Effect of Fiber Waviness

13 Pages·2017·7.1 MB·English

materials
Article
Failure Behavior of Unidirectional Composites under
Compression Loading: Effect of Fiber Waviness
SwaroopNarayananNair1,2 ID,AravindDasari3,* ID,CheeYoonYue2
andSrikanthNarasimalu4 ID
1 EnergyResearchInstituteatNTU/InterdisciplinaryGraduateSchool,NanyangTechnologicalUniversity,
blockS2-B3a-01,50NanyangAvenue,Singapore639798,Singapore;[email protected]
2 SchoolofMechanicalandAerospaceEngineering,NanyangTechnologicalUniversity,Singapore,
50NanyangAvenue,Singapore639798,Singapore;[email protected]
3 SchoolofMaterialsScience&Engineering,NanyangTechnologicalUniversity,50NanyangAvenue,
Singapore639798,Singapore
4 EnergyResearchInstituteatNTU,NanyangTechnologicalUniversity,CleantechOne,1Cleantechloop,
#06-04,Singapore637141,Singapore;[email protected]
* Correspondence:[email protected];Tel.:[phone]
Received:5July2017;Accepted:1August2017;Published:5August2017
Abstract: Thekeyobjectiveofthisworkistohighlighttheeffectofmanufacturing-inducedfiber
wavinessdefectsonthecompressivefailureofglassfiber-reinforcedunidirectionalspecimens. For
thispurpose,in-plane,through-thicknesswavinessdefects(withdifferentwavinessseverities)are
inducedduringthemanufacturingofthelaminate. Numericalandexperimentalresultsshowthat
thecompressivestrengthofthecompositesdecreasesastheseverityofthewavinessdefectsincreases.
A reduction of up to 75% is noted with a wave severity of 0.075. Optical and scanning electron
microscopy observations of the failed specimens reveal that kink-bands are created in the wavy
regionsandleadtofailure.
Keywords: windturbineblades;defects;laminates;in-planefiberwaviness;compressivestrength;
kink-band;failure;numericalandexperimentalanalyses
1. Introduction
Compressivestrengthofcompositelaminatesisoneofthemajordesigndriversinwindturbine
industry. Compressivefailureinthesematerialsiscomplex,suddenandcatastrophicasitinvolves
multiple modes of failure like fiber kinking, splitting, buckling and delamination [1–4]. In 1965,
Rosen[1]attributedcompressivefailuretoelasticinstabilitiesresultinginafiber-bucklingmechanism.
However,subsequentstudieshaveconcludedthatcompressivefailureoffiber-reinforcedcomposites
is predominantly a result of plastic micro-buckling of the fibers in an idealized inelastic matrix
medium [2]. Other modes of failure that have been reported include fiber kinking, splitting, and
delamination. Alongthesamelines,Kyriakydesetal.[5]haveobservedregularlyspacedin-plane
kink-bandswithawidthof~1–1.5mmduringcompressiontestingofthecomposites. Inaddition,
VoglerandKyriakides[6,7]haveshownthatkink-bandformationisapost-bucklingeventandstarts
fromalocalimperfectioninthesample. Inamicromechanicalstudy,Prabhakaretal.[8]haveobserved
aninteractionbetweenthefailuremodeslikekink-bandandsplitting,andconcludedthatmodeII
cohesiveshearstrengthhasagreaterinfluenceonthisfailuremodeinteraction.
Despitethesignificantadvancementsinmaterialsaswellasdesignandmanufacturingofthe
composites, ensuringalongerlifeforthebladeshasbeenagreatchallenge. Windturbinesystem
reliabilityisacriticalfactorforoptimizingthecosts[9]. Severalcollaborativeeffortsbetweenindustry
andacademiahavegoneintounderstandingandimprovingthereliabilityofwindturbineblades,with
Materials2017,10,909;doi:10.3390/ma10080909 www.mdpi.com/journal/materials
Materials2017,10,909 2of13
specificemphasisonflowcharacterizationandmanufacturingdefects[10,11]. Theseandseveralother
studiesonfailedwindturbinebladesbasedonfiber-reinforcedcompositelaminateshavesuggested
thatmanufacturingflawslikevoids,porosity,improperwettingoffiberswithresin,misalignmentof
fibers,andbondingdefectsplayakeyroleintheirfailure[11–14]. A30%–50%dropinthecompressive
strengthofthelaminatehasbeenobservedevenwithaminorfibermisalignmentof~5◦[15]. Athigher
off-axisangles(10◦ <θ<15◦),thecompressivestrengthfurtherdroppedto70%. AdamsandBell[16]
studied two-layer out-of-plane waviness on a unidirectional ply at the middle of an eight-layered
cross-ply laminate. They noted a ~36% reduction in compressive strength of the wavy laminate.
Mandelletal.[17]studiedtheeffectoffiberwavinesswithvariousglassandcarbonfabricsusedin
windturbineblades.Theyalsonotedadropincompressivestrengthwithanincreaseinthepercentage
of 0◦ layers containing waviness. Several other studies have also reported similar observations
of reduced compressive strength in the presence of waviness defects [10,18]. Though there are
manytypesoffiberwaviness,inthepresentwork,wewillbefocusingontheeffectofanin-plane,
through-thicknesssinglesinewavewithdifferentseveritylevelsundercompressionloading. Rather
thandegradationinmaterialproperties,theemphasiswillbeonthefailuremodesandmechanisms.
Thisisimportantbecauselimitedresearchisavailablethatcombinesbothexperimentalandnumerical
approachestoexplainthefailureoftheselaminates.
2. ExperimentalWork
2.1. MaterialsandProcessing
E-glass0◦ (WeeTeeTongUT800,Singapore)fabricswereusedinthisstudyalongwithepoxy
resin as matrix material (Epikote RIMR—135 (HexionTM, Kedah, Malaysia) as base and Epikure
RIMR—137 (HexionTM, Kedah, Malaysia) as hardener). This grade of resin is commercially used
forwindturbineblademanufacturingandhenceadoptedinthisstudy. Anin-planewavylaminate
panelwasmanufacturedbyinducingawavewiththehelpofacylindricalrodoneachlaminaofthe
unidirectionalfabric. ThiswholeprocessisshownschematicallyinFigure1. AsshowninFigure1a,
initially,out-of-planefiberwavinesswasinducedwithawavelengthof≈35mm,andsubsequentlya
uniformshearloadwasappliedfor~5to10minnormaltothefiberdirectionandalongthefiberfabric
planetorenderitin-plane(seeFigure1b). Eachlaminaundergoesthesameprocessbeforestacking
andcuring. Differentwaveseveritieswereachievedbychangingthewaveamplituderatherthan
changingthewavelengthofthedefect(duetosizelimitationsfortestingandanalysis). Anaverage
waveheight(twicetheamplitude)of0.7,1.75,2.45and5.25mmweremeasuredfromeachpanelafter
thecuringandfinalwaveseveritywascalculated.
Thesixlayer([0] )panelswerepreparedwithdifferentwaveseveritylevelsusingunidirectional
6
glassfabrics. Eachlayerhasanaveragethicknessof0.62mm. Thecompositepanelfabricationwas
doneusingVacuumAssistedResinInfusionMethod(VARIM).Thecureprofileemployedwas24h
atroomtemperature,followedbyapost-curingstepinanovenfor15hat60◦C.Thefibervolume
fractionofthecuredpanelswasmeasuredtobeintherangeof0.52to0.57basedonASTMD2584[19].
Materials2017,10,909 3of13

Materials 2017, 10, 909   3 of 13

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outo-uotf‐-opfl‐apnlaenwe awvaevwe withithth teheh heleplpo offa ac cyylilinnddrriiccaall ttuubbee,, ((bb)) oouutt‐-ooff‐-pplalannee fifibberesr safatfetre rthteh erermemovoavl aolf othfeth e
tubtue,b(ec,) (ac)p applypilnyigngin i-np‐lpalnaenes hsheaearrt otom maakkee fifibbeerrss iinn-‐ppllaannee,, ((dd)) aa ttoopp vvieieww oof fththe elalmaminian,a (,e()e p)rpevreievwie wof of
thethine -ipnl‐apnlaenwe awvayvfiy bfiebresr,sa, nadnd(f ()f)d defiefninitiitoionno offfi fibbeerr wwaavvee sseevveerriittyy..  
2.2. Definition of Fiber Wave Severity 
2.2. DefinitionofFiberWaveSeverity
The definition of fiber waviness in the composites was first introduced by Joyce et al. [15,20] as 
The definition of fiber waviness in the composites was first introduced by Joyce et al. [15,20]
follows: (cid:1877)(cid:3404)(cid:1827)sin(cid:4666)2(cid:2024)(cid:1876)/(cid:1838)(cid:4667) for a sinusoidal wave where the mean fiber position is parallel to the 
as follows: y = Asin(2πx/L) for a sinusoidal wave where the mean fiber position is parallel to
longitudinal fiber axis. A statistical approach followed with the help of computer‐aided optical 
thelongitudinalfiberaxis. Astatisticalapproachfollowedwiththehelpofcomputer-aidedoptical
microscope to measure the wave amplitude (A) and wave length (L). The intensity of the fiber 
microscopetomeasurethewaveamplitude(A)andwavelength(L).Theintensityofthefiberwaviness
waviness was quantified with a term called fiber wave severity (Ws), which is the ratio of A to L (see 
wasquantifiedwithatermcalledfiberwaveseverity(W ),whichistheratioofAtoL(seeFigure1f).
Figure 1f). After the curing of composite panels, amplitsude and wavelength of the fiber waviness 
Afterthecuringofcompositepanels,amplitudeandwavelengthofthefiberwavinesswereagain
were again measured with the help of an optical microscope. The final fiber wave severity was taken 
measuredwiththehelpofanopticalmicroscope. Thefinalfiberwaveseveritywastakenbasedonthe
based on the average values measured at different locations of the cured panel. 
averagevaluesmeasuredatdifferentlocationsofthecuredpanel.
2.3. Compression Testing 
2.3. CompressionTesting
Compression tests were conducted as per ASTM D6641 standard [21] on a 100 kN servo‐
CompressiontestswereconductedasperASTMD6641standard[21]ona100kNservo-hydraulic
hydraulic Instron 8801 machine (Singapore) with Zwick Hydraulic Composite Compression Fixture 
Ins(tHroCnC8F8) 0(1Simngaacphoirnee). (ASi ntygpaipcaolr ec)omwpitrhesZsiwonic kexHpeyrdimraeunlti cspCeocimmpeno switeasC 1o4m0 ptor e1s5s0i omnmF ilxotnugr ean(Hd C1C3 F)
(Sinmgmap woirdee). wAitthy painc aulncsoumppporretsesdio gnauexgpe elreinmgtehn tosf p1e3c tiom 2e0n mwmas. 1T4o0 atvoo1id5 0pmremmaltounreg faanildur1e3 omvemr twheid  e
witghagaen luennsguthp,p ao rstmedoogtahu sgpeelceinmgetnh eodfg1e3 atond2 0am sumff.icTioenatv souidrfapcree mroautguhrenefassil uforer othvee rtatbh ebgonagdeinlge nwgaths ,a
smroeoctohmsmpeecnidmeedn [2e2d]g. eThaen ddeafescutf‐ficocnietnaitnsiunrgf ascpeecriomuegnhsn hesasvefo arnt hine‐ptalbanbeo wndaviningewssa dserfeeccot matm theen dgaeudg[e2 2].
Theardeeaf. eAct w-coidnttha ionfi 2n5g mspmec wimase ncsonhsaivdeeraendi fno-rp dlaenfeecwt‐ianvdinuecsesd dsepfeeccitmaetnths e(sgeaeu Fgigeuarree a2.) Ato wmiidntihmoizfe2 5thme m
wapsecrocennstiadgeer eadmfoourndt eoffe cdti-sicnodnuticneudousps efcibimeres ndsu(es etoe Fwiagvuirnees2s) itnocmlusinioimn iinz eththe ecopueprcoenn. tCagomeapmreossuionnt of
distceosnt tfiinxutuoruess fiwbeerres sdeuleectteodw baavseinde ossn icnocmlubsiinoendi nshtheaerc aonudp oenn.dC looamdpinrges [s6io,7n]. tTeshtefi cxotmurbeisnewde reendse alencdte d
bassehdeaor nlocaodms bwienreed asphpeliaerda hnyddreanudlicloaalldy ionng t[h6e,7 c]o.uTphoenc aotm a bcionnesdtaennt dcraonssdhesahde asrpleoeadd osf w1 emrema/mppinli.e d
hydCroamuplirceaslslyivoe nsttrhaiencso wueproen maetaasucroends utasnintgc rsotrsasihne gaadusgpese e(1d2o0 fΩ1) mbomnd/emdi non. Cbootmh psirdeesss iovfe thster acoinuspwone re
megaasuugree darueasi. nTghes tbroanindegda ustgreasin( 1g2a0geΩs )onb obnodthe dsidoens boof tthhes igdaegse opfatrht ewceoreu cpoonnngecatuedg etoa trheea .dTahtae lobgognedre d
for the compressive strain measurement. During the test, failure progression was captured using a 
straingagesonbothsidesofthegagepartwereconnectedtothedataloggerforthecompressivestrain
high‐resolution video camera at the rate of 50 frames/s. Tests on each fiber wave severity specimen 
measurement. Duringthetest,failureprogressionwascapturedusingahigh-resolutionvideocamera
were repeated 5 times for getting statistically significant data. 
attherateof50frames/s. Testsoneachfiberwaveseverityspecimenwererepeated5timesforgetting
statisticallysignificantdata.
Materials2017,10,909 4of13

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Materials 2017, 10, 909   4 of 13

FigurFeig2u.re( a2.) (Sa)c hScehmemataictico off aa ttyyppiiccaal lcocmomprpersesisosnio tnestt espstecsipmeecni,m anend ,(ba)n tdhe( bac)tuthale HaCctCuFa sleHt uCpC wFitshe t up
withssaammppllee. .  
Figure 2. (a) Schematic of a typical compression test specimen, and (b) the actual HCCF set up with 
3. Finite Element Model (FEM) 
3. FiniteEsalmemplee.n  tModel(FEM)
A 3D finite element model of the entire experimental specimen was built in Abaqus/Explicit for 
A3DfiniteelementmodeloftheentireexperimentalspecimenwasbuiltinAbaqus/Explicitfor
3d.i rFeicnti teco Emlepmareinsot nM owdiethl  (FeExMpe)r imental  results.  The  failure  modes  observed  on  unidirectional 
directcomparisonwithexperimentalresults. Thefailuremodesobservedonunidirectionalspecimens
specimens without waviness defects were not detailed in this FEM analysis. A macro‐mechanical 
A 3D finite element model of the entire experimental specimen was built in Abaqus/Explicit for 
withomuotdwela wvians eusssedd ewfeitcht sawn eexreplnicoitt ddyentaamileicd sionlvtehr iast FqEuMasia‐sntaatliyc sliosa.dAingm raacterso. -Tmheec phlaiensi cwaelrme boudieltl was
direct  comparison  with  experimental  results.  The  failure  modes  observed  on  unidirectional 
useduwsiinthg aann e8x‐npoldicei tbdriycnk aemlemicesnotl vweirtha treqduuacseid-s itnatteicgrlaotaiodnin Cg3rDa8tRes a.nTdh eonpel ieelsemweenrte tbhuicikltnuesssi nfogr aenac8h- node
specimens without waviness defects were not detailed in this FEM analysis. A macro‐mechanical 
brickpellye. mIne nthtew aitchturael deuxcpeedriminetnetg, rtahteioren wCa3sD n8oR daanmdaogne etoe lethme etnabt tmhiactkenrieasl safnodr ethaec hadphlye.siIvne tjhoeinat ctual
model was used with an explicit dynamic solver at quasi‐static loading rates. The plies were built 
experuoibsmisneegrnv aten,d t.8h H‐eneroendcewe ,b atrasibcnkso  weldeermaem emnaotg dweeilttlohe drt hebdeaustecadebd o mnin aate thgeirrgaihati lsotanifn fCnd3eDtshs8 egRl aaasdnshd fe iobsneivre  reeeljieonmifnoertncote dbth spiecorklvnyemedses. rf H(oGre FenRaccPeh),  tabs
composite. The entire laminate with in‐plane waviness was meshed in the gage section of the part 
werepmlyo. dIenl ltehde baacstueadl oenxpaerhiimgehnst,t itfhfneeres swgalas snsofi bdearmraegien ftoor ctehde ptaobl ymmaeterr(iaGl FaRnPd) tchoem apdohseistiev.eT jhoiente ntire
geometry. Minimum building block in the model is lamina level, hence all the elements at the wavy 
laminoabtseerwveidth. Hinen-pcela, tnaebsw waevrien mesosdewllaeds mbaesesdh eodn ain hitghhe sgtiaffgneessse gcltaisosn fiboefrt rheeinpfoarrctedg epoomlyemteryr .(GMFRinPi)m  um
regions were oriented through a discrete path (see Figure 3) that looked like the fiber waviness in the 
buildcionmgpbolosictke. iTnhteh eenmtiroed leamliisnlaatme winitahl einv‐epll,ahnee nwceavailnletshs ewealse mmeenshtseda tinth tehew gaavgye rseecgtiioonn sowf tehree poarrite nted
experimental samples. A mesh refinement study was conducted on the waviness‐induced laminate 
througgehomadetirsyc.r Meteinpimatuhm(s beueilFdiignugr ebl3o)ckth iant tlhoeo mkeoddelilk ies ltahmeifinbae lrevweal,v hiennecses ainll tthhee eelxepmeernimts eant ttahles wamavpyl es.A
until the change in predicted failure load was less than 1% (see Figure 4) and an optimum mesh size 
regions were oriented through a discrete path (see Figure 3) that looked like the fiber waviness in the 
meshrefinementstudywasconductedonthewaviness-inducedlaminateuntilthechangeinpredicted
of 0.4 mm was selected. The thickness of the element was similar to the average ply thickness of 0.62 
experimental samples. A mesh refinement study was conducted on the waviness‐induced laminate 
failurmemlo.a Tdhew sapsecleimssenth manod1e%l se(scetieonF iwgausr aeb4o)uat n3d.72a nmmop tthimicku amndm 2e5s mhmsi zweidoef. 0.4mmwasselected. The
until the change in predicted failure load was less than 1% (see Figure 4) and an optimum mesh size 
thicknessoftheelementwassimilartotheaverageplythicknessof0.62mm. Thespecimenmodel
of 0.4 mm was selected. The thickness of the element was similar to the average ply thickness of 0.62 
sectionwasabout3.72mmthickand25mmwide.
mm. The specimen model section was about 3.72 mm thick and 25 mm wide. 

Figure 3. (a) Abaqus model with closely packed mesh, (b) mesh flow in the gage area along the 
waviness path, and (c) element orientation in the waviness region.   
Figure 3. (a) Abaqus model with closely packed mesh, (b) mesh flow in the gage area along the 
Figure 3. (a) Abaqus model with closely packed mesh, (b) mesh flow in the gage area along the
waviness path, and (c) element orientation in the waviness region. 
wavinesspath,and(c)elementorientationinthewavinessregion.
Materials2017,10,909 5of13
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FFiigguurree4 4..M Meesshhr reefifnineemmeennttf oforrt htheew waavveei nindduucceeddm mooddeell( w(waavvees seevveerirtiyty= =0 0.0.07755)).. 
In general, the failure theories included in Abaqus (Max Stress and Max Strain, or Tsai‐Wu and 
In general, the failure theories included in Abaqus (Max Stress and Max Strain, or Tsai-Wu
Tsai‐Hill models) are not based on the individual constituents and result in poor prediction. 
and Tsai-Hill models) are not based on the individual constituents and result in poor prediction.
Therefore, in this work, an Autodesk add‐on for the simulation of composite analysis called Helius 
Therefore,inthiswork,anAutodeskadd-onforthesimulationofcompositeanalysiscalledHelius
PFA (Progressive Failure Analysis) [23] was attached to the Abaqus model to predict the damage in 
PFA(ProgressiveFailureAnalysis)[23]wasattachedtotheAbaqusmodeltopredictthedamageinthe
the composite structures. This plug‐in helps to incorporate the constituent (matrix and fiber) level 
compositestructures. Thisplug-inhelpstoincorporatetheconstituent(matrixandfiber)levelfailure
failure initiation criteria like MCT (Multi continuum theory) based failure [24], Christensen [25], Puck 
initiationcriterialikeMCT(Multicontinuumtheory)basedfailure[24],Christensen[25],Puck[26]
[26] and LaRC02 [27] into the Abaqus software (Dassault systems, v6.13, SIMULIA, Johnston, RI, 
andLaRC02[27]intotheAbaqussoftware(Dassaultsystems,v6.13,SIMULIA,Johnston,RI,USA).
USA). Helius PFA uses separate material manager to include the composite lamina properties. Based 
HeliusPFAusesseparatematerialmanagertoincludethecompositelaminaproperties. Basedonthe
on the input provided to the material manager, Helius PFA provides the constitutive relations for 
inputprovidedtothematerialmanager,HeliusPFAprovidestheconstitutiverelationsforcomposite
composite materials as per the required failure theory to the Abaqus input. As seen in Table 1, the 
materialsaspertherequiredfailuretheorytotheAbaqusinput. AsseeninTable1,thelaminamaterial
lamina material properties were derived from the individual material properties input (fiber and 
properties were derived from the individual material properties input (fiber and resin properties)
resin properties) given to the material manager of Helius PFA. 
giventothematerialmanagerofHeliusPFA.
In the current work, LaRC02 failure criterion (based on an improvement to Hashin’s model) was 
Inthecurrentwork,LaRC02failurecriterion(basedonanimprovementtoHashin’smodel)was
preferred as it combines the fracture plane concept of Puck [26] as well. This criterion identifies the 
preferredasitcombinesthefractureplaneconceptofPuck[26]aswell. Thiscriterionidentifiesthe
fiber failure and matrix cracking in unidirectional composites (initiation and instantaneous damage 
fiberfailureandmatrixcrackinginunidirectionalcomposites(initiationandinstantaneousdamage
progression) [26,28] based on the below mentioned constitutive relations. The uniaxial tensile 
progression)[26,28]basedonthebelowmentionedconstitutiverelations. Theuniaxialtensilestrength
(sStre)n,cgothm p(Sr1e1s),s icvoemstprerensgstihve(- Sstre),nagnthd i(n‐S-p11l)a, naensdh iena‐rpsltarnene gsthhe(aSr s)trwenergetho b(tSa1i2n) ewdefrreo mobtthaeineexdp efrriomme nthtse 
11 11 12
ceoxnpdeuricmteedn.tTs hceonoduut-cotfe-dp.l aTnhee sohueta‐rofs‐tprelanngeth shveaalur esstrSengatnhd vaSluews eSr2e3 aconnds Sid13e wreedree qcuoanlsitdoetrheedi neq-pulaaln teo 
23 13
sthheea irnv‐palluane.e Tshheeatrr avnaslvueer. sTehpea trraamnsevteerrsseS paarnamdeSterws Se2r2e atnadke Sn33a wse√re3 ttaikmeens aosf S√3 .times of S23. 
22 33 23
Individual plies were defined under a composite layup sequence with orthotropic non‐linear 
Individualpliesweredefinedunderacompositelayupsequencewithorthotropicnon-linear
elastic material properties based on experimental measurements. Experiments were conducted on 
elasticmaterialpropertiesbasedonexperimentalmeasurements. Experimentswereconductedon
the same material to determine the maximum tensile, compressive and shear strength properties. The 
the same material to determine the maximum tensile, compressive and shear strength properties.
detailed material properties used for the model are listed in Tables 1–3. Based on the LaRC02 failure 
ThedetailedmaterialpropertiesusedforthemodelarelistedinTables1–3. BasedontheLaRC02
criterion under uniaxial compression loading: (1) Fiber failure is further divided into (1.a) fiber 
failurecriterionunderuniaxialcompressionloading: (1)Fiberfailureisfurtherdividedinto(1.a)fiber
compressive failure with matrix compression, and (1.b) fiber compressive failure with matrix tension. 
compressivefailurewithmatrixcompression,and(1.b)fibercompressivefailurewithmatrixtension.
(2) Matrix cracking is again divided into (2.a) matrix cracking in tension, and (2.b) matrix cracking in 
(2)Matrixcrackingisagaindividedinto(2.a)matrixcrackingintension,and(2.b)matrixcracking
compression. For the current model, due to the presence of fiber waviness imperfections in the cured 
incompression. Forthecurrentmodel, duetothepresenceoffiberwavinessimperfectionsinthe
laminate, it was assumed that majority of failure progression occurred due to fiber kinking. The fiber 
cured laminate, it was assumed that majority of failure progression occurred due to fiber kinking.
compression  failure  scenario  was  explained  due  to  the  collapse  of  fibers  subjected  to  initial 
Thefibercompressionfailurescenariowasexplainedduetothecollapseoffiberssubjectedtoinitial
misalignment, leading to shear kinking and further extending to the supporting matrix [29,30]. 
misalignment,leadingtoshearkinkingandfurtherextendingtothesupportingmatrix[29,30].
Materials2017,10,909 6of13
(1) As mentioned earlier, under fiber compression σ < 0, two stress states (matrix under
11
compressionandmatrixundertension)wereconsideredtoevaluatethefiberfailure[1].
(1.a) Formatrixcompression(σm <0)
22
(cid:12) (cid:12)
(cid:12)τm(cid:12)+ηLσm
FailureindexFI = (cid:104) 12 22(cid:105) (1)
F SL
(1.b) Formatrixtension(σm ≥0)
22
(cid:18)σm(cid:19)2 (cid:18)τm(cid:19)2
FailureindexFI = 22 + 12 (2)
F YT SL
(2) Forthematrixcompressionfailurecriterion,
(2.a) σ ≥YC
11
(cid:32)τT (cid:33)2 (cid:32)τL (cid:33)2
eff eff
FailureindexFI = + (3)
M ST SL
(2.b) σ ≤ YC at this stage the material is in a moderate biaxial compressive state and the
11
conditionis,
(cid:32)τmT(cid:33)2 (cid:32)τmL(cid:33)2
eff eff
FailureindexFI = + (4)
M ST SL
whereτmT andτmLarefunctionsofthefractureangleαwhichwilldetermineduringtheiteration.
eff eff
YT =Valueofσ attransversetensilefailure
22
YC =Valueofσ attransversecompressivefailure
22
SL =Absolutevalueofσ atlongitudinalshearfailure
12
ST =Absolutevalueofσ attransverseshearfailure
23
α =Angleofthefractureplanethatmaximizesthefailureindex(FI)
SubscriptMrepresentsthematrixandFrepresentsthefiber.
BasedontheseconstitutiveequationsofLaRC02failurecriteria, Abaqusidentifiesthefailure
initiationatindividualintegrationpointsinthemodel. TheresultswereinterpretedbasedontheState
DependentVariables(SDV).SDV=1.0,signifiesnodamageinbothfiberandmatrixandSDV=2.0
signifiesfailedmatrix. WhenSDVreaches3.0onaspecifiedlocation,itwasconfirmedthatbothmatrix
andfiberfailedinthatarea.
Table1.ConstituentelasticpropertiesusedintheAbaqusmodel(basedonmaterialdatasheet).
Fiber Matrix
Young’sModulusE (GPa) Poisson’sRatio ShearModulusG (GPa) Poisson’sRatio
f 12
73 0.24 1.2 0.35
Table2.LaminastrengthpropertiesusedintheAbaqusmodel(Experimentallydetermined).
UltimateTensileStrengthXT UltimateCompressiveStrengthXC UltimateShearStrengthG12
(MPa) (MPa) (MPa)
728 630 50
Materials2017,10,909 7of13
Table3.Comparisonoflaminamaterialpropertiesfromexperimentandmodel.
Elasticproperties E11(GPa) E22(GPa) G12(GPa) ν12
BasedonAutodeskHeliusPFA 41.4 9.99 3.58 0.27
Fromexperiment 41.4 10.29 2.78 0.28
3.1. DamageEvolution
The damage evaluation process starts immediately after the damage initiated at any of the
individualintegrationpoints. Aninstantaneousdegradationmethodwasfollowedforthestiffness
degradation. Thedegradationratioforboththematrixandfiberwerepredefinedasusermaterial

Mcoatnersitaalsn 2t0s17(,U 10M, 9C09)  before the analysis. In here, UMC for matrix was set as 0.1 and for fiber, i7t owf 1a3s
1×10−6.
3.2. Boundary Conditions 
3.2. BoundaryConditions
In the model, one end of the specimen was fixed and a quasi‐static displacement load was 
appliIend tohne thmeo odtehle,ro enned.e Fnudlloyf ctohnestsrpaeinceimd ebnouwnadsarfiyx ceodnadnitdioansq wuaersei- satpaptilcieddi sopnl athcee mleeftn (tfilxoeadd) ewnads 
aanpdp ldieisdpolanctehmeeontth berouenndd.aFryu lcloyncdointisotrnasi nweedreb oaupnpdliaerdy tcoo tnhdei tliooands dwireerectaiopnp lbieyd coonnstthraeilneifntg(fi txheed o)tehnedr 
dainrdecdtiiosnpsla tcoe ma erenftebreonucned paoryinct oonnd tihtieo nrisgwhte reendap. pTlhieed retofetrhenecleo apdoidnitr eacntido nthbey ricgohnts etrnadin oinf gthteh emootdheelr 
wdierreec tbioonnsdteoda wreiftehr eannc eeqpuoaintitoonn bthaseerdi gdhitreenctdio.nTahl ecroenfestrreanicnet.p Sooin, tthane ddtihspelraicgehmteenntd goifvtehne tmo otdheel 
rwefeerreebnocne dpeodinwt iwthoaunlde qruefalteicotn tboa tsheed rdigirhetc teionnda flaccoen ostfr tahinet .mSood,ethl.e Fdigisuprlea c5e msheonwtgs itvheen 2toDt hveierwef eorfe tnhcee 
tpriominmtwedo muloddreelfl weicttht o6 ltahyeerrisg ohft pelnyd mfaatceerioafl,t thaeb mboonddeiln.gF iwgiuthre b5oushnodwarsyt choen2dDitivoinesw ato bfoththe etnridms manedd 
tmabo dsiedlews.i th6layersofplymaterial,tabbondingwithboundaryconditionsatbothendsandtabsides.

Figure 5. Boundary conditions at both ends of the sample. 
Figure5.Boundaryconditionsatbothendsofthesample.
4. Results and Discussion 
4. ResultsandDiscussion
4.1. Effect of Waviness Defect on Compressive Strength 
4.1. EffectofWavinessDefectonCompressiveStrength
As listed in Table 4, the mean failure strength of the composites significantly decreases with 
As listed in Table 4, the mean failure strength of the composites significantly decreases with
increase in fiber wave severity. For instance, with a severity of 0.075, a 75% drop in strength is noted. 
increaseinfiberwaveseverity. Forinstance,withaseverityof0.075,a75%dropinstrengthisnoted.
Joyce and Moon [15] have reported a similar but linear trend of decreasing compressive strength with 
JoyceandMoon[15]havereportedasimilarbutlineartrendofdecreasingcompressivestrengthwith
increasing (in‐plane) fiber waviness severity. This has been attributed to the formation of kink‐bands 
increasing(in-plane)fiberwavinessseverity. Thishasbeenattributedtotheformationofkink-bands
at the fiber misorientation sites in the wavy regions leading to a catastrophic failure. In the current 
atthefibermisorientationsitesinthewavyregionsleadingtoacatastrophicfailure. Inthecurrent
work, though a catastrophic failure is observed with defect‐free samples, with waviness defects, the 
work,thoughacatastrophicfailureisobservedwithdefect-freesamples,withwavinessdefects,the
failure is not catastrophic. 
failureisnotcatastrophic.
Table 4. Compression test results of composites with and without waviness defects. 
Sample  Wave Severity (Ws) Mean Failure Strength (MPa) Standard Deviation (MPa) 
A0 (unidirectional) 0  614  19.61 
A1  0.01  479  34.5 
A2  0.025  303  12.25 
A3  0.035  203  13.16 
A4  0.075  158  14.40 
4.2. Mechanisms of Failure 
4.2.1. Unidirectional Laminates without Waviness Defects 
Optical and SEM observations of the failed samples reveal the presence of an angled fracture 
plane due to shear failure (Figure 6). Fiber strand debonding, micro‐buckling and matrix cracking are 
also clearly visible in the gage area. These observations follow the traditional and expected mode of 
failure [31], but the sudden and catastrophic crushing of the gage area during testing has made it 
difficult to differentiate the various failure modes. Fiber micro‐buckling is a result of shear instability 
process that occurs at higher strains in the matrix material due to plastic yielding. It is believed that 
during compression, the presence of fiber misalignment imperfection from the longitudinal direction 
results in the formation of kinks in a localized region. This ultimately leads to the formation of fiber 
kink‐bands followed by compressive kinking failure [32]. However, it is important to note that
Materials2017,10,909 8of13
Table4.Compressiontestresultsofcompositeswithandwithoutwavinessdefects.
Sample WaveSeverity(Ws) MeanFailureStrength(MPa) StandardDeviation(MPa)
A0(unidirectional) 0 614 19.61
A1 0.01 479 34.5
A2 0.025 303 12.25
A3 0.035 203 13.16
A4 0.075 158 14.40
4.2. MechanismsofFailure
4.2.1. UnidirectionalLaminateswithoutWavinessDefects
OpticalandSEMobservationsofthefailedsamplesrevealthepresenceofanangledfracture
planeduetoshearfailure(Figure6). Fiberstranddebonding,micro-bucklingandmatrixcracking
arealsoclearlyvisibleinthegagearea. Theseobservationsfollowthetraditionalandexpectedmode
offailure[31],butthesuddenandcatastrophiccrushingofthegageareaduringtestinghasmadeit
difficulttodifferentiatethevariousfailuremodes. Fibermicro-bucklingisaresultofshearinstability
processthatoccursathigherstrainsinthematrixmaterialduetoplasticyielding. Itisbelievedthat
duringcompression,thepresenceoffibermisalignmentimperfectionfromthelongitudinaldirection
resultsintheformationofkinksinalocalizedregion. Thisultimatelyleadstotheformationoffiber

Materials 2017, 10, 909   8 of 13
kink-bandsfollowedbycompressivekinkingfailure[32]. However,itisimportanttonotethatkinking
stressesareverysensitivetofibermisalignment. Evenamisalignmentangleintherangeof0.8–2.3◦
kinking stresses are very sensitive to fiber misalignment. Even a misalignment angle in the range of 
wasenoughtocausekinking[33]. Moreover,withmisalignedfibers,kinkingstressesarereportedly
0.8–2.3° was enough to cause kinking [33]. Moreover, with misaligned fibers, kinking stresses are 
25%oftheelasticmicro-bucklingstressesofcomposites.
reportedly 25% of the elastic micro‐buckling stresses of composites. 

Figure 6. Catastrophic failure of waviness‐free specimen under compressive loading conditions. 
Figure6.Catastrophicfailureofwaviness-freespecimenundercompressiveloadingconditions.
4.2.2. Unidirectional Laminates with Waviness Defects 
4.2.2. UnidirectionalLaminateswithWavinessDefects
As compared to defect‐free specimens, the failure progression of the wavy specimens is slow 
Ascomparedtodefect-freespecimens,thefailureprogressionofthewavyspecimensisslowand
and gradual (particularly, A4 with a wave severity of 0.075). Figure 7 shows a few selected snapshots 
gradual(particularly,A4withawaveseverityof0.075). Figure7showsafewselectedsnapshotsof
of crack initiation and progression from the video of the test captured with a high‐speed camera 
crackinitiationandprogressionfromthevideoofthetestcapturedwithahigh-speedcameraoperated
operated  at  a  frame  rate  of  50  frames/s.  As  discussed  earlier,  axial  compression  failure  of 
at a frame rate of 50 frames/s. As discussed earlier, axial compression failure of unidirectional
unidirectional composites occurs by plastic kinking in the presence of fiber misalignment sites along 
compositesoccursbyplastickinkinginthepresenceoffibermisalignmentsitesalongwithplastic
with plastic shear deformation in the matrix. Figure 7 shows that the failure initiated with a visible 
fiber kinking followed by an inclined shear crack across the fiber direction in the wavy area and 
ultimately results in fiber strand splitting. Previously, it has been noted that glass fibers fail in 
compression by longitudinal splitting when the uniaxial strain in the composite equals the intrinsic 
crushing strain of the fibers [4]. Nevertheless, the gradual kink‐band formation and the resultant fiber 
kinking failure mode are more evident at higher fiber wave severities (A3 and A4 samples). For 
example, Figure 8 shows the failure progression in A3 with wave severity 0.035.
Materials 2017, 10, 909   8 of 13
kinking stresses are very sensitive to fiber misalignment. Even a misalignment angle in the range of 
0.8–2.3° was enough to cause kinking [33]. Moreover, with misaligned fibers, kinking stresses are 
reportedly 25% of the elastic micro‐buckling stresses of composites. 

Figure 6. Catastrophic failure of waviness‐free specimen under compressive loading conditions. 
4.2.2. Unidirectional Laminates with Waviness Defects 
As compared to defect‐free specimens, the failure progression of the wavy specimens is slow 
and gradual (particularly, A4 with a wave severity of 0.075). Figure 7 shows a few selected snapshots 
Mofa tcerriaalcsk2 0i1n7i,t1i0a,t9io09n and progression from the video of the test captured with a high‐speed ca9moefr1a3 
operated  at  a  frame  rate  of  50  frames/s.  As  discussed  earlier,  axial  compression  failure  of 
unidirectional composites occurs by plastic kinking in the presence of fiber misalignment sites along 
sheardeformationinthematrix. Figure7showsthatthefailureinitiatedwithavisiblefiberkinking
with plastic shear deformation in the matrix. Figure 7 shows that the failure initiated with a visible 
followedbyaninclinedshearcrackacrossthefiberdirectioninthewavyareaandultimatelyresultsin
fiber kinking followed by an inclined shear crack across the fiber direction in the wavy area and 
fiberstrandsplitting. Previously,ithasbeennotedthatglassfibersfailincompressionbylongitudinal
ultimately results in fiber strand splitting. Previously, it has been noted that glass fibers fail in 
splittingwhentheuniaxialstraininthecompositeequalstheintrinsiccrushingstrainofthefibers[4].
compression by longitudinal splitting when the uniaxial strain in the composite equals the intrinsic 
Nevertheless,thegradualkink-bandformationandtheresultantfiberkinkingfailuremodearemore
crushing strain of the fibers [4]. Nevertheless, the gradual kink‐band formation and the resultant fiber 
evidentathigherfiberwaveseverities(A3andA4samples). Forexample,Figure8showsthefailure
kinking failure mode are more evident at higher fiber wave severities (A3 and A4 samples). For 
progressioninA3withwaveseverity0.035.
example, Figure 8 shows the failure progression in A3 with wave severity 0.035. 

Materials 2017, 10, 909   9 of 13
Figure7.SequenceofcrackpropagationbeforecompletefailureinsampleA1:(a)atthestartofthe
Figure 7. Sequence of crack propagation before complete failure in sample A1: (a) at the start of the 
test,(b)crackinitiation(regionwithintheredcoloroval),(c)crackpropagationtowardsthefreeedge,
test, (b) crack initiation (region within the red color oval), (c) crack propagation towards the free edge, 
(d)&(e)wideningofthecrack,and(f)failure.
(d) & (e) widening of the crack, and (f) failure. 

FFiigguurree 88.. ((aa)) FFiibbeerrk kininkkiningga nanddfi bfiebresrp slpitltiitntignagl oanlogntgh ethwea wvyavfiyb efribdeirr edcitrioecntiionns aimn psalemAp3le, (Ab)3k, i(nbk) -kbiannkd‐
vbiaenwd avtiethwe afrt etehee dfrgeee, e(cd)gme,a (gcn) imfieadgnfiibfieerdk fiinbkeirn kginvkieinwga vnidew(d a)nfidb e(dr)b friebaekra bgree.akage. 
A clear transition in the failure mode is evident in composites with and without waviness 
defects. Moreover, the crushing phenomenon during the failure is not seen at higher fiber wave 
severity levels. However, audible crushing and/or knocking sounds are heard in composites with a 
wave severity 0.025 (Sample A2, misalignment angle ~5.7°) and below. Thus, a wave severity of 0.025 
seems to be a transition point in failure mode. The width of the kink‐band increases with increasing 
wave severity. The kink‐band width changed from ~0.1–0.12 mm in A0 sample to ~1.5–2 mm in A3 
sample. 
4.3. Experimental Observations versus Abaqus Model 
As mentioned earlier, a complete specimen model had been developed for direct comparison of 
experimentally observed failure outcomes. Based on the LaRC02 failure criterion, experimental 
observations and results fit well with model predictions (Figures 9 and 10). The advantage of using 
LaRC02 failure criterion is that under compression condition, the fiber failure is caused by shear 
kinking and damage of the matrix. The misalignment of the fibers due to the waviness defects drives 
the failure towards kink‐band formation. As discussed earlier, a similar failure mode trend is seen 
during the experiment.  
In Figure 9b, the elements with blue color have an SDV value of 3 and above, meaning both fiber 
and matrix are damaged in this region. As kink‐band formation is believed to be controlled by the 
misalignment of fibers and the shear strength of the matrix, a shear response analysis has also been 
conducted. It is found that fiber waviness has little influence on shear strength other than the non‐
linear shear response. This once again suggests that fiber waviness does not affect the fiber/matrix 
interfacial strength, which is a key property influencing compressive strength and kink‐band 
formation during failure [6]. Hence, it can be confirmed that waviness is the major reason for the 
kink‐band mode of failure.
Materials2017,10,909 10of13
Acleartransitioninthefailuremodeisevidentincompositeswithandwithoutwavinessdefects.
Moreover,thecrushingphenomenonduringthefailureisnotseenathigherfiberwaveseveritylevels.
However,audiblecrushingand/orknockingsoundsareheardincompositeswithawaveseverity
0.025(SampleA2,misalignmentangle~5.7◦)andbelow. Thus,awaveseverityof0.025seemstobea
transitionpointinfailuremode. Thewidthofthekink-bandincreaseswithincreasingwaveseverity.
Thekink-bandwidthchangedfrom~0.1–0.12mminA0sampleto~1.5–2mminA3sample.
4.3. ExperimentalObservationsversusAbaqusModel
Asmentionedearlier,acompletespecimenmodelhadbeendevelopedfordirectcomparison
ofexperimentallyobservedfailureoutcomes. BasedontheLaRC02failurecriterion,experimental
observationsandresultsfitwellwithmodelpredictions(Figures9and10). Theadvantageofusing
LaRC02 failure criterion is that under compression condition, the fiber failure is caused by shear
kinkinganddamageofthematrix. Themisalignmentofthefibersduetothewavinessdefectsdrives
thefailuretowardskink-bandformation. Asdiscussedearlier,asimilarfailuremodetrendisseen
duringtheexperiment.
Materials 2017, 10, 909   10 of 13

Materials 2017, 10, 909   10 of 13

Figure 9. (a) Experimentally failed specimens and (b) model prediction of both defect‐free and 
FigurFeig9u.r(ea )9E. x(pa)e rEimxpeenritmalelyntfaalillye dfasilpeedc ismpeecnimsaennds (abn)dm (bod) emlopdreedl ipcrteiodnicotifonb oothf bdoetfhe cdt-effreecet‐afrnede wanadv iness
waviwneasvsi ndeesfse dcet‐feccotn‐ctoanintainingin sga smamplpelse.s . 
defect-containingsamples.

FigurFeig1u0r.eE 1x0p. Eerxipmereinmteanltdala dtaataan adndm mododeellp prreeddiiccttiioonnss ooff ccoommpprersessisviev setrsetsrse svss.v dsi.spdliascpelmaceenmt beenhtabvieohra vior
ofA0oaf nAd0 Aan3ds Aam3 spalmesp.les. 
Figure 10. Experimental data and model predictions of compressive stress vs. displacement behavior 
of A0B aansedd A o3n  stahme pAlbesa.q us model (Figure 9b), it is evident that the damage (crack) has initiated at the 
In Figure 9b, the elements with blue color have an SDV value of 3 and above, meaning both
middle of the gage length. However, cracks have appeared at much lower loads in the waviness 
fiberBdaeanfsdeecdmt‐ coaontnr titaxhiena irAnegbd asaqammusap gmleesod. diTenhl et(h Fdiisgisurceorgeni t9oinbnu).,i Atiyt s iiskn ei nvfikibd-ebersan nt( datht faotthr etmh teao tpdio aanmnidasg bbeeo (ltciteorvamce kdo)f th otahbsee  inwciotanivatitrneoedlsl sea dt tbhye 
containing samples) are the weak links in the system and the failure propagation diverted towards 
middle of the gage length. However, cracks have appeared at much lower loads in the waviness 
those areas. In the actual structures, fiber discontinuity would not be present along with the fiber 
defect‐containing samples. The discontinuity in fibers (at the top and bottom of the waviness 
waviness defect unless it were a ply drop situation. In A3, kink angles are measured in the range of 
containing samples) are the weak links in the system and the failure propagation diverted towards 
110° to 118°, and from the model, the angle is ~116°. Hence, we can conclude that the model prediction 
those areas. In the actual structures, fiber discontinuity would not be present along with the fiber 
is closer to the experimental findings. 
waviness defect unless it were a ply drop situation. In A3, kink angles are measured in the range of 
The Abaqus model is a lamina level macro‐mechanical model, and the drop in the stiffness 
110° tpor o1p1e8r°t,i easn dof f rloammi nthaete m poudreelly,  thdeep aenngdlse  iosn ~ 1th1e6 °e. lHemenenctea,l w seti fcfannes cso. nHceluncdee,  tah acth tahneg me oind eelle pmreendti ction 
is cloosreire ntota ttihoen  einx ptheer iwmaevnyt arel gfiionnd irnesgusl.t s in the reduction of elastic modulus in the model. However, in 
Tthhee e xApbeariqmuesn tm, tohde efli biesr  aa nlda mmiantrai xl eavree li nmdiavcirdou‐aml ceocnhsatnitiuceanlt sm aondde tlh, ea fnibde rt hwea vdirnoepss  ianlt etrhse o sntliyf fness 
proptehreti feisb eor fp rloapmeirntiaeste.  Tphuisr iesl ypo sdseibpleyn ad rse aosnon  tfhoer  tehlee smmeanllt arel dsutciftfionne sosb. seHrveendc ein,  eal acsthica nmgoed uinlu se olef ment 
the laminate when compared to the model. For the wavy specimen with a wave severity of over 0.025, 
orientation in the wavy region results in the reduction of elastic modulus in the model. However, in 
a difference greater than 5% in the predicted elastic modulus is observed. Unlike the experimental 
the experiment, the fiber and matrix are individual constituents and the fiber waviness alters only 
data that showed non‐linear behavior, the Abaqus model failed to predict the slight non‐linearity in 
the fiber properties. This is possibly a reason for the small reduction observed in elastic modulus of 
the stress‐displacement curves of waviness defect containing samples. Even the observed fiber 
the laminate when compared to the model. For the wavy specimen with a wave severity of over 0.025, 
breakage and matrix cracking (see Figure 8) could not be predicted with the FEM model. To sum up, 
a difference greater than 5% in the predicted elastic modulus is observed. Unlike the experimental 
Figure 11 shows the effect of manufacturing‐induced fiber waviness on the compressive strength of 
data that showed non‐linear behavior, the Abaqus model failed to predict the slight non‐linearity in 

the stress‐displacement curves of waviness defect containing samples. Even the observed fiber 
breakage and matrix cracking (see Figure 8) could not be predicted with the FEM model. To sum up, 
Figure 11 shows the effect of manufacturing‐induced fiber waviness on the compressive strength of