# Fatigue crack growth behavior of Al7050-T7451 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 flight-by-flight spectrum. In the analysis, the stress intensity factors for through-the-thickness 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.

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**ABSTRACT:**The treatment technics for substrate was researched and improved by experimentations, the technics and additive research of plating for forming ornamental and functional multicomponents alloy was carried out completely, the optimum technics of plating multi-components alloy was been found. The coatings made by optimum technics were excellent in corrosion-resistance, wear-resistance and oxidation-resistance, and also has a smooth, fine, shining surface. It was proved that phosphorus content in the coating is 8.4% by determinations, the coating is amorphous crystal. The properties of Ni-W-P coating were test, the result shown that the combination force between the substrate and the coating was very good, the properties of coating to resist corrosion and abrasion were much better than that of Ni-P alloy by the tests. And the coating was finery in ornamentally also.Physics Procedia. 01/2011; 18:251-255. - [Show abstract] [Hide abstract]

**ABSTRACT:**Many structures such as aircrafts, risers, and offshore pipelines that are in contact with fluids, become subjected to complex variable amplitude loading (VAL) stress-time histories during their service lives. As a result, the structural life assessment and damage-tolerant analyses of such structures are considered as two important design criteria. In this paper, a VAL stress-time history is used to study the fatigue life of 6061-T651 aluminum alloy, with focus on the retardation effect resulting from the applied peak tensile overload cycles (TOLCs). Various so-called “clipping” levels are tested, and the results are compared with those obtained through an analytical method, using the Willenborg retardation approach, in conjunction with the Walker fatigue crack growth model. The results would demonstrate the significant influence of the TOLC present within VAL scenarios on retarding the fatigue crack growth rate of the material. The study also investigates the influence of various clipping levels on the fatigue response of the material, also highlighting the limitations of the analytical approach in estimating the resulting crack growth rate. It is observed that the analytical method predicts a higher fatigue life for the material subjected to VAL, which is non-conservative for design purposes. Some suggestions are provided for fatigue life estimation of the material when subjected to VAL scenarios.Journal of Materials Engineering and Performance 07/2013; · 0.92 Impact Factor - SourceAvailable from: Bao Rui[Show abstract] [Hide abstract]

**ABSTRACT:**Tests with middle-crack tension (M(T)) specimens made of Al 2324-T39 and Al 7050-T7451 are conducted to investigate the influence of low load truncation level on fatigue crack growth. The six different truncated spectra are obtained by removing the small cycles of which amplitudes are less than the specified percentages of the maximum amplitude in the basic flight-by-flight loading spectrum and the remainder of the spectrum is untouched. The tests indicate that the mean level of fatigue crack growth life (FCGL) increases as the load truncation level is enhanced. Considering both the time saving and the influence on FCGL, there is an applicable choice (i.e. spectrum S2 or spectrum S3 in this investigation) for full scale fatigue test. The scatter of FCGL becomes much larger than that under the basic spectrum when the load truncation level is increased to a specified high level, mainly due to the occurrence of crack slanting and branching under the high level truncated loading spectra.Chinese Journal of Aeronautics - CHIN J AERONAUT. 01/2009; 22(4):401-406.

Page 1

Fatigue crack growth behavior of Al7050-T7451

attachment lugs under flight spectrum variation

Jong-Ho Kima, Soon-Bok Leeb,*, Seong-Gu Hongb

aForce Measurement and Evaluation Lab., Korea Research Institute of Standards and Science (KRISS),

Daejeon 305-701, South Korea

bDepartment of Mechanical Engineering, Korea Advanced Institute of Science and Technology,

373-1 Kusong-dong, Yusong-gu, Daejeon 305-701, 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 flight-by-flight spectrum. In the analysis, the stress intensity factors for through-

the-thickness 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 lug-type joint the

lug is connected to a fork by a single bolt or pin.

Generally the structures which have the difficulty

in applying the fail-safe 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.: +82-42-869-3029; fax: +82-42-

869-3210.

E-mail address: sblee@kaist.ac.kr (S.-B. Lee).

0167-8442/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0167-8442(03)00041-7

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

interference-fit 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 through-the-thickness cracks for simple geome-

try subjected to constant-amplitude 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 through-the-thickness cracks. However at initial

stage of fatigue life a corner crack occurs in lugs,

which is the three-dimensional 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-

the-thickness crack at elastic–plastic finite thick-

ness plate was also calculated by three-dimensional

finite element method [7]. However it is not easy to

use the three-dimensional 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

full-scale 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 center-cracked 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

136

J.-H. Kim et al. / Theoretical and Applied Fracture Mechanics 40 (2003) 135–144

Page 3

been analyzed by the rain-flow 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 pre-crack development in the

lugs perpendicular to the load line using an elec-

trical discharge machine (EDM). These slots were

approximately 1 mm radius quarter-circle.

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

KV-25B. 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 constant-amplitude 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 A17050-T7451 under con-

stant amplitude loading.

Fig. 2. Fighter load spectrum: (a) load history; (b) load am-

plitude obtained by rain-flow 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 through-the-thickness 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

three-dimensional 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 through-the-thickness 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 quarter-elliptical

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 through-the-

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

138

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 through-the-thick-

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 through-the-thick-

ness crack

After the transitional crack becomes a through-

the-thickness 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-

the-thickness crack KThruand front crack c. In this

paper the stress intensity factor of a through-

the-thickness 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-

the-thickness 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

through-the-thickness 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 semi-infinite 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 semi-infinite 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

through-the-thickness 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

through-the-thickness 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 through-the-thickness

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 through-the-thickness

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 thin-gauge 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%.

142

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 through-the-

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 through-the-thickness crack

length as just defined [21].

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