Cohesive Zone Modelling in Adhesively Bonded Joints

172 Pages·2014·7.14 MB·English

Cohesive Zone Modelling in
Adhesively Bonded Joints
Analysis on crack propagation in adhe-
sives and adherends
D.C. Noorman
t
f
el
D
f
o
y
t
si
r
e
v
ni
U
al
c
ni
h
c
e
T

C Z M
OHESIVE ONE ODELLING IN
A B J
DHESIVELY ONDED OINTS
ANALYSIS ON CRACK PROPAGATION IN ADHESIVES AND
ADHERENDS
by
D.C.Noorman
inpartialfulfillmentoftherequirementsforthedegreeof
MasterofScience
inMechanicalEngineering
attheDelftUniversityofTechnology,
tobedefendedinSeptember,2014.
Studentnumber: 1309153
Supervisor: Dr.M.Calomfirescu, AirbusDefenceandSpace
Prof.dr.ir.A.vanKeulen, TUDelft
Thesiscommittee: Prof.dr.ir.A. vanKeulen, TUDelft
Ir.A. vanBeek, TUDelft
Ir.C. Ayas, TUDelft
Anelectronicversionofthisthesisisavailableathttp://repository.tudelft.nl/.

P
REFACE
ThisMaster’sthesisisforthoseinterestedinthestructuralmechanicsandfiniteelementanalysisofcom-
positelaminatedbondedjoints.Cracks,ordamagegrowth,withintheadhesivesandadherendsareanalysed
usingatechniquecalledcohesivezonemodelling.Thisthesisassumesthatthereaderpossessesabasicun-
derstandingofstructuralmechanics,finiteelementanalysesandlaminatedcompositesbeforehand,asthe
contentsofthisthesisexpandsonthesetopics.
ThethesiswaswrittenasthefinalexaminationofthetrackSolidandFluidMechanics,intheMasterofSci-
enceprogrammeofMechanicalEngineeringattheTechnicalUniversityofDelft. Thethesiswasperformed
and writtenwithinandfor the departmentof Air Systems ofCassidian, whichisnow Airbus Defence and
Space(Manching,Germany).
Duringthethesis,Iwassupportedbynumerouspeople. Iwouldpersonallyliketothankmysupervisorat
Airbus Defence and Space, Mircea Calomfirescu, who granted me this thesis and guided me throughout.
Also,IwouldliketothankthedepartmentofAirSystemsfortheirfinancialsupportandtheknowledgethey
sharedwithme. IalsowishtothankProf. Dr. Ir. FredvanKeulenforbeingmysupervisorontheuniversity
andacceptingthisthesisasthefinalexaminationofmyMaster’sprogramme,togetherwithAntonvanBeek
andCanAyas.Andfinally,Iwouldliketothankmyparents,brothers,sisterandfriendswhohavesupported
methroughoutmythesis.
D.C.Noorman
Leiden,8thofAugust,2014
iii

A
BSTRACT
Laminated composites is a material that is rapidly being adapted in the aircraft industry and new joining
techniquesarebeingresearchedfornewstructuraldesigns.Onesuchtechniqueisadhesivebonding,which
canresultindecreasedweight,fuelsavingandimprovedstrengthofaircraftcomponents. Robuststrength
andfailureanalysismethodsarerequiredtoassessnewdesignsbeforehand. Oneofthesemethodsisco-
hesivezonemodelling. Cohesivezonemodellingisatechniquebasedoncohesiveforcesandenergywithin
amaterialorinterfaceregionwhichkeepsmaterialtogether. Damagecanbetrackedprogressivelyalonga
regionwithcohesiveelementsanddamagepropagationcanbemonitoredinastructure. Thisthesiswork
reliesoncohesivezonemodellingtomonitordamagepropagationofthebondlineandinbetweenpliesof
simplebondedjoints,togetherwithprogressivefailurecriteriatoassessanyfailurewithinthepliesofajoint.
AcompositeCrackedLapShear(CLS)specimenwastestedwithresultsofapossiblecrackjumpfrom
bondlinetoadherend. Theobjectiveofthisthesiswastoassessandrecreatedamagepropagationandthe
possibilityofajumpofdamagegrowthfrombondlinetoadherendintheCLSspecimen.Thiswasdonebyus-
ingcohesivezonemodellingandprogressivefailurecriteriawiththefiniteelementpackageMSC.Mentatand
itssolverMSC.Marc. Avalidationwithanothertestreportonmixed-modebendingandinterlaminarfailure
wasperformedusingacohesivezonemodelwiththesettingsMSC.Marchastooffer. Thiswieldedaccurate
resultsintermsofloadinganddamage. Withtheaidofthisvalidation,theoptionswithinthecohesivezone
modelwhichhadthebestresultsinthevalidationwereusedforsimulationsoftheCLSspecimen. Cohesive
zoneelementsrepresentingthebondlineandtheadhesivewithinthelaminateadherendsintheCLSmodel
areusedtoassesscohesiveandinterlaminarfailure,whileprogressivefailurecriteriaareusedtoassessin-
tralaminarfailure.Theresultsofthecurrentsimulationsetupswereunsatisfyingasthefailureloadandstrain
resultshadlargeerrors.Furtherdetailedanalyseswillbeneededtorecreatethemultiplefailuremodesinthe
CLSspecimeninMSC.Marcwithacceptableresults.Ontheotherhand,thethesishasproventhatMSC.Marc
anditsowncohesivezonemodelperformwellenoughformixed-modebendingandinterlaminarfailurein
simplegeometries.
v

L F
IST OF IGURES
1.1 Buildingblockapproachintheaircraftindustry.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Overviewofcommonbondedjoints.TakenfromESA[1],Zwinderman[2]. . . . . . . . . . . . . . 5
2.2 Astressdistributioncurveusinganalyticalmethodsfordifferentoverlaplengthsinasinglelap
joint.Stresspeaksattheendsdecreasethelongertheoverlaplengthbecomes.TakenfromKelly
[3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Differenttypesoftaperedendstoreducestresspeaks.TakenfromGleichetal.[4]. . . . . . . . . 6
2.4 Generalised depictions of stress peaks at adhesive and adherend interfaces at the joint end,
denotedbystrengthpresence.TakenfromdaSilvaandCampilho[5]. . . . . . . . . . . . . . . . . 7
2.5 Tapersandroundingsatjointendsandtheirinfluencesonstresspeaksanddistribution.Smaller
angledtapersresultinlowerstressesthroughoutthejointandlargerroundingsresultinamore
spreadoutstressdistributionatthejointends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.6 Correct and incorrect designs of composite bonded joints with optimal fibre orientation de-
pendingondifferentshearandtensileloads.TakenfromESA[1]. . . . . . . . . . . . . . . . . . . 8
2.7 Cohesivefailuremodesinbondedjoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.8 Adhesivefailuremodesinbondedjoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.9 Adherendfailuremodesinbondedjoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.10 Overviewoffailuremodeswithincompositematerial. Fractureresistancedenotion(R),fibre
failure(FF)orinterfibrefailure(IFF),normalfracture(NF)orshearfracture(SF),tension(t)
orcompression(c)andparallel(∥)orperpendicular(⊥)loadingtofibres. SeeTable2.3fora
tabularoverview.TakenfromCuntze[6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.11 Stresssingularitiesatcracktipsandmaterialinterfaces.TakenfromdaSilvaandCampilho[5]. . 12
2.12 ContouroftheJ-integralaroundacracktip.Thecontourenclosesthecracktipwhereplasticity
occurs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.13 Depictionofthevirtualcrackclosuretechnique. Leftfiguredepictsaglobalsystemwhilethe
rightfigureshowsthelocalsystemwherethevirtualworktakesplace.TakenfromKrueger[7]. . 14
2.14 3D coordinate system (x ,x ,x ) of UD composite element, with fibre direction x , laminate
1 2 3 1
mid-surfacex andthicknessdirectionx .Rotationfailureplaneangleθ resultsincoordinate
2 3 fp
system(x ,x ,x ),withfibredirectionx ,normaldirectiontofailureplanex andtangential
1 n t 1 n
directiontofailureplane x . Normalstressesσ arenotedasσ andshearstressσ asτ .
t ii i ij ij
TakenfromPuckandSchürmann[8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.15 FractureenvelopeforPuck’smatrixfailuremodesA,BandC,depictingthedifferentfracture
resistancesandpositionsofthefailuremodesonthestresscoordinatesystem.TakenfromPuck
andSchürmann[8].. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.16 Angleθ representationinPuck’scriterioninMSC.Marc. . . . . . . . . . . . . . . . . . . . . . . . 24
fp
3.1 Simpleillustrationsofacohesivezoneelementresemblingasimplifiedspring-damperconfig-
urationandthedeformationofacohesivezoneelement. TakenfromKregting[9]andBosch
etal.[10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Positionofrelativedisplacementbetweenopposingpointpairsofaloadedbondedjointinthe
tractionlaw. Exampleofabondedjointsincontinuumapproach. TakenfromKhoramishad
etal.[11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Reversibleandirreversiblebehaviourandtheeffectofelasticandplasticloadingandreloading. 29
3.4 Anexampleofabilineartractionlaw.CodefoundinAppendixD. . . . . . . . . . . . . . . . . . . 31
3.5 Anexampleofatrapezoidaltractionlaw.CodefoundinAppendixD. . . . . . . . . . . . . . . . . 31
3.6 Anexampleofanexponentialtractionlaw.CodefoundinAppendixD. . . . . . . . . . . . . . . . 32
3.7 A3Dcohesivezoneelementinareferenceandlocalcoordinatesystem. . . . . . . . . . . . . . . 33
3.8 Thethreedifferentfracturemodes:tensile(ModeI),shear(ModeII)andtear(ModeIII). . . . . 34
vii
viii LISTOFFIGURES
3.9 3D view of a mixed-mode exponential traction law based on Ye’s criterion. Any moment in
mixed-modeloadingcanbetracedtoapointonthesurfaceofthe3Dgraph. Codefoundin
AppendixD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.10 Influenceofmaximumtractionandcriticalenergyreleaserate.. . . . . . . . . . . . . . . . . . . . 36
3.11 3Dinterfaceelementwithareferencesystembasedonanintegrationpoint. TakenfromMarc
2010VolumeA:TheoryandUserInformation[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.12 MSC.Marc’sthreebuilt-intractionlaws:Bilinear(left),exponential(middle),linear-exponential
(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.13 ExampleofMSC.Marc’sbuiltinmixed-modecalculationbetweenpureModesIandIIforan
exponentialtractionlaw.CodefoundinAppendixD. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.14 3Dviewofamixed-modeexponentialtractionlawbasedonMSC.Marc’salgorithm. Therela-
tionsβ andβ arehighlightedasredarrowstodistinguishtheirinfluenceinthemixed-mode
1 2
surfacegraph.CodefoundinAppendixD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1 MMBtestsetups.TakenfromTuronetal.[13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 SimplifiedmodelofMMBspecimenwithlengthx,widthy,totalthickness2z,adhesiveregion
aandinitialcrackregiona . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
0
4.3 Graphicaloverviewofnumericalandexperimentalresultsofallfivesetups. TakenfromTuron
etal.[13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 MSC.Marcmodelofthe0%fracturemode,orDCB,setup. . . . . . . . . . . . . . . . . . . . . . . . 46
4.5 MSC.Marcmodelofthe50%fracturemodesetup. Leverlengthc differsfor20%and80%frac-
turemoderatios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.6 MSC.Marcmodelofthe100%fracturemode,orENF,setup. . . . . . . . . . . . . . . . . . . . . . . 48
4.7 MSC.Marcmodelofthe0%fracturemode,orDCB,setup. . . . . . . . . . . . . . . . . . . . . . . . 50
4.8 MSC.Marcmodelofthe50%fracturemodesetup. Leverlengthc differsfor20%and80%frac-
turemoderatios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.9 MSC.Marcmodelofthe100%fracturemode,orENF,setup. . . . . . . . . . . . . . . . . . . . . . . 52
4.10 DamagelevelsinfirstCZEs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.11 DamageandtractioninaCZE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.1 SimpledrawingofCLSspecimen,withstrap(1),bondlines(2),lap(3),foot(4),clamps(5),strain
gauges(6)andtrigger(7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Reallifespecimenwithstraingauges(orange),bottomview. Footislocatedontheright,and
twoofthethreestraingaugescanbeseen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 Tractionlawsofthecohesivepropertiesoftheadhesives. Notethatthelaminateadhesiveis
strongerinbothmodesthanthebondlineadhesive. . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 SimplifieddrawingofCLSspecimenwithstraingauges:straptopgauge(1),strapbottomgauge
(2)andlapgauge(3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5 Real life CLS experiment results, retrieved with data from the strain gauges and the loading
mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.6 ModelviewsoftheCLSspecimen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.7 ViewofstrapwithreducedelementsizetohighlighttheCZE(blue)betweenthepliesandbulk
region(purple)inthestrapadherend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.8 Close-upsideviewofconstraintsonbothends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.9 Viewoftriggerrestingonlap.Strapismadeinvisible.Notethatthetriggersymbolisestheinitial
crackregiona . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
0
5.10 Strain-LoadresultsofPuckmodel.Thedropinstrainofthelapgaugeindicatesthefailureload. 69
A.1 ContactTablePropertiesfor2Dand3Dmodels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
A.2 Rigidleverasinthe50%moderatiosimulations.Greycircle(1)isthenodewithdisplacement.
Bluecircles(2)arenodesthataretied.Greencircles(3)arenodesthatshareDOF.Theredlines
onthemodelarenodesthataretiedbyDOFtothemiddlenodes. . . . . . . . . . . . . . . . . . . 79
A.3 3Dmodelsindeformedshape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
A.4 Resultsofthe0%fracturemodesetupfor2Dsimulations1through8withvaryingcohesivezone
modelsettings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
A.5 Resultsofthe0%fracturemodesetupfor2Dsimulations1through14. . . . . . . . . . . . . . . . 82