ANL-8_-74

NASA CR-175057

AN-L-85-74

NASA CR-175057

EFFECTS OF A HIGH MEAN STRESS ON THE

HIGH-CYCLE FATIGUE LIFE OF PWA 1480

AND CORRELATION OF DATA BY

LINEAR ELASTIC FRACTURE MECHANICS

by

S. Majumdar and R. Kwasny

[N_SA-CR-175057) EF_ICTS OF A HIGH MEAN

S_RESS ON THE H_GH CYCIE _A_IGUE LIFE OY PWA

1480 AND CORH_.LATICN O_ DATA EY LINEAR

ELASIIC FRACTURE MECHANICS [Argonne National

lab., Ill.) 28 p HC _03)-M} A0| CSCI 20K

"Gob"

%,-,,o,J

ARGONNE NATIONAL LABORATORY, ARGONNE, ILLINOIS

Operated by THE UNIVERSITY OF CHICAGO

for the U. S. DEPARTMENT OF ENERGY

N86-27689

G3/39

under Contract W-31-109-Eng-38

Unclas

43304
Argonne National Laboratory, with facilities in the states of Illinois and Idaho, is

owned by the United States government, and operated by The University of Chicago

under the provisions of a contract with the Department of Energy.

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i

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ANL-85- 74

NASA/CR- 175057

ARGONNE NATIONAL LABORATORY

9700 South Cass Avenue

Argonne, Illinois 60439

EFFECTS OF A HIGH MEAN STRESS ON THE

HIGH-CYCLE FATIGUE LIFE OF PWA 1480

AND CORRELATION OF DATA BY

LINEAR ELASTIC FRACTURE MECHANICS

by

S. Majumdar and R. Kwasny

Materials Science and Technology Division

November 1985

Prepared for the NASA Lewis Research Center, Cleveland, Ohio

under Interagency Order C-91113-D
_E

z

m_

_r_

--=
EFFECTS OF A HIGH MEAN STRESS ON THE HIGH-CYCLE FATIGUE

LIFE OF PWA 1480 AND CORRELATION OF DATA BY

LINEAR ELASTIC FRACTURE MECHANICS*

by

Saurin Majumdar and Rolf Kwasny

ABSTRACT

High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 _xis) at 70°F (room temperature) in air and at 1000°F (538°C) in vacuum (I0 -v torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results

indicate that, although a tensile mean stress, in general, reduces life, the

reduction in fatigue strength, for a given mean stress at a life of one

million cycles, is much less than what is predicted by the usual linear

Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000=F than at 70°F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated

from micropores of sizes of the order of 30-40 _m. Since the macroscopic

stress-strain response in all cases was observed to be linear elastic, linear

elastic fracture mechanics (LEFM) analyses were carried out to determine the

crack growth curves of the material assuming that crack initiation from a

micropore (a = 40 _m) occurs very early in life. The results indicate that

O

the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at

700F as at 1000°F. However, the calculated crack growth rates at other R

ratios, both positive and negative, tend to be higher at 700F than at IO00°F.

Calculated threshold effects at large R values tend to be independent of

temperature in the temperature regime studied. They are relatively constant

with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios. Although there are uncertainties in calculating the

stress intensity factors for the specimen geometry that was tested, the

derived crack growth curve, when extrapolated to moderate stress intensity

region, agrees very closely with the limited crack growth test data (at the

test temperature of interest) available for this material at R = 0.i. The

comparison, if Justified, also tends to show that the threshold stress

intensity factor range may be smaller for specimens with short cracks than

for those with long cracks.

INTRODUCTION

PWA 1480 is a potential candidate alloy for use in the high-pressure

fuel turbine blade of the NASA space shuttle main engine. As a high-pressure

turbine material, it will be subjected to vibratory high-cycle fatigue

loading superimposed on a high mean stress due to centrifugal loading. The

present testing program at Argonne National Laboratory was initiated by NASA

Lewis Research Center to study the effects of a high mean stress on the highcycle fatigue behavior of single-crystal PWA 1480. Since the high mean

stress in an actual turbine blade of the space shuttle main engine occurs
near the root region (where temperatures are relatively low), the temperatures for testing were restricted to 70°F (room temperature) and 1000°F

(538°C). To minimize the effects of oxidation, tests at 1000°F were conducted in a vacuum. Also, since the principal loading direction of interest

is in the [001] direction, only specimenswith their axis oriented in the

[001] direction were tested.

It is known that microporositles are present in PWA1480 and that they

are often the sites of fatigue crack initiation [i]. The present study was

no exception. Although there was a distribution in size, in most cases a

fatigue crack was initiated from the largest (or close to the largest) microporosity present in the gauge section of the specimen. Sometimes these porosities were quite elongated and resulted in large elastic stress concentration factors. It is likely that cracks initiated from these porosities very

early in life. A purpose of the present study was to investigate whether the

generated data could be rationalized on the basis'of a fatigue crack growth

analysis. Fatigue crack growth data on single-crystal PWA 1480 are not

easily available. Some data were reported in Ref. i for tests carried out

generally at much higher temperatures than those used in the present study.

In the absence of a large data base, LEFManalyses were used to estimate the

fatigue crack growth rate properties necessary to obtain a good correlation

between observed and calculated lives, ignoring crack initiation lives.

Although there are uncertainties in the calculations because of uncertainties

in the initial crack size (due to a variability in the size of the microporosity responsible for crack initiation and in the computations of stress

intensity factors), the derived crack growth rates, when extrapolated to

larger stress intensity factors, compare very well with the very limited

experimental data available for this material.

OBJECTIVES

The primary obJectlve of the test program was to conduct high mean

stress high-cycle fatigue tests on single-crystal PWA 1480 in order to

establish the effects of a high mean stress on the high-cycle fatigue life.

Because of the limited scope of the program, the target life was set nominally at one million cycles. A second objective was to carry out metallographic examination of a sufficient number of failed specimens in order to

establish the effects of microstructure on damage. A final objective was to

establish a procedure for correlating the generated data on the basis of LEFM

analyses.

=

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MATERIAL

Straight gauge specimens [5 mm (0.2 in.) in diameter and 15 cm (6 in.)

long], with the specimen axes oriented in the [001] directiom, were supplied

by NASA Lewis Research Center. NASA specifications called for the following

heat treatment before machining:

2345°F in vacuum or protective atmosphere, 4 h, rapid air cooled +

1975°F in protective atmosphere, 4 h, air cooled
3

Additional aging heat treatment of 1600@Ffor 32 h in air followed by

air cooling was given after machining of specimens. The measuredelastic

modulus, proportional stress limit, 0.2% offset yield stress, and ultimate

tensile strength at 70°F and 1000°F are given in Table i. Note that, in

contrast to 70°F, significant strain hardening is present at 1000°F. Thus,

although the proportional limit is reduced with increasing temperature, the

0.2% offset yield stress remains nearly constant.

Table i. Mechanical Properties of As-Received PWA1480 (001)*

Ultimate

Temp, Elastic Proportional 0.2% Offset Tensile

°F Modulus, Limit, Stress, Strength,

x i0 -psi ksi ksl ksi

70 18.4 146 146

I000 16.6 ]25 144

154

*i ksi = 6.895 MPa.

Prior to testing, each specimenwas polished with l-_m diamond paste.

However, the surfaces of each specimen contained manypores, someof which

were as large as 40 _m (Fig. i).

TESTPROCEDURE

In the initial tests, specimenswere subjected to axial strain controlled cycles. However, very little cyclic plasticity was observed. For

example, Fig. 2 shows the hysteresis loop at the tenth cycle of a 0 to 0.8%

strain cycling test at 70°F. The hysteresis loop has almost zero width and

very little cyclic meanstress relaxation occurred during the test. Similar

behavior was also observed at 1000°F. Since almost all the tests were conducted at muchlower strain ranges, where the hysteresis loops have no

measurable widths, it was decided to proceed with the testing under loadcontrol at a frequency of 20 Hz. Becauseof the reduction of the proportional stress limit at 1000°F, plastic yielding occurred at the tensile end

of the first cycle of the high meanstress high-cycle fatigue tests. However, the magnitude of the plastic strain is estimated to be only 0.05%, and

there was no evidence of ratchetting with cycles, shakedownbeing reached

after the first cycle.

The tests at ?O°Fwere conducted in a laboratory air environment. In

order to minimi_e oxidation effects, the tests at IO00°F were conducted in

vacuum (8 x I0- torr). The specimenswere heated by a Lepel induction

heater operating at a frequency of 455 kHz.
4

200/zm

i I

ORIGINAl. PA_E m

OF POOR QUALITY

150

I00

_ 50

0

-5,

-- J CYCLE • I0

0.2 0.4 0.6 0.8

STRAIN (%)

Flg. i

Optical Mlcrograph Illustrates

Typlcal Mlcropore Density in

Unetched Specimen.

Fig. 2

Hysteresis Loop at lOth Cycle

for PWA 1480 (001) Specimen

Subjected to Cycling between

0 and 0.8% Strain Range at

20°C (70°F). I ksl = 6.895 MPa.

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m

F
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=_

Since the stress ranges corresponding to the target life of a million

cycles were not known_ priori, testing at each mean stress was initiated by

cycling for about a million cycles at an estimated stress range. Thereafter,

the stress range was increased successively by about 2 ksi (15 MPa) after

approximately each million cycles until the specimen failed. Barring a few

exceptions, failure of the specimens always occurred at or near the center of

the specimen gauge section. The fracture surfaces of a number of specimens

were examined in an optical or a scanning electron microscope.

TEST RESULTS

A summary of all the tests conducted are presented in Tables 2 and 3 and

in Figs. 3 and 4 for test temperatures of 70°F and 1000°F, respectively.

Note that the material displays a threshold-type behavior at each temperature

where the scatter in llfe is quite large. However, at higher stress ranges

(shorter lives) the tests are quite reproducible. The Goodman diagram corresponding to a life of a million cycles estimated from these tests is shown

in Fig. 5. Note that in contrast to the usual linear drop-off in stress

amplitude with increasing mean stress, PWA 1480 tends to be quite resistant

to mean stress effects at 70°F and somewhat less so at 1000°F. This behavior

is, of course, not unique to slngle-crystal PWA 1480 because it has also been

observed in another polycrystalline superalloy [2]. Interestingly, the fatigue strength at a given mean stress is larger at 1000°F than at 70°F, particularly at low mean stresses. The increase in strength with temperature

may be a result of thermal aging.

METALLOGRAPHIC OBSERVATIONS

Several specimens were examined by optical and scanning electron microscopes after fracture. Each specimen contained a large number of micropores

(Fig. I) ranging in size from a few micrometers to as large as 40 _m and

occasionally formed clusters. Crack initiation always occurred from one of

these micropores, usually one of the larger ones. An example is shown in

Fig. 6 for the specimen from test 1324 which was cycled at 70°F at a stress

range of 60 ksl (414 MPa) with zero mean stress. A similar mode of crack

initiation was also observed (Fig. 7) in the specimen from test 1336 which

was cycled at 70°F at a stress range of 38 ksi (262 MPa) and a mean stress of

120 ksi (827 MPa). The pore initiating the crack is about 40-Bm long and has

an aspect ratio of about 3. Note that the crack is very tight and macroscopical]y appears to grow along crystallographic planes, possibly {lll}-type

planes. In both specimens, the crack that led to failure was initiated by a

crack on a different slip plane (Figs. 6 and 8). Crack growth also appeared

to preferentially follow microporosities (Fig. 9). (The distinct slip band

marks along {lll}-type of planes in the figure are for a test with a rather

large (0.8%) strain range. Such slip bands were not observed in the low

strain range, high-cycle fatigue test specimens.) Crack initiation in specimens tested at 1000°F also occurred at micropores. An example (test no.

1347) is shown in Fig. i0, where the crack initiated at a cluster of microporosities with a major axis of at least 150 _m. The crack propagated radially on what appeared to be a {iii} plane.
Table 2. Summary of Tests on PWA 1480 at 20°C (70°F) In Air (i ksl = 6.895 MPa)

Teat

NO.

Stress, ksi

Range Head

R Frequency, Cycles to Remarks

t{z

Fal]ure

1317

1318

1339

1320

1324

160 +7] 0 1 5,900

151 -7 -1.2 ] 2],800

96 +3 -0.88 I 138,500

56 0 -1 I a 2.73 x ]06

60 0 -i 20 2.33 x 106

Strain cnntro]led O_0.SZ

Strain controlled !O.4_

Strain controlled t0,25_

Falled at bottom l_a.Ro mark

Fal]ed

Increase stress range

Failed

Increase stress ranRe

Fal led

Failed ]/8" above top £augc

mark

Failed

Fal]ed Just above top gauge

mark

Fal]ed

Decrease stress r_n_e

_creaae stress ran_e

Increase stress ranRe

Increase stremm ramRc

Increase stress range

Increase stre_s range

Failed

1321

1322

1325

1336

20 +120 0.85 20 6.75 x 106

30 +120 0.78 20 7.95 x 106

30 +120 0.78 20 12.29 x 106

40 +120 0.71 20 12.59 x 106

40 +120 0.71 20 369,700

38 +120 0.73 20 768,400

1326

1328

3329

60 60 0.33 20 159,400

60 60 0.33 20 141,700

44 60 0.46 20 25.45 x 106

40 60 0.50 20 27.18 x 106

44 60 0.46 20 32.60 x 106

45 60 0.45 20 41.25 x 106

46 60 0.45 20 44.83 x 106

47 60 0.44 20 48.13 x 106

48 60 0.43 20 48.87 x 106

aswltched to 20 llz after 1.2 x ]06 cycles.

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n::

Several Slight differences were observed between specimens with zero and

high mean stress. The specimen with high mean stress (test no. 1336) appeared to have cracks initiated at several sites, whereas the zero mean

stress test (test no. ]324) had a single crack origin. The high mean stress

specimen also had a rougher, more-textured fracture surface, which may be indicative of a higher crack propagation rate. It also contained several

"steps" on the fracture surface (Fig. 8). These steps were probably caused

either by the linking of two parallel cracks on the same type of octahedral

plane or by the intersection of cracks on nonparallel octabedral planes.

LEFM ANALYSIS

Since fracture in all cases initiated from one of the micropores which

often were elongated, and since the macroscopic stress strain response for

all the tests was essentially linear, LEFM analyses seemed appropriate.

However, one complicating factor was that PWA 1480 single crystals are anisotropic and consequently the crack did not grow in a pure mode I fashion

because crack growth was often crystallographic along {lll}-type planes

(Fig. II). This is in contrast to the usual experience [3] in testing

isotroplc polycrystalline materials in mlxed-mode fatigue, where the crack
!a

Table 3. SulmMry of Tests on PWA 1480 st 538°C (i000°F)

in Vacuum (I ksl = 6.895 MPa)

Test Stress, ksl Freq.,

R Cycles Remarks

No. Hz

Range Mean

1346 a 30 105 0.75 1 7 x 104 Increase frequency

30 0.75 i0 2.63 x 106 Increase stress range

32 0.74 12 3.68 x 106 Increase stress range

34 0.72 4.70 x 106 Increase stress range

36 0.71 5.75 x 106 Increase stress range

38 0.69 6.79 x 106 Increase stress range

40 0.68 7.21 x 106 Failed b

1347 40 105 0.68 6 2.52 x 106 Increase frequency

40 0.68 20 9.93 x 106 Increase stress range

42 0.67 14.64 x 106 Increase stress range

44 0.65 16.34 x 106 Increase stress range

46 0.64 18.03 x 106 Increase stress range

48 0.63 19.11 x 106 Failed

1350 50 105 0.62 20 0.65 x 106 Failed

1351 50 105 0.62 20 i.II x 106 Failed

1353 90 60 0.i_ 20 8.06 x 104 Failed

1354 58 60 0.35 20 6.04 x 105 Failed

1364 65 0 -I 20 9.36 x 105 Failed b

1383 66 0 -I 20 6.79 x 106 Increase stress range

68 0 -I 20 8.61 x 106 Increase stress range

70 0 -I 20 10.17 x 106 Increase stress range

72 0 -I 20 10.57 x 106 Felled b

1384 90 0 -I i0 6.10 x 105 Failed

aTh[s specimen had _ 0.004-1n. taper. All other specimens hild a O.010-1n.

taper.

hThe apeclmen failed In the thermocouple region.

|

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eventually turns and propagates in a pure mode I fashion. Assuming a 2-

dimensional edge crack of length a in a {lll}-type plane subjected to a uniaxial stress o in the [001] direction, it is easy to show that the modes I

and II stress intensity factors in an isotropic material are given by

and

KI = 1.12 x 2/3 o x [_a] 1⁄2 (i)

KII = 1.12 x 1/3 o x [_a] 1⁄2 (2)

The effective stress intensity factor for such a configuration is some function of K and KI which is not known for this single-crystal material. For

example, if the e_fective K is taken as
8

I

200 --

O

IOO --

90--

_ 8o

" 70

50

(/)

u_ 40--

n30-- (/)

20--

I0

10'4

Fig. 3.

I

"G I00

80 -

laJ

L9

z 60 -

_:

nu) 40-

&O

bJ

nI--

(n

20 -

I

10 4

Fig. 4.

I IIIIII I I I III111 I

PWA 1480

O

lED

A A

I I IIIII I I I I IIIII

I

SYMBOL MEAN STRESS

(ksi)

0 0

[] 6O

A 120

m

"-_TEST INTERRUPTED --

oo

B--- []_..

m

! I lllilll i , iililll i i iilii,l i I illili

l0 s 106 i07 i0e

CYCLES TO FAILURE

Summary of High-cycle Fatigue Tests of PWA 1480 (001) at

20°C (70QF) at Various Mean Stresses. I ksi = 6.895 MPa.

I i ,Jill I I I I lllll I I I I IIiil I I I I illll

MEAN STRESS

SYMBOL ( ksi )

[3 O

G_-

D

Z_ Z_

0 0

D 60

105 w

"----- TEST INTERRUPTED

0--.-

, ill,ill i , i illi,l I i l ili,ll

105 106 i07

CYCLES TO FAILURE

Summary of High-Cycle Fatigue Tests on PWA 1480 (001)

at 538°C (1000°F) at Various Mean Stresses.

m

m

-- 100

I I IIIIII

108

IO

700 a.

600 _;

500 w

400 z

<

300

(n

(n

200 '"r_

O3

Mil

i;i;i

711

_i!ii

E
MEAN STRESS (MPa)

200 400 600 800 I000

_ LI I I I I

,o. 0 20°C

.,

ul 10

1I:

0 20 40 60 80 I00 120 140

MEAN STRESS (ksi)

o

-- 300 _

UJ

C_

D

-- 200P

,.J

O.

<_

-- I00 _o

tlJ

I160

Fig. 5

Goodman Diagram

for PWA 1480

(001) at 20°C

(70°F) and at

538°C (1000°F).

KEF F = K 2I + KI I

then the crack driving force for the case in hand is

(3)

KEFF = 1.12 (---_3 o)[_a] 1⁄2 , (4)

which, considering that the crack is not really 2-dimensional but is of a

thumbnail type (modes I, II, and III), is sufficiently close to the expression

for a pure mode I crack under a stress o,

K I - 1.12o [_a] 1⁄2 . (5)

Because of simplicity and considering all the uncertainties involved, Eq' (5)

is used as the expression for K in the following analyses, bearing in mind

that the calculated stress intensity factors may be consistently off by some

unknown (possibly close to i) constant factor. The uncertainty in using

Eq. (5) caused by the anisotropy of the material needs to be resolved in the

future.

The fatigue crack growth rate, da/dN, is then assumed to follow a power

law equation,

EC[u(R)AK]n for AK > AKth

I

dN LO for AK < AKth

, (6)
lO

i

X

o

tJ_

ORIGINAL PAGE"IS

OF POOR QUALITY

"el 0

0

0

,el

m 4.1

O _

14.4

_-1 t.M

X _

m 0

r.4 4.1

0 .el

0 .el _

e_. _2u

4.1 0 r/l

[,-.4 .el ,._

o .el

._ CXl 14..i

_ul.4

,g

I

m

g

w

IN

-"iiiiiii

2
ORIGINAL PAQE IS

OF POOR QUALITY

li

_Z

,,-4
12

Fig. 8

Scanning Electron Micrograph

Shows a "Stepped" Fracture

Surface in a Specimen That

Was Cycled at a Stress Range

of 38 ksi (262 MPa) with Mean

StreSs of 120 ksi (827 MPa)

at 20°C (70°F).

AK = stress intensity factor range,

AKTH = threshold stress intensity factor range,

R = ratio of minimum to maximum stress in the cycle,

u(R) = a factor to account for mean stress effects.

The cycles to failure for a loading above the threshold regime can then

be simply obtained by integration,

Nf = / af da

a C[u(R)AK] n

O

, (7)

where a is the initial crack size (_40 _m) and af is the final crack size

(_2-3 m_°). Unfortunately, the material constants for this material at the

temperatures of interest (70 and IO00°F) are not available. Limited crack

growth data at 800°F are reported in Ref. i. However, these data were generated at much larger stress intensity values than are required for the present

analyses.

Therefore, instead of calculating life directly from Eq. (7), it was

decided to compute the necessary crack growth rate properties from the

limited smooth specimen data generated in this program using the following

assumptions:

i. Ignore crack initiation life.

2. Compute the coefficient C and exponent n in Eq. (6) from

fully reversed +tests at 70°F.

-:ii

_i!!i

F,,
13

O9

x

z

bJ

(.3

W

0..

U')

ORIGINAL PAGE IS

OF POOR QUALITY

"0

o,-I

o

.LJ

_0

c_

o

o o

_r_

o

o

CO

°_ eq

o

o

o _

_ °,.-I

o
14 ORIGINAL PAGE IS

OF POOR QUALITY

Fig. I0.

200 _m IO0 _m

Mlcrograph of a PWA 1480 Specimen Tested at 538°C (1000°F),

Showing Crack Initiation from a Cluster of Mlcropores.

iil

i!!

Fig. 11. Typical Crystallographic Fracture of PWA 1480 (001)

Due to High-Cycle Fatigue.
15

3. Assumethe exponent n to be independent of temperature and

R ratio.

4. Determine u(R) and AKTH(R) from correlation with the lives

at high mean stress t_ts.

5. Assume initial and final crack sizes to be 40 _m and 2 mm,

! respectively. The results are insensitive to the actual

: value of the final crack size.

A simple integration of Eq. (7) for cycling at a constant stress range

and R value gives (n # 2)

i l-n/2 l-n/2

a° - af

Nf .... • (8)

(n/2 - i) C[I.12_ Aou(R)] n

;

| A least-squares fit to the life data at R = -1 (fully reversed cycles) gives

i (Fig. 12)

Nf = 3.03 X 1019 Ao-5"04 (Ao in MPa) . (9)

iOOO _ i , , ,,,,iI l I i t,lllI I I i 1,1,1

"-" - 0 20°C

"_ _ A 538°C

"" .Nf = 5.05 x 1019 (AG)'5"04

,oo__

_ W -- W

M_ ¢Y ri-

! - ,o_

,o , I I lli,_l l I I Ill,t1 , J ll,,i,

,o4 ,o_ ,o6 ,o7

Nf

Fig. 12. Zero Mean Stress High-Cycle Fatigue Test Data

on PWA 1480.

]

7
16

A comparison of Eqs. (8) and (9) gives n = 5.04. Normalizing u(R) such that

u(0) = i, and comparing Eqs. (9) and (I0),

Nf 1.258 x 1019 (40 x 10-6) 1"52

= [A_u(R)]-5.04 (10)

ao

where a is the initial crack size in meters. A quick calculation shows that

Eq. (i0_ is approximately valid at IO00°F for R = 0 [u(O) = i]. Equation

(i0) can then be used to compute the values of u(R) as a function of R from

all the high-cycle fatigue tests run, and the results are shown in Fig. 13.

Note that although the function u(R) increases linearly with R value at

IO00°F, at 70°F it increases much more rapidly at positive R values.

Assuming that a = 40 x 10 -6 m, and noting Eqs. (8), and (I0), Eq. (6)

o

can be written as

da 10-15 ]5.04 d--_ffi7.94 x [AK u(R) for AK > gKth .

(ii)

where AKth is as yet to be determined.

1.8

1.6

_.4

=1

1.2

1.0

0.8

0.6

-I,2

I I I I I I I I I

m

O 20°C /_

i I ,,I I, l l I I i

-0.8 -0.4 O 0.4 08

R

Fig. 13

Variation of

the Mean Stress

Correction

Factor u(R) as

a Function of R

Ratio at 20°C

(70°F) and at

538°C (IO00°F).
17

_m

_7

[]

!

|

!

Block Loadin$:

Consider the case where the material is subjected to block loading,

i.e.,

Ao = Aoifor Ni cycles, i = 1,2, ... N (12)

where the cycles N I, N 2, N are applied sequentially. Assuming that

Eq. (6) is valid for each'bloc_ loading so that for the ith block, (assuming

AK i > AKth)

l-n/2

- ai-n/2_ C(n/2 - 1)[l.12_ Ao u(mi)] n Ni ai_ I =

(13)

Summing Eq. (13) for i = 1,2, ... N, it is easy to show that failure occurs

when the following linear damage rule is satisfied:

N N i

Z

i=l Nf i

: 1 (14)

where Nf i = the cycles to failure under constant loading corresponding to the

ith block. Of course, Eq. (14) is not applicable, in general, because of

threshold and crack growth retardation effects. However, in all applications

where the loading is never reduced from one block to the next and where

transient effects can be neglected, Eq. (14) will still be applicable provided the value of Nfi is set equal to infinity for blocks whose loadings

correspond to ranges of stress intensity factor Below the threshold value.

Threshold Stress Intensity Factor Range:

Since all the tests were conducted on nominally smooth specimens without

any macroscopic starter cracks, it was impossible to distinguish between an

endurance limit for crack initiation from a true threshold effect for crack

propagation. Such a distinction can only be made by conducting interrupted

tests and examining the specimens for cracks. In the absence of such detailed

information, it is assumed that crack initiation at the tip of the largest

porosity is always possible and that the tests involving runouts were truly

indicative of threshold effects. A determination of the threshold stress

intensity factor range can be attempted from an analysis of the block load

tests tabulated in Tables 2 and 3. Threshold stress intensity factor of PWA

1480 for the present purposes will be defined as the stress intensity factor

range below which the exponent in Eq. (ii) is significantly above 5.04 so

that a straightforward application of Eq. (14) grossly underestimates the

lives. Of course, the calculated threshold stress intensity factor range

will depend on the size of the initiating micropore. However, since cracks

initiated from micropores in size of the order of 40 _m in most cases where

the specimens were examined, it was assumed that the initiated crack size

in all specimens is 40 _m. The error involved in such an assumption can be

estimated from the square root dependency of the calculated threshold stress

intensity factor range on the initial crack size. Figure 14 shows the estimated ranges of threshold stress intensity factor as a function of R ratio at
18

4 --

3 --

2 --

4 --

3 --

2

I

0

v

3E

h5

I 1

T

I 1

538°C

I I I I

0.2 0.4 0.6 0,8

R

T 20"C

l

\

I I I J

0.2 0.4 0.6 0.8 1.0

R

Fig. 14

Variation of the Threshold

Stress Intensity Factor

Range with R Ratio at 20°C

(70°F) and 538°C (1000°F).

70°F and at 1000°F. Data are too scarce to unambiguously determine the variation of threshold values with R. Dashed lines (independent of temperature)

are included as possible variations of threshold stress intensity factor

range with R ratio that are consistent with the calculated ranges. It

appears that the threshold stress intensity factor range is relatively

independent of R ratio up to about 0.6, beyond which it drops off rapidly

with increasing R. Also, within the accuracy of the present calculations

there appears to be no significant effect of temperature on threshold at

positive R values between 70 and 1000°F. However, at R = -i the threshold

stress intensity factor is greater at i000°F than at 70°F.

=!!

DISCUSSION

The calculated cycles to failure on the basis of crack growth (ignoring

crack initiation) are compared with experimentally observed cycles to failure

for all the tests (including block load tests) in Fig. 15. For block load

tests, observed and calculated cycles include only those blocks for which a

nonzero crack growth is predicted. Otherwise the comparison would be much

more favorable on a total cycles basis. Note that the correlation is equal

to or better than a factor of two in most cases. This, of course, does not

prove that crack initiation life is negligible in this material. To prove

that will require a lot more metallographic work using interrupted tests.

The purpose of this exercise is to show that a credible analysis of the data

can be made using LEFM.
=

i

|

|

i

19

iO e

iO 7 l

E

J

tL

12)

tu_ 106

I.d

..J

(J,

>-

(.)

0

IJJ

I--

<z iO5

J

¢J

U

10 4

---T I I

0 20°C SINGLE BLOCK LOADING

• 20°C MULTIPLE BLOCK LOADING

,_ 538°C SINGLE BLOCK LOADING

• 538°C MULTIPLE BLOCK LOADING --

A0 __

___ I I

104 10 ``5 106

OBSERVED CYCLES TO FAILURE

107

Fig. 15

Comparison of Calculated

Versus Observed Cycles to

Failure.

A comparison between the crack growth rates deduced from the present

exercise and the limited crack growth data reported in Ref. I is shown in

Fig. 16. The excellent agreement both in slope and magnitude may be fortuitous for two reasons. First, there is some uncertainty in the calculations

of stress intensity factors in the present study as discussed earlier.

Second, the crack growth data reported in Ref. i are for large cracks growing

in the [010] direction in a pure mode I fashion, whereas the cracks in the

present study are much shorter and grow principally along {lll} type planes

in a mixed-mode fashion. However, the limited data in Ref. i showed that

crystallographic effects on the crack growth rates are not very large.

Finally, the test data [i] shown in Fig. 16 were obtained from crack growth

tests conducted in air at 800°F whereas the tests in the present studies were

conducted in vacuum at 1000°F. However, the environmental effects at these

temperatures are not expected to be very large. In spite of these reservations, it is evident that the limited crack growth rate data and the derived

crack growth rates in the present study are quite consistent in the moderate

AK regime, which enhances the credibility of using LEFM to correlate the

present life data.

The calculated effects of R ratio on the crack growth rates at 70°F in

air and at I000°F in vacuum are shown in Figs. 17 and 18, respectively.

Crack growth rate at any &K value increases with increasing positive R ratio,

with the increase being somewhat larger at 70°F than at 1000°F. The calculated effects of temperature on the threshold stress intensity factor range

at positive R values is minimal. However, the threshold stress intensity

factor range decreases rapidly with increasing R ratio beyond a value of

R = 0.6. The effects of R ratio on crack growth rates and on threshold

stress intensity factor range are in agreement with similar behavior for

other material [4]. Although the calculated data are broadly in agreement

with the experimental data reported in Ref. i, there are some significant
iO-_ _

io-6 _

,o-_ _

iO-8 _

E

_1z Io.9 _

oo-,O_

l£)-oa _

,o-,2 _

iO-a3

20

,--1I--"1 "T-'r'T__"T I1 I I I

R ,0.1,

,/_ _" 538"C (VACUUM

_ZO_ (AIR)

X DATA AT 4Z?*C --

, ll,,l I I I I llinl

I0 IOO

Fig. 16

Comparison of Derived Crack

Growth Rates at 20°C (70°F)

and at 538°C (1000°F) with

Experimentally Observed

Crack Growth Rate at 427°C

(800°F) in PWA 1480 (001).

Flg. 17

Variation of the Derlved

Crack Growth Rate with R

Ratio at 20°C (70°F).
21

E

v

i0 -II

538"C ,20 Hz

R:

R=0.4

R

X DATA R= 0,IAT 427aC

Fig. 18

Variation of the Derived

Crack Growth Rate with R

Ratio at 538°C (IO00°F).

differences between the two. In contrast to the calculated results, the experimental data show a slight increase in crack growth rate from R = 0.I to

R = -i. However, the experiments were conducted at a higher temperature

1400°F (760°C). Also, the experimental threshold stress intensity factor at

1800°F (982°C) at R = 0.i and at a frequency of 0.167 Hz is of the order of

i0 MPa_m, which is significantly higher than the estimated value of 4 MPa_m

at 20 Hz at 1000°F in the present study. The reason for these differences

was not established. It is suspected that the large difference in crack size

is partially responsible.

It is interesting to speculate on the improvement of the fatigue life of

PWA 1480 achieveable by controlling the size of the microporosities. First,

it should be remembered that the tail end (at the large size) of the size

distribution of the mlcroporosities rather than their average size will control fatigue life. Thus, if the distribution at the tail end can be improved

such that the maximum size of the porosity is reduced significantly below the

existing 40 _m, significant improvement in high-cycle fatigue properties may

be expected. This is shown in Fig. 19 by means of an example where the maximum size of the porosity is reduced successively from 40 to I0 pm. Note

that, although life is extended even at the low-cycle end, the major benefit

to be derived from reducing the maximum size of the porosity is at the highcycle end.
22

hi

CO

Z

n"

(/3

(n

bJ

I--

(n

I000

I00

20°C

a o • IO/_rn_

,,,_o .a 0 • 20#rrl

/o o • 40/zm -_

u

I0_

i I I llllll I , I 1111111 I I I11111

I0 4 I0 5 I0 6 107 I0 8

CYCLES TO FAILURE

¢1

(3.

I000 --"

LI,J

(.9

Z

n."

(,0

(;3

_ IO0 L,J

-- I--

- (,0

I0

10 9

Fig. 19. Possible Improvements in the High-Cycle Fatigue Properties

of PWA 1480 (001) by Controlling the Largest Size Porosity

to Three Different Values.

CONCLUSIONS

i. High mean stress high-cycle fatigue tests on smooth single-crystal

PWA 1480 specimens (001 axis) were carried out. The results show that the

material is quite resistant to mean stress effects at 70°F (room temperature)

in air and less so at IO00°F in vacuum.

2. The stress-straln response In all the tests was linear elastic, and

no significant cycle-dependent creep was observed in any of the high mean

stress tests. The material displayed very little strain hardening at 70°F,

but significant strain hardening was evident at 1000°F,

3. Metallographic studies on failed specimens showed cracks to be nucleated from microporosities of size of the order of 40 pm.

4. Crack propagation occurs crystallographically along {lll}-type

planes in a combined mode I and II fashion.

5. LEFM analyses, ignoring crack initiation llfe, were used to derive

crack growth rates for the material. When extrapolated to moderate AK

regime, the computed crack growth rates compare quite favorably with limited

data available for this material.

6. The computed crack growth rate at a given AK decreases as the temperature increases from 70°F to IO00°F and increases with increasing R ratio,

the increase being more pronounced at 70°F than at IO00°F.
23

7. The computedcrack growth also showsa threshold behavior which is

independent of temperature between 70 and 1000°F at positive R values. The

threshold stress intensity factor range (AKTH)is relatively independent of R

ratio up to a value of R = 0.6, beyond whicN it drops rapidly with increasing

R. The computedAKTHat R = 0.I is significantly smaller than the experimentally observed v_Iue, which implies that AKTHmaybe dependent on crack

size.

8. Significant improvement in fatigue strength, particularly at the

high-cycle end, is theoretically possible by controlling the maximumsize of

the porosities.

ACKNOWLEDGMENTS

The authors would like to thank Professor S. Antlovich and Mr. W.

Mulligan of Georgia Institute of Technology for providing Figs. l, 6, 8,

and i0.

lJ

1

.

.

REFERENCES

D. P. DeLuca and B. A. Cowles, Fatigue and Fracture of Advanced Blade

Materials, Final Report for Period I, August 1982 through August 31, 1984,

Materials Laboratory, Air Force Wright Aeronautical Laboratories Report

ASD-86-0051 (AFSC) (February 1985).

D. M. Moon and G. P. Sabol, "Effect of Mean Stress on the High-cycle

Fatigue Behavior of Udimet 710 at ]000°F, '' in Fatigue at Elevated

Temperatures, ASTM STP 520, American Society for Testing and Materials,

pp. 438-450 (1973).

R. Badaliance, "Mixed Mode Fatigue Crack Propagation," in Mixed Mode

Crack Propagation, Ed. G. C. Sih and P. S. Theocarls, Sijthoff and

Noordhoff, pp. 77-98 (1981).

C. Amzallag, P. Rabbe, C. Bathias, D. Benoit, and M. Truchon, "Influence

of Various Parameters on the Determination of the Fatigue Crack Arrest

Threshold," in Fatigue Crack Growth Measurement and Data Analysis,

ASTM STP 738, American Society for Testing and Materials, pp. 29-44

(1981).

I. RO_XW1No. [2. (3H)_q_men! Acce_NiIG_n No. 3. Ra¢lplenCe CaUlkH_ No.

NASA/CR- 175057 I

4. TIt_ _ _IIM

Effects of a High Mean Stress on the High

Cycle Fatique Life of PWA 1480 and

Correlation of Data by Linear Elastic Fracture

Mechanics

7. Aulhor[s)

S. Majumdar and R. Kwasny

9. Pedonnlng _LzJt_4_ N4m_ =m_ _k_r_Qs

Argonne 9700 SouthNational Cass Avenue Laboratory i} '_. "_ 9

Argonne, Illinois 60439

12. Spormo_r_ _ NmnwD lu_ A(k_'e.

NASA Lewis Research Center

C]eveTand, Ohio

eL_ _a

November 1985

6. Pw/on_lng Oq_in_lofl CQde

& _or_ o_mmw,_ mw_ No.

ANL-85- 74

10. W(_W Unit No.

11. Contmcl or Grant No.

Interagency Order

No. C-91113-D

13. Type of Re.w1 m_l Pwlod Covered

14. 81)o_lw_'lng Aoancy Code

15. $uppllmentk"y Notes

16, Al_trac t

See At.tached

17. Key WOrdS (Suggested by Author(s))

18. _=Id_tl_ 8Mlemenl

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