Fatigue crack growth behavior of Al7050T7451 attachment lugs under flight spectrum variation
ABSTRACT This paper discusses an analytical and experimental investigations of the fatigue crack growth behavior in attachment lugs subjected to a randomized flightbyflight spectrum. In the analysis, the stress intensity factors for throughthethickness cracks initiating from lug holes were compared by weight function method, boundary element method (BEM), the interpolation of Brussat’s solution. The stress intensity factors of a corner crack at a transition region were obtained using two parameter weight function method and correction factors. Fatigue life under a load spectrum was predicted using stress intensity factors and Willenborg retardation model considering the effects of a tensile overload. Experiments were performed under a load spectrum and compared with the fatigue life prediction using the stress intensity factors by different methods. Changes of fatigue life and aspect ratio according to the clipping level of the spectrum were discussed through experiment and prediction. Effect of the spectrum clipping level on the fatigue life was experimentally evaluated by using beach marks of fractured surface.

Article: FATIGUE CRACK GROWTH IN LUGS
[Show abstract] [Hide abstract]
ABSTRACT: Abstract— Crack growth in aluminium alloy lugs was recorded during constantamplitude loading (R= 1/3). Observations were made both for artificial cracks started by a small saw cut and natural cracks started by fretting corrosion between hole and pin. Scatter was low for artificial cracks, whereas considerable scatter applied to the natural cracks as a result of multiple crack initiation at different times and locations. The fastest crack growth was observed for artificial cracks, which appear to be a worst case as compared to natural cracks. Kvalues derived from crack growth results were in good agreement with Kvalues proposed in the literature.Fatigue & Fracture of Engineering Materials & Structures 02/1979; 1(2):185  201. · 0.86 Impact Factor  Engineering Fracture Mechanics  ENG FRACTURE MECH. 01/1969; 1(3):565568.
 [Show abstract] [Hide abstract]
ABSTRACT: The finite element analysis of crack problems often incorporates the asymptotic character of the local solution into the formulation. Embedment of stress or strain singularities can impose serious restrictions on the outcome and inconsistencies in predicting crack and/or growth. These restrictions are discussed in connection with the problem of two diametrically opposite corner cracks near a circular hole subjected to remote uniform tension. Enforced in the numerical treatment is the 1/r character of the strain energy density function local to the corner crack border where r is the radial distance measured from the crack front. The tendency for the corner crack to become a through crack is predicted by assuming that each point of the crack border extends by an amount proportional to the strain energy density factor. The path would correspond to the loci of minimum strain energy density function. Numerical results are displayed graphically and discussed in connection with crack initiation and nonselfsimilar crack growth.Theoretical and Applied Fracture Mechanics  THEOR APPL FRACT MECH. 01/1990; 13(1):6980.
Page 1
Fatigue crack growth behavior of Al7050T7451
attachment lugs under flight spectrum variation
JongHo Kima, SoonBok Leeb,*, SeongGu Hongb
aForce Measurement and Evaluation Lab., Korea Research Institute of Standards and Science (KRISS),
Daejeon 305701, South Korea
bDepartment of Mechanical Engineering, Korea Advanced Institute of Science and Technology,
3731 Kusongdong, Yusonggu, Daejeon 305701, South Korea
Abstract
This paper discusses an analytical and experimental investigations of the fatigue crack growth behavior in attach
ment lugs subjected to a randomized flightbyflight spectrum. In the analysis, the stress intensity factors for through
thethickness cracks initiating from lug holes were compared by weight function method, boundary element method
(BEM), the interpolation of Brussat?s solution. The stress intensity factors of a corner crack at a transition region were
obtained using two parameter weight function method and correction factors. Fatigue life under a load spectrum was
predicted using stress intensity factors and Willenborg retardation model considering the effects of a tensile overload.
Experiments were performed under a load spectrum and compared with the fatigue life prediction using the stress
intensity factors by different methods. Changes of fatigue life and aspect ratio according to the clipping level of the
spectrum were discussed through experiment and prediction. Effect of the spectrum clipping level on the fatigue life was
experimentally evaluated by using beach marks of fractured surface.
? 2003 Elsevier Ltd. All rights reserved.
Keywords: Attachment lug; Load spectrum; Clipping levels; Corner crack; Stress intensity factor; Retardation model; Beach mark
1. Introduction
Attachment lugs are commonly used for aircraft
structural applications as a connection between
components of the structure. In a lugtype joint the
lug is connected to a fork by a single bolt or pin.
Generally the structures which have the difficulty
in applying the failsafe design need the damage
tolerance design. Advantages of lugs follow: the
joint allows an easy mounting and dismounting;
and since clamping of the fork is not applied, the
lug can act as a pivot without local bending mo
ments. However, flaws or cracks can nucleate in
attachment lugs due to corrosion, stress corrosion
cracking, fretting, tool marks, material defects,
and fatigue. The presence of such flaws or cracks
raise the stresses and strains considerably in the
vicinity of these imperfections, which increases the
possibility of abrupt failure or reduces the lug?s
*Corresponding author. Tel.: +82428693029; fax: +8242
8693210.
Email address: sblee@kaist.ac.kr (S.B. Lee).
01678442/$  see front matter ? 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S01678442(03)000417
Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
www.elsevier.com/locate/tafmec
Page 2
operating life. Attachment lugs are particularly
critical components in crack initiation and growth
because of their inherently high stress concentra
tion levels near the lug hole. For these reasons, it
is important to develop analytical as well as expe
rimental procedures for assessing and designing
damage tolerant attachment lugs to ensure the
operational safety of aircraft. Over the years, sev
eral extensive studies [1,2] have been made on lug
fatigue performance, involving both experimental
and analytical means. Cold working and the use of
interferencefit bushings were suggested as the
methods providing potential benefit for practical
application [3].
In the study of fatigue crack growth and fracture
behavior of attachment lugs, an accurate calcula
tion of the stress intensity factor is essential. Over
the years several methods have evolved to compute
the stress intensity factors for structural compo
nents containing cracks. These methods include
analytical as well as experimental approach. The
experimental backtracking approach was used to
derive empirically the stress intensity factors for
structural components using the growth rate data
of throughthethickness cracks for simple geome
try subjected to constantamplitude loading [4]. A
simple compounding method of superposition of
known solutions has been applied to lugs [5]. Most
of the researches mentioned above are applicable
to throughthethickness cracks. However at initial
stage of fatigue life a corner crack occurs in lugs,
which is the threedimensional crack of a finite
body, therefore the studies mentioned above have
been extremely limited. Meanwhile, the stress in
tensity factor of corner cracks near circular hole
was evaluated using the strain energy density
function based on the finite element method [6].
Additionally the stress intensity factor of through
thethickness crack at elastic–plastic finite thick
ness plate was also calculated by threedimensional
finite element method [7]. However it is not easy to
use the threedimensional finite element method to
predict the fatigue life of the corner crack at at
tachment lugs, especially under spectrum loading
condition. The finite element method can be ap
plied easily to the propagation of the crack under
constant amplitude loading condition, but it is
difficult to use under random loading conditiondue
to the complexity of modeling the retardation
behavior of the crack (crack closure effect sug
gested by Elber), which can be introduced by over
loadings. Therefore, instead of using the strain
energy density function based on the finite element
method, the approximate stress intensity factor
equation [8,9] is used to predict the fatigue life of
the corner crack at attachment lugs.
Increasing the magnitude or the frequency of
the highest peaks in the repetitive spectrum load
ing produces significant retardation effects in crack
propagation, because high positive loads introduce
large plastic deformations at the crack tip. How
ever, negative high loads are not so efficient in
destroying the positive effects of tensile overloads,
so that in all the balance is in favor of the retar
dation effects. In order to predict the fatigue life
under spectrum loading, Willenborg retardation
model is used due to its relative simplicity [10]. To
evaluate the effects of stress intensity factors on the
crack growth, the predictions of fatigue crack
growth were performed using some stress intensity
factors. The application of very high loads in a
fullscale fatigue test should be avoided, because
they introduce beneficial retardation effects on
crack growth and moreover aircraft will not en
counter such high loads in its operative life. The
effects of clipping high loads on the fatigue crack
growth were also evaluated through tests and
compared with the predictions.
2. Experiment
In order to predict fatigue crack growth in at
tachment lugs under a load spectrum, the basic
crack growth rate was obtained for the 7050–
T7451 aluminum alloy, the attachment lug mate
rial. Fig. 1 shows the basic crack growth rate ob
tained using the centercracked tension (CCT)
specimens. The CCT specimen is 70 mm wide, 10
mm thick and in a L=T orientation. The initial
artificial through crack in the specimen was made
by means of a hole of 12 mm in diameter and a
starter saw cut. In experiments the stress ratios R
of )0.2, 0.0, 0.3 are used. Fig. 2(a) shows one test
block of load spectrum taken from a fighter spec
trum of a training aircraft. The stress sequence has
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J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
Page 3
been analyzed by the rainflow cycle counting
method. Fig. 2(b) shows the result of load ranges
as a function of the number of occurrences.
Fig. 3(a) shows the specimen tested. The lug
specimen has a hole of 26 mm diameter (2Ri) with
35 mm outer radius (Ro) and 10 mm thick (B). The
beryllium copper bushing in both the lug and pin
was installed with a very mild 0.1 mm diametrical
interference which, coupled with its relative thin
ness and low stiffness, produced no appreciable
residual stress. The steel was installed with a very
slight clearance providing a ‘‘near fit’’. Small slots
were introduced for precrack development in the
lugs perpendicular to the load line using an elec
trical discharge machine (EDM). These slots were
approximately 1 mm radius quartercircle.
Fatigue tests of simple attachment lug with
initial corner crack are conducted at 7 Hz and
compared with analytical predictions. The total
fatigue life of lug was defined from initial flaw to
a final fracture. The crack growth in the surface
crack was monitored by crack propagation gage
KV25B. The growth of depth crack was obtained
later by measuring the failure surfaces produced
with the marker cycle loads. The beach marks were
made by applying constantamplitude loading
with stress ratio of 0.85 while keeping the maxi
mum stress level constant [11]. The fracture tough
ness KC necessary to prediction of fatigue life is
40 MPa [12].
Fig. 1. Basic crack growth rate of A17050T7451 under con
stant amplitude loading.
Fig. 2. Fighter load spectrum: (a) load history; (b) load am
plitude obtained by rainflow cycle counting.
Fig. 3. Specimen geometry: (a) an attachment lug with a corner
crack; (b) corner crack in a transitional region. Dimensions in
mm.
J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
137
Page 4
3. Analysis of stress intensity factors
A corner crack in a lug is more difficult to ana
lyze than a throughthethickness crack because
it has both surface length c and bore depth a as
shown in Fig. 3(a). In a rigorous analysis, it should
be assumed that the crack grows with different
growth rates at all points along the periphery of
the crack front. In the present analysis, it is as
sumed that the crack front shape is a quarter
ellipse and, thus, only the points of intersection of
the crack front with the lug surface and the hole
wall need to be considered. The method of calcu
lating the stress intensity factors for a corner crack
in a lug is as follows.
3.1. Stress intensity factor of a corner crack
The calculation of stress intensity factor at
threedimensional corner crack as shown in Fig.
3(a) is not simple. To calculate the stress intensity
factor, the following equations using two para
metersweightfunctionapproximationisapplied[8].
KðAÞ
I
¼ r0
ffiffiffiffiffi
ffiffiffiffiffi
pc
p
aTð0Þ
ffiffiffiffiffi
?
An
p
c
Ri
MðAÞ
I
Fffiffiffiffi
Iffiffiffiffi
Q
p MB
ð1Þ
KðCÞ
I
¼ r0
pc
p
aT
?
ffiffiffiffiffi
An
p
MðCÞ
p
Q
ð2Þ
where
An? Min
?
where KThru is the stress intensity factor of crack
length c at throughthethickness crack.
a
c;1:0
??
and
r0¼
P
2RoB
aT
c
Ri
?
¼
KThru
r0
ffiffiffiffiffi
pc
p
ð3Þ
Q ¼ 1:0 þ 1:464ðAnCnÞ1:65
where
c
a;1:0
ð4Þ
Cn? Min
??
MðAÞ
I
¼ ½1:0 þ 0:025Cnþ 0:0965ð1:0 ? AnÞ?
ffiffiffiffiffi
Cn
p
ð5Þ
MðCÞ
I
¼ ½1:0 þ 0:214Cn? 0:0925ð1:0 ? AnÞ?
ffiffiffiffiffi
An
p
ð6Þ
F ¼ 1:0 ? 2:09S þ 9:635S2? 23:37S3þ 25:485S4
?10:403S5
where
c
c þ Ri
1:0
1:0 þ
B
ð7Þ
S ¼
MB¼
a > c
a6c
a
??ð1:8þAnÞð0:92 ? 0:82AnÞ
(
ð8Þ
It is assumed that for a given number of applied
load cycles, the extension of the quarterelliptical
crack border is controlled by the stress intensity
factors at two points, namely, the intersections of
the crack periphery with both the hole wall and the
lug surface. In general, the stress intensity factors
at these two locations are different, resulting in
different crack growth rates. Therefore, the aspect
ratio of the new flaw shape after each crack growth
increment differs from the preceding one. The as
pect ratio of the new flaw shape is computed using
the new crack lengths at both the hole wall and lug
surface. The preceding process can be repeated
until the crack depth a becomes equal to the lug
thickness. Then the crack breaks through the back
side of the lug and finally becomes a throughthe
thickness crack after a transitional crack growth
period.
3.2. Stress intensity factor of a transitional crack
When a corner crack grows through the thick
ness, the remaining net section is usually small in
comparison to the front crack size. Therefore, a
proper transitional crack growth criterion is nee
ded for the transition period from when the crack
penetrates the back surface until the crack lengths
are essentially equal on the front and back sur
faces. Fig. 3(b) shows the transitional crack ge
ometry, in which cFand cBare crack lengths on the
front and back surfaces, respectively. A stress in
tensity magnitude factor for the crack tip at the
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J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
Page 5
back surface of a surface crack was proposed as
Eq. (9) [9];
"
bt¼
1
f1 ?
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 ? c2
B=c2
F
p
g
#1=2
for cB> 0
ð9Þ
It should be noted that when the back side crack
length equals the front side crack length, the
magnification is unity and the throughthethick
ness crack has achieved a uniform front. The above
magnification factor is used to calculate the stress
intensity factor at the back surface of the transi
tional crack using the equation
?
Assuming an imaginary crack length along the
hole wall direction, a0, instead of a, the stress in
tensity factor at the front crack is calculated using
Eq. (2) as
?
The imaginary crack length a0can be deter
mined by fitting the elliptical equation through
points C and D as
(
cF
KB¼ r0
ffiffiffiffiffiffiffiffi
pcB
p
aT
cB
Ri
?
bt
ð10Þ
KðCÞ
I
¼ r0
ffiffiffiffiffiffiffiffi
pcF
p
aT
cF
Ri
?
ffiffiffiffiffi
An
p
MðCÞ
Iffiffiffiffi
Q
p
ð11Þ
a0¼ B 1
?
cB
??2)1=2
ð12Þ
3.3. Stress intensity factor of a throughthethick
ness crack
After the transitional crack becomes a through
thethickness crack with a uniform front, the stress
intensity factors are calculated as following equa
tion.
?
As mentioned above, the stress intensity factors
for a growing corner crack depend on aTdefined in
Eq. (3), i.e., the stress intensity factor of a through
thethickness crack KThruand front crack c. In this
paper the stress intensity factor of a through
thethickness crack is obtained using following
methods.
KD¼ KC¼ r0
ffiffiffiffiffi
pc
p
aT
c
Ri
?
ð13Þ
4. Calculation of stress intensity factor of a through
thethickness crack
4.1. Weight function method
First of all, Bueckner?s weight function is
adopted to calculate the stress intensity factor,
KThruusing the following equation [13]
mðx;cÞ ¼H
2K
oc
where H equals E for plane stress and E=ð1 ? m2Þ
for plane strain, K is the stress intensity factor, and
uðx;cÞ is the crack opening displacement at x for a
throughthethickness crack of lengthc. The weight
function was shown to be unique under a given
structural geometry and crack size regardless of
the stresses acting on the product of this function
[13,14], and the stress distribution along the crack
boundary gives the stress intensity factor as fol
lowing,
Z
where pðxÞ is the stress distribution that would
exist along the crack boundary if the crack were
not there. Since the weight function is independent
of the loading condition, it can be determined for
one condition and then utilized to obtain the stress
intensity factor for another. The present develop
ment of the weight function for a hole utilizes the
exact weight function derived by Bueckner for an
edge crack in a semiinfinite plate. These functions
are modified by a geometry correction factor to
obtain the desired result. The final equation for an
approximate weight function for a hole is
ouðx;cÞ
ð14Þ
K ¼
c
pðxÞmðx;cÞdx
ð15Þ
mðx;cÞ ¼ mecU1U2U3
ð16Þ
mec¼ ðc ? xÞ?1=21
?
þ 0:6147 1
?x
c
?
ffiffiffiffiffiffiffiffi
?x
c
?
þ 0:2502 1
?
?2?
ð
2=p
p
Þð17Þ
U1, U2and U3are given in the Appendix A. The
term mecis Bueckner?s weight function for an edge
crack in a semiinfinite plate, and x is measured
from the edge of the plate toward the crack tip.
The analytical technique described above provides
J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
139
Page 6
a method of computing the stress intensity factor
for cracks in holes for any loading condition. The
additional information required for this analysis is
the lug stress distribution that would exist along
the crack boundary if the crack were not there.
Fig. 4 shows the stress distribution based on a two
dimensional boundary element solution for a pin
loaded lug with the geometry of the specimen. The
throughthethickness variation in stress is con
sidered to be small due to the relatively large dia
meter of the lug hole compared to its thickness.
The steel near fit pin was also modeled for the
boundary element analysis to produce the correct
pin bearing pressure on the inside surface of the
lug hole. This result shows the elastic gross section
stress concentration factor is about five, which is
compared to about three for a fastener hole with
zero bearing load. The stress intensity factor is
then obtained by inserting this stress distribution
into Eq. (15).
4.2. Comparison of the stress intensity factors
Contact pressure distributions of the unflawed
cases have been assumed to remain unchanged
even though a crack develops in most numerical
analyses including weight function method of
throughthethickness cracks emerging from lug
holes. Some researcher [15] confirmed the large
effect of the contact pressure distribution on the
stress intensity factor and demonstrated its de
pendence on crack length. To verify these phe
nomena, the crack in the lug was modeled with
boundary element program BEASY [16] consid
ering the contact between lug and pin. The stress
intensity factors were obtained using boundary
element method (BEM). Fig. 5(a) reveals that the
mode II stress intensity factor occurs due to the
geometry of the outer radius of lug but it is about
one tenth of the mode I stress intensity factor in
magnitude. This mode II stress intensity factor
causes a crack to propagate slantly, especially at
the lug of a small gap between lug and pin.
Fig. 5(b) shows the comparison of the stress
intensity factors obtained using BEM, Weight
function method and Brussat?s result. The Brus
sat?s result was obtained using the interpolation
from the established results for a simple geometry
[9]. The stress intensity factors among BEM and
interpolation method of the established Brussat?s
result are somewhat similar but have some differ
ence as the crack propagates. The weight function
Fig. 4. Elastic stress distribution in a loaded lug obtained by
BEM.
Fig. 5. Stress intensity factors of the throughthethickness
crack in a lug: (a) mode I and II stress intensity factors obtained
by BEM; (b) mode I stress intensity factors obtained by BEM,
weight function and Brussat?s result.
140
J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
Page 7
method among the three results showed the largest
value. Fig. 6 presents the stress intensity factors
ratio Ka=Kcof the corner crack for aspect ratio a=c
of 1.0, 1.5, and 2.0, using Eqs. (1) and (2) and the
stress intensity factor of the throughthethickness
crack obtained by BEM. These results indicate
that as aspect ratio a=c becomes larger, change of
the ratio Ka=Kcbecomes smaller.
5. Retardation model
A computer program was developed to predict
crack growth under a load spectrum such as shown
in Fig. 2(a). This program utilized these stress in
tensity factor solution and the approximate curve
fitting function for a crack growth rate shown in
Fig. 1. In the analysis, the corner crack aspect ratio
a=c is not held constant but is allowed to vary
as the crack grows. After the crack depth reaches
the back surface, the transition behavior is also
included. To evaluate the retardation of crack
growth under random loading, a simple Willen
borg?s model was adopted [10].
Assume that ap is sum of the crack length at
which the overload occurred and the overload
plastic zone size, while the crack length ai at ith
loading cycle exists within plastic zone caused by
overload. The stress intensity factor Kreq
related to the distance of ap? aias follows.
1
ap
rYS
maxcan be
Kreq
max
??2
¼ ap? ai
ð18Þ
where a ¼ 2 for plane stress, a ¼ 6 for plane strain
and rYSis yield stress of material.
The compressive stress intensity factor Kcomp
due to the elastic body surrounding the overload is
the difference between the maximum stress inten
sity factor occurring at the ith cycle Ki
stress intensity factor Kreq
max,
Kreq
maxand the
max? Ki
Therefore, the actual effective stress intensity
factor range DKeffand the effective stress ratio Reff
become as following equations.
max¼ Kcomp
ð19Þ
Keff
Keff
max¼ Ki
min¼ Ki
max? Kcomp
min? Kcomp
ð20Þ
DKeff¼ Keff
Reff¼Keff
max? Keff
min¼ Ki
max? Ki
min
ð21Þ
min
Keff
max
ð22Þ
Both DKeff and Reff can be determined and then
da=dN can be calculated from the following For
man equation based on effective values.
CðDKeffÞm
ð1 ? ReffÞKC? DKeff
where C and m are empirical fatigue material con
stants and KCis the applicable fracture toughness
for the material.
da
dN¼
ð23Þ
6. Results and discussion
6.1. Clipping effects on the fatigue life
One of the most controversial basic problems
in spectrum loading is the choice of peak load
clipping level. It was revealed that the choice of
clipping level is particularly acute for the testing
of thingauge damage tolerant materials because
tensile peak loads cause large and persistent de
creases in fatigue crack growth rates [17]. Another
important decision about the spectrum concerns
the minimum load range to be included in the full
scale test. Cyclic frequency in tests cannot be
higher than a few cycles in a second owing to the
large displacements of real structures. It is there
fore of great economical importance to reduce
Fig. 6. Normalized stress intensity factors of corner cracks on
the aspect ratio a=c, 1.0, 1.5 and 2.0.
J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
141
Page 8
testing time by excluding the very numerous small
cycles, which do not contribute significantly to
fatigue damage. The only retardation evaluations
caused by high loads were performed, since the
load spectrum in Fig. 2 does not contain numerous
small cycles. The threshold stress intensity factor,
DKth, was not considered, since all load spectrum
have an influence effect on the crack growth rate. If
the maximum load among original loads spectrum
in Fig. 2(b) is defined as clipping 100%, then the
clipping 90% means that the higher loads than 90%
of the original maximum load were clipped. Clip
ping 80% is similarly defined. The maximum load
among spectrums of clipping 100% is 21 kN which
corresponds to 80.7 MPa of bearing stress.
The fractured surfaces on clipping levels shown
in Fig. 7 were obtained by applying the marker
cycle load per 100 times of one flight spectrum. It
is found that as the clipping level becomes lower,
the distance between beach mark becomes wider.
However the distance between beach mark of clip
ping 90% is larger than that of clipping 80%. This
result shows that clipping 80% has the fatigue life
larger than clipping 90%.
Fig. 8 shows the aspect ratios a=c on the clip
ping levels measured from fractured surface and
the stress intensity factor ratios Ka=Kc obtained
using aspect ratios. The aspect ratios regardless of
clipping levels increase as the cracks grow. On the
other hand, the stress intensity factor ratios Ka=Kc
obtained using aspect ratios is approximately 1.0
regardless clipping levels. This result means that
the stress intensity factors of each direction a, c
under growth of the corner crack have approxi
mately same value. The fretting caused by contact
between pin and lug as shown in Fig. 7 made the
depth crack a propagate fast. Artificial initial
corner crack causes the aspect ratios a=c to have
some difference at the beginning of crack growth.
Because the aspect ratios a=c have an approximate
fitting function regardless of clipping levels, the
prediction of fatigue life was conducted using only
one variable c not two variables a, c. It was re
vealed that the aspect ratios depend on the geo
metry of attachment lug and scatters in aspect
ratios under constant amplitude loading can be
reduced considerably by increasing the ratio of
outer radius over inner radius [18].
Fig. 9(a) represents the results of surface crack
length versus block by the experiment and predic
tion on the clipping 100% using the stress intensity
factor obtained by BEM, weight function method
and interpolation of Brussat?s result. The fitting
function of the aspect ratio a=c measured from the
experiment is used for fatigue crack growth. The
Fig. 8. Aspect ratios a=c and normalized stress intensity factor
ratios Ka=Kc obtained using the measured aspect ratios on
clipping levels.
Fig. 7. Fractured surfaces on clipping level: (a) clipping 100%; (b) clipping 90%; (c) clipping 80%.
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J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
Page 9
surface crack length prediction using BEM and
Brussat?s result were similar to the experiment,
while the prediction using weight function method
had the shortest life. This reason is due to the
shortcoming of weight function method performed
on the condition that the load distribution transfer
between the pins and lug is exactly during the crack
propagates. From the extensive investigations of
lug problems [19,20], however, it has been shown
that the load transfer between the bushing and hole
of lug change significantly when a crack increases.
The change of the load transfer occurs because
bushing exerts increasingly higher pressure on the
mouth of the crack with increase of the crack size.
Thus, the reduction of the stress intensity factor
finally causes the corner crack to propagate slowly.
Fig. 9(b) shows the results of surface crack
length versus block by the experiment and predic
tion on the clipping 100%, 90% and 80% using
BEM?s stress intensity factor for an attachment lug.
Similar to the result of beach marks mentioned
above, results of clipping 100%, 80% show that the
retardation effect decreases with increase of the
clipped cycles. However, the fatigue life of clipping
90% has shorter fatigue life than clipping 80% as
shown in Fig. 7. This means that if clipping level is
lower than clipping 90%, the fatigue life is in
creased by cutting off the amplitudes inducing fa
tigue crack growth among load spectrum. It is
recommended that the basic fatigue crack growth
rate at several stress ratios is required to predict the
more exact fatigue life, since the Willenborg model
considers only stress ratio effect of cycle loads.
7. Conclusions
Predictions and experimental investigations for
fatigue life of an attachment lug under random
spectrum were performed. From this investigation
followings are concluded.
1. Fretting caused by contact between bushing
and pin makes the depth crack a propagate fast
and finally decrease the fatigue life of an attach
ment lug.
2. Regardless of clipping levels, aspect ratio a=c
measured from the fractured surface has an ap
proximately same value and the corresponding
stress intensity factor ratios Ka=Kc was almost
1.0.
3. The fatigue crack growth prediction by stress
intensity factor obtained using both BEM and
Brussat?s result except weight function method
was similar to experiments relatively.
4. The fatigue life of an attachment lug decreases
as clipping level increases, because the clipping
of high load cycles reduces the retardation ef
fect.
Acknowledgements
This work has been supported partly by CARE
(Computer Aided Reliability Evaluation) National
Research Laboratory in KAIST.
Fig. 9. Comparison of the fatigue life: (a) fatigue life on clip
ping 100% obtained using BEM, weight function method and
Brussat?s result; (b) BEM?s fatigue life on clipping 100%, 90%
and 80%.
J.H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144
143
Page 10
Appendix A
The terms U1, U2and U3are used to adjust the
weight function for single crack to finite width
effects. They are given by the following equations,
where c is the crack length and R is the hole radius
and W is the width of a plate specimen.
c
R
c
R
c
R
U1¼ 1 ? 0:6449
??
þ 0:8964
c
R
c
R
c
R
??2
?4
?6
? 0:7327
?
?
?3
?5
þ 0:3335
?
?
? 0:0781
þ 0:0073
ðA:1Þ
U2¼ 1
ðA:2Þ
?
?
ðA:3Þ
U3¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2R
W
2
sec
2Rþc
W ?c
?
??
?
p
? ?
p
?
sec
?
?
sin
?
2Rþc
W ?c
?
??
2c
W
2c
W
?
??
2Rþc
W ?c
?
? ?
???
v
u
u
u
u
t
u
The geometry correction factor U1was obtained
as the ratio of the stress intensity for a crack em
anating from one side of a hole in an infinite plate
to the stress intensity for an edge crack in a semi
infinite plate. The term U2 was derived using an
assumption that the crack or cracks and hole can
be represented by a single effective throughthe
thickness crack equal in length to the diameter of
the hole plus the length of the crack. The term U3
was determined using finite width correction fac
tors and the effective throughthethickness crack
length as just defined [21].
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