Fatigue Crack and Delamination Growth in Fibre Metal Laminates under Variable Amplitude Loading

Stellingen

behorende bij het proefschrift

Fatigue Crack and Delamination Growth

in

Fibre Metal Laminates

under Variable Amplitude Loading

Sharifullah Khan

Stellingen 1

In tegenstelling tot metalen profiteren vezelmetaallaminaten maar marginaal van de toepassing van

overbelastingen. [ dit proefschrift ]

In contrast to metals, Fibre Metal Laminates benefit only marginally from the application of

over-loads. [ this thesis ]

Stellingen 2

In vezelmetaallaminaten wordt de vorming van afschuiflippen verhinderd door vezeloverbrugging.

[ dit proefschrift ]

In Fibre Metal Laminates, shear-lip formation is prevented by fibre bridging. [ this thesis ]

Stellingen 3

Om een gelijkwaardige nauwkeurigheid in de voorspelling van vermoeingsscheurgroei te verkrijgen,

impliceert een toenemende materiaalcomplexiteit (van monlitisch metaal naar vezelmetaallaminaat)

niet een toenemende complexiteit van het model. [Dit proefschrift]

To achieve similar accuracy in predicting fatigue crack growth, increasing material complexity (from

monolithic metals to fibre metal laminates) does not imply increasing model complexity. [ this thesis ]

Stellingen 4

Belasting met variable amplitude benvloedt wel de vorm van de delaminatie, maar niet de

delami-natiegroei. [Dit proefschrift]

Variable amplitude loading affects the delamination shape but not the delamination growth.

[ this thesis ]

Stellingen 5

Om incidenten in een industrie te vermijden kunnen procedures worden gedefinieerd, maar alles komt

neer op de mens die de vereiste handeling uitvoert.

Procedures can be defined to avoid incidents in an industry but everything funnels down to the human

taking the required action.

Stellingen 6

In de olie en gas industrie is roestvast staal niet de optimale oplossing voor het aanpakken van

cor-rosieproblemen.

In oil & gas industry, stainless steel is not the optimum solution to tackle corrosion issues.

Stellingen 7

Een goed wetenschapper is een goed communicator.

Good scientist should be good communicator .

Stellingen 8

Een individu kan geen CO2-neutraliteit bereiken.

[Naar een toespraak van Michael Braungart bij de Shell Ecomarathon 2012, Rotterdam]

An individual cannot achieve carbon neutrality.

[After Michael Braungart speech at Shell Ecomarathon 2012, Rotterdam.]

Stellingen 9

De wetenschap zou sneller vooruitgang boeken als alle goed gedocumenteerde experimenten, die in

tegenspraak zijn met de geteste hypothese, gepubliceerd zouden worden.

Science would progress faster if all well-documented experiments that are in disagreement to tested

hypothesis are published.

Stellingen 10

Het geld dat een land uitgeeft aan onderwijs, onderzoek en ontwikkeling moet worden beschouwd als

een investering en niet als een kostenpost.

The money spent by a country on education, research, and development should be considered

invest-ment and not expenditure.

Deze stellingen worden opponeerbaar en verdedigbaar geacht en zijn als zodanig goedgekeurd

door de promotor, Prof. dr. ir. Rinze Benedictus.

These propositions are regarded as opposable and defendable, and have been approved as such

by the supervisor, Prof. dr. ir. Rinze Benedictus.

FATIGUE CRACK & DELAMINATION

GROWTH

IN

FIBRE METAL LAMINATES

FATIGUE CRACK & DELAMINATION

GROWTH

IN

FIBRE METAL LAMINATES

under Variable Amplitude Loading

Proefs hrift

terverkrijging van degraadvando tor

aan deTe hnis he Universiteit Delft,

opgezag van de Re tor Magni usProf.ir.K.C.A.M. Luyben,

voorzittervan hetCollege voorPromoties,

inhet openbaarteverdedigen opmaandag 7 januari2013om

10:00uur

door

Sharifullah KHAN

MasterofS ien ein Aeronauti al Engineering,



E oleNationaleSuperieure de l'Aeronautique etdel'Espa e,

Toulouse, Fran e

Prof.dr.ir.R.Benedi tus

CopromotorDr.ir.R.C.Alderliesten,

Samenstellingpromotie ommissie:

Re torMagni us voorzitter

Prof.dr.ir.R.Benedi tus Te hnis heUniversiteitDelft,promotor

Dr.ir.R.C.Alderliesten Te hnis heUniversiteitDelft, opromotor

Dr.-Ing.T.Beumler AirbusDeuts hlandGmbH

Prof.dr.ir.R.Marissen Te hnis heUniversiteitDelft

Prof.dr.ir.A.deBoer UniversityofTwente

Prof.dr.W.VanPaepegem GhentUniversity

Prof.dr.P.Horst Te hnis heUniversitatBrauns hweig

Prof.dr.Z.Gurdal Te hnis heUniversiteitDelft(reservelid)

Keywords: FibreMetalLaminates,VariableAmplitudeLoading,Fatigue

Cra kGrowth,DelaminationGrowth,Plasti Zone.

Copyright

2012bySharifullahKhan

Allrightsreserved. Nopartofthematerialprote tedbythis opyright

noti emaybereprodu edorutilizedinanyformorbyanymeans,

ele troni orme hani al,in ludingphoto opying,re ordingorbyany

informationstorageandretrievalsystem,withoutthepriorpermissionof

theauthor.

ISBN978-90-8891-555-0

The greatest weakness of most humans is their

hesitancy to tell others how much they love them

while they are alive

_{-Optimus Prime}

Dedicated to my Beloved Wife,

Contents

Contents

i

List of Figures

vii

List of Tables

xi

Nomenclature

xiii

1 INTRODUCTION

1

1.1 S ienti Resear hMotivation. . . 2

1.2 InitialResear hProblem&Framework . . . 3

1.3 Stru tureofthisDissertation . . . 4

Referen es . . . 5

2 FIBRE METAL LAMINATES

7 2.1 Nomen latureofFMLs . . . 9

2.2 PropertiesofFMLs. . . 9

2.3 Manufa turingPro ess . . . 10

2.4 PostStret hing . . . 11

2.6 FatigueinFibreMetalLaminates . . . 13

2.6.1 FatigueCra kPropagation . . . 13

2.6.2 Cra kBridgingandRestraintonCra kOpening . . . . 14

2.6.3 DelaminationattheInterfa e . . . 14

2.6.4 AdhesiveShearDeformation . . . 16

2.6.5 Ee tonFatiguePerforman eofFMLs . . . 18

2.7 VariableAmplitudeLoading . . . 18

2.8 FatigueCra kGrowthRetardationModel. . . 19

2.8.1 Formetals. . . 19

2.8.2 ForFMLs . . . 19

2.8.3 Cra k-TipPlasti ity . . . 20

2.8.4 TheIrwinApproa h. . . 21

2.8.5 Des riptionofWheelerYieldZoneModel . . . 22

2.8.6 ModiedWheeler Model. . . 24

2.8.7 Cra k losuremodels . . . 24

2.9 Summary . . . 29

Referen es . . . 30

3 DELAMINATION GROWTH

37 3.1 DelaminationGrowthRateCal ulations . . . 39

3.2 Experimental Program . . . 40

3.2.1 TestSpe imen. . . 40

3.2.2 TestEquipment&Pro edure . . . 41

3.2.3 TestMatrix . . . 42

3.3 Results&Dis ussion . . . 42

3.3.1 Blo kLoadSequen es . . . 42

3.3.2 FlightLoadSequen es . . . 46

3.3.3 DelaminationBehaviourofARALL&GLARE . . . 49

3.4 Summary . . . 57 Referen es . . . 58

4 DELAMINATION SHAPE

63 4.1 EXPERIMENTALPROGRAM . . . 66 4.1.1 Testspe imens . . . 66 4.1.2 TestMatrix . . . 66

4.1.3 TestEquipment&Pro edure . . . 68

4.1.4 MeasurementTe hnique-DigitalImageCorrelation . 69 4.2 RESULTS&DISCUSSION . . . 72

4.2.1 ObservedDelaminationShape . . . 72

4.2.2 Ee tofDelaminationShape. . . 77

4.3 Summary . . . 80

Referen es . . . 80

5 CRACK-TIP PLASTICITY

83 5.1 Plasti ZoneMeasurementTe hniques . . . 86

5.2 ExperimentalProgram . . . 88

5.2.1 TestMatrix . . . 88

5.2.2 TestEquipment&Pro edure . . . 88

5.3 Results&Dis ussion . . . 88

5.3.1 Shear-LipFormation&Topology . . . 93

Referen es . . . 97

6 PREDICTION MODEL

101 6.1 LinearDamageA umulation(LDA). . . 102

6.2 YieldZoneModel . . . 104

6.3 Cra kClosureModel . . . 104

6.4.2 TestEquipment&Pro edures . . . 107

6.5 ResultsandDis ussion . . . 109

6.5.1 Lineardamagea umulation . . . 109

6.5.2 YieldZoneModel . . . 112

6.5.3 Cra kClosureModel . . . 120

6.6 Summary . . . 122

Referen es . . . 123

7 PREDICTIONS:POST-STRETCHED LAMINATES

127 7.1 Mathemati alModelingofPost-Stret hing . . . 130

7.2 TestSpe i ations . . . 131

7.3 ResultsandDis ussion . . . 132

7.4 Summary . . . 137

Referen es . . . 138

8 CONCLUSION

141 8.1 PhenomenaunderVariableAmplitudeLoading. . . 142

8.1.1 Delaminationgrowth . . . 142

8.1.2 Delaminationshapes . . . 143

8.1.3 Cra k-tipplasti ity . . . 144

8.1.4 Shear-lipformation . . . 144

8.2 Predi tionModel. . . 145

8.2.1 LinearDamageA umulation . . . 145

8.2.2 ModiedYieldZoneModel . . . 145

8.2.3 Cra k- losuremodel . . . 145

8.3 FutureWork . . . 145

Appendices

B Post-Stretched Classical Laminate Theory

151

B.1 Cal ulationoftheResidualInternalStressDistribution . . . 157

B.1.1 Non-Stret hedFMLs . . . 157

B.1.2 FMLsStret hedinOnePrin ipleMaterialDire tion . 157 Referen es . . . 158

C Model Validation

159 C.1 ARALL . . . 159

C.1.1 TWISTandMiniTWIST . . . 159

C.1.2 EXPERIMENTALPROGRAM. . . 159

C.1.3 Results&Dis ussion . . . 161

C.2 HSS-GLARECra kgrowthresults . . . 163

Referen es . . . 163

D Plastic Zone and Delmination Shape Experiments

165 D.1 spe imen . . . 165 D.2 TestingSetup . . . 165 D.3 TestMatrix . . . 167

Summary

171

Samenvatting

175

Publications

181

Acknowledgments

185

List of Figures

1.1 Atypi alFibreMetal LaminateLay-up[8℄ . . . 2

2.1 Residualstressesinaluminiumlayers[15℄ . . . 10

2.2 Post-stret hingstressandstrain urve . . . 12

2.3 Cra kbridginganddelamination. . . 13

2.4 Cra kopeningdispla ement[22℄ . . . 15

2.5 S hemati of ra kgrowthretardation[24℄ . . . 17

2.6 Classi ationofFatigue ra kgrowthretardationmodels . 19 2.7 S hemati stressdistributionatthe ra k-tip . . . 20

2.8 Relativesizesofplasti zonesintheYieldZoneModels.[56℄ 23 2.9 Plasti Zone . . . 24

2.10 The ra kopeningstresslevela ordingtodierentrelations 26 2.11 Ahump reatedbyanoverloadand attenedbyanunderload 27 3.1 Illustrationoftypi aldelaminationandCCTspe imens[21℄ 38 3.2 Earlyfailureofinta tmetallayers . . . 40

3.3 Testingsetup . . . 41

3.4 Delaminationgrowthtests-blo kloading . . . 44

3.6 DeburredmetallayersandTe ontapelo ation. . . 46

3.7 Delaminationgrowthtests-Periodi spe tra. . . 46

3.8 Delaminationgrowthtests-Programedspe tra . . . 47

3.9 Delaminationgrowthtestsresults-ARALLandGALRE . . . 48

3.10 Delaminationpaths. . . 49

3.11 Fatiguedelaminationsurfa einARALL[1℄ . . . 50

3.12 Delaminationsurfa eofbreside . . . 52

3.13 Illustrationofthebre/matrixadhesion . . . 53

3.14 Delaminationmarkings(striation) . . . 54

3.15 Delaminationmarkings-LO-HISpe trum . . . 55

3.16 Delaminationmarkings-Periodi spe trum . . . 56

3.17 Dis ontinuityobservedinDelaminationmarkings(striation). 57 4.1 DelaminationShapewithandwithoutoverload . . . 64

4.2 Illustrationofdelaminationextensionafterappli ationofOL 65 4.3 Postmortemspe imengeometry . . . 67

4.4 DelaminationshapeusingDIC. . . 70

4.5 Delaminationshape-postmortemspe imens . . . 71

4.6 Delaminationshape:Predi tedanda tual . . . 73

4.7 Delaminationgrowthtestresults-Postmortem . . . 74

4.8 Delaminationgrowthtestresults . . . 76

4.9 Ee tofdelaminationshape-postmortemspe imen . . . . 78

4.10 Ee tofdelaminationshape-newspe imens . . . 79

5.1 Cra kgrowth urves . . . 84

5.2 Planestress/strainformation . . . 85

5.3 DICoutputs-Monolithi metal . . . 89

5.4 DICoutputs-AluminiumLaminate . . . 90

5.5 DICoutputs-FMLs . . . 91

5.8 Shearlip-Monolithi metal . . . 95

5.9 Shearlip-Aluminiumlaminate . . . 96

5.10 Shearlip-FMLs . . . 97

5.11 Shearlip omparison . . . 98

6.1 FlowdiagramoftheLDA ra kgrowthpredi tionmodel . 103 6.2 FlowdiagramforthemodiedWheelermodel . . . 105

6.3 FlowdiagramfortheCra k losuremodel. . . 106

6.4 Correlation:Experimentandpredi tions-SingleOL . . . 110

6.5 Correlation:Experimentandpredi tions-MultipleOLs . . . 111

6.6 Correlation:Experimentandpredi tions-LO-HI . . . 113

6.7 Correlation:Experimentandpredi tions-HI-LO . . . 114

6.8 Correlation:Experimentandpredi tions-Spe trumI . . . . 117

6.9 Correlation:Experimentandpredi tions-Spe trumII . . . . 118

6.10 Correlation:Experimentandpredi tion-Spe trumIII . . . . 119

6.11 Thereasonofmismat hfor omplexspe tra . . . 120

7.1 ResidualstressesinthealuminiumandbrelayersofARALL 128 7.2 Ee tofpost-stret hinglevelonthe ra kgrowth[2℄ . . . 129

7.3 Fatigue ra kgrowthofstret hedandun-stret hed [3℄ . . 130

7.4 Flowdiagramforthe ra kgrowthpredi tionmodel . . . . 131

7.5 Testspe imendimensions . . . 132

7.6 Correlation:GLARE1-3/2,GLARE1-3/2-150MPa,0.05. . . 134

7.6 Correlation:GLARE1-5/4-150MPa,0.05 . . . 135

7.7 Correlation:GLARE1-3/2,GLARE1-3/2-120MPa,0.05. . . 136

7.7 Correlation:GLARE1-4/3,GLARE1-5/4-120MPa,0.05. . . 137

A.1 The hangeofstresslevelsafterdelamination . . . 147

B.1 Positiverotationofprin ipalmaterialaxes . . . 153

C.2 Spe imengeometry. . . 160

C.3 Testandpredi tion omparisonforARALL . . . 162

C.4 Delaminationshapes . . . 163

C.5 Correlation: ExperimentalandYieldZoneModelpredi tion 164

D.1 DICspe imengeometry . . . 166

List of Tables

2.1 IdentiedadvantagesofvariousbresforFMLs . . . 8

2.2 Commer iallyavailablebremetallaminates. . . 8

2.3 Me hani alpropertiesofMetalandPrepreg[16℄ . . . 11

3.1 Delaminationtestmatrix . . . 43

3.2 Possible ausesofdierentdelaminationbehaviour . . . 51

4.1 Postmortemspe imentestmatrix. . . 68

5.1 Plasti zonesizemeasurementte hniques . . . 87

5.2 Plasti zonemeasurement . . . 94

6.1 Fatigue ra kgrowthtestmatrix . . . 108

7.1 GLARE1testmatrixforvalidationof al ulations . . . 133

B.1 MaterialProperties[1℄ . . . 152

C.1 TWIST ight-simulationloadspe trum ightsdetail[1℄ . . . 160

C.2 TestMatrix . . . 161

D.2 Monolithi metalspe imentestmatrix . . . 169

Nomenclature

da

dN

Cra kgrowthrate mm/ y le

db

dN

Delaminationgrowthrate mm/ y le

A

i j

Extensionalstinessmatrixofalaminate

-b

Delaminationlength mm

B

i j

Couplingstinessmatrixofalaminate

-C

d

, n

d

Paris onstantsfordelaminationgrowthrelation

-C

cg

, n

cg

Paris onstantsfor ra kgrowthrelation

-D

i j

Bendingstinessmatrixofalaminate

-E

Young'sModulus MPa

G

ShearModulus MPa

G

d

Strainenergyreleaserate MPamm

j

Numberofbre/metalinterfa es

-k

Surfa e urvatureofalaminate

-n

Numberoflayers

-N

i

Externalloada tingonthelaminate N

P

Externalloadperunitlength N/mm

-S

Ti

Deviatorstress MPa

T

Temperature

◦

_C

t

Materialthi kness mm

U

Elber's ra k losure oeÆ ient

-α

i

CoeÆ ientofthermalexpansion

C

−1

δ

Displa ement mm

γ

Shearstrain mm/mm

ν

Cra ktipopening mm

σ

Appliedstress MPa

σ

e

Ee tivestress(VonMises) MPa

σ

0

.2

Yieldstress MPa

θ

Anglefromthex-axistothe1-axis

◦

υ

Poisson'sratio

ε

i

,pl

Poststret hingstrain mm/mm

ε

Strain mm/mm

ε

0

.2

Plasti strain mm/mm

Indi es

∞

Far-eld

0

Middlesurfa eproperties

1

, 2, .., 6

Prin iplematerial oordinates

al

Aluminium

al

, P

Aluminiumlayer(Delaminated)

br

Bridging

cr

Cra kedmetalli layers

cure

As ured onditions

e f f

Ee tive

f

Fibre

f

, 0

0

◦

bresrelated

f

, 0, P

0

◦

delaminatedbres

f

, 90

90

◦

bresrelated

f

, 90, P

90

◦

delaminatedbres

f

, r

Fibre/Resin

k

k

th

layer

lam

Laminate(ARALL,GLARE)

max

Maximumvalue

mean

Meanvalue

min

Minimumvalue

OL

Overload

p

Corre tedplasti zonesize

pl

Plasti strainduetoyield

postr

Poststret hed onditions

pp

Prepregrelated

residual

Componentduetoresidualstress

T

Duetothermalexpansion

T R

Transition

use

Roomtemperature onditions

x

, y, z

Laminate oordinates

y

Irwinplasti zonesize

Abbreviation

ARALL AramidReinfor edAluminiumLaminate

CCT Centre-Cra kTension

DCLS Double-Cra kLapShear

FMLs FibreMetalLaminates

GLARE GLAss-REinfor ed

LDA LinearDamageA umulation

OL Overload

VA VariableAmplitude

Chapter

1

INTRODUCTION

A goal without a plan

is just a wish.

Antoine de Saint Exupery

(1900-1944)

F

ibreMetallaminates onsistofalternatinglayersof

unidire -tionalimpregnatedbrelaminaandthinmetalli sheets

adhe-sivelybondedtogether,asshowninFigure1.1. FMLsare

hy-bridmaterialshavingbetterme hani alanddamagetoleran e

propertiesthantheindividual onstituents. FMLshavebeendeveloped

pri-marilyforair raftstru turesasasubstitutetohighstrengthaluminium

al-loys.Tomanufa tureFMLs,asta kofpliesis uredatelevatedtemperature

andpressure. This uringpro ess resultsin residualtensilestress inmetal

layersand ompressivestressesinbrelayer.Post-stret hingissometimes

usedtoreversethisun-favourableresidualstressdistributionbyplasti ally

deforming the metalli layers. This te hnique improvesthe fatigue ra k

growth properties but an only be applied touni-dire tional FMLs.

Uni-dire tionalFMLsaremainlyusedinstringersandstraps[1℄.

offatigue ra kgrowth andrelated me hanisms [1℄. Major part ofthese

investigations[2℄ on ernConstantAmplitude(CA)loadinginorderto

un-derstand thebasi phenomenafollowed by limited work dealing with

Va-riable Amplitude (VA) loading [3{6℄. This suggests that the behaviour of

FMLsunderVAloadingneedstobefurtherinvestigated.

AtDelftUniversityofTe hnology,intensiveresear hhasbeendoneinorder

tostudythedierentfatiguerelatedphenomenaofFMLs.In1988afatigue

ra k growth predi tion model for ARALL was developed [7℄ followed by

anothermorea urateandgeneri modelin2005[8℄.These ondmodelis

apable ofpredi ting fatigue ra kgrowth,bridgingstressdistributionand

delaminationshape(prole)underCAloading.

Figure1.1:Atypi alFibreMetalLaminateLay-up[8℄

1.1 S ienti Resear h Motivation

FMLs are developed mainly for aerospa e appli ations [9{12℄. In servi e

theywillbesubje tedtovariableamplitude(VA)loadingrangingfromsimple

overloadstomore omplexloadings(e.g.take-o/landing,gust,et .).

Constantamplitude(CA)predi tionmethods anbeused topredi tthe

fa-tigue ra k growth of a stru tural omponent under VA loading.

Beum-ler[13℄ has dis ussedspe trum fa torstotranslate thefull spe truminto

fa tors[13℄remainsanintelligentguess. The onden elevelofthese

VA predi tions an be overed by in reasing the safety fa tor. This

safetyfa tormaysolvetheissuebutatthe ostofweight,dueto

over-designed omponents.

2. In addition, ra k growth retardation due to ra k-tip plasti ity and

otherVA loadingrelatedphenomenawill notbe addressedin theCA

ase. If ra k-tipplasti ityisnot onsidered,spe trumfa tors anonly

bedeterminedforea hVAseparatelybytests. Nogeneri fa tor an

bedeterminedwithoutunderstandingtheVAsequen eee ts.

Inordertodevelopageneri predi tionmodel,addressingtheabove

men-tionedissues,itbe omesne essarytodeveloptheunderstandingaboutthe

fatigueand ra kgrowthphenomenaexistinginFMLsunderVAloading.

Aftera quiringdetailedunderstandingofphenomenainFMLsunderVA

loa-ding, the next step is the development ofan analyti al predi tion model.

However,itisne essarytothinkabouttheOEMs' on erninthepredi tion

model. OEMs' need an ee tive and eÆ ient predi tion model requiring

lesspro essortime.

1.2 Initial Resear h Problem & Framework

To ometoapredi tion modelforVAloading in FMLs,allrelatedaspe ts

needtobeinvestigated.

Themainquestion addressedinthisthesisis: Whi haspe tsrelatedto

ar-bitraryloadsequen eshaveanadditionalee tonthe urrentlyidentied

fra tureme hanisms? Howshouldthesein uen esbedes ribed,with

pra -ti al onstraintsofanee tive,eÆ ientandsimplepredi tionmodel.

Theresear hisdetailedintospe i questions

1. When onlydelamination growthis onsidered, ananyadditional

in- uen ebeobservedattributedtoarbitraryloading? Ifso, how anit

bea ountedforinthepredi tionmethod?

2. When onsideringthe ombinationof ra k-delaminationgrowth, an

theinformationa quiredinstep-1explainobservationson

delamina-tion. Ifnot,whatareadditionalin uen es?

4. Considering ra kgrowth,willmetalinFMLsbehavesimilarto

mono-lithi metal underVAfatigue? Can the ontribution ofhybrid lay-up

bequantiedinthemethodology?

Toanswerallthesequestions,a ombinedexperimental-analyti alapproa h

hasbeenadopted.Fatigue ra kgrowthanddelaminationgrowthtestshave

beenperformedtounderstandtheme hanismsortheintera tionofdierent

me hanismsinFMLsunderVAloading. Fordelaminationstudy,

delamina-tiongrowth(db/dN)anddelaminationshapehavebeeninvestigated. In

or-dertoinvestigatedelaminationgrowthindependentoffatigue ra kgrowth,

double- ra klap shearspe imenshavebeenused. Whilefordelamination

shape, entre ra ktensionspe imenshavebeenused. Inaddition, digital

image orrelation(DIC)hasbeenused asstrainmeasurementte hniqueto

observethedelamination shapesin-situ testing. Forfatigue ra kgrowth,

entre ra ktensionspe imenshavebeentestedundersele tiveVAloading

and ight spe trum loading. This delamination and fatigue ra k growth

observationsandunderstandingisusedinthedevelopmentofananalyti al

predi tionmodelforVAloading.

1.3 Stru ture of this Dissertation

Chapter2brie yintrodu esFMLsandrelevantfatigueme hanisms. In

ad-ditionthesigni an eofVAloadingisalsoexplainedinthis hapter.

Details aboutthe delamination growth spe imen, pro edure and setup as

wellasdis ussionoftheresultsaregivenin hapter3.

Detailedinvestigationoftheee tofVAloadingonthedelaminationshape

isgivenin hapter4.

Chapter 5 presents the investigation of the behaviour of metal layers in

FMLs.The omparisonisperformedbasedon ra ktipplasti ityanalysis.

ThedevelopmentofanAnalyti alpredi tionmodelforFMLsunderVA

loa-ding, using all the aboveresear h is given in hapter 6. Followed by the

development of a sub-routine to predi t the fatigue and delamination in

post-stret hedFMLs,givenin hapter7.

Referen es

[1℄ A.Vlot,J.Gunnink,FiberMetalLaminates-Anintrodu tion,Kluwer

A ademi Publishers,Dordre ht,TheNetherlands,2001.

[2℄ R. C. Alderliesten, On the available relevant approa hes for fatigue

ra kpropagationpredi tioninglare,InternationalJournalofFatigue

29(2007)289{304.

[3℄ R.C. Alderliesten,H.J.M. Woerden,Load historyee tsduring

fa-tigue ra kpropagationinGLARE,in: M.Guillaume (Ed.),Fatigueof

Aeronauti alstru turesasanEngineeringChallenge,Vol.I,2003,pp.

509{530.

[4℄ H.M.Plokker,R.C.Alderliesten,R.Benedi tus,Cra k losureinber

metal laminates, Fatigue and Fra ture of Engineering Materials and

Stru tures30(2007)608{620.

[5℄ J.S hijve,F.J.Wiltink, V.J.W. Van Bodegom,Flight-simulation

fa-tiguetestsonnot hedspe imensofber-metallaminates,Te h.Rep.

ReportNo.LRV-10,DelftUniversityofTe hnology,TheNetherlands

(1994).

[6℄ G.H.J.J.Roebroeks,Fibre-metallaminatesre entdevelopmentsand

appli ations,InternationalJournalofFatigue16(1)(1994)33{42.

[7℄ R. Marissen, Fatigue ra k growth in arall - a hybrid

aluminium-aramid ompositematerial,Te h.rep.,DelftUniversityofTe hnology,

Delft,LR-574(1988).

[8℄ R.C.Alderliesten,Fatigue ra kpropagationanddelaminationgrowth

inglare,Ph.D.thesis,DelftUniversityofTe hnology,Delft(2005).

[9℄ C.A.J.R.Vermeeren,Anhistori overviewofthedevelopmentofbre

metallaminate,AppliedCompositeMaterials10(2003)189{205.

[10℄ A.Vlot,L.B.Vogelesang,T.F.Vries,Towardappli ationofbremetal

laminatesin largeair raft,Air raftEngineering & Aerospa e

Te hno-logy71(1999)558{570.

[11℄ S.Karishnakumar,Fibermetallaminates-thesynthesisofmetalsand

omposites,MaterialandManufa turingpro ess.9(2)(1994)295{354.

[12℄ L. B. Vogelesang, A. Vlot, Development of bre metal laminates for

Te h-[13℄ T.Beumler,Flyingglare-a ontributiontoair raft erti ationissues

on strengths properties in non-damaged and fatigue damaged glare

Chapter

2

FIBRE METAL LAMINATES

The most difficult part was deciding where to begin read.

The bookshelves extended out of sight, their information

stretching as if to eternity.

by Brandon Sanderson

(1975-)

This hapterprovidestheabriefintrodu tiononFibreMetalLaminates,theirmain

hara te-risti s,manufa turingandinspe tionpro ess.Inaddition,themajorphenomenaobservedin

thefatigueme hanismsofFibreMetallaminatesaredis ussed. Finally,VariableAmplitude

loadinganditsee tonthe ra kgrowthisdis ussed.

L

ooking atthehistoryofFMLdevelopment, it seemsthatthe

maindriverofthedevelopmentistheavailableexpertiseand

knowledgeonmetal ombinedwiththeidentied benetsof

ompositematerials. Resear honappli ationofbrestothe

bondlinehasbeenstartedinseventiesatFokkerfa ilities,Netherlands[1℄.

Atthesametime,thefavourablebehaviouroflaminatedaluminiumsheets

hasbeenidentiedatDelftUniversityunderCAloading[2℄.In1978,FMLs

having arbonandaramidbreshavebeentestedunder ightspe trum

loa-ding,tostudytheee tsof dierent bres[3℄. Thesetestsshowed quite

promisingresults. Duringthedevelopmentphasedierentbretypeswere

high-Table2.1:IdentiedadvantagesofvariousbresforFMLs

Fibre Advantage Disadvantage Available

laminates

Aramid lowweight lowstrength ARALL[5℄

Glass highstrength highweight GLARE[6℄

highfailurestrain lowstiness

Carbon lowweight lowfailurestrain TIGr[7℄

' highstiness orrosionissue CARALL[8℄

highstrength expensive

Table2.2:Commer iallyavailablebremetallaminates

Grade Metal Metal Fibre Fibre Stret hed Chara teristi s

type thi kness layer dire tion

(mm) (mm) (

◦

) % ARALL 1 7075-T6 0.3 0.22 0/0 0.4 Fatigue,strength 2 2024-T3 0.3 0.22 0/0 0.0 Fatigue, formabi-lity 3 7475-T76 0.3 0.22 0/0 0.4 Fatigue,strength, exfoliation 4 2024-T8 0.3 0.22 0/0 0.0 Fatigue, elevated temperature GLARE 1 7475-T61 0.3-0.4 0.266 0/0 0.4 Fatigue,strength, yieldstress 2 2024-T3 0.2-0.5 0.266 0/0,90/90 0.0 Fatigue,strength 3 2024-T3 0.2-0.5 0.266 0/90 0.0 Fatigue,impa t 4 2024-T3 0.2-0.5 0.266 0/90/0,90/0/90 0.0 Fatigue, strength in0/90dire tion 5 2024-T3 0.2-0.5 0.266 0/90/90/0 0.0 Impa t 6 2024-T3 0.2-0.5 0.266 +45/-45,-45/+45 0.0 Shear, o-axis properties

lightstheadvantagesanddisadvantagesofvariousbres. Whilethe

a tivi-tiesregardingtheoptimizationofthisnewmaterial on eptwereterminated

atFokker,DelftUniversity ontinueditsresear h. Detailsaboutthe

deve-lopmentofFMLsarewelldo umentedin[4℄.

ARALL (AramidReinfor ed Aluminium Laminate) was the rst FML

om-mer ially available for the air raft industry [9℄. In 1983, two grades of

ARALL were ommer ialized, but later in 1987 twomore grades were

re-leased(detailsaboutthese gradesareshownin table 2.2). Despitethe

ad-vantages, theM Donald-Douglas C-17 aft argodoor was theonly major

appli ationforARALL [10℄. Major drawba ksofARALL werebre

mi ro-bu kling,prematurefailurewhensubje tedto ompressiveloadsand

inasu essorofARALL,namedGLARE(GLAss-REinfor ed).InGLARE

high-strength glass bres areeither present in

0

◦

,

90

◦

,

45

◦

or in a ombination (detailed in table 2.2). Instead of ARALL, GLARE is urrently applied in

theair raftindustry[12,13℄be auseofthebetterme hani alanddamage

toleran eproperties,espe iallyunder ight(spe trum)loading.

2.1 Nomen lature of FMLs

Similartoa traditional omposite,dierent FMLlay-ups arepossible and

toidentifyor ategorizetheselaminates,a odingsystemispreferred. This

odingsystemisimportantfordesign,produ tionandmaterialquali ation.

The odeforanarbitrarylaminateis

GLAREAx-B/C-t

where

AdenesthegradeofthelaminateasdenedinTable 2.2

xgivesinformationonthe prepregplyorientation with respe ttoloading

dire tion

Bindi atesthenumberofaluminiumalloyplies

Cindi atesthenumberofglassbreprepregplies

tindi atesthethi kness ofthealuminiumalloylayers

Forexample, GLARE 3- %5/4 - 0.3is Glare 3 with 5 metal and 4 prepreg

layers. Themetallayersare0.3mmthi k.

2.2 Properties of FMLs

FMLshaveanumberofadvantageswhen omparedwith onventional

alu-miniumalloysorevenbrereinfor edplasti s. FMLshaveasuperior ra k

growthratesandfatigueperforman ewhi hallowlonginspe tionintervals.

In omparisonto omposites,theyoersimplemaintenan emethods,easy

inspe tionduringservi e, higherimpa tresistan eand lessenvironmental

degradation.

UnlikeARALL,GLAREhasgoodfatiguepropertiesin ombinationwith

om-pressiveloading[5℄.Besidetheex ellentfatigue hara teristi s,GLAREalso

has good impa t and damage toleran e hara teristi s [14℄. In addition,

thebre/epoxylayersa tasbarriersagainst orrosionoftheinnermetalli

wellasgoodthermalinsulationproperties. Someoftheadvantagesofbres

usedinFMLsareshowninTable2.1.

Temperature - [C]

Temperature - [C]

S

a

l

-[M

P

a

]

0

50

100

-10

0

10

20

30

40

50

2/1 Layup

5/4 Layup

Curing Temperature-T

_CURE

Figure2.1:Residualstressesinaluminiumlayersasfun tionoftemperature[15℄.

2.3 Manufa turing Pro ess

Thealuminium layers in GLAREhave athi kness of0.3- 0.5mmand are

pretreatedbeforebeinglaminatedintoapanel.Thispre-treatment onsists

of hromi a idorphosphori a idanodizing andsubsequentpriming with

BR-127adhesivesystems[17℄. Thebresaredeliveredasaprepreg

in lu-dingtheFM94adhesivesystemfromCyte [18℄.

Thealuminiumandprepreglayersarebondedtogetherin anauto lave

u-ring pro ess at an elevated temperature of

120

◦

C

at a maximum pressure of6 to 11bar. This implies thatthelayersare bondedtogether ata high

temperatureandare ooled downin bonded ondition. As aresult ofthe

dieren ein oeÆ ientsofthermalexpansion,giveninTable2.3,the

alumi-niumlayerswanttoshrinkmorethan theprepreglayers. Assumingarigid

bondbetweenthealuminiumandprepreglayersduring ooling,thisresults

Table2.3:Me hani alpropertiesofAluminium2024-T3andPrepregS2/FM94 [16℄

Unit 2024-T3 S2-glass,FM-94

k

Fibreaxis

⊥

Fibreaxis

Thi kness of

singlelayer

mm 0.3 0.133

Young'sModulus MPa 72,400 48,900 5,500

ShearModulus MPa 27,600 5,550

Poisson'sratio

ν

xy

- 0.33 Poisson'sratio

ν

yx

- 0.33 0.0371 Thermal expan-sion oeÆ ient

10

−6

C

−1

22 6.1 26.2 Curing tempera-ture

◦

_C

- 120 2.4 Post Stret hing

Figure2.1showsthat ooling downresultsinatensilestressin the

alumi-niumlayers,ofwhi hthemagnitude dependsonthelay-up. Thisresidual

stressisunfavorableforfatigueloading. Thestressallowsanin reased ra k

openingandsoenlargesthestressintensityfa toratthe ra ktip.

Post-stret hing of ured bre-metal laminates is sometimes performedto

over omepotentialnegativeee tsoftheseresidual tensile stressesinthe

metallayers. Theresidual tensile stress inthealuminiumlayers anbe

re-versedintoa ompressivestressbyyieldingthelaminatetoasmall(positive)

strain per entage. Ithas beenproventohaveabene ialee t onthe

fa-tigueproperties[15,19℄.Post-stret hing anbeseenasameanstoalterthe

internalstressdistributionin thelaminatestoobtaindesirableproperties.

Thepost-stret hingme hanismisillustratedingure2.2.Furtherdetailhas

beenprovidedintheChapter7.

2.5 Inspe tion & Quality Control

Theultrasoni C-s anmethod anbeappliedtoinspe tandverifythequality

Fibre Layer

Stress

Strain

Aluminium

Fibre

Metal

Laminate

σ

Aluminium

σ

_{Fibre Layer}

_σ

Aluminium

σ

_{Fibre Layer}

Residual

stress in

as-cured

Residual

stress in

stretched

laminate

laminate

Stretching

Strain

Figure2.2:Illustrationofpost-stret hingpro esswithstressandstrain urves

Theobje tiveofnon-destru tiveinspe tionmethodistodeterminewhether

thes annedpanel anbea eptedorshouldbereje ted.

Thedefe tsinGLAREpanels anbeduetoforeignmaterial ontamination,

likewrappingfoils, rawmaterial ontamination,su h asglass splinters,or

porositiesordelaminationsduetoairin lusions. ThisC-s anmethodisalso

usedtodete tanypositioningerrorin aseofspli esordoublersoreventhe

breorientation.

Toa eptorreje taGLAREpanelbasedonC-s anevaluation,itisne essary

toestablish ertain riteria. Asmentioned by VanMeer andCoenen[18℄,

D D

D

Crack

crack

D=Delamination Boundary

M

E

T

A

L

FI

B

R

E

M

E

T

A

L

Part of the load is

“BRIDGED”

over the crack

Figure2.3:Cra kbridgingofthebresanddelaminationofthelayers

2.6 Fatigue in Fibre Metal Laminates

2.6.1 FatigueCra kPropagation

InFMLs, fatigue ra k propagation an be divided into twomain

me ha-nisms: ra k propagation in metal layers and delamination at the

metal-breinterfa e. Inreality, bothof these me hanisms form a balan ed and

so- alled oupledpro ess. Theseme hanismsareshowningure2.3.

Thefatigue ra kgrowth behaviour in FMLs anbe des ribed with Linear

Elasti Fra tureMe hani s(LEFM).This impliesthat, likemonolithi

me-tals,the ra kgrowthrateinFMLsisrelatedtoa ra k-tipstressintensity

fa tor. Butit is not thatsimple, be ause in FMLs the ra k-tip stress

in-tensity fa tor is in uen ed by the ontribution ofbridging bres, whi his

ee tedbythedelaminationatthebre-metalinterfa e.

Whenthe ra ksinthemetallayersstartgrowing,thebresremaininta tin

thewakeofthe ra k. Thesebresprovideapathoftheloadtransferover

the ra kandrestrainthe ra kfromopening. Asa onsequen e,lessload

needstobetransferedaroundthe ra k-tipinthemetallayers,resultingin

alower ra k-tipstressintensityfa tor.

distribu-Thisredistribution,resultsin analmost onstant ra k-tipstress intensity

fa torduringmajorpartofthe ra kgrowthlife. Thebrebridging

me ha-nism depends on a number of fa tors, su h as the stiness and thi kness

ofea hindividuallayer,thenumberofmetal-breinterfa es,thedire tion

ofea h bre-adhesive layer with respe t to theloading dire tion, the

ap-plied loading, the ra k onguration (surfa e ofpart through ra ks) and

theenvironmental onditions(temperature)[20℄.

Delaminationgrowthisapro essinwhi hthelayersadja enttothe ra ked

metalli layersdelaminateduetothe y li shearstressesthato ur,be ause

ofloadtransferatthebre-metalinterfa e[21℄. Nostresseso urbetween

thelayersin thedelaminated area. Butthe stress relaxation will o urin

thebrelayersitself[22℄. Theadvantageofdelaminationgrowthisthefa t

thatthein reaseinthelengthofthebridgingbresredu esthestrainsand

stressesinthebres,preventingbrefailure.

Inthefollowingse tions,theseme hanismswillbedis ussedindetail.

2.6.2 Cra kBridgingand Restrainton Cra kOpening

The bres in FMLs are insensitive to fatigue. They transfer a signi ant

partoftheloadoverthe ra kandrestrainthe ra kopening, asshownin

gure 2.3. Due to thisrestraining, the ra kopening in GLAREis smaller

as omparedto monolithi metal. Theamount of load thatis transferred

around the ra k in the metal layersis smaller due to the transfer of the

major part through the bres, over the ra k. This me hanism resultsin

smaller ra k-tipstressintensityfa toras omparedtomonolithi metal,for

equal ra klengthandappliedload.Moreover,the ra k-tipstressintensity

fa torisnotsigni antlyin uen edbythein reaseofthe ra klengthwhi h

is ontrarytowhatisobservedinmonolithi metals.

Cra kbridgingbe omesmaximumlyee tiveaftera ertain ra k lengthis

rea hed,whi hmeans,afterthe ra kopeningdispla ement rea heda

er-tain magnitude. A small ra kopening meanslow strain in thebresand

asa onsequen elowbridgingstress. Therefore,thebrebridgingandthe

restrainton ra kopeningwillbesmallforsmall ra klengths,butwill

be- omeee tiveafterthe ra klengthrea hesa ertainsize[21,22℄.

2.6.3 Delamination atthe Interfa e

Marissen[21℄hasreportedthat ra kopeningduringthe ra kpropagation

phaseisduetothetwomainfa tors:

ALUMINIUM

ALUMINIUM

ADHESIVE

ADHESIVE

FIBRES

DELAMINATION

COD

CRACK FLANKS

P

P

(a)

SHEAR DEFORMATION

IN THE ADHESIVE

COD

CRACK FLANKS

P

P

ADHESIVE

ADHESIVE

FIBRES

ALUMINIUM

ALUMINIUM

(b)

ALUMINIUM

ADHESIVE

FIBRES

ADHESIVE

COD

CRACK FLANKS

P

P

( )

Figure2.4:Cra kopeningdispla ementduetodelamination(a),adhesiveshear

•

Adhesivesheardeformation(Figure.2.4(b)).

Inaddition, Guo andWu [23℄, mentioned thedeformation of metal layer

(Figure. 2.4( )), but assumed it tobe insigni ant in omparison with the

othertwofa tors.

The y li shearstressesatthemetal-breinterfa eduetotheloadtransfer

from the metal to bre layers are ausing this delamination growth. The

magnitudeof y li shearstressis determined by thematerialandloading

parameters,su hasthethi knessandstinessoftheindividuallayers,the

lay-up,thebreorientationintheprepreg,andtheminimumandmaximum

appliedstress.

Inadditiontothelevelofthese y li shearstresses,thedelaminationgrowth

ratedependsonthedelaminationresistan eoftheprepreg. In reasingthe

delaminationresistan eprovidesbetterbrebridging[21℄.

Duringloading, when the ra k- anks areopened in aluminium layer, the

inta tbresare elongated over thedelamination length. This meansfora

given ra kopening,thatthedelaminationlengthdeterminesthestrainand

thusthestressinthebrelayers. Largedelaminationlengthsresultinsmall

bridgingstresses,with small y li shearstresses atthe interfa e indu ing

smalldelaminationgrowthrates. Inotherwords,thedelaminationgrowth

rate and the bridging stress are in balan e, ontinuously in uen ing ea h

other.

Thebridgingstressalso ontributestothestressintensityfa toratthe ra k

tipinthealuminiumlayers,whi hdeterminesthe ra kgrowth rate. High

bridgingstressesalongthe ra kresultinlowstressintensitiesatthe ra k

tipandthussmall ra kgrowthrates.

Thismeansthatthefatigue ra kgrowthme hanisminGlareis hara terised

bythepro essesof ra kgrowthin thealuminiumlayersanddelamination

growthattheinterfa es, whi h ontinuouslyin uen eea h other. The

ra-tiobetween ra klengthanddelaminationlengthdependsonthelaminate

lay-up and on the ra k growth hara teristi s of the aluminium and the

delaminationresistan eoftheinterfa e.

2.6.4 AdhesiveShearDeformation

Besidestheelongationofbres,Marissenattributesapartofthe ra k

ope-ningtothedeformation oftheadhesive ri hlayersin theprepreginArall.

Dueto bre bridging, the load has to be transferred from the aluminium

Marissen on luded that in the ideal situation of an innitely sti

adhe-sive between thelayers, the ra kopening and the stress intensity fa tor

wouldbezeroforalaminatewithoutastarternot handwithout

delamina-tion. However,inthea tualsituationduetolo alsheardeformationofthe

adhesive,some ra kopeningwillo ur. Thisis s hemati ally represented

inFigure2.4(b). Asresultoftheslightly opened ra k,thestress intensity

fa torinthealuminiumlayersisnolongerzero.

Intheabovedis ussion,theee t ofdelamination was negle ted. If

dela-minationofthelayerso urs,thelengthoverwhi hthebreswillelongate

in reases,resultingin lowerbrestresses. Thesituation,however,will be

qualitativelythesame.

OL-Cycle

N

D

N

CA

No. of cycles, N

N

D

a

OL

Δa

OL

a

D

C

ra

c

k

l

e

n

g

th

,

a

Crack length, a

C

ra

c

k

g

ro

w

th

r

a

te

d

a

/d

N

Δa

OL

a

OL

Figure 2.5: S hemati of ra k growth retardation following an overload in

2.6.5 Ee ton FatiguePerforman eof FMLs

Thefatigue ra kgrowth behaviour ofGlare was des ribedwith thestress

intensityfa torapproa hinaqualitativeway. Theargumentofthisthesisis

thatthestressintensityfa toratthe ra ktipdeterminesthe ra kgrowth

rate in thealuminium layers. Control ofthestress intensity fa tor means

ontrolofthe ra kgrowthratesintheGlarematerial. Thestressintensity

fa toratthe ra ktip anberedu edby[21℄

•

In reasing the stiness of the bre layers. This an be obtained by applyingbreswithahigherYoungsmodulus,orbyin reasingthebre

layer thi kness or by in reasing the bre volumefra tion within the

prepreg. Thebridgingstressesinthese aseswillbehigheratthesame

ra kopeningdispla ement.

•

De reasingthestinessofthealuminiumlayersbyde reasingthe thi- knessofthealuminiumlayers.

•

In reasing the delamination resistan e. The delamination areas will besmaller,resultingin higherbridgingstressesandthuslower stress

intensities.

•

In reasingtheadhesiveorprepregshearstiness,whi hrestrainsthe ra kopeningmoreandlowersthestressintensityatthe ra ktip. In

general, thefatigue hara teristi sofGlare an beenhan edby

opti-mizationofthelaminatewithrespe ttobresandadhesivesin

om-binationwiththelaminatelay-up.

2.7 Variable Amplitude Loading

Theretardationee tson ra kgrowthresultingfromasingleoverload y le

isillustrated in Figure2.5. During theoverload y le,yielding of the

ma-terial near the ra ktip o urs, reatingalargeplasti zone[25{31℄. Due

to the presen e of this plasti zone in front of the ra k-tip, surrounded

inanelasti allydeformed region,the ra k-tipexperien esasqueezing

ef-fe t, whi h resultsin the development of residual ompressivestresses at

and around the ra k-tip. The ompressive stress eld redu esthe

avai-lable ra k-tipdrivingfor eand ausesasigni antredu tioninfatigue ra k

growth rate[26,28,32℄. The ra kretardationzone,i.e. the ra kextent

over whi h retardation of ra k growth is experien ed, may be

hara teri-zedby parameters,

a

D

(overload ae ted total ra k length) and

N

D

(delay y les), andis s hemati ally representedin gure2.5. After the ra khas

intheabsen eofotherretardationee ts. This isthetypi alphenomenon

observedinmetals,however,FMLshavingmetalasa onstituentshowthe

sameretardationphenomenonbutpresen eofbreredu ethisee t.

2.8 Fatigue Cra k Growth Retardation Model

2.8.1 Formetals

Fatigue ra kgrowthretardationmodels anbedividedintotwomain

a-tegories: thosebasedon ra kgrowth througha plasti zoneaheadofthe

ra ktipandthosebasedon ra k losureinthewakeofthe ra k(see

Fi-gure2.6).Earlyintera tionmodelswerebasedon ra k-tipplasti itywhi h

wasassumed tobethemajor ause offatigue ra kgrowthretardation. A

well-known andsimple modelofthis ategoryis the Wheeler Model[33{

47℄. These ra k-tip plasti ity models were followed by the advan e and

omplexfatigue ra kgrowthpredi tionmodels basedonthe ra k losure

inthe wake ofthe ra k asthe major ause offatigue ra kgrowth

retar-dation. These models are ategorized in semi-empiri al models (su h as

ONERA,PREFFASand CORPUS)andStrip-yieldmodels. Detailsonthese

modelsaregivenin[48℄

FATIGUE CRACK GROWTH RETARDATION

MODEL

WHEELER Model

Semi-Empirical Models

Strip-Yield Models

CORPUS

ONERA

PREFFAS

Based on Crack Closure in the

Wake of the Crack

Based on Crack Closure due to

Crack-Tip Plasticity

WILLENBORG Model

Figure2.6:Classi ationofFatigue ra kgrowthretardationmodels

2.8.2 ForFMLs

InFMLs,allthemetal relatedphenomenaaretosomeextentredu eddue

mo-loading.Thishighlightsthat omplexandadvan emodelsmaynotbe

requi-redin aseof omplexmaterialslikeFMLsunderVAloading. Asimplied

intera tionmodel( ra k-tipplasti ity)isusedforfatigue ra kgrowth

pre-di tionsunderVAloadinginFMLs.Thedetailsaboutthe ra k-tipplasti ity

modelaredis ussedinthisse tion.

2.8.3 Cra k-TipPlasti ity

A ordingtothetheoryofelasti ity,thestressatthetipofthe ra kbe omes

innitewhenastru tureisloaded.Inreality,the ra k-tipbe omesblunted

uponloading. Additionally,foradu tilematerial,thetheoreti al ra k-tip

stressesex eedtheyieldstrengthofthematerial,

σ

0

.2

,resultinginyieldingin frontofthe ra k-tip.Asaresult,azoneofplasti allydeformedmaterialof

theoreti alsize

r

p

isformedaheadofthe ra ktip,asillustratedingure2.7.

Whenthe ra kedstru tureisloadedintensionthetotalelasti andplasti

strain within the plasti zonebe omes larger than theelasti strain ofthe

surroundingmaterial. Duringthesubsequentunloadingstage,the

surroun-dingelasti materiala tslikeaspringthat lampstheresidualstrainwithin

theplasti zoneand exerts ompressivefor esontothezone. As aresult,

azoneof ompressiveresidualstressaheadofthe ra k-tipis reatedafter

unloading(fromtensileappliedstress).

Theoretical (Elastic)

Stress Distribution

Yielded, Redistributed

(Elastic-Plastic) stress

Plastic Zone

Blunted Crack

_rp

x

σ0.2

σyy

ry

y

sin etheresidual stressinterfereswith theappliedstresstothe ra k-tip.

Theinterferen eofthe residual stress with theappliedstress is knownto

have a signi antee t on the fatigue ra k growth ratesof the stru ture

underVAloading. Intheeventofatensile overload,amoreextensiveand

largerzoneof ompressiveresidualstressis reatedaheadofthe ra k-tip.

As the ra k advan es through the zone during subsequentfatigue y les,

the ompressiveresidualstress ontributestothewell-knownfatigue ra k

growthretardationinthesubsequent y lesfollowingatensileoverload.

2.8.4 TheIrwin Approa h

Irwinmadeasimpleestimationoftheplasti zonealongthe ra kplanefor

elasti ,perfe tly-plasti materials. The simplestestimate anbe made by

substituting

θ

= 0

in

σ

0

.2

=

K

I

√

2

π

r

cos

θ

2



1

+ sin

θ

2

sin

3

θ

2



(2.1)

andsolvingforadistan e,

r

y

,atwhi h

σ

y

=

σ

0

.2

,detailsaboutthisequation aregivenin[49{51℄. Thisleadstotheequation:

r

y

=

1

2

π



_K

σ

0

.2



2

(2.2)

The distan e

r

y

is s hemati ally illustrated in gure 2.7. This estimate of plasti zone is in orre t, be ause it is based on an elasti stress

distribu-tion [49{51℄. Figure 2.7 also shows the elasti -plasti stress distribution

withplasti zonesize

r

p

. Theareasunderelasti and elasti -plasti stress distribution must be the same in order to satisfy for e equilibrium in

y-dire tion. This ondition an bemet bymaking

r

p

su h thatthefollowing equationissatised:

r

p

Z

0

K

I

√

2

πr

dx

−

σ

0

.2

r

y

=

σ

0

.2

(r

p

− r

y

)

(2.3)

Solvingfor

r

p

gives:

r

p

= 2r

y

=

1

π



_K

σ

0

.2



2

(2.4)

Equation2.4isderivedforplanestress ondition.Forplanestrain ondition it anbemodiedas

r

p

,plstrain

=

1

3

r

p

=

1

3

π



_K

σ

0

.2



2

(2.5)

2.8.5 Des ription ofWheeler Yield ZoneModel

A ordingtoGallagher[52℄andS hijve[53℄,themodelsthattrytoexplain

theintera tionee tby onsideringthe onditioninfrontof ra ktip(plasti

zone)arelabelledasYieldZoneModels. Wheeler[54℄startedthis

genera-tionof predi tion models involvingintera tion ee tsin thepredi tion of

ra kgrowth.

TheWheeler predi tionmodel usesthemodiedlinear damage

a umula-tionrelation,

a

= a

0

+

n

∑

i

=1

f

(

∆

K

, r, ..) = a

0

+

n

∑

i

=1

∆

a

i

(2.6)

usingasimpleretardationparameter

C

P

,

a

= a

0

+

n

∑

i

=1

C

P

f

(

∆

K

, r, ..)

(2.7)

Thelineardamagea umulation providesapredi tionofVAfatiguelifeby

adding y le-by- y le ra k growth in rements

∆

a

i

, mathemati ally repre-sented in equation 2.7. The modied ra k length and ra k growth rate

equations anbewrittenas:

da

dn

= C

P

·C

cg

∆

K

n

cg

(2.8)

where

C

P

variesfrom0 to1dependingonthelo ationofthe ra ktipin a previously reatedlargerzone(

r

p

,OL

ingure2.1)andtheplasti zonesizeof the urrentload y le

r

p

,i

. The

C

P

is al ulatedusing:

C

P

=



_r

p

,i

(a

OL

+ r

p

,OL

) − a

i



m

when

a

i

+ r

p

,i

< a

OL

+ r

p

,OL

(2.9) or

C

P

= 1 when a

OL

+ r

p

,OL

≤ a

i

+ r

p

,i

(2.10)

where

r

p

,i

is the urrentplasti zonesize,

r

p

,OL

is theoverloadplasti zone size,

a

OL

isthe ra klengthatoverloading,illustratedingure2.8. misthe experimentally al ulated exponent whi hdepends onthestress level, the

ra kshapeaswellastheloadspe trum.

Wheeler assumed that m, on e alibrated, an be used for other spe tra.

Butlateritwasshownthatthea ura yofpredi tionswillsuerifdierent

loading spe tra are used with the same m value [33, 55℄. For metalli

stru tures,theWheelermodelisunabletopredi tthephenomenonof ra k

arrestafterahighoverload,be ausethepredi tedretardationfa tor

imme-diatelyaftertheoverloadwillnotbezero[35℄.Se ondly,theWheelermodel

didnotre ognizetheo urren eofdelayedretardation. A tually,the

mo-delassumesverysimple ra kgrowthbehavior;whereasimmediatelyafter

appli ationofpeakloadstherealphenomenaarevery omplex.

r

_p,OL

a

p

a

_OL

a

i

r

p,i

∆a

Current effective

plastic zone

Overload Effective

Plastic Zone

σ

_OL

σ

max

σ

min

σ

max,i

∆σ

2.8.6 ModiedWheelerModel

IntheoriginalWheeler model,theParis equationisused for ra kgrowth

al ulation. AproblemoftheParisequationisitsdependen yonthestress

ratio. Toin lude thestress ratio ee tin theCA ra kgrowth predi tion,

a number of equations have been proposed in the literature [57℄.

Gal-lagher [52℄ used the Walker [58℄ ra k growth relation, while Pereira et

al.[59℄andFinney [33℄used theForman relation [60℄. HeretheS hijve

relation[61℄(Equation2.11)isusedforthe

CA

baselinestressratio orre -tion.

∆

K

e f f

= (0.55 + 0.33R + 0.12R

2

) ·

∆

K

(2.11) TheoriginalWheeler's ra kgrowthrelation(Equation2.8)ismodiedas

da

dn

= C

P

·C

cg

∆

K

e f f

n

cg

(2.12)

2.8.7 Cra k losuremodels

Monotonic Plastic Deformation

Reversed Plastic Deformation

Figure2.9:Plasti Zone

Theo urren eof ra k losureofafatigueatapositivetensilestresslevel

afterremovingtheloadonthespe imenisaphysi alreality[62℄.Inorder

tobea urate,thisphenomenon shouldbeanessential elementofa ra k

growthpredi tion model. During ra kgrowth, theplasti zoneis moving

withthetip ofthe ra kaswellasin reasingin size, gure2.9. Thesame

willbetrueforthereversedplasti zone. Thisdeformationinvolves

elonga-tioninthey-dire tion. Asaresultofthiselongationthe ra kwill lose(at

surfa esarepressedtogether byplasti deformationleftinthewakeofthe

ra k,theresidual ompressivestressesaretransmittedthroughthe ra k.

Thisphenomenoninliteratureisreferredtoas\Cra kClosure". Itwasrst

observedbyElber[62℄.anditissometimesreferredtoastheElber

Me ha-nism. Thepresen eofthisphenomenon anbejustiedeither bystiness

measurement[61℄,whi hisnotana uratewayofmeasurement,orbythe

ee tonfatigue ra kgrowth.

Elbersuggestedthatonlythatpartoftheload y lewill ontributeto ra k

extensionwherethe ra kisfullyopenuntilthe ra ktip,be ause ra ktip

singularitydoesnotexistduringthepartoftheload y lewhenthe ra ktip

is losed. Thisleadstothedenitionofanee tivestressrangeandstress

intensityfa tor.

∆

S

e f f

= S

max

− S

op

;

∆

K

e f f

= K

max

− K

op

(2.13) Elberdevisedthefamous ra k losurerelationinvolvingthestressintensity

fa torandstressratio.

U

=

∆

_∆

K

e f f

K

=

∆

S

e f f

∆

S

= 0.5 + 0.4R

(2.14)

Figure2.10 omparesthedierent ra k losurerelationsasafun tionofR.

Elber'srelation indi ate that

S

op

is in reasingagain foranegative R-value whi hisphysi allyunrealisti . Analyti alworkofNewman[63℄hasshown

thatit shouldbeade reasingfun tion for

R

− > −1

. Forthisreason, S hi-jve[64℄proposed anewrelation between UandRbased onthetrendsas

predi tedbyNewman.

U

= 0.55 + 0.35R + 0.1R

2

(2.15)

Thisrelationshowsa ontinuouslyde reasing

S

op

forade reasingR-value. Thistrendshould beexpe ted be ause fora ertain

S

max

value, a lower R-valueimpliedalower

S

min

value. Theweaknessofthisapproa histhe im-pli itandunprovenassumptionsthat ra k losureisresponsibleforallload

ratioee tsandthatthese anbe orrelatedbyanequation. Butthis

rela-tionisprovedtobetheonly ra k losureestimationmethoddue to

una-vailabilityofa uratedire t ra k losuremeasuringte hniques[3℄.

After the introdu tion ofthe ra k losure on eptby Elber [62℄, a lot of

eort was putin understandingthe phenomenon topredi t ra kgrowth.

These eorts in lude the early phase work whi h were mainly numeri al

te hniques (niteelementanalysis) asdetailedbyNewman [65℄ andOhiji

Stress Ratio - R

γ

=

S

O

P

/S

m

a

x

-0.8

-0.4

0

0.4

0.8

0

0.2

0.4

0.6

0.8

1

Elber Relation

Schijve Relation

ONERA Model

PREFAS Model

CORPUS Model

Figure2.10: The ra kopeningstresslevela ordingtodierentrelations

the al ulation ostsandtime,whi hmades ientistsdevelopingsimple

ana-lyti al ra k losuremodels [67{69℄. Cra k losure models forVA-loading

require y le-by- y le al ulation ofthe ra k openingstress, Sop andthe

orresponding

K

op

. Thethreemainmodelswhi harebasedonElbers ra k losureassumptionwereprimarydevelopedtopredi tfatigue ra kgrowth

under ightsimulationloading[70℄.Thesemodelsare:

1. ONERAModel

2. CORPUSModel

3. PREFFASModel

predi -TheCORPUSModel

Figure2.11:Ahump reatedbyanoverloadand attenedbyanunderload

The CORPUS model (Computation Of Retarded Propagation Under

Spe -trumloading)wasproposedbyDeKoning[71℄in1981.Thismodel

develo-pedusedfor ra kgrowthpredi tionunder ightsimulationloadsequen es.

TheCORPUSmodelwas basedonthehumpme hanism, i.e. ra k losure

isvisualized by thehumpformation (gure 2.11)on ra k surfa es. There

isnoeviden e supportingtheformation ofthehumpsonthe ra ksurfa e

presentedinliterature. However,only s hemati sareavailableto

unders-tandthehump reationand attening. In aseofanoverload,alargerhump

willbe reatedandwillbe attenedbyalater ompressiveloadinthe

spe -trum. In every y le, ahump is reatedwith asso iated

S

op

level, and for theestimationof

S

op

a y le-by- y le al ulation isrequired,sin e

S

op

isan essentialpartofCORPUSmodelfor ra kextension.

DeKoning[71℄wasabletointrodu eafewnew on eptsinthe ra kgrowth

models.Thesewererelatedtothe on eptofprimaryandse ondaryplasti

zones, the onsideration of plane strain/plane stress for plasti zone

esti-mationandthemultipleoverloadee t. Althoughthe on eptbehind the

modelisquitesimple,themathemati alinterpretationofthemodelappears

tobefairly omplex. Padmadinata[72℄andPutra[73℄explainedthe

COR-PUSmodelverysystemati allyintheirthesis. Thedes riptioninthispaper

ismainlyattributedtobothauthorsandisbasedontheiranalyses.

Inordertodes ribe thehumpbehaviour after appli ation ofan

overload-underload ombination,a formsimilartoElber's fun tionwas determined

empiri allyfor7075-T6and2024-T3material:

U

_{= (−0.4R}

4

+ 0.9R

3

_{− 0.15R}

2

_{+ 0.2R + 0.45); R > 0}

U

_{= (−0.1R}

2

_{+ 0.2R + 0.45); −0.5 < R < 0}

(2.17)

UsingFiniteElementAnalysis,Newman[74℄demonstratedthat

S

op

depends on

S

max

,n

,

S

min

,n

and on thelevel of

σ

max

in omparison to the yield stress, whi hNewmanassumedasanaverageyieldstress. Inordertoin orporate

the in uen e of high load levels, De Koning dened a orre tion fa tor

h

forthe

S

op

values. The orre tionfun tion was obtainedby a urvetting pro eduretoNewman'sresults.

Anoverload is playing amajor rulein reating thehump while an

under-loadwill redu ethehumpandhump openingstresses. Alower underload

de reasestheSopleveloftheprevious y leswhileanoverloadhigherthan

thepreviousoverload y lesin reasestheSoplevel.

AnimportantfeatureoftheCORPUSmodelisthatitalsodierentiates

bet-ween a plasti zone developing into virgin (elasti ) material and a plasti

zoneextendingin alreadyplasti ally deformedmaterial. Therstones are

alled PrimaryPlasti Zone (PPZ)andthelatterones are alled Se ondary

Plasti Zone(SPZ).

DeKoningformulatedaspe ialequationbymodifyingtheIrwin[75℄

equa-tionaswellastheDixonnitewidth orre tionfor entrally ra ked

spe i-men,inordertoa ount foralargezoneif

S

max

approa hesthenetse tion yield-limit. This resultedin afairly ompli atedequationfor al ulating a

PPZinvolvinga variable forthestress state assumption. Theplasti zone

size has an important role in the delay swit h and the material memory

onsideration.

Intera tions between an overload with an overlapping PPZ auses an

in- rease of the ra k opening levels, whi h will give more ra k growth

re-tardation. This ee t plays animportantrolein theCORPUS model. The

humpopeningstressgivenbytheequations2.16and2.17isvalidforasingle

overload

S

max

,n

ombinedwithanunderload

S

min

,n

. Ifaseriesofoverloadsis applied,deKoningassumesthat

S

op

,n

willrea hanupperboundstationary leveldenedby

1

+ m

st

,n

 1

U

− 1



(2.18)

Where

m

st

,n

isastationaryparameterwhi hdependsonthe ra kgrowth in- rement

∆

a

betweentheoverloadsandtheplasti zonesize

D

n

ofthe over-load. FortheCA ase

∆

a

/

D

n

goestozeroandgivesavalue of

m

st

=0.1. Fi-nally, if the ra k has grownthrough the overload plasti zone (

∆

a

/

D

n

>1), theoverload intera tionis ignored and equation 2.13 is used to al ulate

Aftertheappli ation oftheoverload,thevalueof

S

op

,n

isin reased stepby step. To omputetheloadintera tionee t,arelaxationfa tor

δ

wastaken into onsideration(0.28for2024-T3). Thisvalueisvalidfortheintera tion

ee tsofoverloadsofthesamelevelinplanestress ondition.Forageneral

ase,whereoverloadofdierentlevelsintera tatdierentstatesofstress,

two orre tionfa torswereintrodu ed. The orre tedrelaxationfa toris

δ

= 0.28

δ

1

δ

2

(2.19)

δ

1

a ounts forintera tionof dierent overload levels and

δ

2

a ounts for theee tofredu edintera tioninplanestrain ondition.Itshouldbekept

inmindthatonlyintera tionbetweenthere entoverloadandtheoverload

asso iatedwithdominanthumpis onsidered.

Con eptsadoptedintheCORPUSmodelarerelatedto ra k losure(Elber

me hanism),plasti zonesize,lo ationof ra ktipinplasti zone,humpand

retardationme hanism.

After omparingthe predi tedand tested results,Padmadinata stated the

following on lusions:

1. Cra kgrowthinmostsevere ightswasunderestimated.

2. The CORPUSmodelgivesmu h importan etoa rarelyo urring

ne-gative loadif that loadis more ompressive(gust load) thanthe

fre-quentlyo urringgroundstresslevel. Thepredi tionisina uratebut

onservativeinthat ase.

3. Someimprovementshavetobedoneontheloadsequen e,asinsome

aseswithsimpleloadsequen es,asequen eee twaspredi tedbut

itwasnotobservedinthetestseriesandsometimesito urredintests

butCORPUSmodeldidnotpredi tit.

4. The CORPUS model predi ts a higher ra k growth rate for a lower

yieldstressiftheothermaterial onstantsarenot hanged. Thelatter

onditionisnotrealisti ,butitindi atesthatrelevantCA ra kgrowth

ratesareessentialforgoodpredi tions.

5. TheCORPUSmodeldoesnot onsiderthemultipleoverloadee tson

the7075alloy.

2.9 Summary