocouples attached at the ends of the 

specimen in the grip region.5

 A thermocouple was also attached to the center of 

the test section to determine the temperature at that point. An optical pyrometer 

was used to compare the center thermocouple temperature with the temperature 

of the rest of the uniform section. Adjustments were made to the induction 

heating coils such that the temperature deviation in the uniform section was less 

than ±1%.5 

The specimen was strained elastically to obtain the P versus ε behavior for 

calculating E at 21°C. The specimen was then heated to the test temperature of 

649°C to within ±1%. P versus ε behavior was again recorded to calculate E at 

649°C. Strain-controlled fatigue testing was then performed at 0.33 Hz with a 

triangular waveform. 

Plots of load versus strain were recorded at regular intervals during cycling. 

Cycles to crack initiation, Ni, was subjectively determined when a rapid change in 

the load versus time history plot occurred (Figure 4.6).5 Tests were conducted 

until failure, Nf, which was defined as either specimen fracture or a change in the 

maximum stress to 30 percent of its original value. 

 For each specimen, the following parameters were calculated at the start of 

the test upon reaching the test strain range: cycle, N; stress range, ∆σ ; 

maximum stress, σmax; and minimum stress, σmin. At approximately half the 

specimen life, additional parameters were calculated: elastic modulus, E; the 

elastic strain range, ∆εel; and the inelastic strain range, ∆εin. ∆ε, ∆εel, and ∆εin

were determined from the load versus strain hysteresis plots following standard 

methods.7

 Ni and Nf were also obtained from each test. 

Figure 4.6 Example of crack initiation point in load, strain time history 

plot.5
NASA/TM—2005-213873 35 

Statistics

 The fatigue strain-life results were evaluated following a simple linear model 

in log-log coordinates: 

( )

ζ N = Z %∆ε f Eqn. 4.9 

where the constant, Z, and exponent, ζ, were to be determined and %∆ε is the 

percent total strain range. Thus, 

log(N ) = log Z +ζ log(%∆ε ) f Eqn. 4.10 

Linear regression analysis of the log-log transformed fatigue strain-life data 

was then conducted to determine Z and ζ for both Rε = 0 and Rε = -1. The linear 

regressions were tested for significance based upon the null hypothesis method 

at the 99.95% confidence level.10 The coefficient of determination, R2

, was also 

calculated. Normal distribution of the data was checked, data removed, and the 

regression revised as necessary.10 A test for lack-of-fit was done to check 

whether the linear model was correct.10 Also the Foster-Burr test was performed 

to check for outliers in the data. 10 Finally 99.95% prediction intervals were 

calculated for both data sets. 10 

Method of Universal Slopes

The Manson-Hirschberg Method of Universal Slopes11 (MUS) was used to 

estimate strain life with zero mean stress based only upon tensile properties: 

 

el in ∆ε = ∆ε + ∆ε Eqn. 4.11 (Ref. 11) 

( ) ( ) c

f

b ∆ε = C1 N f + C2 N Eqn. 4.12 (Ref. 11)

 

() () 0.6

0

0.12 0.6 5 0 3. − − ∆ = f + f f

UTS N N

E

ε

σ

ε Eqn. 4.13 (Ref. 11)

 where C1, C2 = constant coefficients 

 Nf0 = cycles to failure under zero mean stress 

 εf = true fracture ductility 

 = ⎟

⎠

⎞ ⎜

⎝

⎛

100 − RA

100 ln Eqn. 4.14 (Ref. 11) 

 

Average tensile properties were calculated based upon the four tensile tests 

performed. ∆εel and ∆εin were calculated by inserting the averaged tensile 

properties into Eqn. 4.13. ∆ε is the sum of ∆εel (first term) and ∆εin (second term) 

in Eqn. 4.13. Thus, Nf0 can be estimated based upon a given ∆ε. 
NASA/TM—2005-213873 36 

Halford-Nachtigall Method

To estimate the effect of mean stress on cyclic life, the Halford-Nachtigall 

Method was used with the MUS: 

N N Vσ

b

f

b

fm = − − −

0 Eqn. 4.15 (Ref. 4) 

 where Nfm = cycles to failure in presence of mean stress 

 b = fatigue strength exponent 

 Nf0 = cycles to failure under zero mean stress 

 Vσ = ratio of mean stress to stress amplitude 

The relationship is derived from: 

( ) b

f m N fm

− ∆σ = σ −σ ' 2 Eqn. 4.16 (Ref. 4) 

 where ' σ f = fatigue strength coefficient [MPa] 

 σm = mean stress [MPa] 

This is Morrow’s original equation (Eqn. 4.14) except that Nfm is used instead of 

2Nfm. 

The value for b was -0.12 from the MUS. Nf0 from Eqn. 4.14 was calculated 

using the ratio of the inelastic strain range and the elastic strain range from the 

MUS at ratios of 0.3, 0.2, 0.1, 0.08, 0.05, and 0.02. Veff was substituted for Vσ in 

Eqn. 4.14 (Ref. 4): 

where σ σ

σ V k kV

a

m

eff = = Eqn. 4.17 (Ref. 4) 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∆

∆ = −

2

exp 70

el

in k

ε

ε Eqn. 4.18 (Ref. 4) 

 Veff = effective ratio of mean stress to stress 

 amplitude 

 k = transfer function 

 σa = stress amplitude [MPa] 

The ratio of the mean stress to stress amplitude is assumed to be unity at the 

start of each strain-life test. This assumption is correct if the stress-strain 

hysteresis loop is completely elastic. However, with increasing cyclic plasticity, 

mean stress relaxation may occur and the ratio of the mean stress to stress 

amplitude would decrease. 
NASA/TM—2005-213873 37 

Finally, the variation of mean stress and range of stress was plotted against 

increasing strain amplitude at the specimen half-life. 

Morrow Strain Life Equation

 The Morrow Strain-Life equation was used to model Rε = -1 strain-life data: 

() ()c

f f

b

f

f

a N N

E

2 2

2

'

'

ε

σ

ε

ε = = +∆ Eqn. 4.19 (Ref.12) 

 where εa = strain amplitude 

 

' σ f = fatigue strength coefficient [MPa] 

 b = fatigue strength exponent 

 

'

f ε = fatigue ductility coefficient 

 c = fatigue ductility exponent 

The coefficients and exponents of the Morrow strain-life equation were 

determined as follows:13

1. A plot was made on log-log coordinates of 2

e ∆ε

 versus 2N f . By definition, 

( )b

f

f N

E

2

' σ

 is equal to 2

e ∆ε . Thus, the y-intercept of the regression at 2N f =1

is equal to E

f

' σ . ' σ f was determined given E. Finally, the slope of the 

regression is equal to b.

2. A plot was made on log-log coordinates of 2

p ∆ε

 versus 2N f . By definition, 

( )c

f 2N f

' ε is equal to 2

p ∆ε

. Thus, the y-intercept of the regression at 2N f =1

is equal to the '

f ε . Finally, the slope of the line is equal to c. 

Modified Morrow with Mean Stress Effects

The Modified Morrow equation was used to account for mean stress effects in 

the Rε = 0 tests: 

( ) ( )c

f

b

c

f

m

f

b

f

f

f m

a N N

E

1 2 1 2 '

'

'

'

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − σ

σ

ε

σ

σ σ

ε Eqn. 4.20 (Ref. 7) 
NASA/TM—2005-213873 38 

The coefficients ( ' σ f , E, '

f ε ) and exponents (b and c) initially used were 

calculated from the Morrow Strain-Life Equation (Eqn. 4.18). For each of the 30 

fatigue strain-life tests, the mean stress was determined by the average of the 

maximum and minimum stress values at the cyclic half-life. εa was then 

calculated for each specimen. Finally, the coefficients and exponents of the 

Modified Morrow equation were optimized by minimizing the residual between 

the experimental strain amplitude and the calculated strain amplitude from 

Eqn. 4.19. Also, constraints were imposed on exponents b and c as follows: 

 -0.12 ≤ b ≤ -0.05 Eqn. 4.21 (Ref. 7) 

 -0.9 ≤ c ≤ -0.5 Eqn. 4.22 (Ref. 7) 

Using these optimized coefficients and exponents, the Modified Morrow equation 

was then used to plot strain amplitude versus cycles to failure along lines of 

constant mean stress with values ranging from -345 MPa to 690 MPa. This plot 

was compared to experimental data. 

Fractographic Examination

The fracture surfaces of fatigued specimens were cleaned in acetone, alcohol 

rinsed, and air dried to facilitate fractographic examination. 

Surfaces were examined using light stereomicroscopy and scanning electron 

microscopy (SEM) using secondary electron (SE) and backscattered electron 

(BE) modes to determine crack initiation sites. 

4.4 Results and Discussion: Tensile Behavior 

Properties

Average tensile properties of four tensile tests for the Grainex Mar-M 247 

material are shown in Table 4.2. The ultimate tensile strength and 0.2% offset 

yield stress were found to be 1064 and 821 MPa, respectively. 

Table 4.2 Tensile test results for Grainex Mar-M 247 at 649°C 

 E [GPa] σUTS [MPa] σy(0.2%) [MPa] %RA %EL f

~

σ [MPa] f

~

ε

Average 194.3 1064.4 821.0 16 6.9 1268 0.177

Standard 

deviation 12.6 19.8 18.3 1 1.0 31 0.015
NASA/TM—2005-213873 39 

The Grainex Mar-M 247 tensile properties determined from the sacrificial NASA 

disk were within 5 to 10% of values reported from literature (Table 4.3).2,14 The 

exception was in the %RA data where the sacrificial NASA disk %RA was 30 to 

40% higher than that reported in the literature. The higher values were most 

likely due to a slight amount of necking observed in the gage sections of the 

tensile test specimens. 

Table 4.3 Comparison of average Grainex Mar-M 247 

tensile properties at 649°C with literature 

 NASA Disk* Kaufman*,2 Howmet14 

No. Samples 4 2 N/A 

E [GPa] 194.3 N/A 179.3 

σUTS [MPa] 1064.4 1011.5 1027.3 

σy(0.2%) [MPa] 821.0 799.1 827.4 

%RA 16 9.7 10.7 

%EL 6.9 7.1 7.0 

* average data 

Fractographic Examination

Crack initiation sites were observed by light stereomicroscopy at the surface 

of the gage section of the specimens. Little if any necking of the gage section 

was observed on the tensile specimens. Shear lips were not observed. The 

overall fracture surface appearance was consistent with brittle fracture (Figure 

4.7). Examination of the fracture surfaces by SEM in BE mode did not reveal 

any evidence of interior initiation, supporting the visual observations that fracture 

initiated at the surface (Figure 4.8). 
NASA/TM—2005-213873 40 

Figure 4.7 Typical SEM (SE mode) image of Grainex Mar-M 247 tensile 

specimens conducted at 649°C. 

Figure 4.8 Typical SEM (BE mode) image of Grainex Mar-M 247 tensile 

specimens conducted at 649°C (same fracture surface as in 

Figure 4.7). 
NASA/TM—2005-213873 41 

4.5 Results and Discussion: Fatigue Strain-Life Behavior 

Rε = -1 

Ni and Nf were determined for each of the Rε = -1 fatigue strain-life tests at 

649°C (Table 4.4). 

Table 4.4 Grainex Mar-M 247 fatigue strain-life test results 

 at 649°C, Rε = -1. Specimen identifications refer to the 

location on the NASA disk where the specimens 

were obtained (Figure 3.1a and Figure 3.1b) 

Specimen 

Identification %∆ε Ni Nf

66L 0.50 * 429420 

86L 0.50 * 120171 

CB1L 0.50 * 110545 

57L 0.58 115737 116335 

76L 0.58 31362 31486 

CA9L 0.58 43555 44313 

47L 0.67 4618 6624 

CA7L 0.67 6836 8018 

CB8L 0.67 3175 5231 

27L 0.78 1464 1668 

CA4L 0.78 1004 1586 

CB6L 0.78 1773 2279 

15L 0.90 192 484 

CA2L 0.90 393 875 

CB3L 0.90 317 451 

*Switched to load-control after approximately 100,000 

cycles. No crack-initiation life was available. 

Linear regression analysis of Eqn. 4.9 for the Rε = -1 total strain life versus Ni 

data resulted in an exponent, ζ, of -11.49 and a coefficient, Z, of 75.86 with 

R2

 = 0.94. The exponent and coefficient were significant to a 99.95% confidence 

level. The residuals were normally distributed. A histogram of the residuals 

found one possible outlier (57L) and subsequent linear regression analysis 

resulted in an exponent, ζ, of -10.55 and a coefficient, Z, of 91.20 with R2 = 0.96. 

The exponent and coefficient were again significant to a 99.95% confidence 

level. The lack-of-fit test showed that the linear model was acceptable to a 

99.9% confidence level. The Foster-Burr test showed no outliers in the data to a 

99% confidence level. Prediction intervals were calculated to a 99.95% 

prediction level (Figure 4.9). 
NASA/TM—2005-213873 42 

Cycles to Crack Initiation, Ni

102 103 104 105

Total Strain Range, %∆ε

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Data

Linear Regression

99.95% Prediction Intervals

Figure 4.9 Crack initiation strain-life results for Grainex Mar-M 247, 

Rε = -1, 649°C, triangular waveform, 0.33 Hz. By convention, Ni

was plotted on the abscissa while %∆ε was plotted on the 

ordinate. 

Linear regression analysis of Eqn. 4.9 for the Rε = -1 total strain life versus Nf 

data resulted in an exponent, ζ, of -10.10 and a coefficient, Z of 165.96 with 

R2 = 0.95. The exponent and coefficient were significant to a 99.95% confidence 

level. The residuals were normally distributed. A histogram of the residuals 

found three outliers (57L, 66L, and CA2L) and subsequent linear regression 

analysis resulted in an exponent, ζ, of -9.53 and a coefficient, Z, of 165.96 with 

R2 = 0.99. The exponent and coefficient were again significant to a 99.95% 

confidence level. The lack-of-fit test showed that the linear model was 

acceptable to a 99.9% confidence level. The Foster-Burr test showed no outliers 

in the data to a 99% confidence level. Prediction intervals were calculated to a 

99.95% prediction level (Figure 4.10). 

A comparison of the outliers found in the Rε = -1 data (Specimens 66L, 57L, 

and CA2L) with their respective strain-ranges revealed the following: 

1. Crack depth was approximately 1/3 of the gage cross-section regardless 

of the strain-range. 

2. The outlier specimens had a 2x to nearly 4x longer life, Nf, than specimens 

tested at the same strain range (Table 4.4). Subsequent life predictions 

would have been non-conservative. 

3. Comparing SEM of specimens at the same strain range showed that the 

outlier specimens had fewer crack initiation sites and that crack growth 

was limited to fewer facets. 
NASA/TM—2005-213873 43 

Cycles to Failure, Nf

102 103 104 105

Total Strain Range, %∆ε

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Data

Linear Regression

99.95% Prediction Intervals 

Figure 4.10 Cycles to failure strain-life results for Grainex Mar-M 247, 

Rε = -1, 649°C, triangular waveform, 0.33 Hz. By convention, Nf

is plotted on the abscissa while %∆ε is plotted on the ordinate. 

The NASA Grainex Mar-M 247 Rε = -1 strain-life data at 649°C was compared 

with available literature at 427°C (Figure 4.11). The data showed that the cyclic 

life of the Grainex Mar-M 247 sacrificial NASA disk material was similar to that 

reported by Macha et al.3 Specifically, data reported by Macha et al. were 

Cycles to Failure, Nf

102 103 104 105

Total Strain Range, %∆ε

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

NASA, 649C , R = -1

Macha, 427C , R = -1

Figure 4.11 Comparison of NASA Grainex Mar-M 247, Rε = -1 strain-life 

data with literature.3
NASA/TM—2005-213873 44 

comparable with the sacrificial NASA disk data at the design point of 0.5% ∆ε. It 

should be noted that the values reported by Macha et al. in the early 1980s were 

when the Grainex process was first introduced and that refinements in the 

process (i.e., the Grainex examined in this study) appear to have led to equal if 

not improved strain-life at higher temperatures. Normally, at higher temperatures 

the strain-life decreases for identical strain ranges. However it was seen that the 

strain-life at 649°C for the NASA disk Grainex Mar-M 247 material is equal to if 

not higher than that reported by Macha et al. data at 427°C. 

Rε = 0 

Ni and Nf were determined for each of the Rε = 0 fatigue strain-life tests at 

649°C (Table 4.5). 

Table 4.5 Grainex Mar-M 247 strain-life test results at 649°C, Rε = 0. 

Specimen identifications refer to the location on the NASA disk 

where the specimens were obtained (Figure 3.1a and Figure 3.1b). 

Specimen 

Identification %∆ε Ni Nf

67L 0.50 * 127523 

77L 0.50 25917 26939 

CA8L 0.50 9557 10697 

56L 0.58 12266 12566 

87L 0.58 2450 2842 

CB2L 0.58 5910 7970 

46L 0.67 2056 3056 

CA1L 0.67 3114 3842 

CB5L 0.67 1322 2234 

35L 0.78 585 723 

CA3L 0.78 792 1352 

CB7L 0.78 680 1254 

26L 0.90 513 889 

CA6L 0.90 ** 1142 

CB9L 0.90 *** 554 

* Switched to load control after approximately 100,000 cycles. 

** Recorder malfunction. Ni occurred between 415 and 847. 

***Recorder malfunction. Ni occurred between 295 and 500 cycles. 

Linear regression analysis of Eqn. 4.9 for the Rε = 0 total strain life versus Ni

resulted in an exponent, ζ, of -6.48 and a coefficient, Z of 162.18 with R2 = 0.86. 

The exponent and coefficient were found to be significant to a 99.95% 

confidence level. The residuals were found to be normally distributed. A 

histogram showed no outliers. The lack-of-fit test showed that the linear model 
NASA/TM—2005-213873 45 

was acceptable to a 99.9% confidence level. The Foster-Burr test showed no 

outliers in the data to a 99% confidence level. Prediction intervals were 

calculated to a 99.95% prediction level (Figure 4.12). 

Cycles to Crack Initiation, Ni

102 103 104 105

Total Strain Range, %∆ε

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Data

Linear Regression

99.95% Prediction Intervals

Figure 4.12 Crack initiation strain-life results for Grainex Mar-M 247, Rε = 0, 

649°C, triangular waveform, 0.33 Hz. By convention, Ni was 

plotted on the abscissa while %∆ε was plotted on the ordinate. 

Linear regression analysis of Eqn. 4.9 for the Rε = 0 total strain life versus Nf

resulted in an exponent, ζ, of -6.26 and a coefficient, Z of 295.12 with R2 = 0.80. 

The exponent and coefficient were found to be significant to a 99.95% 

confidence level. The residuals were found to be normally distributed. A 

histogram of the residuals found two possible outliers (67L and CA6L) and 

subsequent linear regression analysis resulted in an exponent, ζ, of -5.62 and a 

coefficient, Z, of 316.23 with R2

 = 0.87. The exponent and coefficient were again 

significant to a 99.95% confidence level. The lack-of-fit test showed that the 

linear model was acceptable to a 99.9% confidence level. The Foster-Burr test 

showed no outliers in the data to a 99% confidence level. Prediction intervals 

were calculated to a 99.95% prediction level (Figure 4.13). 
NASA/TM—2005-213873 46 

Cycles to Failure, Nf

102 103 104 105

Total Strain Range, %∆ε

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Data

Linear Regression

99.95% Prediction Intervals

Figure 4.13 Cycles to failure strain-life results for Grainex Mar-M 247, 

Rε = 0, 649°C, triangular waveform, 0.33 Hz. By convention, Nf

is plotted on the abscissa while %∆ε is plotted on the ordinate. 

Testing at Rε = 0 and 649°C addressed the actual localized conditions the 

Grainex Mar-M 247 NASA disk bolt holes encounter in the Turbine Seal Test 

Facility. Specifically, the NASA disk is strained from a zero to maximum strain 

when the surface speed increases from zero to maximum during testing. The 

-99.95% prediction interval (1 failure in 2000 samples) on cyclic life was chosen 

since it was more conservative than the mean cyclic life by a factor of 

approximately 10 (Table 4.6). As expected, more data scatter was observed at 

the lower strain ranges. Overall the cyclic life to crack initiation of the Grainex 

Mar-M 247 NASA disk bolt holes at the 0.5% design strain, Rε = 0, and -99.95% 

prediction interval was found to be 1100 cycles (Figure 4.12). This was nearly 6 

times less than the cyclic life predicted from previous analyses1

 and more than 

10 times less than the cyclic life extrapolated using the Rε = -1, Ni , -99.95% 

prediction interval data at %∆ε = 0.5 (see Table 4.6). 

Comparison of the NASA Grainex Mar-M 247 Rε = 0 strain-life data with 

reported data by Kaufman2 showed good agreement (Figure 4.14). As observed, 

the NASA data at 649°C fell in between the 427°C and 760°C data reported by 

Kaufman.2

 As expected, cyclic lives decreased with increasing temperature for 

a constant strain range. 
NASA/TM—2005-213873 47 

Cycles to Failure, Nf

102 103 104 105

Total Strain Range, %∆ε

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Data: NASA, 649C, R = 0

Regression: NASA, 649C, R = 0

Data: Kaufman, 205C, R = 0

Regression: Kaufman, 205C, R = 0

Data: Kaufman, 427C, R = 0

Regression: Kaufman, 427C, R = 0

Data: Kaufman, 760C, R = 0

Regression: Kaufman, 760C, R = 0

Figure 4.14 Comparison of NASA Grainex Mar-M 247, Rε = 0 strain-life data 

with literature.2

Table 6 summarizes the mean and -99.95% prediction cyclic life for both 

Rε = -1 and Rε = 0 data at both Ni and Nf at the 0.5% design strain range of the 

Grainex Mar-M 247 NASA disk (see also Figure 4.9, Figure 4.10, Figure 4.12, 

Figure 4.13). 

Table 4.6 Grainex Mar-M 247 mean and -99.95% cyclic life predictions at 

649°C, %∆ε = 0.5. 

Rε → -1 0 

Statistic → Mean -99.95% Mean -99.95% 

Ni (cycles) >100000 14500 14500 1100 

Nf (cycles) >100000 40000 15500 1600 

Method of Universal Slopes

The estimated Nf was plotted against ∆ε for the Grainex Mar-M 247 material 

using tensile data (Table 4.2) as input for the MUS (Figure 4.15). The plastic and 

elastic strain lines were also plotted. Nt was found to be 400 cycles to failure. 
NASA/TM—2005-213873 48 

Figure 4.15 Method of Universal Slopes equation using Grainex Mar-M 247 

Tensile Data at 649°C. 

Halford-Nachtigall Method

Comparison of the Halford-Nachtigall Method with the MUS, Rε = 0 data, and 

Rε = -1 data for the Grainex Mar-M 247 material is shown (Figure 4.16). 

Figure 4.16 Comparison of MUS, Halford-Nachtigall method, and data for 

Grainex Mar-M 247 at 649°C. 
NASA/TM—2005-213873 49 

Assuming the ratio of mean to alternating stress was equal to 1 at the start 

of the strain-life tests, Vσ (Eqn. 4.15) was compared at the beginning and 

approximate half-life for each test (Table 4.7). The variation of mean stress and 

range of stress was then compared with increasing strain amplitude Figure 4.17). 

Point P1 through point P2 defines elastic behavior. Point P2 defines where the 

mean stress and range of stress are equal. Point P3 defines the point of zero 

mean stress. Finally, point P3 to P4 is the region of zero mean stress. 

Table 4.7 Comparison of Vσ at Nf = 1 and Nf/2 for Grainex 

Mar-M 247 at 649°C, Rε = 0 

at N = 1 at Nf/2 at Nf/2 strain 

range Vσ

σm

[MPa] 

σa

[MPa] Vσ

0.50 1 344.1 463.3 0.74 

0.50 1 281.0 472.7 0.59 

0.58 1 295.1 513.7 0.57 

0.58 1 247.9 562.3 0.44 

0.58 1 265.8 556.1 0.48 

0.67 1 227.5 598.5 0.38 

0.67 1 206.9 600.6 0.34 

0.67 1 180.6 608.1 0.30 

0.78 1 100.3 745.0 0.13 

0.78 1 153.8 669.5 0.23 

0.78 1 106.9 706.7 0.15 

0.90 1 88.6 734.7 0.12 

0.90 1 60.0 781.2 0.08 

Figure 4.17 Variation of mean stress and range of stress with strain 

amplitude at Nf/2 for Grainex Mar-M 247 at 649C, Rε = 0.15
NASA/TM—2005-213873 50 

Comparison between MUS, Halford-Nachtigall, and Data 

Both the MUS and the Halford-Nachtigall method provide a means to predict 

fatigue strain-life by use of only tensile data. It was expected that the MUS would 

over-predict the Rε = 0 data (Figure 4.16) since the MUS is generally used in 

predicting Rε = -1 data. At the design point of 0.5% total strain, the MUS 

predicted Nf0 at 100,000 cycles. This is 5 times greater than the average Rε = 0 

data at 0.5% total strain of approximately 20,000 cycles. In comparison, the 

Halford-Nachtigall method predicted a life of approximately 23,500 cycles. Thus, 

a more accurate prediction was found at the 0.5% total strain design point using 

only tensile data and modifying the MUS with the Halford-Nachtigall Method to 

account for mean stress effects. 

Morrow Strain-Life Equation 

' σ f and b were determined from a plot of 2

el ∆ε versus 2Nf (Figure 4.18). A 

linear regression of the Rε = -1 data resulted in a y-intercept at 2N f =1 of -2.09 in 

log-log coordinates. In linear coordinates the y-intercept was 3 8.13 10− × ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

= E

f

' σ . 

Given an average E of 186 GPa, calculated from the Rε = -1 data, ' σ f was 

calculated as 1510 MPa. The fatigue strength exponent, b, was -0.0928. 

Figure 4.18 Grainex Mar-M 247 elastic strain-amplitude data, Rε = -1, 649°C. 
NASA/TM—2005-213873 51 

'

f ε and c were determined from a plot of 2

in ∆ε versus 2Nf (Figure 4.19). A 

linear regression of the Rε = -1 data resulted in a y-intercept of -1.78 in log-log 

coordinates. In linear coordinates the y-intercept was 0.0166 (= '

f ε ). The fatigue 

ductility exponent, c, was -0.628. 

Figure 4.19 NASA Grainex Mar-M 247inelastic Strain-Amplitude Data, 

Rε = -1, 649°C. 

Thus, the Morrow strain-life equation was determined to be 

 ( ) ( ) 3 0.0928 0.628 8.13 10 2 0.0166 2 − − −

a = × N f + N f ε Eqn. 4.23 

and was compared with Rε = -1 data (Figure 4.20). 
NASA/TM—2005-213873 52 

Figure 4.20 Comparison of Morrow Strain-Life equation with Grainex Mar-M 

247 data at 649°C. 

The Morrow Equation conservatively predicted the cyclic life when compared 

to the strain-life data at Rε = -1 and 649°C. At 0.9% total strain range (∆ε/2 = 

0.0045) the predicted reversal to failure, 2Nf, was 400 which was 2 times lower 

than that given by the Rε = -1 data (2Nf = 950). At the design strain (∆ε = 0.5%), 

the difference between predicted (155,000) and experimental data (240,000) is 

nearly 100,000 reversals. One source of error was the low resolution in the 

plastic strain data used to calculate the fatigue ductility coefficient and exponent. 

This was due to the low resolution of the pen plotter used to plot the cyclic load 

versus strain curves for each of the strain-life tests. 

Modified Morrow with Mean Stress Effects

Optimization of the coefficients and exponents for the Modified Morrow 

equation resulted in an R2

 value of 0.928. The coefficients and exponents 

(Table 4.8) were used in the Modified Morrow equation. The results of the 

Modified Morrow equation were compared to experimental Grainex Mar-M 247 

strain-amplitude data (Figure 4.21). 
NASA/TM—2005-213873 53 

Table 4.8 Optimized coefficient and 

exponent values for the Modified Morrow 

Equation for Grainex Mar-M 247 at 649°C 

Coefficients original optimized

' σ f (MPa) 1507 1507

'

f ε 0.117 0.027

Exponents 

b -0.0928 -0.090

C -0.628 -0.627

Life, Nf

100 101 102 103 104 105 106

Strain Amplitude, ε

a

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.020

0.001

0.010

Data R = -1

Data R = 0

σm= -345 MPa

σm= -172 MPa

σm= 0 MPa

σm= 172 MPa

σm= 345 MPa

σm= 517 MPa

σm= 690 MPa

0.5% total strain level

σ

'

f = 1507 MPa

ε

'

f = 0.027

b = -0.090

c = -0.627

( ) ( )c

f

b

c

f

m

f

b

f

f

f m

a N N

E

1 2 1 2 '

'

'

'

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ + − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − σ

σ ε σ

σ σ ε

Figure 4.21 Comparison of NASA Grainex Mar-M 247 data at 649°C with 

predictions from the Modified Morrow equation. 
NASA/TM—2005-213873 54 

As expected, higher mean stresses were observed at lower strain levels while 

lower mean stresses were observed at higher strain levels (see also Figure 

4.17).15 This is because the larger the strain range, the greater the degree of 

relaxation of the initial mean stress imposed by the Rε = 0 strain condition. The 

effect of mean stress on cyclic life was more pronounced at lower strain levels 

(Table 4.7). For example, at the design strain level of 0.5% total strain, the 

average mean stress was 313 MPa, while at 0.9% total strain, the average mean 

stress was 74 MPa. 

Also, cyclic life decreased as mean stress increased for constant strain 

amplitude. For example, at the design point of ∆ε = 0.5% (εa = 0.0025) the 

difference in cyclic life between the σm = 0 MPa line and the σm = 172 MPa line 

was nearly a factor of four. The Rε = 0 data were observed to trend towards a 

zero mean stress at the highest strain range (εa = 0.0045). Finally, as expected, 

compressive mean stresses predict an increase in cyclic life. 

Fractographic Examination

 The majority of the crack initiation sites were observed at or near the surface 

of the gage cross-section perimeter and initiated at carbides. The fracture 

surfaces exhibited 3 areas of cracking – crack initiation, propagation, and 

overload. 

The crack initiation site could be traced by following river patterns which point 

back to the crack initiation site (Figure 4.22 - Figure 4.24).16 By contrast, the 

overload surfaces were faceted in appearance at low magnification (Figure 4.25 

and Figure 4.26). 

No relationship was determined between crack initiation direction on the 

fracture surface in relation to the specimen’s location in the NASA disk, to Rε, 

level or %∆ε. Dual crack initiation sites (Figure 4.25) were observed in most 

specimens tested at higher strain ranges, which is in agreement with literature17. 
NASA/TM—2005-213873 55 

Figure 4.22 SEM Micrograph SE mode for specimen 77L at 100x. River 

patterns pointing back to crack initiation site. 

Figure 4.23 SEM (SE mode), 87L, 100x. River patterns pointing back to 

crack initiation site. 
NASA/TM—2005-213873 56 

Figure 4.24 SEM (BE mode), 87L, 100x. Crack propagation showing river 

patterns pointing back to crack initiation site. (See also 

Figure 4.23) 

Figure 4.25 SEM Micrograph in backscattered electron mode for specimen 

26L at 25x. Unstable fracture with dual crack initiation sites. 
NASA/TM—2005-213873 57 

Figure 4.26 SEM (SE), 86L, 100x. Typical overload fracture. 

 Of the 30 fracture surfaces examined, 25 exhibited surface crack initiation. 

Twenty-one of the 25 surface initiated cracks occurred at a carbide (Figure 4.27). 

Three of the remaining 4 specimens with surface initiated cracks contained voids 

(Figure 4.28). SEM examination of the complementary surface of the specimens 

may determine if a carbide was present. One specimen with surface initiated 

cracks (Specimen 47L) showed both a void and a carbide at surface locations. 

Five of the 25 surface initiated cracks that started at a carbide also showed 

evidence of grain boundary cracking (Figure 4.29). Five of the original 30 

surfaces showed subsurface crack initiation. Four of the 5 initiated at carbides 

(Figure 4.30 and Figure 4.31) while the last (Specimen 15L) was indeterminate. 

 Table 4.9 summarizes specimen crack, void and carbide locations. 
NASA/TM—2005-213873 58 

Figure 4.27 SEM (BE), CA1L, 500x showing surface carbide crack initiation. 

Figure 4.28 SEM (BE), 86L, 100x showing void at surface crack initiation 

site. 
NASA/TM—2005-213873 59 

Figure 4.29 SEM (BE), CA3L, 500x. Observed grain boundary cracking. 

Figure 4.30 SEM (BE), 77L, 500x. Subsurface carbide crack initiation 

occurring at a carbide. 
NASA/TM—2005-213873 60 

Figure 4.31 SEM (BE), CA9L, 100x. Carbide cracking within grain. 
NASA/TM—2005-213873 61 

Table 4.9 Summary of scanning electron microscope results for Grainex 

Mar-M 247 strain-life specimens at 649°C

Specimen Rε %∆ε Nf

Crack Information

‘clock’ location, surface/subsurface, carbide/void 

CB1L -1 0.50 104433 0200, surface, no carbide present 

86L -1 0.50 120171 0230, surface, void 

66L -1 0.50 429420 0900, surface, void 

76L -1 0.58 31486 0900, surface, carbide 

CA9L -1 0.58 44313 0100, subsurface, carbide within grain 

57L -1 0.58 116335 0930, surface, void 

CB8L -1 0.67 5231 0530, surface, carbide 

47L -1 0.67 6624

Crack 1, 1100, surface, carbide 

Crack 2, 1100, surface, void 

CA7L -1 0.67 8018 0800, surface ,carbide 

CA4L -1 0.78 1586

0430, surface, carbide + boundary, 

0730, surface, multiple carbides 

27L -1 0.78 1668

Crack 1, 1000, surface, carbide 

Crack 2, 1200, surface, multiple carbides 

CB6L -1 0.78 2279 0800, surface, carbide 

CB3L -1 0.90 451 0730, surface, carbide 

15L -1 0.90 484 Indeterminate, surface likely, carbide likely 

CA2L -1 0.90 875

Crack 1, 0300, surface, carbide 

Crack 2, 1200, surface, multiple carbides 

CA8L 0 0.50 10697 0500, surface, void 

77L 0 0.50 26939 0400, subsurface, carbide 

67L 0 0.50 127523 middle, within grain, carbide 

87L 0 0.58 2842 1100, surface, carbide + boundary 

CB2L 0 0.58 7970 0900, surface, carbide 

56L 0 0.58 12566 0700, subsurface, carbide 

CB5L 0 0.67 2234 0130, surface, carbide 

46L 0 0.67 3056 0900, surface, carbide 

CA1L 0 0.67 3842 0500, surface, carbide 

35L 0 0.78 723 0900, surface, multiple carbides & voids 

CB7L 0 0.78 1254 1030, surface, carbide 

CA3L 0 0.78 1352 0100, surface, carbide + grain boundary 

CB9L 0 0.90 554 0230, surface, carbide + grain boundary 

26L 0 0.90 889

Crack 1, 0700, surface, multiple carbides 

Crack 2, 0900, surface, multiple carbides 

CA6L 0 0.90 1142 1030, surface, carbide + grain boundary 
NASA/TM—2005-213873 62 

Discussion Summary

Tensile properties for the Grainex Mar-M 247 NASA disk at 649°C were 

presented and compared with literature data. Fatigue strain life data for the 

same material were also presented at 649°C at strain ranges of 0.50%, 0.58%, 

0.67%, 0.78%, and 0.90%. Both the tensile and Rε = 0 strain-life data were 

comparable with literature. 

Evaluation of mean stress effects showed a large effect on cyclic life. The 

Halford-Nachtigall Method used with the MUS was practical for predicting Rε = 0 

life using only tensile data at 649°C. A difference of only 18% in cyclic life was 

observed between predicted and experimental lives at the design point of 0.5% 

strain range. The 10,000 cycle limit suggested by the Modified Morrow analysis 

at the 0.5% design strain range can be reduced accordingly to 1500 cycles using 

an equivalent –3σ reduction factor and probabilistic accounting for the 6 bolt 

holes using Eqn. 1.1. 

 During operation, the NASA disk is generally cycled at zero to maximum 

strain conditions (Rε = 0). At the design strain of ∆ε = 0.5% the Rε = 0 results 

lead to, at the -99.95% prediction level, a cyclic crack initiation life of 1100 cycles 

which is nearly 6 times less than the initial predicted cycles to failure obtained 

previously by Tong and Steinetz.1 Probabilistic accounting for the 6 bolt holes by 

using Eqn. 1.1 gives the most conservative result of 665 cycles with 6 bolt holes. 

Thus, using the experimental data at a -99.95% prediction level and the 

presence of 6 bolt holes it was found that the NASA disk should be inspected for 

surface cracks after 665 cycles based on a total strain range of 0.50% at 649°C. 
NASA/TM—2005-213873 63 

 

Chapter 4 Works Cited 

1. Tong, Mike and Bruce Steinetz. “Mar-M 247 Disk Finite Element Thermal 

and Stress Analysis”, NASA Glenn Research Center, Cleveland. 30 January 

1997. 

2. Kaufman, M. “Properties of Cast Mar-M-247 for Turbine Blisk Applications.” 

 Superalloys 1984. Ed. Maurice Gell et al. Warrendale: Metallurgical 

 Society of AIME, 1984. 43-52. 

3. Macha, D.E., G.R. Cole, and J.A. Butzer. “Fine Grain, Investment-Cast 

 Integral Turbine Wheels.” Grain Refinement in Castings and Welds. Ed. 

 G.J. Abbaschian and S.A. David. New York: The Metallurgical Society of 

 AIME, 1983. 197-219.

4. Halford, G.R., and A.J. Nachtigall. “Strainrange Partitioning Behavior of an 

Advanced Gas Turbine Disk Alloy AF2-1DA.” Journal of Aircraft, 17.8 

(1980) 598-604. 

5. Mar-Test. “Tensile and Strain-Life Test Descriptions” email to Irebert 

Delgado. 15 Oct. 2003. 

6. Mar-Test. “Tensile Test Specimen Geometry.” Fax to Irebert Delgado. 03 

May 2001.

7 . Dowling, Norman E. Mechanical Behavior of Materials : engineering 

methods for deformation, fracture, and fatigue. Upper Saddle River: 

Prentice-Hall, Inc., 1999.

8. Neugebauer, Bob. “Mar-Test Strain-Life Specimen Geometry.” Personal 

communication by Irebert Delgado. 22 September 2000.

9. ASTM Committee E-8 on Fatigue and Fracture. “ASTM E-606 – 92 

 (Reapproved 1998): Standard Practice for Strain-Controlled Fatigue 

 Testing.” Annual Book of ASTM Standards 2001: Section 3 Metals Test 

 Methods and Analytical Procedures: Volume 03.01 Metals—Mechanical 

 Testing; Elevated and Low-Temperature Tests; Metallography. ASTM. 

 West Conshohocken: ASTM, 1998. 543-557. 

10. Keller, Dennis. Introduction to Regression: Theory, Methods, Applications. 

Fairview Park: RealWorld Quality Systems. 

11. Manson, S.S. “Fatigue: A Complex Subject.” Experimental Mechanics. 5.7 

(1965) 193-226. 

12. Manson, S.S. “Predictive Analysis of Metal Fatigue in the High Cyclic Life 

 Range.” Methods for Predicting Material Life in Fatigue. Ed. W.J. 

 Ostergren and J.R. Whitehead. New York: ASME, 1979. 

13. Lapointe, N.R. “Monotonic and Fatigue Characterizations of Metals,” 

 Proceedings of The SAE Fatigue Conference P-109. Warrendale: Society 

 of Automotive Engineers, Inc., 1982. 

14. Howmet Turbine Components Corporation. TB 3000: Grainex Cast Mar-M 

 247 Alloy. Greenwich: Howmet Turbine Components Corporation. 
NASA/TM—2005-213873 64 

 

15. Conway, Joseph B., and Lars H. Sjodahl. Analysis and Representation of 

Fatigue Data. Materials Park: ASM International, 1991. 

16. Kerlins, Victor, and Austin Phillips. “Modes of Fracture.” Metals Handbook 

Volume 12 Fractography. 9th ed. Metals Park: ASM International. 1987. 

17. Hertzberg, Richard W. Deformation and Fracture Mechanics of Engineering 

Materials. 3rd ed. New York: John Wiley & Sons, Inc. 1989. 
NASA/TM—2005-213873 65 

5. Fatigue Crack Growth Behavior of Grainex Mar-M 247 

5.1 Introduction 

 The possibility exists that surface cracks would develop over time in the bolt 

holes of the Grainex Mar-M 247 NASA disk (Figure 1.1, Figure 3.1a, and 

Figure 3.1b) used in NASA’s Turbine Seal Test Facility. An inspection interval of 

the bolt holes can be implemented using strain-life data and fatigue crack growth 

data to preclude catastrophic NASA disk failure. The present chapter focuses on 

the fatigue crack growth behavior of the Grainex Mar-M 247 material. 

The purpose for characterization of the fatigue crack growth behavior is to 

predict the cycles to failure of a surface crack growing from an initial flaw to a 

critical crack length. 

5.2 Materials and Methods 

Experiment

Tests were conducted at 649°C, at a load ratio of R = 0.05, with a sinusoidal 

waveform at a cyclic frequency of 0.33 Hz. A surface flaw (or Kb) specimen 

(Figure 5.1) was used to simulate the growth of a flaw within a disk bolt hole. 

The Kb specimen was first developed by Coles et. al.1 for evaluating turbine 

engine components. 

 The Kb specimen was fabricated by electro-discharge machining (EDM) a 

cylinder from the sacrificial Grainex Mar-M 247 NASA disk that was 41 mm long 

by 14 mm in diameter. A total of 8 fatigue crack growth specimens were 

fabricated from the sacrificial NASA disk (Figure 3.1a). The cylinders were 

removed at locations adjacent to the NASA disk bolt holes and oriented 

perpendicular to the bolt hole axis. This oriented the machined surface flaw on 

the Kb specimen perpendicular to the applied cyclic stress, since cracks tend to 

initiate within bolt holes from circumferential and radial disk stresses during 

rotation.2

 The axial direction is parallel with the bolt holes of the NASA disk 

(Figure 3.1b). 

 Inconel 718 cylinders were inertia-welded to both ends of the Grainex Mar-M 

247 cylinders. The ends of the resultant specimen were machined to a 

buttonhead for gripping by the fatigue testing machine. The surface flaw was 

plunge EDM’d on one side of the rectangular gage section in the shape of a halfcircle (Figure 5.2). Note that the depth and width of the surface flaw were 

approximately doubled from those dimensions shown in Figure 5.2 after failures 

outside the gage section occurred in initial tests. Thus, the final surface flaw size 

that was used was 0.46 mm in depth by 0.91 mm in width. This enlargement of 

the EDM notch was necessary to encourage crack growth at the surface flaw. All 

fatigue crack growth specimens (Figure 5.3) were fabricated at Mar-Test in 

Cincinnati, Ohio. 
NASA/TM—2005-213873 66 

Figure 5.1 Surface flaw (Kb) specimen geometry for the Grainex Mar-M 247 

fatigue crack growth tests at 649°C. 3 Dimensions are in 

millimeters. 
NASA/TM—2005-213873 67 

Figure 5.2 Surface flaw geometry for the Kb specimen.3 Dimensions are in 

millimeters. See also Figure 5.1 for location of notch on Kb

specimen. 

 

Figure 5.3 Kb specimen with alumel wire attachments for potential drop 

crack growth measurement. 
NASA/TM—2005-213873 68 

Fatigue crack growth tests were performed at the NASA Glenn Research 

Center fatigue and fracture laboratories. A Materials Test System 810 (MTS 

Corporation, Minneapolis, Minnesota) was utilized (Figure 5.4). The system is 

computer-controlled by a custom program, MATE (Material Analysis and Test 

Environment), which also acquires the raw fatigue crack growth data.4

 Crack 

length computations for the Kb specimen are based on a closed-form analytical 

model by Gangloff et.al. that has been experimentally confirmed.5,6,7 

 Fatigue crack growth of the Kb specimen was measured using the direct 

current electrical potential difference (dcEPD) method. The method was initially 

developed by Gangloff8 for small surface cracks in hour-glass shaped 

specimens. The method was modified by Vanstone and Richardson9 for 

specimens having rectangular cross sections with semi-circular EDM notches. 

Fatigue crack growth in a semi-circular crack is related to voltage through an 

analytical model developed by Roe and Coffin8. To facilitate potential drop 

measurements, 0.13 mm diameter alumel wires were tack-welded to either side 

of the EDM notch (Figure 5.5). 

Figure 5.4 Fatigue crack growth test equipment and controls at NASA’s 

fatigue and fracture laboratories. 

 
NASA/TM—2005-213873 69 

Figure 5.5 Alumel wire location at the notch area of the Kb specimen. 

 

Figure 5.6 Nominal fatigue crack growth pre-test measurements for the Kb

specimen surface flaw geometry. 

Measurements of the EDM notch geometry were taken prior to installing the 

Kb specimen in the load frame (Figure 5.6). Measurements were taken with a 

Nikon Measurescope 10 (Nikon, Tokyo, Japan) and a Nikon SC-102 X-Y digital 

readout (Nikon, Tokyo, Japan). The Measurescope has an accuracy of 

±0.0025 mm. 

Alumel wire 

2bc

2cc 

2Lpmax

2Lpctr

2Lpmin 

notch

tack-weld

Key

2bc crack height 

2cc crack width 

2Lp potential probe spacing

Nominal Measurements [mm]

2bc 0.152 

2cc 0.953 

2Lpmin 0.523 

2Lpctr 0.732 

2Lpmax 0.955 
NASA/TM—2005-213873 70 

The measurements were used as input into MATE to calculate crack length, 

maximum load, and dcEPD voltage during the test. An assumption on the EDM 

crack depth was initially inputted into MATE, based on original EDM notch 

specifications, and was subsequently corrected for in post-test calculations. 

The Kb specimen was installed into the MTS load frame with 12-gage copper 

leads attached to the buttonheads. A constant 10 amps was applied to the 

leads, forming a circuit through the specimen having a voltage across the Alumel 

wire locations (Figure 5.5). The voltage increased with increasing crack length 

and depth. Baseline voltage measurements were taken to adjust for 

thermoelectric influences.

10 

Prior to starting the pre-cracking portion of the test, initial voltages were taken 

at 0 N and 17.8 KN axial load on the KB specimen. The specimen was precracked at room temperature to grow the notch to approximately 0.81 mm in 

depth. Pre-cracking was conducted to ensure that fatigue crack growth occurred 

beyond the recast layer resulting from the EDM notch. Pre-cracking was 

performed with a sinusoidal waveform at 3 Hz, and R = 0.05 (Pmax = 25.8 KN). 

Both crack length voltages and number of cycles were acquired. After precracking, reference voltage measurements (VN) were again taken at 0 N and 

17.8 KN axial load. These voltages were used to correct for voltage drift and for 

normalizing the acquired crack length voltages for data reduction. Reference 

voltages were taken prior to the pre-crack test and the actual crack-growth test at 

649°C. 

Three type-K thermocouples were tack-welded to the gage section of the Kb

specimen (Figure 5.7). Thermocouple 1 (T/C 1) measured the Kb specimen test 

temperature. T/C 2 and T/C 3, spaced 6.35 mm from the center thermocouple, 

were used for temperature control. 

Two half-section resistance furnaces (Figure 5.4) were then positioned 

around the Kb specimen. The specimen was heated to 649 ± 1°C at zero load 

with the Kb surface temperature read out through a digital meter. Initial voltage 

potentials were measured at axial loads of 0 N and 17.8 KN. An initial voltage 

was also taken to account for thermoelectric influences. The test was conducted 

with a sinusoidal waveform at 0.33 Hz, and a ratio of R = 0.05 (Pmax = 27.4 KN). 
NASA/TM—2005-213873 71 

Figure 5.7 Thermocouple locations on the Kb specimen gage section 

indicated by the arrows. Thermocouples not shown. 

 

 For each acquisition, MATE recorded the cycle count, total crack length, 

maximum load, corrected dcEPD voltage, number of dcEPD points acquired, 

thermoelectrically induced voltage, and input load ratio. Data was taken 

approximately every 0.0508 mm of crack extension.11 For back-up, voltage and 

load history were recorded with a strip chart recorder and data acquired by 

MATE was printed. 

 The crack was allowed to grow to 2.54 mm. This crack length limitation was 

due to the 4.32 mm gage thickness. Experience has shown that crack length 

voltage accuracy begins to drop off for crack lengths at approximately 65% of the 

gage thickness.12 Final voltages were again taken at axial loads of 0 N and 

17.8 KN. At the conclusion of the test, the test specimen was brought to failure 

by monotonically increasing the load to failure. 
NASA/TM—2005-213873 72 

Data Reduction

 Crack depth data was corrected based on post-test measurements of the 

fracture surface (Figure 5.8 and Figure 5.9). 

 

Figure 5.8 Fracture surface measurements for the Grainex Mar-M 247 Kb

specimen (13K). Dimensions are in millimeters. 
NASA/TM—2005-213873 73 

Figure 5.9 Fracture surface measurements for the Grainex Mar-M 247 Kb

specimen (32K). Dimensions are in millimeters. 

The solution was automated within the MATE program where iterations were 

performed which compared the measured voltage for a calculated crack depth to 

the voltage predicted by the Roe-Coffin potential solution9

 for a semi-elliptical 

surface notch. 

The Roe-Coffin solution, given by Gangloff,8

 has the form 

( , , , , , , ) c c c n n n p

N

f a b c a b c L V

V = Eqn. 5.1 (Ref.8) 

where V = crack length voltage [volts] 

 VN = reference voltage [volts] 

 ac = crack depth [mm] 

 bc = crack half-height [mm] 

 cc = crack surface half-width [mm] 

 an = initial EDM crack depth [mm] 
NASA/TM—2005-213873 74 

 bn = initial crack half-height [mm] 

 cn = initial crack surface half-width [mm] 

 Lp = potential probe spacing half-width [mm] 

The crack depth and length were iterated within the MATE program such that 

the difference between the measured and predicted voltages of the crack depth 

and length were minimized. This was done by holding constant VN

V , an, bn, cn, 

and Lp, and holding constant the aspect ratio, c

c

a

c , for each increment of crack 

depth acquired during the test. Thus, crack depth was generated for each cycle. 

 The crack growth rate, dN

dac , was calculated using the incremental polynomial 

method, per ASTM E647.13 The stress intensity range, ∆K, was calculated within 

MATE using stress-intensity factor equations developed by Newman and Raju 14 

for a semi-elliptical surface crack subjected to tensile loading: 

= ( , , ,Φ)

c

c c

c

c

S

c

I b

c

t

a

c

a F

Q

a K s π Eqn. 5.2 (Ref.14) 

where KI = stress-intensity factor (Mode I) [MPa m ] 

 s = remote uniform tensile stress [MPa] 

 Q = shape factor 

 Fs = boundary correction factor 

 t = through thickness of test specimen [mm] 

φ = ellipse parametric angle [radians] 

Kmax was determined by inputting the maximum recorded load at each data point 

into Eqn. 5.2, which is programmed into MATE. Finally, ∆K was calculated using 

∆K = K (1− R) max Eqn. 5.3 (Ref. 15) 

where ∆K = stress intensity range [MPa m ] 

 Kmax = maximum stress intensity factor [MPa m ] 

 R = stress ratio 

The resultant 

dN

dac versus ∆K data were then plotted on log-log coordinates. 
NASA/TM—2005-213873 75 

The fatigue crack growth behavior over the entire range of data that was 

collected was modeled using: 

( ) c m C K

dN

da = ∆ Eqn. 5.4 (Ref.15) 

where 

dN

dac = fatigue crack growth rate [mm/cycle] 

 C = coefficient ( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

m

MPa m

mm cycle

 m = exponent 

This relationship was used to estimate fatigue crack growth life of the Grainex 

Mar-M 247 material. The entire range of data was evaluated with this 

relationship to provide a conservative estimate of fatigue crack growth life. 

Statistics

 Linear regression analysis was conducted to evaluate the log-log transformed 

data: 

() ( ) C m K

dN

dac ⎟ = + ∆ ⎠

⎞ ⎜

⎝

⎛ log log log Eqn. 5.5 

A statistical comparison between regression lines was performed to 

determine if the individual slopes and intercepts were statistically similar at a 

confidence level of 95%. A test of equal variances on the error terms for each 

regression line was first done to validate a comparison between regression 

lines.16 To test for similar slopes and intercepts, a reduced statistical model was 

determined which combined data sets from successful fatigue crack growth tests. 

The reduced statistical model was: 

Yij Xij ij = β + β + ε 0 1 Eqn. 5.6 (Ref.16) 

where Yij = predicted value 

β0 = intercept of reduced model 

β1 = slope of reduced model 

 Xij = independent variable 

εij = error term 
NASA/TM—2005-213873 76 

A test statistic, F*, was calculated and compared with the F value determined 

from F-tables based on significance level and degrees of freedom. F* is defined 

as: 

4

( )

2

( ) ( ) *

1 + 2 − ÷ − = n n

SSE R SSE F SSE F F Eqn. 5.7 (Ref.16) 

where SSE(R) = sum squared error of reduced model 

 SSE(F) = sum squared error of full model 

 n1 = number of data points for data set 1 

 n2 = number of data points for data set 2 

 For F* ≤ F(1-a; 2, n1 + n2 - 4) a conclusion can be made that the slopes and 

intercepts of both regression lines are equal. Note that “a” is the desired 

percentile level. 

Small Crack Growth Behavior

Because of the small size of the EDM notch dimensions (Figure 5.2) with 

respect to the Grainex Mar-M 247 grain size (1.6 mm, See Chapter 3), it was 

possible that fatigue crack growth would occur in the small crack growth regime. 

Small cracks are defined as having dimensions equal to or smaller than the 

dimension of greatest microstructural significance, such as grain size.15 Small 

cracks are characterized by higher growth rates and their ability to grow at ∆K 

values below the threshold stress intensity range, ∆Kth (Figure 5.10). Small 

cracks may decelerate and arrest or approach a minimum in fatigue crack growth 

rate, then accelerate, and merge with long crack growth behavior. Thus, the 

fatigue crack growth behavior and respective crack size relative to the grain size 

was evaluated to determine if fatigue crack growth followed small crack behavior. 
NASA/TM—2005-213873 77 

Figure 5.10 Typical small-crack growth behavior.17

Linear-Elastic Fracture Mechanics (LEFM)

 An assessment of the validity of linear-elastic fracture mechanics (LEFM) was 

made based on specimen geometry. LEFM limitations were compared to 

specimen geometry based on 

( )

( )

2

0.2%

4 max , , ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ≥

y

c c

K

a t a h

π σ

 Eqn. 5.8 (Ref. 15) 

where ac = crack depth [mm] 

 t = through thickness of the test specimen [mm] 

 h = half-height of the Kb specimen gage section 

 from the EDM notch [mm] 

Plastic-Zone Size

The plastic zone size was compared with the average grain size of Grainex 

Mar-M 247. The plastic zone size for plane stress conditions, 2r0σ, was 

estimated by: 

2

(0.2%)

max

0

1 2 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

y

K

r

π σ σ Eqn. 5.9 (Ref.15) 
NASA/TM—2005-213873 78 

Fractographic Examination

Fatigue crack propagation surfaces from each specimen were prepared for 

examination by carefully removing the gage section with a cut-off wheel. The 

surface was cleaned and then mounted. Fracture surfaces were examined using 

a light microscope and a scanning electron microscope (SEM) under secondary 

electron (SE) and backscattered electron (BE) modes. 

Fracture surface features were identified including: initial and final EDM 

notches; pre-crack region; low ∆K (= 23.3 to 26.4 MPa m ) and high ∆K (= 35.7 

to 39.1 MPa m ) regions; and the overload region. SEM micrographs of the low 

and high ∆K regions were taken, respectively, at 1.00 – 1.25 mm and 2.00 to 

2.25 mm from the EDM notch origin. A comparison was made between crack 

growth rate and crack depth. The microscopic crack growth rate was determined 

for the low and high ∆K regions by measurement of striation spacings. 

A comparison was made between the experimentally applied ∆K and the 

calculated ∆K based on striation spacings at the low and high ∆K fracture surface 

regions using the Bates and Clark relationship18: 

 striation spacing 

2

6 ⎟

⎠

⎞ ⎜

⎝

⎛ ∆ = E

K Eqn. 5.10 (Ref.18) 

where Young’s modulus, E, was taken to be 194 GPa (see Chapter 4). The 

experimental ∆K used to compare with the Bates and Clark relationship was 

taken from the averaged ∆K determined from the low ∆K regime (24.85 MPa m ) 

and high ∆K regime (37.40 MPa m ). 

5.3 Results and Discussion 

Test Summary

Of the original eight Kb specimens, two tests (13K and 32K) were successfully 

conducted after doubling the EDM notch width and depth. Four Kb specimens, 

previously tested, failed prematurely outside the EDM notch. The remaining two 

were untested. Hereafter, the results pertain only to Kb specimens 13K and 32K. 

Experimental Data

The fatigue crack growth behavior for the two tests specimens is shown in 

Figures 5.11 and 5.12 and the coefficient, C, and exponent, m, from Eqn. 5.4 are 

given for each specimen in Table 5.1. 
NASA/TM—2005-213873 79 

Figure 5.11 Fatigue crack growth behavior for Grainex Mar-M 247 at 649°C 

(Kb specimen 13K). 

Figure 5.12 Fatigue crack growth behavior for Grainex Mar-M 247 at 649°C 

(Kb specimen 32K). 
NASA/TM—2005-213873 80 

Table 5.1 Regression results of Eqn. 5.4 for fatigue crack growth 

behavior of Grainex Mar-M 247 Kb specimens at 649°C for the 

entire stress intensity range tested (13K and 32K) 

Specimen intercept slope R2 constant C exponent m 

13K -11.98 5.80 0.93 1.05x10-12 5.80 

32K -10.53 4.82 0.90 2.94x10-11 4.82 

 

The deceleration and then acceleration of the dac/dN data in the low ∆K 

region may be due to the crack approaching microstructural barriers such as 

grain boundaries or due to crack closure.17,21 This small crack growth behavior 

generally transitions into long crack growth behavior at higher ∆K values19, and 

this appears to have been the case in this study. 

Statistics

Fatigue crack growth data with regressions from both data sets were 

analyzed for similarity. The variances between the individual regressions were 

found to be equivalent to a 95% confidence level. Thus a comparison between 

the regressions for similarity was valid. The reduced model (Eqn. 5.6) was 

determined with β0 = -11.20 and β1 = 5.28. Finally, F* (Eqn. 5.7) was calculated 

as -72.56. From standard F-tables, F(0.999, 2, 120) was 7.32. Thus F*≤ F and 

the slopes and intercepts were equal to within a 99.9% confidence level. The 

data from the two specimens were thus combined into one data set and an 

overall coefficient, C, and exponent, m, were determined (Figure 5.13). 

∆K [MPa (m0.5)

20 25 30 35 40 45 50

dac/dn [mm/cyc]

10-5

10-4

10-3

10-2

data: 2 tests

regression

C = 6.34 x 10-12

m = 5.28

( ) c m C K

dN

da = ∆

Test Conditions

Specimen Type: Kb

Temperature: 649C

R = 0.05

Frequency = 0.33 hz

Waveform = sine

Figure 5.13 Regression results using both specimen data sets for Grainex 

Mar-M 247 fatigue crack-growth Kb data. 
NASA/TM—2005-213873 81 

To be conservative in predicting fatigue crack growth life, both data sets (13K 

and 32K) were used with regression analysis over the entire experimentally 

determined range. The steeper dac/dN versus ∆K slope in both data sets at low 

∆K was thus taken into account as well as the shallower slope at high ∆K. This is 

appropriate since a conservative inspection interval is needed for the turbine seal 

rig facility (see Chapter 6). 

Small Crack Growth Behavior

Small crack growth behavior (Figure 5.10) was observed for both fatigue 

crack growth specimens (Figure 5.11 and Figure 5.12). That is, the crack growth 

rate for both specimens was observed to initially decelerate to a minima and then 

to transition into the long crack growth regime. 

In this study, the transition from small crack growth to long crack growth 

appeared to occur at approximately ∆K = 30 MPa m (dac/dN = 4e-4 mm/cycle) 

for both fatigue crack growth tests (Figure 5.13), based on the similarity in dac/dN 

versus ∆K behavior above the transition. Consistent with this, the corresponding 

range of crack depths at that stress intensity was between 1.55 and 1.65 mm 

(see Figure 5.17 below). This coincides with reported Grainex Mar-M 247 

average grain sizes of 1.6 mm. In other words, once the crack grows larger 

than the grain size, long crack growth behavior is expected. 

Linear Elastic Fracture Mechanics, LEFM

Initial and final crack lengths for both fatigue crack growth test specimens 

were compared to the Kb specimen geometry to determine LEFM applicability 

using Eqn. 5.8 (Table 5.2). Initial crack lengths did not meet LEFM criteria for 

either specimen. Final crack lengths and remaining gage specimen thickness 

(i.e. t – ac) also did not meet LEFM criteria. 

Table 5.2 Comparison of initial and final crack lengths to Kb specimen 

geometry (13K and 32K) for LEFM applicability (Eqn. 5.8) at 649°C 

Initial 13K 13K 

Criteria Pass/Fail Initial 32K 32K Criteria Pass/Fail

ac [mm] 0.846 0.963 Fail ac [mm] 0.884 0.919 Fail 

(t- ac) [mm] 3.472 0.963 Pass (t- ac) [mm] 3.434 0.919 Pass 

h [mm] 7.976 0.963 Pass h [mm] 7.976 0.919 Pass 

Final 13K 13K 

Criteria Pass/Fail Final 32K 32K Criteria Pass/Fail

a [mm] 2.550 3.840 Fail ac [mm] 2.560 3.607 Fail 

(t- ac) [mm] 1.768 3.840 Fail (t- ac) [mm] 1.758 3.607 Fail 

h [mm] 7.976 3.840 Pass h [mm] 7.976 3.607 Pass 
NASA/TM—2005-213873 82 

The use of an LEFM approach for fatigue crack growth tests assumes that 

plasticity is limited to a local region that is small compared to the specimen 

dimensions.15 Predicted gross yielding of the specimen calls into question the 

use of an LEFM approach. In this study, during fatigue crack growth testing, the 

initial maximum stress level at the gage section, calculated using the uncracked 

ligament, was approximately 79% of the 0.2% offset yield stress at 649°C. The 

final maximum stress level at the gage section, calculated using the uncracked 

ligament, was nearly 118% of the 0.2% offset yield stress. Thus, the fatigue 

crack growth behavior in these tests may have been influenced by gross yielding 

in the gage region. This suggests that the fatigue crack growth behavior of 

Grainex Mar-M 247 may be worse than the experimentally-obtained data. 

Fatigue crack propagation tests of Grainex Mar-M 247 using a specimen 

geometry that meets LEFM criteria would help answer this question. Because of 

the uncertainty in the data, a safety factor of 2 is used to predict fatigue crack 

growth life (see Chapter 6). 

Plastic Zone Size

The initial and final plane stress plastic zone sizes for both specimens 13K 

and 32K (Eqn. 5.9) can be found in Table 5.3. 

Table 5.3 Initial and final plastic zone sizes for Grainex 

Mar-M 247 Kb fatigue crack growth specimens, 

13K and 32K, for plane stress conditions at 649°C 

Plane Stress Plastic Zone Size 

Specimen 

Initial [mm] Final [mm] 

13K 0.241 0.960 

32K 0.230 0.902 

The final plane stress plastic zone size did not exceed the average grain size 

of 1.6 mm determined from results in Chapter 3 (Material Cut-Up and 

Characterization). Thus, the recorded dac/dN versus ∆K behavior was likely 

microstructurally-sensitive.20 

Fractographic Examination

The fracture surface of specimen 13K is shown in SE mode (Figure 5.14 and 

Figure 5.15) Fracture surface features for Kb specimen 32K were similar. 
NASA/TM—2005-213873 83 

Figure 5.14 Grainex Mar-M 247 fatigue crack growth fracture surface for 

Kb specimen 13K (649°C). Dotted area enlarged in Figure 5.15 

Figure 5.15 Close-up of Grainex Mar-M 247 fatigue crack growth fracture 

surface features for Kb specimen 13K at 649°C. Low ∆K 

region: 23.3 to 26.4 MPa m . High ∆K region: 35.7 to 39.1 

MPa m . SEM (SE mode). The initial EDM notches are 

indicated in blue and the initial pre-crack region (conducted 

at 649°C) is indicated in red. 
NASA/TM—2005-213873 84 

Figure 5.16 Grainex Mar-M 247 fatigue crack growth fracture surface for Kb

specimen 13K at 649°C showing grain boundary near 

beginning of fatigue crack growth (SEM – BE mode) 

Under BE mode, grain boundaries were observed in the fatigue crack 

propagation region beginning between 0.75 and 1.00 mm radii from the EDM 

notch origin (Figure 5.16). Note that the 649°C fatigue crack growth began at 

approximately 0.82 mm from the EDM notch origin. 

The decreasing crack growth rate at low ∆K (Figure 5.11) at a crack depth 

between 0.85 and 0.90 mm may be related to the grain boundary (Figure 5.16) 

between 0.75 and 1.50 mm from the notch origin. This deceleration in crack 

growth rate may be due to the crack front encountering a microstructural barrier 

such as a grain boundary. In fact, the minima in the fatigue crack growth rate 

was found to correspond to a crack depth of 0.88 mm (Figure 5.17) for specimen 

13K. This is consistent with findings by Taylor17 and Suresh et.al. 21 

Grain Boundary
NASA/TM—2005-213873 85 

Figure 5.17 Fatigue crack growth rate versus crack depth for Grainex 

Mar-M 247 Kb specimen (13K) at 649°C. 

The low ∆K region (Figure 5.18) of specimen 13K between 1.00 to 1.25 mm 

from the EDM notch origin showed pockets of fatigue striations. The 

microstructural fatigue crack growth rate per cycle was approximately 

2.5 x 10-3 mm/cycle (Figure 5.17). In contrast, the high ∆K region (Figure 5.19) 

shows more organized and delineated striations and the microstructural fatigue 

crack growth rate is approximately 5 x10-3 mm/cycle (Figure 5.17). Specimen 

32K showed similar results. 
NASA/TM—2005-213873 86 

 

Figure 5.18 Low ∆K fatigue striations of Grainex Mar-M 247 fatigue crack 

growth fracture surface for Kb specimen 13K at 649°C (SEM –

SE mode) (See also Figure 5.15). ∆K range from 23.3 to 26.4 

MPa m . Arrow indicates crack growth direction. 

Figure 5.19 High ∆K fatigue striations of Grainex Mar-M 247 fatigue crack 

growth fracture surface for Kb specimen 13K at 649°C (SEM –

SE mode) (See also Figure 5.15). ∆K range from 35.7 to 39.1 

MPa m . Arrow indicates crack growth direction. 
NASA/TM—2005-213873 87 

Table 5.4 compares the experimentally applied ∆K and the calculated ∆K 

based on striation spacings taken from the low and high ∆K regions. The stress 

intensity ranges were overestimated by the Bates and Clark relationship, 

(Eqn. 5.10), by a factor of 5 for both low and high ∆K regions. 

Table 5.4 Comparison between experimental ∆K and calculated ∆K from 

striation spacing measurements for Grainex Mar-M 247 at 649°C 

∆K 

region 

∆K (experimental)*

[MPa m ] 

Striation Spacing 

[mm/cycle] 

∆K (Bates & Clark18) 

[MPa m ] 

Low 24.85 2.5 x 10-3 125.2 

High 37.40 5.0 x 10-3 177.1 

*average 

Adjusting Eqn. 5.10 by the percent striated area of the fracture surface may 

result in better agreement between the experimental and calculated ∆K.18 A 

rigorous survey of the fractographic area would be needed to determine if the 

Bates and Clark relationship would be a reliable predictor of cyclic stress 

intensity. 

Comparison of Data to Literature

The regression of the combined experimental data was compared to literature 

at 426°C and 538°C (Figure 5.20 and Table 5.5). The fatigue crack growth rate 

increases with test temperature at constant cyclic stress-intensity. Data reported 

by Macha et. al. 22, , MacIntyre et.al. 23, Helmink et.al. 24, and Alloy Digest,25

support this observation. The data from this study had the highest fatigue crack 

growth rate, since tests were conducted at the highest test temperature, 649°C. 
NASA/TM—2005-213873 88 

Figure 5.20 Comparison of Grainex Mar-M 247 to literature.22,23,24,25 

Table 5.5 Comparison of experimental Grainex Mar-M 247 test 

parameters with reported data from available literature.22,23, 24,25

This Study Macha MacIntyre Alloy Digest Helmink 

Specimen Type Kb C-T unknown unknown Unknown 

Temp [°C] 649 426 538 538 538 

Frequency [Hz] 0.33 30 0.33 unknown Unknown 

Load Ratio 0.05 0.1 0.05 0.05 Unknown 

Waveform sine sine unknown unknown Unknown 
NASA/TM—2005-213873 89 

Summary 

Small crack growth behavior observed by minima in the fatigue crack growth 

rate was likely related to microstructural barriers such as grain boundaries. The 

data transitioned towards long crack growth behavior at higher ∆K. The fatigue 

crack growth behavior is likely microstructurally sensitive because the final plane 

stress plastic zone size was predicted to be smaller than the average grain size. 

Data sets from both fatigue crack growth tests were combined to account for 

the higher crack growth rates in the low ∆K region. However, since gross 

yielding was predicted at the fracture surfaces and LEFM criteria were not met, 

this may indicate a more severe dac/dN versus ∆K behavior than given by the 

data. Thus, an arbitrary factor of 2 safety was used for determining fatigue crack 

growth life (see Chapter 6). 

 

Chapter 5 Works Cited 

1. Coles, A., R.E. Johnson, and H.G. Popp. “Utility of Surface-Flawed Tensile 

 Bars in Cyclic Life Studies.” Journal of Engineering Materials and 

 Technology. 98 (1976) 305–315.

2. Diez, Andrew. “Crack formation in bolt holes.” Personal communication by 

 Irebert Delgado. 03 August 2000. 

3. Kantzos, Pete. “Kb specimen geometry.” Personal communication by 

Irebert Delgado. 31 March 2000. 

4. Hartman, G.A., and N.E. Ashbaugh. “A Fracture Mechanics Test 

 Automation System for a Basic Research Laboratory.” Applications of 

 Automation Technology to Fatigue and Fracture Testing, ASTM STP 1092. 

 Eds. Braun, A.A., N.E. Ashbaugh, and F.M. Smith. Philadelphia, ASTM, 

 1990. 95-110. 

5. Ashbaugh, N. and G. Hartman. “Direct Current Electric Potential 

Workshop.” MATE Workshop. University of Dayton Research Institute. 

6. Gangloff, R. P., D. C. Slavik, R. S. Piascik, and R. H. Van Stone. “Direct 

Current Electrical Potential Measurement of the Growth of Small Cracks.” 

Small-Crack Test Methods, ASTM STP 1149. Eds. Larsen, J. M., and J.E. 

Allison. Philadelphia: ASTM, 1992. 116-168. 

7. Hartman, George. “Questions on MATE program.” Personal communication 

by Irebert Delgado. 17 September 2002. 

8. Gangloff, R.P. “Electric Potential Monitoring of Crack Formation and 

 Subcritical Growth from Small Defects.” Fatigue of Engineering Materials

 and Structures. 4.1 (1981) 15-33. 

9. VanStone, R.H., and T.L. Richardson. “Potential-Drop Monitoring of Cracks 

 in Surface-Flawed Specimens.” Automated Test Methods for Fracture and

 Fatigue Crack Growth, ASTM STP 877. Eds. Cullen, W.H., R.W. Landgraf, 

 L.R. Kaisand, and J.H. Underwood. Philadelphia: ASTM, 1985. 148-166. 
NASA/TM—2005-213873 90 

 

10. Shannon, Brian. “Accounting for thermoelectric influences.” Personal 

 communication by Irebert Delgado. 07 August 2000. 

11. Shannon, Brian. “FCG data acquisition rate.” Personal communication by 

Irebert Delgado. 24 July 2003. 

12. Telesman, Jack. “Crack growth limitations.” Personal communication by 

 Irebert Delgado. 07 September 2002. 

13. ASTM Committee E-8 on Fatigue and Fracture. “ASTM E-647-95a 

 Standard Test Method for Measurement of Fatigue Crack Growth Rates.” 

 Annual Book of ASTM Standards 2001: Section 3 Metals Test 

 Methods and Analytical Procedures: Volume 03.01 Metals—Mechanical 

 Testing; Elevated and Low-Temperature Tests; Metallography. ASTM. 

 West Conshohocken: ASTM, 1998. 577-613.

14. Newman, J.C., Jr., and I.S. Raju. “Stress-Intensity Factor Equations for 

Cracks in Three-Dimensional Finite Bodies.” Fracture Mechanics: 

Fourteenth Symposium—Volume I: Theory and Analysis, ASTM STP 791. 

Eds. Lewis, J.C., and G. Sines. Philadelphia: ASTM, 1983. I-238 - I-265. 

15. Dowling, Norman E. Mechanical Behavior of Materials : engineering 

 methods for deformation, fracture, and fatigue. Upper Saddle River: 

 Prentice-Hall, Inc., 1999.

16. Neter, John, and William Wasserman. Applied Linear Statistical Models. 

Homewood: Richard D. Irwin, Inc. (1974). 

17. Taylor, David. Fatigue Thresholds. London: Butterworths, 1989. 

18. Bates, R.C., and W.G. Clark Jr. “Fractography and Fracture Mechanics.” 

ASM Transactions Quarterly. 62.2 (1969) 380-389. 

19. Taylor, D. A Compendium of Fatigue Thresholds and Growth Rates. 

London: Chameleon Press LTD. (1985).

20. Hertzberg, Richard W. Deformation and Fracture Mechanics of Engineering 

Materials. 3rd Ed. New York: John Wiley and Sons, Inc. (1989). 

21. Suresh, S., and Ritchie, R. O. “Propagation of short fatigue cracks.” 

International Metals Reviews. 29.6 (1984) 445-476. 

22. Macha, D.E., G.R. Cole, and J.A. Butzer. “Fine Grain, Investment-Cast 

Integral Turbine Wheels.” Grain Refinement in Castings and Welds. Ed. 

G.J. Abbaschian and S.A. David. New York: The Metallurgical Society of 

AIME, 1983. 197-219.

23. MacIntyre, Cal A. and P. Neil Agarwal. “Development of Fine Grain Cast 

Mar-M 247 Axial and Radial Turbine Wheels.” Advanced Aerospace 

Materials Technology: SP-597. Warrendale: Society of Automotive 

Engineers, Inc., 1984. 35-45.

24. Helmink, R.C. et. al. “Advanced Superalloys and Tailored Microstructures 

for Integrally Cast Turbine Wheels.” Superalloys 2000. Ed. T.M Pollock et 

al. Warrendale: TMS, 2000. 171-179.

25. “Microcast-X Mar-M 247.” Alloy Digest May 1995. 
NASA/TM—2005-213873 91 

6. Determination of the NASA Disk Inspection Interval 

6.1 Introduction 

As discussed in Chapter 1, eddy-current inspections are used to examine the 

NASA disk bolt holes after a set number of cycles at maximum operating 

conditions. In general, engine companies use eddy current inspection or other 

non-destructive evaluation procedures for turbine disks, such as the Grainex 

Mar-M 247 NASA disk, to prevent disk failure by growth of an existing crack to a 

critical crack length, acrit. The inspection interval is based on a critical crack 

length, acrit, determined at a specific cyclic life from KIC tests at a specific test 

temperature, stress level, and detectable threshold crack size. 

This chapter discusses the eddy-current inspection interval determined for the 

Grainex Mar-M 247 NASA disk based on strain-life and fatigue crack growth 

results from previous chapters. 

6.2 Methods 

Although the dac/dN versus ∆K behavior was estimated in Chapter 5, a critical 

crack length was not determined because of a lack of valid KIC tests. However, 

an estimate of the critical crack length at failure is required to predict cyclic life. 

Data reported by Kaufman1

 indicates that the plane-strain fracture toughness, 

KIC, for Grainex Mar-M 247 is greater than 55 MPa m at 760°C. The maximum 

∆K value of 40.83 MPa m , attained at the end of the fatigue crack growth tests, 

can be used as a conservative estimate of KIC. This is reasonable since the 

fatigue crack growth behavior was observed to be well-behaved at the end of the 

test (i.e. stable crack growth rate). 

Assuming KIC to be approximately 40 MPa m , the critical crack length, acrit, 

for a cyclic stress intensity range of 40 MPa m was determined. Using the 

regression values for coefficient, (C = 6.34x10-12), and exponent, (m = 5.28), for 

the combined data (Chapter 5, Figure 5.13) with an initial crack size of 0.381 

mm (the threshold level for eddy-current inspection2

), the crack length versus 

cycles can be calculated iteratively and plotted.3

 Assuming the initial crack 

length, ai, occurs at cycle 1, the following crack length at cycle 2 is calculated as 

follows: 

1. Calculate ∆K based on ∆K = F∆σ πai ˆ . ∆σ is 699 MPa from 

analyses by Tong and Steinetz.4 Fˆ is 1.12 for a half-elliptical 

surface crack.5

 

2. Calculate dac/dN per Eqn. 5.4 (Chapter 5) using the values for C 

and m found for the combined data set. 

3. Recalculate the crack length for cycle 2 by adding the previous 

crack length, ai, to the value dac/dN calculated in step 2. The 

estimated crack growth length for the following cycle is dac/dN. 

4. Repeat steps 1 – 3 until ∆K is approximately 40 MPa m . 
NASA/TM—2005-213873 92 

6.3 Results and Discussion 

The calculated critical crack length was 0.831 mm at 734 cycles at 

∆K = 40 MPa m (Figure 6.1). An average crack growth of 0.016 mm per 

50 cycles was calculated from cycle 0 to approximately cycle 350. 

An arbitrary safety factor of 2 on cyclic fatigue crack growth life was used 

since results from Chapter 5 indicate that LEFM conditions were not met and 

gross yielding was predicted at the gage section. Thus, the calculated cyclic life 

of 734 cycles is reduced, by half, to 367 cycles. Also, the corresponding crack 

depth is reduced from 0.831 mm to a crack depth of 0.501 mm. 

The total fatigue life of a material often encompasses approximately 90% 

fatigue strain-life and 10% fatigue crack growth life.6

 Recall Figure 4.12 which 

gives the Rε = 0 fatigue strain-life crack initiation curve at 649°C. At the design 

strain of 0.5% the mean life to crack initiation is approximately 15,000 cycles. 

Combining this with the predicted fatigue crack propagation cycles to failure, 734, 

in Figure 6.1 gives a total life of 15,734 cycles. This approach suggests that, for 

the Grainex Mar-M 247 NASA disk operating at 649°C air temperature, crack 

initiation represents 95% of the cyclic life of the NASA disk while the remaining 

5% is used to propagate the crack to failure. 

Figure 6.1 Grainex Mar-M 247 NASA disk fatigue crack growth rate with 

increasing cycles at 649°C. 
NASA/TM—2005-213873 93 

 However, considering the environment in which the NASA disk is used and 

the safety required for personnel and equipment, statistical and other safety 

factors must be used to estimate the inspection interval. Specifically, using the -

99.95% prediction interval shown in Figure 4.12, the cyclic life to crack initiation, 

with statistically 1 failure in 2000, is 1100 cycles at the design strain of 0.5% at 

649°C. Accounting for the 6 bolt holes using the system life analysis as 

previously discussed in Chapter 1, the resultant crack initiation life is 665 cycles. 

Combining this with the predicted fatigue crack propagation cycles of 367 cycles 

(using a factor of safety of 2) gives a total cyclic life for the Grainex Mar-M 247 

NASA disk bolt holes of 1032 cycles at a crack length of 0.501 mm at maximum 

disk operating conditions. 

Since the eddy-current detection threshold is currently 0.381 mm, an initial 

NASA disk bolt hole inspection is recommended starting at approximately 665 

cycles to detect crack initiation. Inspection intervals are then recommended 

approximately every 50 cycles thereafter to adequately monitor fatigue crack 

growth. The NASA disk should be retired from service upon attaining either 1032 

cycles or a crack depth of 0.501 mm (Figure 6.2). One possible implementation 

plan is given in Figure 6.3. 

Figure 6.2 Total fatigue life of Grainex Mar-M 247 at maximum operating 

conditions of the NASA Turbine Seal Test Rig. 
NASA/TM—2005-213873 94 

Figure 6.3 Decision tree for implementing eddy-current inspection 

interval for Grainex Mar-M 247 NASA disk. 

 

Chapter 6 Works Cited 

1. Kaufman, M. “Properties of Cast Mar-M-247 for Turbine Blisk Applications.” 

 Superalloys 1984. Ed. Maurice Gell et al. Warrendale: Metallurgical 

 Society of AIME, 1984. 43-52. 

2. Curtis Industries, Inc. “Reference Standard Calibration for GX Mar-M 247.” 

Inspection report for reference standard. Curtis Industries, Inc., 

Pennsylvania. 12 May 2003. 

3. Broek, David. Elementary Engineering Fracture Mechanics. 3rd ed. 

Hingham: Kluwer Boston, Inc., 1984. 

4. Tong, Mike and Bruce Steinetz. “Mar-M 247 Disk Finite Element Thermal 

and Stress Analysis”, NASA Glenn Research Center, Cleveland. 30 January 

1997.

5. Dowling, Norman E. Mechanical Behavior of Materials : engineering 

methods for deformation, fracture, and fatigue. Upper Saddle River: 

Prentice-Hall, Inc., 1999. 

6. Kerlins, Victor, and Austin Phillips. “Modes of Fracture.” Metals Handbook 

Volume 12 Fractography. 9th ed. Metals Park: ASM International. 1987. 
NASA/TM—2005-213873 95 

7. Future Work 

7.1 Effect of Material limitations 

 The size and number of test specimens (tensile, strain-life, and fatigue crack 

growth) were limited due to the single Grainex Mar-M 247 NASA disk available 

for cut-up. This also limited preferential cutting planes for microstructural 

examination of the NASA disk from the rim to the centerline. 

Priorities were set on the specimens taken out of the NASA disk based on the 

data that was needed. For example, fatigue crack growth specimens were taken 

near the bolt hole locations since they were the structural feature most limiting in 

terms of fatigue strain-life per analyses by Tong and Steinetz.1

 A large number 

of strain-life specimens were taken out of the NASA disk to obtain a statistical 

prediction of the cyclic crack initiation life at design conditions with a high degree 

of confidence (i.e. 99.95%). Tensile specimens numbered the fewest because 

the results were used to confirm previous data and to make general comparisons 

to fatigue strain-life prediction models. Finally, specimen cut-out plans were 

necessary to ensure that an adequate cross-section of the NASA disk was 

available for metallurgical analysis. 

 The biggest disadvantage to having limited materials for test specimens was 

that fracture toughness tests could not be carried to out to determine KIC. Even 

with available material for fatigue crack growth tests, size limits on Kb test 

specimen thicknesses brought into question the applicability of LEFM for these 

fatigue crack growth analyses to predict a fatigue crack growth life. Further tests 

are needed to determine KIC from adequately sized fracture toughness 

specimens. 

Finally, because of inherent differences in processing from casting to casting, 

the Grainex Mar-M 247 material study was limited to the set of disks (7 total 

including sacrificial disk) used at NASA’s Glenn Research Center Turbine Seal 

Test Facility. 

7.2 Effect of Test Parameter Limitations 

 Tests were limited to the 649°C bolt hole temperature as predicted from 

analysis.1

 This was based on the limited material available and because the bolt 

hole region had the lowest predicted strain-life limits in terms of maximum 

operating temperature and stress. 

 Strain-life specimens were limited to two strain ratios with 5 strain-levels at 

each R-ratio. Work with statisticians aided in setting the proper number of 

repeats (three) at each strain-level to ensure a statistical analysis could be 

carried out for each R value. Other parameters were held constant, such as 

frequency and waveform and thus limited the study accordingly. Further, 

cumulative fatigue damage effects were not tested. 

 
NASA/TM—2005-213873 96 

 Fatigue crack growth tests were also limited to one set condition (R = 0.05, 

waveform = sine, temperature = 649°C, frequency = 0.33 Hz). Thus effects of 

these parameters were not within the scope of the study. Hold-times were also 

not considered nor was threshold limit testing. 

7.3 Eddy-Current Limitations 

 Eddy-current threshold crack size limits (0.381 mm) currently place limitations 

on the detectable defect size. Thus, -99.95% prediction intervals were placed for 

the strain-life cycles to crack initiation. Also, an arbitrary safety factor of 2 was 

imposed for the fatigue crack growth critical crack size. 

7.4 Recommendations for Further Research or Improvements 

 Material availability for KIC testing would improve on the predicted critical 

crack length to failure calculation. Conclusions made on the fatigue crack growth 

study were done in consideration of the available literature data and specifically 

on the range of ∆K tested. 

 Characterization of the material microstructure would benefit from a complete 

chord slice from the NASA disk rim to the disk center. Also, Grainex Mar-M 247 

disks used in the turbine seal test facility that would eventually be retired from 

service could possibly be used to study the effects of temperature and stress 

over time on the microstructure. 

 Finally, strain-life and fatigue crack growth as well as creep tests from 

material at the NASA disk rim should be considered. These areas experience 

higher operating temperatures but not necessarily the same magnitude of stress 

seen at the hub location. Nevertheless, creep is an additional issue and would 

complement the work done on characterizing the bolt hole location on the 

Grainex Mar-M 247 NASA disk. 

 

Chapter 7 Works Cited 

1. Tong, Mike and Bruce Steinetz. “Mar-M 247 Disk Finite Element Thermal 

and Stress Analysis”, NASA Glenn Research Center, Cleveland. 30 January 

1997. 
NASA/TM—2005-213873 97 

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NASA/TM—2005-213873 98 

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ARL–TR–3528

E–15243

111

Grainex Mar-M 247 Turbine Disk Life Study for NASA's High Temperature High

Speed Turbine Seal Test Facility

Irebert R. Delgado

Fatigue life; Fatigue crack propagation; Grainex Mar-M 247; Turbine Seal Test Facility;

Inspection interval

Unclassified -Unlimited

Subject Category: 26

WBS–22R–714–30–0402–01

1L161102AF20

This report was submitted as a thesis in partial fulfillment of the requirements for the degree of Master of Science to Case

Western Reserve University, Department of Mechanical and Aerospace Engineering, Cleveland, Ohio 44106. Responsible

person, Irebert R. Delgado, organization code Z, 216–433–3935.

An experimental and analytical fatigue life study was performed on the Grainex Mar-M 247 disk used in NASA’s Turbine

Seal Test Facility. To preclude fatigue cracks from growing to critical size in the NASA disk bolt holes due to cyclic

loading at severe test conditions, a retirement-for-cause methodology was adopted to detect and monitor cracks within the

bolt holes using eddy-current inspection. For the NASA disk material that was tested, the fatigue strain-life to crack

initiation at a total strain of 0.5 percent, a minimum to maximum strain ratio of 0, and a bolt hole temperature of 649 °C

was calculated to be 665 cycles using –99.95 percent prediction intervals. The fatigue crack propagation life was calculated

to be 367 cycles after implementing a safety factor of 2 on life. Thus, the NASA disk bolt hole total life or retirement life

was determined to be 1032 cycles at a crack depth of 0.501 mm. An initial NASA disk bolt hole inspection at 665 cycles is

suggested with 50 cycle inspection intervals thereafter to monitor fatigue crack growth.