NASA
Technical
Memorandum
81942
(NASA-Ta-819U2)
PREDICTION
OP
FATIGUE-CRACK
Ndl-
19480
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VABlABLEAiIPLlTUDE
AND
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USING
A
CLOSURE
MODLi
(NASA)
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PREDICTION OF FATIGUE-CRACK GROWTH
UNDER VARIABLE-AMPLITUDE AND SPECTRUM
LOADLNS
USING
A
CLOSURE MODEL
Janua
rv
1981
Langley
Research
Center
!idr-rlp:
-
,v
'r;,,>,4
36t35
PREDICTION OF FATIGUE-CRACK GROWTH
mDER
VARIABLE-AMPLITUDE
AND
SPECTRUM
LOADING
USING
A
CLOSURE
MOOEL
J.
C.
Newman,
Jr.
NASA
iangley
Research
Center
Hampton, Virginia
23665
ABSTRACT
The present paper
is
concerned wtth the application of an existing
analytic~l criack-closure model to study crack growth under varisus load his-
tories.
The model was based
cr.
a concept
like
the D~gdale mod~l, but modified
to
leave
plastically-deformed material in the wake of the advanciag crack tip.
The
model was used to correlate crack-growth rates under constant-amplitude
loading,
and to pr.adi;t crack growth under variable-amplitdde and aircraft-
spec
trua Loading on 2219-T851
aluminum
alloy sheet material. The predicted
crack-growth lives agreed well
with experimental data. For
80
crack-growth
tests
subjected
to
various load histories, the ratio of predicted-to-experimental
lives
(Np!NT)
ranged from
0.5
to
1.8.
The
mean value
of
Np/NT
was
0.97
and
the standard deviation Gas
0.27.
SYMBOLS
material crack-growth constants
(k
-
1.5)
half-length of crack,
m
half-length of final crack,
m
half-length of initial crack, m
half-length
of
starter notch,
m
half-length
of
crack plus tensile plastic zone,
m
b~undary-correction factor on stress intensity
maximum stress-intensity factor,
MPa
-
m
112
elastic-plasttc fracture toughness,
Wa
-
m
1/2
frdcture toughness parameter
number of cycles
number of crack-growth
delay cycles
number of cycles predicted from analysis
number
of
cycles from test specimen
stress ratio
(Smin/Snaxj
applied stress,
MPa
maximum applied stress, MPa
minimum applied stress,
M?a
crack-opening stress, MPa
specimen thickness, m
specimen width,
rn
corstraint factor,
n
=
1
for
plane stress
.jnd
cx
-
3
for plane strain
stress-intensitv factor range,
?Pa
-
m1-I2
effective stress-intensity
factor
range,
MFa
-
m 1/2
%
effectiw threshold atrees-int-ity factor range, WPa
-
m
1/2
&th thre~hold atrere-inturoity factor
r.nga,
MPa
-
m
1/
2
ASeff effective stress range,
HPa
P
length of te~ile plastic rone,
m
P~~
plastic-zone &ire calculated from overload,
m
f
I'
;
OO
flow streas (average between Uys and
uU),
MPa
.
r
1
u
YS
yield stress
(0.2
percent offset), MPa
a,
ultimate tensile strength,
MPa
u
length of compressive plastic zone,
m
INTRODUCTION
Fatigue cracks remain closed during part
of
the load cycle under fatigue
loading.
The crack-closure concept has been used to correlate crack-growth
rates under constant-amplitude loading
[1,2] and is a significant factor in
causing load-interaction effects on crack-growth rates
(retardation and
acceleration) under
variable-amplitude loading.
Fatigue-crack closure is
caused by residual plastic deformations remaining in the wake of an advancing
crack.
The crack-closure
pt~enomenon has been analyzed using two-dimensional,
elastic-plastic, finite-element methods
[3-61.
The finite-element analyses
were shown to be quite accurate, but were very complicated and required large
computing facilities.
There
have elso been several attempts to develop simple
analytical models of crack closure
[3,7-121.
All of these trjdels were based on
a
cdncept similar to the Dugdale mdel
[13] or strip-yield model, but modified
to leave plastically-deformed material in the wake of the crack.
Newman
131,
Budisnsky and Hutchinson
[a],
and ~Liir1.n~ and Seager [10,11] studied only the
crack-closure behavior.
But,
Dill and Saff
[7],
Mrdrath, Neua~en, Elber and
Poe
[9],
and Newman [12]
used
the crack-opening stresses
from
the
models to
predict crack growth under
spectrur loading.
The purpose of the present paper is to apply
an
existing
analytical crack-
closure model
[12],
which simulates rlane-strees and plane-strain conditions,
to crack growth under various load histories.
The
model was based on the
Dugdale model [13], but modified to leave plastically-deformed material along
the crack surfaces as the crack advances.
Plane-stress and plane-strain condi-
tions
vere simulated by using a "constraint" factor on tensile yielding.
The crack-closure model, developed in reference
12,
was for
a
central
crack in a finite-width plate that was subjected to a uniformly applied stress.
To calculate Elber's effective stress-intensity factor range
[2], crack-opening
stresses were calculated from the model under constant-amplitude loading at
various applied stress levels and stress ratios.
Experimental crack-growth rate
data from 2219-T851 aluminum alloy sheet material under constant-amplitude
loading
[14] were correlated with the effective stress-intensity factor range
for a wide range of stress levels and stress ratios.
An
equation relating
crack-growth rate to effective stress-inteusity factor range, threshold
stress-
intensity factor range, and fracture toughness, developed in reference 12, was
applied herein over the total range of crack-growth rates.
The closure model
was then used to predict crack growth in 2219-T851 aluminum alloy sheet
material under variable-amplitude and aircraft-spectrum loading
1141.
ANALYTICAL
CRACK-CLOSURE
MODEL
The following section is a brief description of the analytical crack-
closure model developed in reference
12.
