crack growth analyses

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CRACK GROWTH ANALYSIS IN AIRCRAFT WING LUG SECTION

AND FATIGUE LIFE ESTIMATIONK.Mookaiya1, S.R.Balakrishnan2

PG scholar 1 , Director/H.O.D2

1, 2, Department of Aeronautical Engineering, Nehru institute of engineering and technolog1 [email protected]

Abstract

A computational model for estimating the residual

fatigue life of attachment lugs is proposed. !n strength

analsis, the lug "ith single #uarter$elliptical corner

crac% as "ell as "ith single through the thic%ness crac%is e&amined. 'tress intensit factor, as an important

parameter for fatigue life estimation, is determined (

appling analtical and numerical methods. )he model

is *erified using e&perimental fatigue crac% gro"th

data. Predictions of fatigue crac% propagation

(eha*iours are in a good agreement "ith analtical

o(ser*ations.

Keywords — Notched 'tructural +omponents, Analtic '!

of lugs, inite elements , Crack growth.

1. Introdct!onSurface and through-thickness cracks

frequently initiate and grow at notches, holes

in structural comonents. Such cracks are

resent during a large ercentage of the useful

life of these comonents. !he lug tye "oint

consists of two or three arts connected with

only one fastener. #n the lug tye "oint, the

com$ination of high concentration and fretting

could otentially lead to aearance of the

crack initiation, and then crack growth under

cyclic loading. %atigue, as a comle& rocess,could $e so dangerous and e'en to cause

failure of lug, i.e. comonents that are

connected $y lug tye "oint. (ue to re'ious

reasons it is 'ery imortant to assess, analyse

and)or redict the crack initiation and crack

growth $eha'iour of lugs.

#n general, when analysing crack growth

hase, the most often it is ossi$le to identify

corner cracks, as well as through-the-thickness

crack in the lugs. %rom the engineering oint

of 'iew corner crack are usually aro&imated $y quarter-ellitical crack. %or relia$le

rediction of crack growth rates and fracture

strengths of attachment lugs accurate stress

analysis is needed.

!hese tools include *omuter +ided (esign

*+(, %inite lement Modelling %M and+nsys Structural +nalysis. *omuter can $e

used to redict fatigue crack growth and

residual strength in aircraft structures. !hey

can also $e useful to determine in ser'ice

insection inter'als, time-to-onset of

widesread fatigue damage and to design and

certify structural reairs. !he aim of this work

is to in'estigate the strength $eha'iour of an

imortant aircraft notched structural elements

such as cracked lugs and ri'eted skin.

". #robab!$!st!c %&&%cts !n crac' (ro)t*Bent looks at how to include random effects in a risk

analysis of fatigue failure. + study $y /ang looks at

crack roagation in fastener holes of aircraft structuresand in a centre cracked anel with $oth su$"ected to

random sectrum loading. /ang models the crack

roagation rate as a lognormal rocess using0 #ngeneral, to accurately assess fatigue growth of quarter-

ellitical corner crack in the lug it is necessary to

analyse fatigue growth $eha'iour at the oint ofma&imum crack deth and at the oint of surface crack

interaction with the surface. (ue to re'ious reason, thecrack roagation rocess can $e descri$ed $y two

couled equations for crack growth rate as follows0

here *+ and *B are material constantse&erimentally o$tained, K+, KB, Kma&+, Kma&B

are the ranges and ma&imum 'alues of stress intensityfactor at the deth + and surface B oints, resecti'ely.

%inal num$er of loading cycles for the lug with cornercrack can $e estimated for $oth directions if e&ressions

for crack growth rate are integrated for deth direction0

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and for surface direction0

Since relationshis for stress intensity factors are

comle& functions, numerical simulations ha'e to $e erformed to comute fatigue life of attachment lugs u

to failure f 3. Stress intensity factoror $othdirections.

3. Str%ss !nt%ns!t+ &actor#n general geometry of notched structural

comonents and loading is too comle& for the stress

intensity factor S#% to $e sol'ed analytically. !he S#%

calculation is further comlicated $ecause it is afunction of the osition along the crack front, crack si4e

and shae, tye loading and geometry of the structure.#n this work analytic and %M were used to erform

linear fracture mechanics analysis of the in-lugassem$ly. +nalytic results are o$tained using relations

deri'ed in this aer. 5ood agreement $etween finiteelement and analytic results is o$tained. #t is 'ery

imortant $ecause we can to use analytic deri'ede&ressions in crack growth analyses. 6ugs are essential

comonents of an aircraft for which roof of damagetolerance has to $e undertaken. Since the literature does

not contain the stress intensity solution for lugs which

are required for roof of damage tolerance, the ro$lem osed in the following in'estigation are0 selection of asuita$le method of determining of the S#%,

determination of S#% as a function of crack length for'arious form of lug and setting u a comlete formula

for calculation of the S#% for lug, allowing essential

arameters. !he stress intensity factors are the key

arameters to estimate the characteristic of the crackedstructure. Based on the stress intensity factors, fatigue

crack growth and structural life redictions ha'e $eenin'estigated. !he lug dimensions are defined in %ig. 1.

%#57R 10 5eometry and loading of lugs

!he stress analysis can $e considered $y alyinganalytical and numerical aroaches. !he resent

authors tackled $oth aroaches for stress intensity

factor e'aluation of the attachment lugs. +s the in-

loaded lug with single quarter-ellitical corner crack8%ig.19 is in'estigated.

#n addition to the in-loaded lug with the quarter-ellitical corner crack, the resent authors tackle the lug

with single through-the-thickness crack %ig.1. (ue to re'ious reason, the e&ression for the stress intensity

factor in the case of lug with single quarter-elliticalcorner crack is reduced.

%urthermore, a numerical aroach is emloyed forthe stress analysis $y alying the finite element

method. #n the ackage +:S/S, quarter-oint ;-<

singular finite elements are used to simulate the through-the-thickness crack growth in attachment lugs.

,. N-%r!ca$ R%s$ts!o illustrate comutation model for crack growth

analysis of attachment lugs with one quarter-ellitical

corner crack emanating from the hole or through-the-thickness crack, a few numerical e&amles are resented

in this Section. !hese e&amles e&amine stress analysisas well as fatigue life estimation. #n order to 'erify the

'alidation of resented model for crack growthsimulation o$tained results are comared with

e&erimental data.

,.1 Str%ss ana$+s!s o& an attac*-%nt $(#n this e&amle, stress intensity factor calculation

of the lug with single through-the-thickness crack was

carried out. !he lug made of =>=? !=3?1 +luminium+lloy was su$"ected $y cyclic loading with constant

amlitude a ma&imum force <ma&@ A3=1A : and stressratio R @ >.1. 5eometry characteristics of the lug with

single through-the-thickness crack are0 w @ 3.3 mm, (@ C> mm, t @ 1? mm, $> @ ?.33 mm the lug :o.A.

Material characteristics are as follows0 Du@ C32 M<a,D>.2@ 33C M<a.

#n addition to analytical aroach for stressintensity factor e'aluation, numerical aroach $ased on

finite element method is introduced in this aer. !he

lug with single through-the-thickness crack is tackled ascontact ro$lem. %or this urose singular si&-node

finite elements 81?9 are used. +ctually, ste-$y-ste, foreach increment of crack length different meshes aremodelled $y using suer-elements around crack ti.



%#57R 20 5eometry of cracked lug

%#57R 3. %inite lement Model of cracked lug

with stress distri$ution!he ste-$y-ste rocedure is reeated until the

comuted crack growth is 'ery close to the final failureof the attachment lug. + reresentation of the finite

%#57R 3.1. %inite lement Model of cracked lug withstress distri$ution

lement analysis for the lug with single through-the- icthickness crack $ @ ?.33 mm is resented in %ig.2 and

%ig.3. Moreo'er, for the same geometry of lug the stressintensity factor is calculated $y alying analytical

aroach (ifferences $etween analytical and numerical%M aroaches are resented in !a$le 1. 6ug multi crack comression

6ug

multicrack

Stress a Stain !otal

deformationa

6ug 1st

crack 2.=CA?e=ma&

E.>C2e?min

>.>>>3A3ma&

1.2=3Ae-Amin

1.2=2e-?ma&

> min

6ug 2

nd

crack 2.=>1e=ma&

1.133e?

>.>>>3E1?Ama&

1.AAAAe-A

1.E3e-?ma&

> min

min min

6ug 3rd

crack

3.C=2?e=

ma&=?3A min

>.>>>CE>

ma&1.>A1?e-A

min

2.131e-?

ma&> min

6ug Cth

crack

3.?2??e=

ma&=>2?? min

>.>>>CEA??

ma&E.E?1e-=

min

2.1E=e-?

ma&> min

!a$le C. lug multi crack comression.

C.1 S!RSSS-6#% *7RFS, S-:

%ig C S-: cur'e in aluminium alloy.

S-: *ur'es o$tained under torsion or $ending load-control test conditions often do not ha'e data at the

shorter fatigue li'es say 1>3or 1>Ccycles and less due

to significant lastic deformation.

!orsion and $ending stress equations

and D@M/)# can only $e used for nominal elastic

$eha'iour. !he num$er of cycles to form this smallcrack in smooth un notched or notched fatigue

secimens and comonents can range from a few recent to almost the entire life, as illustrated

schematically. !he fatigue limit has historically $een a rime consideration for long-life fatigue design.



%ig C.1 S-: cur'e in %atigue crack growth.Rotating Bending %atigue 6imits or %atigue

Strengths Based on 1>*ycles for +luminium +lloys.*ast wrought

%ig C.2 Rotating fatigue strength in aluminium alloy.

!here is a tendency to generali4e that Sf increases

linearly with Su. !hese figures show this is incorrect anddata $ands tend to $end o'er at the higher ultimate

strengths.

,." Constant A-$!td% Load!n(

!hese load histories are tyical of those found in

real-life engineering situations. %atigue from 'aria$leamlitude loading in'ol'ing histories such as these is

discussed. *onstant amlitude loading is introduced inthis aer.

!o o$tain material fatigue $eha'iour)roerties for usein fatigue design, Some real-life load histories can

occasionally $e modelled as essentially constant

amlitude.

%ig C.2.1 *onstant amlitude load in aluminium alloy.

%ig C.3 *onstant amlitude load in fully re'ersed inaluminium alloy.

R@-1 and R@>

Stresses can $e relaced with load, moment,

torque strain, deflection, or stress intensity

factors. %atigue loading calculation.

/. Conc$s!ons !he aer resents a comutational model for the

crack growth analysis of the attachment lug with single

quarter-ellitical crack as well as with single through-

the-thickness crack. !he roosed model e&amines thestress analysis, the fatigue life estimation and the crack

ath simulation. #n the stress analysis, $oth analyticalaroaches are emloyed to determine the stress

intensity factor. #n the finite element analyses areconducted using the ackages +:S/S and quarter-oint

;-< finite elements are emloyed to simulate the stressfield around the crack ti.

0. R%&%r%nc%s819 Katarina Maksimo'ic 2>>E. G%atigue *rack

5rowth +nalysis of (amaged Structural *omonents.

Scientific !echnical Re'iew, Fol.6#H, :o.1, 2>>E.

829 Marko +nttila, 2>>. %atigue 6ife stimation

If +n +ircraft 7sed #n +ir$orne 5eohysical

Sur'eying. soo, January E, 2>>

839 Katarina Maksimo'ic, Fera :ikolic, Ste'an

Maksimo'ic 2>>C. fficient *omutation Method #n

%atigue 6ife stimation If (amaged Structural



*omonents0 Mechanics, +utomatic *ontrol and

Ro$otics Fol.C, :o 1A, 2>>C, . 1>1 11C

8C9 S. Maksimo'ic, L. Bur4ic, K. Maksimo'ic .J.

2>>C. %atigue 6ife stimation If :otched Structural

*omonents0 *omutation and &erimental

#n'estigations. F!#- +eronautical #nstitute, Katanie'a

1?, 11>>> Belgrade.

8?9 Slo$odanka Bol"ano'ic, Ste'an Maksimo'ic

+.N. 1EE. Strength +nalysis of +ttachment 6ugs under

*yclic 6oading. F!# +eronautical #nstitute, Ratka

Resano'ica, Belgrade, Ser$ia.

8A9 Katarina Maksimo'ic, Mir"ana (uric, Miodrag

Janko'ic, +.N. 2>11. %atigue 6ife stimation of

(amaged Structural *omonents 7nder 6oad Sectrum.

Fol.A1,:o.2,.1A-23

8=9 Jaa Schi"'e. %atigue (amage #n +ircraft

Structures, :ot anted, But !oleratedO (elft 7ni'ersityof !echnology, %aculty of +erosace ngineering

Kluy'erweg 1, 2A2E NS, !he :etherlands.

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