Design of Composite Structures ContainingBolt Holes and Open Holes

by

Tomas Ireman

Department of AeronauticsKungliga Tekniska Högskolan(Royal Institute of Technology)

SE-100 44 StockholmSweden

Report No. 99-03

ISSN 0280-4646

i

PREFACE

Thework presentedin this doctoralthesiswascarriedout betweenJanuary1991andOctober1998at SaabAB andat the Royal Instituteof Technology, Departmentof Aeronautics.Thework wascarriedout on part time basis.The thesisconsistsof five separatepapers,of whichtwo were a part of my licentiate thesis presented in December 1994.

The work was financially supportedby SaabAB and the SwedishNational AeronauticalForum.

First I would like to thank my supervisor, Dr. Ingvar Eriksson, for his support andencouragementthroughout this study and ProfessorJan Bäcklund for giving me theopportunity to carry out this work within the department.

I also want to thank all my colleaguesat SaabAB, and especiallymy former headsLarsSjöströmand HansAnsell for their supportand Christina Altkvist, AndersBredberg, andTonny Nyman for their helpfulness and for many hours of stimulating discussions.

Finally, I thank my wife ChristinaBradley Iremanand my children Emilie, Amanda,andWilhelm for their patience and support during the course of this study.

Linköping, January 1999

Tomas Ireman

ii

ABSTRACT

This thesisis concernedwith stressanalysisandstrengthpredictionin compositelaminatescontainingbolt holesandopenholes.It coversbothtwo- andthree-dimensionalanalyses,andexperimentshavebeencarriedout to determinecriteriaparametersandto validatetheanalysismethods.

Theobjective of thework on two-dimensionalanalysismethodshasbeento developaccurateand cost-efficient stressanalysisand failure predictionmethodsvalid for complex loadingconditions.Boththefinite elementmethodandamethodbasedonLekhnitskii’scomplex stressfunctionshave beenusedto determinethe stressdistribution aroundthe hole. In the caseofbolted laminates,the frictionlesscontactbetweenthe bolt and the hole hasbeentaken intoaccount.Differentfailurecriteria,includingthePointStressCriterion(PSC)andtheDamageZoneCriterion (DZC) have beenusedto predict the strengthof testspecimenssubjectedtocomplex loading conditions. In the caseof bolted laminates,simple failure criteria forpreliminary designare proposed.The validity of thesecriteria is demonstratedon multi-fastenertension-and shear-loaded test specimens.A comprehensive test programmewascarriedout to establishcriteriaparametersandto generatedatato validatethestressanalysisandstrengthpredictionundercomplex loadingconditions.A specialtestfixture wasdesignedfor this purpose. Good agreement was found between predicted and measured results.

Theobjective of thework on three-dimensionalmethodshasbeento developtools for three-dimensionalstressand failure analysesand to study the effect of various factors on thestrengthof single-lapjoints. An experimentalprogrammewasconductedto characterizethefailure mechanismsand to measuredeformation, strain, and bending effects. A three-dimensionalfinite elementmodelof a boltedsingle-lapjoint hasbeendevelopedto determinethenon-uniformstressdistributionthroughthethicknessof thelaminatein thevicinity of thehole. The model was validated against measuredstrains and displacementsfrom theexperimentalprogramme.The agreementbetweenpredictedand experimentalresultswasgenerallygood. In the failure characterisationpart of the experimentalprogramme,it wasfoundthatthefailure of thejoints wasdominatedby kinking. A failure analysisprocedureforthepredictionof bearingfailure dominatedby kinking hasbeendeveloped.In this procedure,failure is predictedusing a quadraticfailure criterion evaluatingfibre stressand transverseshearstressat a characteristicdistancefrom the edgeof the bolt hole. Experimentalresultswere used to validate the analysis procedureand good agreementwas found betweenpredictedand experimentalfailure loads.The analysisprocedurewere then usedstudy theeffect of eight different parameterswhich affect the strengthof boltedcompositelaminates.The parametersstudiedwere: laminatethickness,lay-up, bolt diameter,bolt configuration(countersunkor protrudinghead),friction, clampingforce,clearanceandlateralsupport.Theparametricstudy was organisedas a reducedtwo-level factorial test. The resultsfrom theparametricstudyshowthatlaminatethickness,friction, clampingforceandbolt configurationare the parameters which have the strongest influence on the strength of the joints.

iii

CONTENTS

PREFACE..........................................................................................................................i

ABSTRACT......................................................................................................................ii

CONTENTS.....................................................................................................................iii

DISSERTATION..............................................................................................................iv

INTRODUCTION............................................................................................................1

1 Background.............................................................................................................1

2 Stress analysis..........................................................................................................3

2.1 Laminates with open holes.................................................................................4

2.2 Bolted laminates.................................................................................................5

3 Failure prediction.....................................................................................................9

3.1 Failure prediction in laminates with open holes.................................................9

3.2 Failure prediction in laminates with bolted joints............................................13

4 Design methods.....................................................................................................15

SUMMARY OF APPENDED PAPERS.........................................................................17

DIVISION OF WORK BETWEEN THE AUTHORS...................................................19

REFERENCES...............................................................................................................20

PAPER A................................................................................................................A1-A33

PAPER B.................................................................................................................B1-B37

PAPER C.................................................................................................................C1-C46

PAPER D................................................................................................................D1-D35

PAPER E.................................................................................................................E1-E28

iv

DISSERTATION

This dissertation consists of an introduction and the following five papers:

PAPER A: Ireman T., Nyman T. and Hellbom K., “On Design Methodsfor BoltedJoints in CompositeAircraft Structures”,Revised version of paperwithsametitle, publishedin Composite Structures, Vol. 25,pp.567-578,(1993).Theoriginalpaperwaspresentedat theSeventhInternationalConferenceonCompositeStructures(ICCS/7),9-11July 1993in Paisley, whereit receivedthe Elsevier Composite Structures Award.

PAPER B: IremanT. and ErikssonI., “Strengthof CompositeLaminatesContainingHoles and Subjected to Complex Loading Conditions”, Journal ofComposite Materials, Vol. 31, pp. 1214-1248, (1997).

PAPER C: Ireman T., Ranvik T. and Eriksson I., “On Damage Development inMechanically Fastened Composite Laminates”, To be submitted forpublication inComposites Part B.

PAPER D: IremanT., “Three-dimensionalStressAnalysisof BoltedSingle-lapJoints”,Accepted for publication inComposite Structures.

PAPER E: IremanT. andPurinP., “Rankingof FactorsAffectingtheStaticStrengthofBoltedCompositeLaminates”,Extendedversionof thepaper“EvaluationofFactorsAffecting the Designof Bolted CompositeLaminates”which hasbeenacceptedfor presentationat the internationalconference“Joining andRepair of Plastics and Composites”16-17 March 1999, IMechE HQ,London and publication in the Conference Transactions.

1

INTRODUCTION

1 Background

A compositematerialconsistsof two or morematerialsmixedtogetherto giveamaterialwithgood properties.A typical compositematerialconsistsof a materialwith high mechanicalstrengthandstiffness(reinforcement),for exampleunidirectionalor wovenfibres,embeddedin a materialwith lower mechanicalstrengthandstiffness(matrix).To tailor thepropertiesofthe compositematerial, a laminate is formed by stackingon top of eachother layers ofreinforcement oriented in different directions.

Compositematerialshave an old history. Compositesare often found in natureitself. Forexample,woodis aunidirectionalcompositematerialwherecellulosefibresareembeddedin alignin matrix, and this materialhasbeenusedby humansin all times in different typesofapplications.Thefirst compositelaminatesweremadeby bondingtogetherthin pliesof woodwith differentfibre orientations.This typeof laminateis known underthenameply-woodandhasbeenusedin many different applications.The classicallaminatetheory was originallydeveloped for ply-wood.

Compositematerialssuch as glass-,aramide-,boron- and carbon-fibre-reinforcedplasticshavebeenusedfor a few decades,especiallyin theaircraftindustry. At Saab,compositeswereintroducedin the fighter aircraft J35 Draken which was developedin the beginning of thefifties. TheDrakenhaspartsof theair inletsmadeof glass-fibre-reinforcedepoxyresin.Theuseof compositeshassincethenbeengraduallyincreased.On theJA 37 Viggen,thefin andlanding geardoorsare honeycomb sandwichconstructionswith skins of carbon-reinforcedepoxyresin.Thedefinitebreakthroughfor compositescamewith theJAS 39 Gripenin whichabout20%of thestructuralweight is composites.Theuseof compositesin JAS 39 Gripenisshown in Fig. 1. The major composite structural parts are: the wing, fin and canard.

Fig. 1. The use of composites on the JAS 39 Gripen.

Equipment doorCanard

Fillet Leading edgeflaps

Vertical fin

Nose landing gear doors

Radome

Main landing gear doors

2

Compositematerials,if properlyused,offer many advantagesover metals.Examplesof suchadvantagesare: high strength and high stiffness-to-weightratio, good fatigue strength,corrosionresistanceandlow thermalexpansion.Nevertheless,conventionalcompositesmadeof pre-impregnatedtape or fabric also have somedisadvantages,such as poor transverseproperties,inability to yield andsensitivity to moistureandhigh temperatures,which mustbeaccounted for in the design.

Among the most important elementsin aircraft structuresin general and in compositestructuresin particularare mechanicallyfastenedjoints. Improperdesignof the joints mayleadto structuralproblemsor conservative designleadingindirectly to overweightstructuresandhigh life-cycle costof the aircraft. Typical examplesof mechanicallyfastenedjoints incompositeaircraftstructuresare:theskin-to-spar/ribconnectionsin e.g.a wing structure,thewing-to-fuselageconnectionandtheattachmentof fittings etc.Examplesof suchjoints in theJAS 39 Gripen aircraft are shown in Fig. 2.

Fig. 2. Examples of bolted joints in the JAS 39 Gripen.

Aircraft structuresalso include a large numberof open holes and cut-outse.g. holes forelectric wires and hydraulic pipesor holes requiredfor assemblyor maintenance.This isexemplifiedin Fig. 3, whereatypicalwing sparfrom JAS 39Gripenis shown. This is a typicalexampleof a casewherea laminatecontainingopenholesis subjectedto shearloadingi.e. a

AL-fitting

CFC-skin

CFC-skin

CFC-sparCFC-skin

Wing to fuselage attachmentSkin to spar attachment

3

two axial loadingcase.To avoid theproblemsdueto improperdesignmentionedabove,andtofully utilize the material,the designmethodsmustbe applicableto generalin-planeloadingcases.

Fig. 3. Typical wing spar from the JAS 39 Gripen.

This study can be divided into two parts.The first part, is focusedon designmethodsforlaminatescontainingbolt holesand openholessubjectedto multi-axial loading conditions.The second part is focused on three-dimensional effects in bolted composite single-lap joints.

Theobjectiveof thefirst partof this studywasto developaccurateandcost-efficientmethodsfor thestressandfailure analysisof compositelaminatescontainingbolt holesandopenholessubjectedto multi-axial loadingconditions.Theobjectiveof thesecondpartof this studywasto characterizeexperimentallythe bearingfailure modein single-lapjoints, to developtoolsfor three-dimensionalstressandfailure analysesandto studytheeffectof variousfactorsonthe strength of single lap joints.

2 Stress analysis

Design methodsfor laminatescontaining bolt holes and open holes require a detailedknowledgeof the stressdistribution in the vicinity the hole. This stressdistribution can bedeterminedby analyticalmethodsandnumericalmethodssuchastheFinite ElementMethod(FEM), dependingon thedegreeof simplificationintroduced.In this chapter, differentaspectson stressanalysismethodsfor boltedlaminatesandlaminateswith openholesarediscussed,and the areas addressed in this work are pointed out.

4

2.1 Laminates with open holes

Considera laminatedcompositeplateof arbitraryshapecontaininganopenholeandsubjectedto general in-plane loading, as shown in Fig. 4.

Fig. 4. Laminatedcompositeplatecontainingaholeandsubjectedtogeneralin-planeloading.

To determinefully thestressstatein theplate,a three-dimensionalanalysisis required.A threedimensionalstressstateappearsat free edgessuchashole edgesdue to the so-called“freeedge” effect causedby the mis-match of Poisson’s ratios betweenplies with differentorientationsin a laminatedplate.This givesrise to interlaminarshearandnormalstressesatthe free edge.An accurateanalysisof the stressstateat a “free edge” requiresthat all theindividualpliesandpreferablyalsotheresin-richzonebetweenthepliesarerepresentedin themodel.If thefinite elementmethodis used,averyfinemeshis neededcloseto thefreeedgeinorderto capturethesteepstressgradients,unlesselementswith a high degreeof interpolationpolynomialsare used.This, in combinationwith the model requirementsin the thicknessdirection, leads to large FE-models which require much computer power for their solution.

Several authors[1-7] have performedFE-analysesto determinethe three-dimensionalstressstatein laminateswith circularholes.In mostof thestudies[1-4], conventionalsolidelementswereused.Singularelementswereusedin [5] andspecialelementswith a seriesexpansioninthe thicknessdirection were usedin [6]. Nyman and Friberg [7] usedthe p-adaptive FE-systemSTRIPE.With two exceptions,thework by Carlsson[4] andthework by NymanandFriberg [7], all studieswere performedon laminateswith only a few plies. The analysisperformedby Carlsson[4] wasrepeatedin an unpublishedwork by Andersson[8] who also

0o

90o +45o

-45o

5

usedthep-adaptive FE-systemSTRIPE.In a p-adaptive FE-method,it is possibleto increasethedegreeof theinterpolationpolynomial,up to ahigh level. Theresultsof thisstudydifferedconsiderablyfrom thosein [4], indicatingthatFE-solutionsusingconventionalelements,evenwith very fine meshes, can be unreliable when “free edge” stresses are involved.

Analytical methodswith somesimplificationshave alsobeenusedby someinvestigators[9-17] to determinethe three-dimensionalstressstatecloseto the hole boundary. In all casesclassicallaminatetheory was combinedwith boundarylayer theory in the boundarylayerregion close to the hole. In two of the studies[11-12], the problem was simplified to afictitious straightedgeproblemby assumingthat thecurvededgecanbedividedinto a seriesof one-dimensionalstraightedgeproblems.With this simplification,it is importantto accountfor the interlaminar stresses caused by the in-plane stress gradient [12].

Considerablesimplificationscanbemadeif the interlaminarstressescloseto theedgeof thehole are omitted, i.e. if the laminateis treatedas a homogeneousanisotropicplate usingclassicallaminatetheory. Thestressanalysisis performedeithernumericallywith FEM usingmembraneor shellelementsor by analyticalmethodsusinga complex variableapproach.FE-analyses of this kind are well established and will not be further treated here.

The methodof complex functions was developedby Muskhelisvili [18] and extendedtoanisotropicmaterialsby Lekhnitskii [19] andSavin [20]. Theoriginal papers[19,20] includedexactsolutionsfor infinite plateswith circular and elliptical holesas well as approximatesolutionsfor oval, rectangularand triangularopenings.The complex variableapproachhasbeenusedby many authors[e.g.21-29].In mostof thesestudies,circularandelliptical holeswere considered.Quasi-rectangularholes were treated in [23] and [24]. Simplifiedapproximatesolutionsfor infinite orthotropicplateswith circular and elliptical holeswerederived in [22] and[25]. Theexactsolutionsobtainedwith thecomplex variableapproachislimited to infinite plates.Thestandardprocedure,well known for metals,is to usefinite widthcorrectionsto overcomethis limitation. Thefinite width correctionfactorsfor isotropicplateshave frequentlybeenusedfor orthotropicandanisotropicplates.Thevalidity of doing this isquestionablesincethe finite width correctionfactorsfor isotropic platesare not in generalvalid for orthotropicandanisotropicplates.Expressionsfor finite width correctionfactorsforanisotropic plates have been presented in [30].

In thepresentwork, thestressanalysiswaspreferablycarriedout in two steps.In thefirst step(loaddistributionanalysis),thefar-field stressdistribution in thelaminatewasdetermined,andin thesecondstep,adetailedstressanalysisof theregioncontainingtheholewasperformedinorder to determinethe stressdistribution aroundthe hole. The load distribution analysisiscarried out using FEM. For the detailedstressanalysis,a methodbasedon Lekhnitskii’scomplex stress functions was developed and implemented in a computer code.

2.2 Bolted laminates

The analysisof laminatescontaining bolt holes is considerablymore complex than theanalysisof laminatescontainingopenholes.The stressstatein the vicinity of a bolt holedependson many complex parameterssuchas friction. The most importantparametersare:

6

geometryandstiffnessof the joined members,joint configuration,friction propertiesof themembersbeingjoined,clampingforceandloadingconditions.To includeall theseparametersdirectly in a stressanalysisof a joint is almost impossible,even with the most powerfulcomputers now available.

Theanalysisof a boltedjoint in a complex structuresuchasanaircraft is preferablydividedinto two or morestepsasshown in Fig. 5. In thefirst step,theinternalloaddistribution in thejoint is determinedusing one or a few successively refined analyses.The local stressdistribution in thelaminatearoundthefasteneris thendeterminedin adetailedstressanalysis.

Fig. 5. Overall design procedure for bolted joints.

For a joint with complex geometryandloadingconditions,FEM is theonly way to determinethe load distribution. Load distribution analysiswith FEM hasbeenbriefly discussedby thepresentauthorandhis co-authors[31] andby Eriksson[32]. Poon[33] broughtup thesubjectin his literaturereview on thedesignof mechanicallyfastenedjoints in compositestructures.A FE-baseddesignprocedureincludingbothloaddistribution anddetailedstressanalysishas

1 2

3

1 2

3

Load distribution analysis

Local stress analysis

Global structural analysis

7

beendevelopedby Erikssonet al. [34]. It shouldbe pointedout that the load distributionanalysisis a very importantstepin the designof boltedjoints in compositestructures.If theload distribution analysisis of poor quality it doesnot matter how good the local stressanalysisandfailurepredictionare.Improvedmodellingtechniquesaswell asdetailedstudiesof the joint behaviour are needed.

The determinationof the local stressdistribution in a bolted laminateis in generala three-dimensionalproblem.The three-dimensionalstressstate is due to bendingeffects and toclampingof thefastener. Therearethreekindsof bendingeffects:primarybending,secondarybendingand fastenerbending(Fig. 6). Primary bendingis causedby an external bendingmomentactingon thejoint, whereassecondarybendingis causedby theeccentricityin e.g.asingleshearjoint. Fastenerbendingoccursto someextent in every joint with a shear-loadedfastener. Thebendingandtilting of the fastenergive rise to a non-uniformstressdistributionthroughthethicknessof thelaminate,asillustratedin Fig. 7 whereanormalizedcontactstressdistribution for the bolt-hole contact in a single-lap joint is shown. Becauseof the largeamountof modellingwork andthecomplexity of theanalysis,three-dimensionalanalysesofcomposite bolted joints are relatively sparse. Only a few studies [35-48] have been reported.

Fig. 6. Bending effects in bolted joints.

c) Fastener bending

a) Primary bending

b) Secondary bending

8

Fig. 7. Normalized contact stress distribution in a single-lap joint.

Two-dimensionalanalysesin which thelaminateis treatedasa homogeneouscontinuumhavebeenperformedby several authors[31] and [49-70]. The local stressdistribution in thevicinity of theholehasbeendeterminedeitherwith thecomplex variableapproach[31, 49-57]or numerically by FEM [35-48] and [58-70].

Thecontactbetweenthebolt andthelaminatehasbeentreatedin severaldifferentways.Onesimple way is to assumea contact stressdistribution. The sinusoidalstressdistribution(frequently used for isotropic materials) has also been frequently used for orthotropicmaterials[51,58,60-62].If the bolt is assumedto be rigid, the prescriptionof zero radialdisplacementsat an assumedcontactareaof the hole boundaryis anothersimple way ofmodellingthecontact[35,59,68].Chang[69] usedthesametechniquebut addedan iterativeprocedurein which theextentof thecontactareawasdetermined.In [36], theholeperipherywas loadedby an arrangementof pin-jointedbarsconnectedbetweenthe centreof the holeandnodesat the loadededgeof the hole. The forcesin the barswere thenexaminedby aniterative procedure.If theaverageof thebar forcesin the thicknessdirectionwastensile,thebarswereremovedfrom themodel.A similar approachwasusedin [66,67]wherenodepairson the bolt and laminatewere connectedby non-linear truss elementswith zero tensionstiffness.In [63] and[65], a nodalpoint iterationtechniquewasusedto determinethecontactstressdistribution. The complex variableapproachhasalso beenusedto solve the contactproblem [31,49-57]. In nearly all cases the collocation method has been used, i.e.undeterminedcoefficientsin anassumedseriesexpansionhave beendeterminedby imposingthecontactconditionsin anumberof pointsat theholeboundary. Theextensionof thecontactareais determinedthroughaniterativeprocedure.A rigid bolt wasassumedin all studiesusingthecomplex variableapproach,exceptin thework by Hyer et al. [50,55,56].Theeffect of anelastic bolt on stress distributions in the vicinity of the bolt hole was shown to be very small.

0

0.25

0.5

0.75

1

0

90

180

270

3600

0.5

1

1.5

2

2.5

3

normalized thicknessangle [deg]

norm

aliz

ed c

onta

ct p

ress

ure

Nor

mal

ized

con

tact

pre

ssur

e,

Angle, α (degrees)z t1⁄–

pp 0⁄

9

Friction hasbeenincludedin [37,50,52-57,63-65].The effect of multiple holeson the localstressdistributionsin thevicinity of thebolt holeswasconsideredin [53,57,60].Infinite plateswere consideredin most of the studies.Only in the studiesin [51,52,57]were finite platesconsideredusing a boundary collocation method and a boundary integration method,respectively.

In the first part of the presentwork, a stressanalysismethodbasedon the complex variableapproachwasdeveloped,the frictionlesscontactbetweenthe bolt and the hole being takeninto account.This methodand FEM have beenusedto calculatethe stressdistributions inthreedifferentpin-loadedlaminateswith two differentwidths.Two FE-modelswith differentmeshdivisionswereusedto studythe influenceof the meshdensityon the calculatedstressdistribution.Theagreementbetweenthestressdistributionsobtainedwith thetwo methodsisgood.Thestressanalysismethodbasedon thecomplex variableapproachis apartof adesignprogramfor compositeboltedjoints usedat SaabAB. In this program,thestressanalysiscanbe performedon anisotropiclaminatessubjectedto bolt loadsand to combinednormalandshear by-pass loads.

In thesecondpartof thework, a three-dimensionalFE modelwasdevelopedto determinethenon-uniformstressdistribution throughthethicknessof thelaminatein thevicinity of theholein single-lapjoints. To validate the model, an experimentalprogrammewas conductedinwhich strainsin thevicinity of theholeandrelative displacementsbetweenthejoint membersweremeasured.Computedandmeasuredstrainsanddisplacementswerecomparedandgoodagreement was generally obtained.

3 Failur e prediction

Designmethodsfor laminateswith openholesand laminatesin bolted joints also requirecriteriafor strengthprediction.In thissection,strengthpredictionfor laminateswith bothopenholesandbolt holesarediscussed.The first part of the presentwork focuseson the strengthpredictionof laminatescontainingopenholesandbolt holesandsubjectedto generalin-planeloads.Thesecondpart focuseson thestrengthpredictionof tension-loaded,boltedsingle-lapjoints where through-the-thickness effects are taken into account.

3.1 Failur e prediction in laminates with open holes

Consideragain the in-planeloadedlaminatedplateshown in Fig. 4. The load at which theplate is unableto supportany additional load is definedas the failure load. At this point,damagedueto differentfailuremechanismsmaybepresentin thelaminate,dependingon thestacking of the laminate. Fig. 8 shows some of the internal failure types that may occur.

10

Fig. 8. Failure modes in a composite ply.

Thesefailure modesarefibre failure,matrix cracking,fibre-matrixfailure anddelamination.Matrix crackingusuallyoccursfirst and the crackdensityincreaseswith increasedloading.Whenthematrixcracksaresufficiently close,afibre-matrixfailurebetweentwo matrixcracksoccursforming a small delamination.If the primary loadingis compressive, local instabilitywill occurwhena certainlevel of delaminationandmatrix crackingis reached.If theprimaryloadingis tensileandthe stackingis well mixed, the final failure will be controlledby fibrefailure.Delaminationmayalsooccurdueto high interlaminarstressese.g.at thefreeedgeofan open hole.

The existing methodsfor strengthpredictioncanbe divided into two main groups:laminatefailurecriteriaandlaminafailuremodels.To thefirst groupbelongcriteriawhicharebasedonlaminatestrengthdata,whereasthe secondgroup containsmodelswhich are basedon plystrengthdata.A comprehensive review of currentfailuremodelsespeciallywith respectto thefirst group is given by Awerbuch and Madhukar [71].

Oneof thefirst attemptsto predictthestrengthof notchedlaminateswasmadeby Waddopsetal. [72], who usedthe principlesof linear fracturemechanics(LEFM) to form the Inherent

Section A

Section B

Section AMatrix cracks

Fibre failure Fibre failure

Fibre-matrix failure

Section B

Delamination

Fibre-matrix failureMatrix cracks

11

Flaw Model (IFM). The useof LEFM hasbeenquestionedby Kanninenet al. [73], whopointedout that damagein a compositelaminatecausedby several failure modesis quitedifferent from a simple through-the-thicknesscrack in metals,and that self-similar crackgrowth is not likely to occur in a composite laminate.

Strengthpredictionsbasedon the maximum stressat the hole edge are in generalveryconservative for compositelaminates.In orderto overcomethe severeconservatismin usingthemaximumtangentialstressat theholeedge,Whitney andNuismer[74,75] introducedtheprinciple of evaluatingthe stresslevel at a characteristicdistanceaway from the hole edge.They formulatedthewell-known PointStressCriterion(PSC)andtheAverageStressCriterion(ASC). Thesecriteria aresimple to apply andarethereforeattractive to designers.Both thePSCandASC have beenwidely usedto predictthestrengthof laminateswith openholesandbolted laminates[25] and[76-80]. Oneproblemwith thesemodelsis that the characteristiclengthis a functionof bothnotchtypeandnotchsizefor thesamelaminate.For circularholes,this problemwasaddressedby Karlak [81] andPipeset al. [82], who proposedrelationshipsbetween the characteristic distance used in PSC and the hole radius.

Bäcklund[83] concludedthat IFM, PSCandASC areall semi-empiricalin thesensethat thecriteriaparameterscannotbecalculatedor postulatedon thebasisof fundamentaldatafor thecompositematerial. A new model, the Fictitious Crack Model (FCM), later renamedtheDamageZoneModel (DZM), wasproposedfor compositematerials.TheDZM simulatesthedamagedevelopmentin the stress-intenseregion at the edgeof the notch by introducingacrackwith cohesive stressesactingat thecracksurfaces.Thecohesive stressesareassumedtobe linear functions of the crack opening. The model is basedon the two fundamentalparameters,the unnotchedtensilestrengthand the apparentfractureenergy. The DZM hasbeenusedin a numberof studiesto predict the strengthof laminatescontainingcracksandholesof variousshapes[84-86]. Very good agreementbetweenpredictedand experimentalstrengthhasbeenobtainedin all studies.Thenumericalprocedureof theDZM makesit lessattractive to designers than e.g. ASC and PSC.

ErikssonandAronsson[87] developedtheDamageZoneCriterion(DZC), which is basedonthetwo fundamentallaminateparametersunnotchedtensilestrengthandcritical damagezonelength. The failure load is determinedfrom a simple equilibrium equationat the point offailurewhenthedamagezonehasreachedacritical size.Thestresseswithin thedamagezoneareassumedto beconstantandequalto theunnotchedstrengthof thelaminate,andthestressdistribution aheadof thedamagezoneis assumedto have thesameshapeasthelinearelasticstress distribution.

The lamina failure criteria can be divided into two groups:first-ply failure and progressivefailurecriteria.Thefirst groupcontainscharacteristicdistanceapproachesappliedat theply-level [89-95]. Garbo and Ogonowski [89] evaluated the Tsai-Hill failure criterion at acharacteristicdistancefrom the hole while El-Zein andReifsnider[90] usedthe principle oftheAverageStressCriterion (ASC) at theply level by assumingthat failureoccurswhentheaverageply fibre stressover a characteristicdistanceis equalto the critical fibre stress.Tan[91-95] evaluateda fibre failure criterion and the Tsai-Wu criterion along a characteristiccurve.

12

In the progressive failure criteria, the stiffnesspropertiesof the material are successivelydegradedas the plies fail. The failure of a ply is predictedusing e.g. Tsai-Wu, Tsai-Hill,Hashinetc.andthematerialdegradationis accomplishedby settingsomeof thecomponentsin the lamina stiffnessmatrix to zero dependingon the type of failure. Examplesof suchdamagemodelsare found in [96-100]. Delaminationwas included in someof the models[96,98,99]by using stress-basedpolynomial criteria in termsof the interlaminarshearandpeel stresses.

Predictionsof delaminationonsetat thefreeedgeof holesin compositelaminatesaremadein[5] and [12-16]. Ericsonet al. [5] useda fracturemechanicsapproachevaluatingthe totalstrain energy release.Shalev and Reifsnider [13] useda criterion basedon the order ofsingularityof the stressfield andthe energy releaserate.Stress-basedpolynomialcriteria intermsof the interlaminarstressesevaluatedat a characteristicdistancefrom the hole edgewere used in [12] and [14-15].

In most of the studies of laminateswith holes, uniaxial loading conditions have beenconsidered.Only a few authors [21,94,101-104]have consideredlaminateswith holessubjectedto morecomplex loadingsituationssuchasbiaxialandshearloading.Whitsideetal.[21] included a biaxial tension-tensiontest in their comprehensive experimentalstudy ondifferent types of fibre-reinforcedepoxy laminates.A similar test procedurewas usedbyLiebowitz and Jones[101] and by Daniel [102,103]who performedbiaxial tension-tensiontestswith differentratiosbetweentheloadsin thetwo loadingdirections.Tan[94] performedsheartestson laminateswith elliptical holesusing a rail sheartest fixture. GamziukasandCarlsson [104] performed shear tests on I-beams with an irregular cutout.

Studieson thestrengthpredictionof notchedlaminatessubjectedto generalin-planeloadingsituationssuchasbiaxial loadingareeven moresparsethanthe experimentalstudieson thesubject.Lee [96] analysedthe biaxial testsin [101] usinga progressive failurecriterion.Tan[94] analysedsheartestsaswell as the biaxial test by Daniel [102,103]usinga ply-failureapproachappliedat a characteristicdistancefrom the hole edge.Hollman [88] analysedtheshear-loadedgraphite/epoxybeamwith an irregular cut-out in [104], using the Point StressCriterion (PSC) and the Damage Zone Model (DZM) for strength prediction.

The major advantageof the laminatestrengthpredictionmethodsover the lamina strengthpredictionmethodsis thatthecomplex mechanismsof laminatefailureincludingfibre failure,matrix cracksanddelaminationcanbe taken into accountin a simpleandaccurateway. Ageneral limitation of these methods is that tests have to be made on each laminateconfigurationusedin thedesignin orderto determinethe laminatefractureparameters.Thislimitation can,however, be effectively overcomeby establishinganalyticalandexperimentalmodels to determine the fracture parameters using only a limited amount of test data.

The laminamodelson the otherhandhave the advantagethat the strengthof the laminateispredictedfrom basicstrengthparametersfor the ply, i.e. the amountof testingrequiredtopredictthe strengthfor a wide rangeof laminateconfigurationsis generallylessthanfor thelaminatemodels.It is, however, very difficult to find a failure criterion which is capableofpredicting the strengthof a laminate containing several fibre orientationsusing strength

13

parametersdeterminedfrom testswith unidirectionallaminates.Anotherdisadvantageof thelamina progressive failure modelsis that the analysisis expensive and time-consuming.Amoredensefinite elementmeshis generallyrequiredfor thelaminaprogressive failuremodelsthan for the laminate models for accurate predictions.

In this work, a seriesof experimentswith both uniaxially loadedlaminatesand laminatessubjectedto combinedtensionand shearloading was carried out. The strengthsof thesespecimenswerepredictedusingthe PSCandthe DZC extendedto generalin-planeloadingsituations.Good agreementbetweenpredictedand experimentalstrengthsis obtainedwithboth criteria.

3.2 Failur e predictions in laminates with bolted joints

A boltedjoint in a compositestructurecanfail in a numberof waysasshown in Fig. 9. Boltfailure is often a secondaryfailure modein compositestructuresi.e. the bolt fails after thelaminatehasfailed in bearing.Pull-throughfailure is the predominantfailure modein jointswith axially loadedfastenersor a secondaryfailure modein a singleshearjoint with shearloadedfasteners.This failure modewill not be treatedhere.The remainingfailure modes:bearing,net-sectionandshear-out are the basicfailure modesof a laminatein a compositebolted joint with shear-loadedfasteners.The shear-out failure modeoccursmainly in jointswherethe distancebetweenthe hole edgeandthe edgeof the laminateis shortor in highlyorthotropiclaminatessuchascross-plylaminates.Theshear-out failuremodecanbeavoidedby usingappropriatedesignrulesfor edgedistancesandstackingsequences.Shear-out failurewill not therefore be further addressed here.

Fig. 9. Failure modes for composite bolted joints.

a) Net-section failure b) Bearing failure c) Shear-out failure

d) Fastener failure

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Net-sectionfailurein tensionor compressionis assumedto occurby thesamemechanismsasfor laminateswith open holes. The samefailure criteria as for open holes which weredescribedin theprevioussection,arethereforeusedto predictnet-sectionfailureof laminatesin bolted joints.

Bearingfailure is primarily a compressive failureoccurringcloseto thecontactregion at thehole edge.The failure is causedby the compressive contact stressesacting on the holeboundary. Bearingfailure is, like any compressive failure in a compositelaminate,associatedwith delaminationand ply-buckling, which implies that the bearing strength is stronglyaffectedby thelateralconstraintof thematerialsurroundingtheloadedhole.Theeffect of thelateral constraintson the bearing strengthhas been shown experimentally in [105-109].Eriksson[112] formulateda bearingstrengthpredictionmodel, the DelaminationBucklingModel (DBM), from stability considerations.Thebearingstrengthis alsostronglydependenton the layup of the laminate[110] andis sensitive to environmentalconditionssuchashightemperature and high moisture content in the laminate [111].

With theexceptionof theDBM, thestrengthpredictionmethodsfor bearingfailureareeitherof thelaminatetype[51,59]or thelaminatype[58,61,66-68,113],accordingto thedescriptionin theprevioussection.At thelaminatelevel, theASC [51,59] in termsof theradialstresshasbeen used to predict the bearing strengthwith characteristicdistancesdeterminedfrombearingstrengthtests.In the strengthpredictionsstudieswith lamina methods,variousplyfailure criteria suchasDistortionalEnergy, Tsai-Wu, Yamada-Sunhave beenusedeither incombination with a characteristic distance or as progressive failure models.

Relatively few authorsdealwith the failureanalysisof a boltedjoint on thebasisof a three-dimensionalstressstate[39,42,46,47].ChenandLee[39] usedthemaximumstresstheorytopredict in-planefibre, matrix and shearfailure and the Ye delaminationcriterion [41] in aprogressive damagemodel. A progressive fatigue modelling techniquewhich includes aprogressive failureanalysishasbeendevelopedby Shokriehet al. [45]. A setof stress-basedfailure criteria were usedto predict matrix tension,matrix compression,fibre tension,fibrecompression,fibre-matrix shearout, delaminationtension and delaminationcompression.Gambleetal. [42] usedamodifiedversionof theHill-criterion in aprogressivedamagemodel.Thecriterionwasableto predictfibre failure,matrix splittinganddelamination.Delaminationinitiation in laminateswith pin-loadedholeswaspredictedbyPerssonetal. [47] usingthestrainenergy density criterion.

In the first part of this work, two very simple stress-basedcriteria were proposedfor thepredictionof tensionand bearingfailure in compositebolted joints, and the validity of thecriteriahasbeendemonstratedin testswith realistictension-andshear-loadedmulti-fastenerjoints. Comparisonsbetweenexperimentsand predictionsshow that the strengthof thesejoints is fairly well predicted with the simple failure criteria.

In the secondpart, an experimentalprogrammewas conductedto characterizethe damagedevelopmentin single-lapjoints. Basedon the resultsfrom this experimentalinvestigation,afailure analysisprocedurefor the prediction of bearingfailure dominatedby kinking wasdeveloped. The failure analysis procedurewas validated against experimentsand good

15

agreementbetweenpredictedand experimental results was generally found. The failureanalysisprocedurewas then used togetherwith three-dimensionalFE analysesto studynumerically the effect of different factors on the strength.

4 Design methods

Several analysisprogramsfor compositebolted joints are available for compositestructuredesigners.Snyderet al. [114] examinedsix differentanalyticalprogramsanddiscussedtheirmerits and disadvantages.In addition to theseprograms,Madenci [115] has developedadesign and analysis program which is capable of handling multi-fastener joints withinteraction betweenthe fasteners,finite geometry, friction and by-passloading. All theprogramsareanalyticallybasedandmostof themusethecomplex variableapproach.Thereisonly oneprogramamongthoseexaminedin [114] andtheprogramdevelopedby Madenciinwhich the contactstressdistribution betweenthe bolt andthe hole is determined.Thereare,however, acoupleof FE-basedprogramsin whichthecontactstressdistribution is determined,[32] and [34,116].

Thestressanalysismethodbasedon thecomplex variableapproachusedin this work for theanalysisof laminatesin boltedjoints andlaminateswith openholeshasbeenusedasa basisfor a designprogramfor bolted joints calledCOBOLT. COBOLT is capableof analysingalarge numberof joints using both simple and more advancedfailure criteria. It is possibleeitherto solve thefrictionlesscontactproblemor to useafixedcosinedistribution in thestressanalysis.

All the designandanalysiscodesalreadymentionedaretwo-dimensionalwhereasthe stressstatein a bolted joint is in generalthree-dimensional.To accountfor the three-dimensionaleffects,thetwo-dimensionalanalyseshave to becorrectedby correctionfactors.A designtoolbasedona three-dimensionalanalysiswouldmake it possibleto includethebendingeffectsinthe local stressanalysisand therebyreducethe conservatism in the design.As a first steptowardssucha designtool, a meshgenerationprogrammewhich generatesthree-dimensionalFE modelsof anisolatedregion arounda fastener(Fig. 10) hasbeendeveloped.This tool haspartly been used for the generation of three-dimensional FE models in this work.

16

Fig. 10. Three-dimensional FE model of an isolated region around a fastener.

1 2

3

1 2

3

17

SUMMARY OF APPENDED PAPERS

PAPER A

Theproblemsrelatedto thedeterminationof theloaddistribution in amulti-row fastenerjointusingthefinite elementmethodarediscussed.Bothsimpleandmoreadvanceddesignmethodsused at Saab Military Aircraft are presented.The stressdistributions obtained with ananalyticallybasedmethodandanFE-basedmethodarecompared.Failurepredictionswith asimpleanalyticallybasedmethodandthemoreadvancedFE-basedmethodof multi-fastenertensionandshear-loadedtestspecimensarecomparedwith theresultsof experiments.Finally,complicating factorssuch as three-dimensionaleffects causedby secondarybendingandfastener bending are discussed and suggestions for future research are given.

PAPER B

Stressand failure analysesof compositelaminatescontainingholesarepresented.Both thefinite elementmethod(FEM) andananalyticalmethod,basedoncomplex stressfunctions,areusedto determinethestressdistributionsaroundtheholes.Failurecriteria,includingthePointStressCriterion(PSC)andtheDamageZoneCriterion(DZC), areusedto predictthestrengthof testspecimenssubjectedto complex loadingconditions.A comprehensive testprogramwascarriedout to establishcriteriaparametersandto generatedatato validatethestressandfailureanalysis.For this purpose,a specialtest fixture was designed.Good agreementwas foundbetween predicted and measured results.

PAPER C

A comprehensive experimentalprogram was conductedto measureand characterizethedevelopmentof damagein thevicinity of fastenerholesin graphite/epoxycompositelaminates.Thiswascarriedout to generatedatawhichcanbeusedfor developmentof appropriatefailurecriteria.Testspecimenswereloadedin quasi-staticcycleswith successively increasingloads,anddamagedevelopmentin thevicinity of thebolt holeswasdetectedusingdifferentmethodssuchasstrainmeasurements,acousticemission,X-ray andmicroscopicexamination.Severalfailuremodesweredetectedin a seriesof eventsstartingat load levels far below the level atwhich the first visible evidenceof damageappearedon the load-displacementcurve. Failuremodes included matrix cracking, fibre fracture, delamination, and kinking.

PAPER D

A three-dimensionalfinite elementmodelof boltedcompositejoints hasbeendevelopedtodeterminenon-uniformstressdistributionsthroughthethicknessof compositelaminatesin thevicinity of a bolt hole.An experimentalprogrammewasconductedto measuredeformation,strain,andbolt load on test specimensin order to validatethe numericalmodeldeveloped.Strainsin the radial direction at different radii and different angleswere measuredin thevicinity of thebolt holeat theshearplanebetweentheplates.Thedegreeof secondarybending

18

in the joints wasdeterminedfrom strainmeasurementsat certainpointson both sidesof thelaminate. In the experiments,a numberof parameterssuch as laminate lay-up, laminatethickness,bolt diameter, bolt type, clamping force and lateral supportwere varied. Eachspecimenconfigurationwas analysedusing the three-dimensionalfinite elementmodel. Ingeneral, the computed and experimental results showed good agreement.

PAPER E

A systematicparametricstudyhasbeencarriedout to determinethe effect of eight differentparameterswhich affect the strengthof boltedcompositelaminates.The parametersstudiedwere:laminatethickness,lay-up,bolt diameter, bolt configuration(countersunkor protrudinghead),friction, clampingforce,clearanceandlateralsupport.The parametricstudyhasbeenorganisedasa reducedtwo level factorialtest.Finite elementanalyseswereusedto simulatetheexperiments.Three-dimensionalfinite elementanalyseswereusedto determinethestressdistributions in the vicinity of the bolt hole. Failure waspredictedusinga quadraticfailurecriterionevaluatingfibre stressandtransverseshearstressat a characteristicdistancefrom theedgeof thebolt hole.Experimentalresultswereusedto validatetheanalysisprocedure.Goodagreementbetweenpredictedandexperimentalfailureloadswasfound.Thestressandfailureanalyseswere thenusedin the numericalparametricstudy. The resultsfrom the parametricstudy show that laminatethickness,friction, clampingforce and bolt configurationare theparameters with the strongest influence on the strength of the joints.

19

DIVISION OF WORK BETWEEN THE AUTHORS

PAPER A:

IremanandNymandevelopedtheanalyticalmethod.Iremanimplementedthe methodinto acomputercodeandcarriedout all the analyses.Hellbom contributedwith the experimentalresults. Ireman wrote the paper and initiated the work.

PAPER B:

IremanandEriksonextendedDZC to two axial loadingconditions.Iremaninitiatedthework,plannedtheexperiments,implementedthemethod,carriedout all theanalysesandwrote thepaper.

PAPER C:

Iremaninitiatedthework andwrotetheoverall testplan.Ranvik carriedout theexperiments.All authors contributed to the writing of the paper.

PAPER E:

Iremandevelopedthe failure criterion.Purin createdthe FE modelsandcarriedout someofthe analyses. Ireman initiated the work and wrote the paper.

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