Damage accumulation analysis of cfrp cross-ply laminates under different tensile loading rates

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Delft University of Technology

Damage accumulation analysis of cfrp cross-ply laminates under different tensile loading

rates

Li, X.; Saeedifar, M.; Benedictus, R.; Zarouchas, D.

DOI

10.1016/j.jcomc.2020.100005

Publication date

2021

Document Version

Final published version

Published in

Composites Part C

Citation (APA)

Li, X., Saeedifar, M., Benedictus, R., & Zarouchas, D. (2021). Damage accumulation analysis of cfrp

cross-ply laminates under different tensile loading rates. Composites Part C, 1, [100005].

https://doi.org/10.1016/j.jcomc.2020.100005

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ContentslistsavailableatScienceDirect

Composites

Part

C:

Open

Access

journalhomepage:www.elsevier.com/locate/jcomc

Damage

accumulation

analysis

of

cfrp

cross-ply

laminates

under

diﬀerent

tensile

loading

rates

Xi Li, Milad Saeedifar, Rinze Benedictus, Dimitrios Zarouchas

∗

Structural Integrity & Composites Group, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS, The Netherlands

a

r

t

i

c

l

e

i

n

f

o

Keywords:

Transverse matrix crack Inter-laminar crack Acoustic emission Digital image correlation Cross-ply laminate

a

b

s

t

r

a

c

t

Thispaperinvestigatestheloadingrateeﬀectonbothmechanicalpropertiesanddamageaccumulationprocess of[0°

2/90°4]Scarbonﬁber-polymerlaminatesundertensileloading.In-situedgeobservations,AcousticEmission

andDigitalImageCorrelationtechniqueswereutilizedsimultaneouslytomonitorthestateofdamageinrealtime. Resultsshowedthattheaxialmodulusandstrengthwerelesssensitivetoloadingratesthanfailurestrain,which increasedwiththedecreaseoftheloadingrate.Intheviewpointofdamageaccumulationprocess,highdensity anduniformdistributionoftransversematrixcracks,andH-shapecrackpatterns,incorporatinginter-laminar cracks,weremorelikelytooccuratlowloadingrateswhilevariablecrackspacingoccurredathigherrates. Whenloadingrateswerelowerthanacertainlevel,maximumtransversematrixcrackdensitydecreasedslightly duetotherestrictionofrelativelywidelygeneratedinter-laminarcracks.Furthermore,thecumulativeacoustic emissionenergyoflow-frequencysignalswaslinearlycorrelatedtotransversematrixcrackdensity,providinga promisingwaytoquantifycrackaccumulationinrealtime.Finally,spatialconsistencewasobservedbetween transversematrixcracksatedgesandstressconcentrationsattheexterior0° ply,andthepeaksofaxialstrainat localconcentrationregionslocateeithernearthenewestcracksorattheplacewithminimumcrackspacing.

1. Introduction

Compositestructuresmayexperienceloadingcombinationswhich vary fromstatic loadsinducedby itsown weighttohigh-strain-rate loadslikeimpact.Consideringtheuncertainserviceenvironment,itis importanttoexploreandunderstandtheloadingrateeﬀectsonthe me-chanicalresponseanddamageaccumulationprocess.

Aplethoraofstudiesexistfordifferenttypesofpolymermaterials thatdealwiththemechanicalresponseunderdifferentloadingrates, mainlycarbonandglassfiberreinforcedpolymers(CFRPandGFRP), andlay-upconfigurations,suchasunidirectional(UD)laminates[1–3] , multi-directionallaminates[2 ,4 ,5] ,wovencomposites[3] .These stud-ies show that CFRPs aregenerally less sensitiveto loadingrates in comparisonwithGFRPs[4 ,5] .Zhangetal.[3] foundthat loading-rate-dependencyofthetensilestrength,Young’smodulusandfailurestrain ofUDCFRPlaminate,wasnotobviousunder20s−1_while_a_remarkable

increasewasobservedattherateover20s−1_._Taniguchi_et_al._[1]

re-portedthatthetensilemodulusandstrengthwereindependentof load-ingratesfor[0°_]_laminates,_but_an_increase_of_the_tensile_modulus_and

strengthwiththeincreaseofloadingrateswasobservedfor[90°_]_and

[45°_]_specimens._Gilat_et_al._[2]_concluded_that_the_{loading-rate-eﬀect}

onthemaximumstressof[45°_]_and_[_±₄₅°_]

Sspecimenswasmore

sig-niﬁcantthanof[90°_]_and_[10°_]_specimens.

∗_{Corresponding}_author.

E-mailaddress:d.zarouchas@tudelft.nl(D.Zarouchas).

Thefactthatoff-axislaminatesaresensitivetoloadingratesimplies thattheirdamageaccumulationprocess,especiallyformatrix-related damagemechanisms,isdifferentfordifferentloadingrates.Few stud-ies[6–8] dealtwiththeloadingrateeffectsontheevolutionof trans-versematrixcracks,andBertheandRagonet[8] concludedthattherate sensitivityisstrongerforlowstrainratesthanforintermediatestrain rates.Azadietal.[9] foundthattheloadingratedidnotalterthe dom-inantdamagemechanism,butthequantityofeachdamagemechanism changedwithdifferentloadingrates,anobservationthattheauthors believeneedsfurtherresearch.

Forthenon-transparentCFRPcomposites,themainchallengeisto quantitativelyidentifymatrix-relateddamagemechanismsinrealtime [10] .Asthemostdirectway,opticaledgeobservationbycamerasor microscopesiscapabletotrackthecrackaccumulationforthe rectan-gularlaminatedcouponswithoﬀ-axisplies[11–14] .However,inview thathighresolutionandlargeobservationwindowareusuallyhardto beachievedsimultaneously,in-situcrackcharacterizationinthe large-sizeviewwindowremainschallengesfornon-interruptedtests.Inmost cases,specimensneedtoberemovedfromthetestingmachines,ortests needtobeinterruptedforex-situ/in-situdamageinspections,whichcan inducethestressrelaxationandfurtheraﬀectthecrackingprocess[10] . Choetal.[15] foundthatboththecrackdensityandmaximumstress duringtheloadingandunloadingphaseoftensiletestswerestrongly

https://doi.org/10.1016/j.jcomc.2020.100005

Received22April2020;Receivedinrevisedform13July2020;Accepted15July2020

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Fig.1.Theschematicdiagramofspecimen di-mensions,AEsensors’locations,measurement areaofDICandclampingregions(a); Experi-mentalequipment(b).

dependenton theparticularloadingsequence,andatime-dependent increaseinmatrixcracksoccurredthroughouttheholdperiod.

Advancedin-situ monitoringtechniqueslike DigitalImage Corre-lation(DIC)[10–12 ,16 ,17] ,infraredthermography(IR)[8 ,18 ,19] and AcousticEmission(AE)[9 ,11–13 ,19–22] havealsobeenwidelyapplied forCFRPcompositestohelpdetectdiﬀerentfailuremechanismsand monitorthedamageaccumulationprocess.

ByapplyingDIC,Tessemaetal.[16] investigatedthematrixcrack initiationandgradualpropagationofquasi-isotropiclaminatesusingthe localconcentrationof axialandshearstrainasdamageindicators of intra-laminarandinter-laminarcracks.Mehdikhanietal.[10] quanti-fiedtheevolutionoftransversematrixcracksofcross-plylaminatesby countingthepeaksofthestrainprofileviabothmacro-andmeso‑ scale DICanalysis.However,detectingthedamageaccumulationinthisway ishighlyaffectedbytheplythicknessandthestackingsequenceof lam-inates[11] .

Asfor IR,thevariationof surfacetemperature canrepresent the degradationanddissipativemechanismsofmaterial[18] ,butdiﬀerent damagemechanismsarehardtobepreciselycharacterizedand local-izedaccordingtotheheatsources,especiallyformatrixcrackswhich dissipateslessthermalenergythanﬁberdamageandinterfacefailure [19] .Recently,BertheandRagonet[8] haveachievedthemonitoring ofmatrixcrackingappearancebyusingpassiveinfraredthermography measurementsforcross-plylaminateswith41mmfreelengthbetween tabs.

ComparedwithDICandIR,AEprovidesmoreinformative damage-relatedresultsanditis regardedasthemostpromisingtechniqueto uncovertheinitiationandprogressionofdifferentdamagemechanisms [11] .IntensiveeffortshavebeenmadeontheinterpretationsofAE ac-tivitiesbyanalysingmultipleAEfeatureswithclusteringalgorithms in-volved.Arecentreviewonthedamageanalysisofcompositestructures usingAEhighlightsthepotentialofthismonitoringtechnique[25] . Am-plitudeandfrequencyaretreatedasthemostpreferredAEfeaturesto classifydifferentAEactivities[11 ,19 ,20 ,22–24] .TocorrelateAE clus-terstodifferentdamagemechanisms,someresearchershaveexecuted

destructive testson theindividualconstituentmaterials,forexample couponsmadeofpureresinorfiberbundles,toobtaintheAEfeatureof eachdamagemechanismseparately.TheseAEfeatureswerethenused asthereferencepatternstocorrelateeachAEclustertoaspecific dam-agemechanism[9 ,22–24] .Ageneraltrendhasbeenestablishedwhich relatesAEwaveformswithlowpeakfrequencyandamplitudeto matrix-cracking-relateddamagemechanisms[22–24] .However,doubtsexistin viewthatAEfeaturesforeachdamagemechanismmightbedifferentfor compositesampleswithdifferentdimensions[21] orstackingsequences [11] .

Therefore,itisnecessarytocombineAEandothermonitoring sys-temsduringtheteststoprovideareliableinterpretationofAEactivities andcorrespondingfeatures.Ozetal.[11 ,12] correlatedAEclusters ob-tainedfromk-means++algorithmtodiﬀerentdamagemechanisms(e.g. matrixcracksatthesurfaceandinner90°_plies,_micro_and_macro

de-lamination,etc.)monitoredfromopticaledgeobservationandDIC.They foundthatthedepthofdamagesourcecanaﬀectthecorrespondingAE featuresandhighfrequencycouldalsobeinducedbythematrix crack-ingwhen90°_plies_approach_to_mid-section_of_specimens._Baker_et_al.

[13] concludedthatwaveform-basedAEenergycanbeusedto iden-tify matrixcrack initiationobserved bytheoptical microscopefrom theedge.These observationsindicate AEactivitiescould be compre-hensivelyinterpretedtoidentifydifferentdamagemechanisms,andthe evolutionofAEfeaturesfromdifferentclustersareexpectedtoactas theindicatorstoquantitativelyrepresenttheaccumulationofdifferent damagemechanismsinthefuture.

Theobjectivesofpresentworkweretoinvestigatethe loading-rate-dependencyof bothmechanicalpropertiesanddamageaccumulation processforCFRPcross-plylaminatesundertensileloading,andto ex-plore thecorrelationsofdamage-relatedresultsfrom diﬀerentin-situ monitoringsystems.Inthetestcampaign,thick90°_block_in_the

mid-dleofcross-plylaminatesweredesignedtoprovidedetectablecracks, andopticaledgeobservation,DICandAEwereappliedsimultaneously tomonitorthecrackaccumulationprocess.Themaincontributionof presentworkistheachievementofin-situcharacterizationoftransverse

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Table1

Thecontrolmode,loadingrate,runningtimeandstrainrateundereachload condition.

Control mode Loading rate Running time (s) Strain rate (s −1 )

Load 0.019 kN/s 1470.25 ± 40.14 9.77 × 10 −6 0.19 kN/s 140.72 ± 1.78 9.98 × 10 −5 1.9 kN/s 14.21 ± 0.03 9.56 × 10 −4 19 kN/s 1.54 ± 0.01 8.52 × 10 −3 Displacement 1 mm/min 196.80 ± 3.05 7.19 × 10 −5 Table2

Mechanicalpropertiesofcross-plylaminatesunderdiﬀerentloadingrates. Loading rate Axial modulus (GPa) Tensile strength (MPa) Failure strain 0.019 kN/s 51.45 ± 0.65 706.81 ± 14.91 0.0144 ± 0.0002 0.19 kN/s 50.54 ± 0.70 684.99 ± 7.82 0.0140 ± 0.0002 1.9 kN/s 51.26 ± 1.01 691.01 ± 15.69 0.0136 ± 0.0001

19 kN/s 51.32 ± 2.18 ± 8.34 0.0131 ± 0.0000

1 mm/min ± 0.32 699.33 ± 6.94 0.0141 ± 0.0002

matrixcracksandinter-laminarcracksinalargeviewwindow(100mm) withoutinterruptingthetensiletests,whichfurtherenrichesthe analy-sisofloading-rate-eﬀectonthestatisticaldistributionoftransverse ma-trixcracksandenhancesourunderstandingonhowinter-laminarcracks constrainthegenerationoftransversematrixcracks.

2. Experimentalmethods

2.1. Materialandspecimens

Thespecimensusedinthepresentstudyweremanufacturedfrom theUDcarbon fiberPrepregnamedHexply○R _F6376C_–HTS(12_K)₋_5– 35%.ThisPrepregsystemcontainshightenacitycarbonfibres(Tenax○R -E-HTS45)andhigh-performancetoughepoxymatrix(Hexply○R _6376). ThenominalfiberweightratioandthicknessofthePregregare65% and0.125mm,respectively.ThematerialpropertiesoftheUD-Prepreg layerincuredconditioncanbefoundin[26] .

Two600×300mm2_panels_were_laminated_following_the_stacking

sequencesof[0°

2/90°4]S.Theywerethencuredinsideanautoclave

ac-cordingtothemanufacturer’srecommendation[27] .Afterwards,the panelswerecut,usingawater-coolingdiamondsaw,intorectangular specimensof250mm×25mmaccordingtoASTMD3039/D3039M-17 standard[28] ,asshowninFig. 1 (a).

Thickpapertabswereglued onbothends ofthespecimen using cyanoacrylateadhesive inorder toincreaseclampinggrip. Addition-ally,bothedgesofthespecimenwerecoveredwiththinwhitepaintto enhancethequalityforthedamagemonitoringwiththeedgecameras. Finally,awhitebasecoatwaspaintedonthefrontsurfaceofspecimen andthendesignedspecklepatternwiththedotsizeof0.18mmwere printedonthesurfaceusingaVICspecklerollertopreparetheDIC in-spectionarea.

2.2. Testset-up 2.2.1. Tensiletest

Tensiletestswerecarriedoutona60kNfatiguemachinewith hy-draulicgrips,asshowninFig. 1 (b).Fivelevelsofloadingrateswere per-formedunderloadanddisplacementcontrolmode,aslistedinTable 1 . Thecorrespondingrunningtimeandstrainrateateachratearealso presentedinTable 1 .Here,thestrainrateequalstothestrainatpeak loadsdividedbytherunningtime.The1mm/minand0.19kN/scan beregardedassimilarloadingratesbasedonthestrain-ratelevel.

Toguaranteetherepeatabilityoftestresults,ﬁvespecimenswere testedundereachloadingratewhilespecimensthatfailattheclamps wereexcludedfromtheanalysis.TheAE,DICandedgedamage moni-toringsystemsweresynchronizedwiththetestingmachinetocreatea synergisticworkenvironmentamongdiﬀerentdevices.

2.2.2. Edgedamagemonitoringsystem

Two 9Megapixelcameras with50 mmlens and150 frames-per-secondwereplacedatleftandrightsideofthetestingmachineto mon-itorcracksoccurredonbothedgesofthespecimen,asshowninFig. 1 (b). Atotallengthof100mmforeachedgewasobservedduringthetest. Aftertesting,thenumberandpositionofcracksatthe90°_plies_were

obtainedthroughauser-definedMATLABcode.Initially,theacquired imageswereprocessedusingaBottom-hatfilteringinordertocompute themorphologicalclosingoftheimage.Then,thefilteredimageswere subtracted fromtheoriginalonesallowingthecontrast ofcrack and un-crackedregionsattheedgestobeenhanced.Finally,theprocessed imageswereconvertedtobinaryimagesinordertolabelthecracksas regionsofcontiguouswhitepixels,forbeinglatercountedandlocalized. 2.2.3. AEsystem

TwobroadbandVS900-MAEsensorswithadiameterof20.3mm andafrequencyrangeof100–900kHzwereclampedonthespecimen. Thedistancebetween twosensorswasfixedto100mm forall tests, asshowninFig. 1 (a).Vacuumedsilicongreasewasusedbetweenthe AEsensorandthespecimensurfacetocreategoodacousticalcoupling. TheAMSY-68-channelVallensystemwasusedtorecordtheAEactivity andtwopre-amplifierswithgainof34dBandband-passfilterof20– 1200kHzwereusedtoconnectthesensorstotheAEsystem.Beforeeach test,pencilleadbreakswereperformedtocalibratethedataacquisition system.Inalltests,thesamplingrateandthresholdweresetas2MHz and45dB,respectively.

2.2.4. DICsystem

TheDICwasemployedtomeasurethedisplacementandstrain dis-tributionsoftheexterior0°_ply._In_the_present_study,_two_diﬀerent

po-sitionsofaspecimencan beappliedwithDICsystemtomonitor the strain/displacementdistributionsduringthetest,i.e.theedgeandthe exterior0°_ply._Considering_the_thickness_of_the_specimens_(~1.5_mm),

itisextremelydifficulttomonitortheentireedgewithaccurate mea-surements.Furthermore,thespecklepattern,appliedontheedges,could affectthecontrastofedgeimagesanddisturbtheidentificationof trans-versematrixcracksduringthepostimageprocessing.Therefore,apair of5Megapixelcameraswith23mmlensand75frames-per-secondwas

Table3

Loadlevelandlocationwhenthetransversematrixcrackinitiatedatdiﬀerentloadingrates.

Loading rate Load level F / F max (%) Location X (mm)

Specimen #1 Specimen #2 Specimen #3 Specimen #1 Specimen #2 Specimen #3

0.019 kN/s 81.88 61.32 85.66 79.49 29.15 88.95

0.19 kN/s 82.43 52.50 66.07 35.42 71.59 24.75

1.9 kN/s 83.24 85.00 78.79 91.33 66.26 38.67

19 kN/s 73.02 75.01 87.12 67.94 44.50 18.77

1 mm/min 76.30 69.51 81.00 61.13 73.07 16.05

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Table4

Matrixcrackdensityandcrackspacingatthe90°_plies_under_diﬀerent_loading_rates.

Loading rate Maximum matrix crack density 𝜌max (mm −1 ) Crack spacing d (mm)

daverage dmin dmax dmax - d min

0.019 kN/s 0.24 ± 0.02 3.64 ± 0.15 1.12 ± 0.75 9.07 ± 1.05 7.95 ± 0.30

0.19 kN/s 0.30 ± 0.04 3.33 ± 0.47 0.57 ± 0.26 10.03 ± 3.59 9.46 ± 3.63

1.9 kN/s 0.16 ± 0.01 5.59 ± 0.32 0.63 ± 0.19 16.43 ± 6.03 15.80 ± 6.12

19 kN/s 0.14 ± 0.02 5.84 ± 0.47 0.44 ± 0.06 19.57 ± 7.71 19.13 ± 7.65

1 mm/min 0.25 ± 0.02 3.84 ± 0.37 0.91 ± 0.67 14.24 ± 3.89 13.33 ± 4.56

Fig.2. Histogramofcrack spacingbetweenadjacenttransverse matrixcracksandrelatedtwo-parameterWeibulldistributionsatdiﬀerentloadingrates:(a) 0.019kN/s,(b)0.19kN/s,(c)1.9kN/s,(d)19kN/s,(e)1mm/min.

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placedinthefrontsideofthespecimen,asshowninFig. 1 (b),to mea-suretheglobalaxialdeformationandthestraindistributionscloseto thecrackedregionsof90°_plies._{Post-processing}_was_performed_using

thecommercialsoftwareVIC-3DbyCorrelatedSolutions.Asubsetsize of29pixelsandstepsizeof7pixelswereselectedforcorrelation anal-ysis.Thelengthoftheviewﬁeldforin-situ strainmeasurementwas approximately70–80mm.

3. Resultsanddiscussion

3.1. Mechanicalproperties

Theelasticmodulus,tensilestrengthandfailurestrainofthe speci-mensunderdiﬀerentloadingratesarelistedin

Table 2 .Themoduluswascalculatedbasedondatagatheredwithin theaxialstrainrangelessthan0.5%.Failurestraincorrespondstothe globalstrainofspecimensatthemaximumload.Theglobalstrainwas obtainedbytrackingthedisplacementoftwopointsnearthetopand bottomoftheDICmeasurementregion.Anincreasecanbeobservedfor thefailurestrainwhentheloadingrateisreduced,whichisconsistent withtheresultsreportedbyGilatetal.[2] .Thisfactindicatesthat spec-imensbehavedinamoreductilewayatlowerloadingrates[29] .Asthe matrixisloading-rate-dependent,itsductileresponse,suchasthestress relaxationandplasticdeformation,canbemoreeasilytriggeredatlow loadingrates[30 ,31] .Ontheotherhand,theaxialmodulusand ten-silestrengthﬂuctuatedatarelativelynarrowbandandtheywereless loading-rate-dependentcomparedwiththefailurestrainresponsedue totheloading-rate-insensitivenatureofcarbonﬁbres[32] .Therefore,it canbeconcludedthatthematrixdominantlydeterminesthesensitivity ofcross-plylaminatestostrainratesinthepresentstudy[2] .

3.2. Damageontheedge 3.2.1. Transversematrixcracks

Table 3 liststhepositionsandtheloadlevelswhentheﬁrstmatrix crackoccursatthe90°_plies_for_three_specimens_at_each_rate._For_all

specimens,theﬁrstmatrixcrackoccurredatanarbitrarypositionof theinner90°_plies _and_the_{corresponding} _load_level _is_distributed_in

therangefrom52.50%to87.12%.Thisfactisattributedtotheinherent materialdefectsinsidethespecimenslikemicro-cracksandvoids,which highlyaﬀecttheoriginsofthetransversematrixcrack[33] .

Thenumberofcracksateachsidewasthesameateachloading mo-ment,indicatingthatthetransversematrixcracksrapidlypropagated throughtheentirewidthdirection.Table 4 liststhemaximummatrix crackdensityandthecrackspacingforthediﬀerentloadingrates.Here, themaximummatrixcrackdensity𝜌maxequalstoN/2L,whereNisthe

totalnumberoftransversematrixcracksonbothedgesbeforespecimens failedandListhelengthoftheedgeobservationregion.Thematrix crackdensitydecreasedwiththeincreaseofloadingrates,exceptfor the1mm/minand0.019kN/scaseswhereaslightdecreaseofmatrix crackdensityisobserved.Furthermore,crack-spacingrelatedvariables arealsolistedinTable 4 .Crackspacingdmeansthedistancebetween everytwoadjacenttransversematrixcracks.Theaveragecrack spac-ingdaverage,themaximumcrackspacingdmaxandthediﬀerences

be-tweenthemaximumandminimumcrackspacingd_max-d_minwerelarger at1mm/min(7.19×10−5_s−1₎_than_those_at_0.19_kN/s_(9.98_×₁₀−5

s−1_)._This_indicates_that_transverse_matrix_cracks_distributed_more

un-evenlyunderdisplacementcontrolmodethanunderloadcontrolmode whenthestrain-ratelevelissimilar.Intheload-controlledcases,dmax

anddmax-dminincreasedwiththeincreaseofloadingrates,reﬂectingthe

moreuniformdistributionoftransversematrixcracksatlowerloading rates.

Nevertheless,thedeviationsofallcrack-spacingvariableswere sig-niﬁcant,whichhighlightsthespatialstochasticprocessesoftransverse matrixcrack[34] .Choetal.[15] attributedthisphenomenontothe

Fig.3. Thegrowingtrendofmatrixcrackdensitywiththeloadlevel.

factthatthelocationofsubsequentcracksisverysensitivetominor lo-calvariationsinmatrix.Torepresentbetterthestatisticalvariationin crackspacing,variablematerialproperties,i.e.strengthandfracture en-ergy,areusuallyassumedduringcrackevolutionprocesses[15 ,35 ,36] . Fig. 2 presentsthehistogramofcrackspacingbetweenadjacent trans-versematrixcracks.Atwo-parameterWeibulldistributionisutilizedin todescribetheprobabilisticdistributionofcrackspacing.Underlower loadingrate,crackspacingismorelikelytoconcentratebetween2and 4mmwithnarrowerscatterband,whileamoreuniformprobability dis-tributionispresentedunderhigherloadingratewithwiderscatterband. Thisphenomenonfurtherreﬂectsthelargescatteringincrackspacing athigherloadingrate.

Fig. 3 presentsthematrixcrackevolutionversustheloadforevery loadingrate.TheloadlevelF/F_maxisrepresentedasthepercentageof thecurrentloadFtothemaximumloadFmax.Underallloadingrates,

matrixcrackdensity remainedconstantorpresenteda slowgrowing trenduptotheloadlevelaround85%andthenincreasedsigniﬁcantly uptotheﬁnalfailure.Thehigherloadingrates(1.9kN/sand19kN/s) exhibitedslowerincreaseofmatrixcrackdensitythantheotherthree loadingratesforwhichthecurvesofmatrixcrackdensityweresimilar amongeachother.

Moreover,thelocationXandloadlevelF/Fmaxwheneachtransverse

matrixcrackgenerated,andthelocalcrackdensityatevery20mmedge regionareshowninFig. 4 .Foraclearvisualization,onlyone represen-tativespecimenateachloadingrateisselectedhere.Nexttothestraight transversecracks,fewcurvedcrackswereobservedduringthetests,as markedbytheblackarrowsinFig. 4 andseeninFig. 5 b(specimens 3,4,5for).Grovesetal.[37] reportedthatthecurvedcracksaredriven bythestressstateresultingfromtheadjacentstraightcracksandHu et al.[38] proposedthat theyonlyoccur whenthecrack densityof straight cracksexceedsthecriticalvalue.Inthepresentwork,itwas foundthattheywerepronetooccurunderhighloadlevelandlocate nearonepriorstraightcrackwiththespacinglessthan1mm.

Furthermore,thefirstthreetransversecrackswerealsolabelledin Fig. 4 anditassumedthattheyoccurredattheregionwherethelocal crackdensityisrelativelyhigh.Thenewcracksarelocatedaroundthe priorcracks,whichisdifferentfromwhatsomemodelspropose;that newcracksformmidwaybetweenexistingcracks[39 ,40] .Moreover, amongalllocalcrackregions,aremarkablehighcrackdensitywas pre-sentedwhereboththecurvedcracksandoneofthefirstthreecracks coexisted.Inaddition,whentheloadingrateincreased,mosttransverse matrixcracksinitiatedatthehighloadlevel.Forinstance,at19kN/s, nearlyhalfoftotalcracksformedjustbeforethefinalfailure.

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Fig.4. Thelocationandloadlevelwheneachtransversematrixcrackoccurred(scatterplot),andthelocalcrackdensityatevery20mmedgeregion(batchart) underdiﬀerentloadingrates.

3.2.2. Inter-laminarcracks

Similartotransversematrixcracks,inter-laminarcrackslocatedat 0°_/90°_interfaces_were_more_likely_to_occur_at_low_loading_rates._The

inter-laminarcrackspromote energyabsorptionandstress redistribu-tion,butontheotherhandtheyrestricttheoccurrenceofnewtransverse matrixcracksnearby wheninter-laminarcracksarerelativelywidely distributedalongtheedge[40] .

Duringthetests,inter-laminarcracksalwaysoriginatedatthetips oftransversematrixcracks.Fig. 5 presentstwolocalregionsalongthe loadingdirection(i.e.0≤X≤25mmand50≤X≤75mm),wheretypical morphologiesoftheco-existingoftransverseandinter-laminarcracks atthepeakloadarehighlighted,shapingH,LandTforms.Thecrack patternHmainlyoccurredatthelowloadingrates.Thisisbecause spec-imenshavemoretimetoredistributetheloadandabsorbenergyatlow

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Fig.5.Thedistributionpatternsofco-existing transverseandinter-laminarcracksattwo lo-calregionsofthespecimenedgewhenreaching thepeakloadforeachloadingrate.

rates,andasaresultinter-laminarcracksaremoreprobablytooccurat bothtipsofthetransversematrixcrackandpropagatealongbothsides ofthecracktip.

3.3. AEactivityanalysis

Inthepresentwork,peakfrequencywasappliedasarepresentative featuretointerpretAEactivities,becauseitislessaﬀectedbythe attenu-ationhappenedduringthewavepropagationincomparisonwith ampli-tude,duration,etc.[41] .Fig. 6 presentsthreebandsofpeakfrequency (i.e.100–200kHz,300–400kHzand>400kHz)amongAEactivitiesat eachrate,andthecorrespondinggrowingtrendsofcumulativeenergy Ecumwiththeincreaseoftheloadlevel.Here,Ecumrepresentsthe

sum-mationofenergiesofeachAEactivity,astheyarerecordedbythedata acquisitionsystem-VallenSysteme[42] .TheAEdataat19kN/swere notfurtheranalysedbecausealmost95%ofthenumberofAEactivities occurredatthefailureandpostfailurephases.Theformationofdistinct frequencybands,asaresultofdamageaccumulation,isdeterminedby materialproperties,plyconﬁgurationsandloadconditionsgiventhe samesensorsandacquisitionsystem.

TheﬁrstAEactivitywasrecordedataround10%to30%ofthe fail-ureloadunderalltheloadingrates,whilethecumulativeenergystarted toincreaseatloadlevelsaround60%to80%.TheoriginoftheearlyAE activitieswithnegligiblecumulativeenergyindicatesthedevelopment ofmicro-cracksbeforetransversematrixcracksinitiated.Thehighest cumulativeenergyduringthetestswasprovidedbyAEactivitiesinthe peakfrequencyrangefrom100kHzto200kHz,whichalsopresented slowergrowingtrendsofcumulativeenergyinmostcasesthanotherAE activitieswithhighfrequency.

AmongthethreegroupsofAEactivitiesclassiﬁedbypeakfrequency, similargrowingtrendsofmatrixcrackdensityandcumulativeenergy asafunctionoftheloadlevelF/Fmaxwereobservedforthelow

fre-quencyband(100–200kHz),aspresentedinFig. 7 .Here,bothcrack densityandcumulativeenergywerenormalizedbytheirvaluesatthe peakload,asexpressedas𝜌/𝜌maxand𝐸𝑐𝑢𝑚∕𝐸𝑐𝑢𝑚_𝑚𝑎𝑥respectively.Each

jumpon𝜌/𝜌maxcansuﬃcientlycorrelatetocertainsteppingincreaseof

𝐸𝑐𝑢𝑚∕𝐸𝑐𝑢𝑚_𝑚𝑎𝑥.Therefore,AEactivitiesinthelowfrequencylevelwere

dominantlyrelatedtotransversematrixcracks.Thisconclusionisin co-incidencewiththemajorityﬁndingsinliterature[22–24] ,butitdoes notmatchwithwhatOzetal.reported[11] .Theauthorsobservedthat matrixcracksattheinner90° _plies_usually_generate_AE_activity_with

peak-frequencyofhigherrangesandtheyexplainedthatthedepthof thedamagesourcecanaﬀecttheAEcharacteristics.Inourstudy,the thicknessofexterior0°_plies_is_only_0.25_mm,_thus_the_through_thickness

distanceofamatrixcracktoAEsensorscanbarelyaﬀectthe correspond-ingAEcharacteristics.

Furthermore, thenormalizedmatrixcrack density𝜌/𝜌max is

plot-tedagainstthenormalizedcumulativeAEenergy𝐸𝑐𝑢𝑚∕𝐸𝑐𝑢𝑚_𝑚𝑎𝑥of

low-frequencyAEactivities(i.e.100–200kHz),wherealinearcorrelationis found,seeFig. 8 .Thisplotdemonstratesthatthecumulativeenergyof low-frequencyAEactivitiescandescribetheaccumulationoftransverse matrixcracksforcross-plylaminates,whichfurtherpavesapromising wayforthereal-timequantiﬁcationoftransversematrixcrackevolution basedonAEfeature.

3.4. Axialstraindistributions

Fig. 9 showstheaxialstraindistributionsattheexterior0°_ply_for_all

testedloadingratesunderfourdiﬀerentloadinglevels(i.e.85%,90%, 95%and100%ofthemaximumload).Forthesameloadlevel,itis ob-servedthatthelocalstrainatlowloadingrateswasgreaterthanthatat highloadingrates.Whenthetransversematrixcracksstartedtoinitiate, strainconcentrationswithnarrowstrips(2.8mmto5.2mm)occurred throughthewidthofthespecimens.Astheloadincreased,someofthese stripsexpandedorconnectedwiththeirneighbourstoformlargestrain concentrations.Atmaximumload,thelargeststrainconcentrationarea attheloadingdirection,38mm,wasfoundfor0.019kN/s.

Tofurtherinvestigatethedevelopmentofstrainconcentrations,the distributionoftransversematrixcracks,obtainedfromedge observa-tions,wascomparedwithaxialstraindistributionsasmeasuredbyDIC. Agoodcorrelationofmatrixcracksattheinner90°_plies_and_strain

con-centrationsattheexterior0°_ply_under_diﬀerent_loading_rates_is_shown

inFig. 10 .Thereddashboxesatthefrontsurfaceofspecimenswere usedtolabelthestrainconcentrationregionswithmorethanone

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trans-Fig.6.ThreebandsofpeakfrequencyamongAE activitiesandthecorrespondingcumulative en-ergyplottedwiththeincreaseofloadlevel un-derdiﬀerentloadingrates:(a)0.019kN/s,(b) 0.19kN/s,(c)1.9kN/s,(d)1mm/min.

versematrixcracks,generatedfromtheedgethicknessandtherelated transversematrixcracksatthelocalregionwithstrainconcentration, weremarkedbythecurlybracketsatedges.Thesemarkedregionswere alsotheplaceswhereexpansionsorconnectionsofstrainconcentration withnarrowstripsoccurredateachloadingrates.Asobserved,the ma-trixcracksat90°_plies_cause_uneven_distribution_of_strain_at_the₀°_plies.

Inviewthattheinter-laminarcrackswerenotwidelydistributedalong theedgeandtheydidnotpropagatebroadlyinsidethespecimensunder tensileloading,theireﬀectsonthedistributionspatternofaxialstrain arenegligibleinthepresentstudy.

The strain proﬁle of a line slice along the loading direction (as markedwiththewhitesolidlineinFig. 10 )andrelatedglobalstrain (asplottedwiththedashline)atthreediﬀerentmoments(i.e.t1,t2and

t3)werealsopresentedinFig. 11 .Here,t1isthemomentthatno

ex-pansionsorconnectionsamongindividualstrainconcentrationsoccur; t2isthemomentthatlocalstrainconcentrationsstarttoexpandor

con-nectwiththeirneighbours;t3isthemomentofthemaximumload.The

ﬁrstexpandingdirectionoflocalstrainconcentrationsismarkedwith redarrowatt₂andthenumberedstrainconcentrationregionsatt₃(red dashboxesatthefrontsurfaceofspecimens)inFig. 10 werealsoshown

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Fig.7. ThenormalizedmatrixcrackdensityandnormalizedcumulativeenergyofAEactivitieslocatedatdiﬀerentfrequencybandsasafunctionoftheloadlevel underdiﬀerentloadingrates:(a)0.019kN/s,(b)0.19kN/s,(c)1.9kN/s,(d)1mm/min.

Fig.8. Therelationshipbetweennormalizedmatrixcrackdensityand normal-izedcumulativeenergyoflow-frequencyAEactivitiesatdiﬀerentloadingrates.

inthestrainproﬁleforeachloadingrateinFig. 11 .Beforet1,strain

concentrationsappearedasthenarrowstripsatthecracklocation. Af-terwards,thenewcracksaﬀecttheearly-emergedstrainconcentrations, andthisisdeterminedbythedistancebetweenthenewcracksandtheir

neighbours.Ifthecrackspacingissmallenough,lessthan4mm,the originalstrainconcentrationexpandstocovertheregionwiththehigh localcrackdensity.Otherwise,onlynewstrainconcentrationstripsare induced.Thisfurtherexplainswhythelargeststrainconcentration re-gionwasgeneratedatthelowestloadingratebecausethereexiststhe widest localregionwithhighmatrixcrackdensityat0.019 kN/s,as showninFig. 10 .

Asforthepeaksoflocalstrainateachlabelledconcentrationregion, theirnumbersandlocationsarerelatedtoboththeoccurringsequences andpositionsoftransversematrixcracks.Bothsinglepeakandmultiple peaksoflocalstrainproﬁlesexistinthelabelledstrainconcentration regions duringthetests,asFig. 11 presents.Inthesingle-peakcase, thelocationofthepeakstrainalmoststaysattheinitialplace(asshown fromt1tot2inFig. 11 (a)-(c),(e))iftheupdatedminimumcrackspacing

isalwayslocatedaroundtheﬁrstcrackgeneratedatthelabelled concen-trationregion.Otherwise,itshiftstothepositionnearthenewestcrack (asshownfromt1tot2inFig. 11 (d)),orturnstomulti-peakcases(as

shownfromt₂tot₃inFig. 11 ).Inthemulti-peakcases,valleysusually existamongneighborpeaksateachstrainconcentrationregionandthe straindiﬀerencesofeachpairofvalleyandpeakaredeterminedbythe relatedcrackspacing.Thelargerthecrackspacingis,higherstrain dif-ferencesoccur.Furthermore,similartothelocationofthesingle-peak case,thehighestpeakinthemulti-peakregionispositionedateither thelocationofthenewestcrackorneartheplacewiththeminimum crackspacing.

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Fig.9. Axialstraindistributionsattheouter0°_ply_under_four_diﬀerent

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Fig.10. Correlationbetweenstrain concentra-tionsattheexterior0°_ply_and_transverse_matrix

cracksgeneratedfromtheedgethicknessatthe maximumloadunderdiﬀerentloadingrates.

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Fig.11. Strainproﬁleofalineslicealongtheloadingdirectionatthreediﬀerentmoments:(a)0.019kN/s,(b)0.19kN/s,(c)1.9kN/s,(d)19kN/s,(e)1mm/min.

4. Conclusion

This paper investigated the loadingrate eﬀectson the mechani-cal properties and the damage accumulation process of [0°

2/90°4]S

carbon ﬁber-polymer laminatesunder tensile loading.Emphasis was givenoncharacterizingthedistributionoftransversematrixcracksand howtheoccurrenceofinter-laminarcrackscouldinﬂuencethe trans-versematrixdensity.Threein-situmonitoringtechniques,edge-camera, DICandAEwereemployedtomonitorsimultaneouslyand

synergisti-callythedamageaccumulationprocess.Themainconclusionsarelisted hereafter:

1) Theaxialmodulusandstrengtharelesssensitivetodiﬀerentloading ratesthanthefailurestrain,whichdecreaseswiththeincreaseofthe loadingrate.

2) At low loading rate, the maximum density of transverse matrix cracksishigh,andinter-laminarcracksatthe0°_/90°_interfaces_are

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localdamagepattern hasa H-shapewheretransversematrixand inter-laminarcracks coexist.Whentheloadingrateis lowerthan 0.19kN/s,thedensityoftransversematrixcracksslightlydecreases duetotheconstrainsimposedbytheinter-laminarcracks. 3) Transversematrixcracksdistributedmoreuniformly underlower

loadingrates,accompaniedwithsmallerscatterofcrackspacingat localregions,whileamorerandomdistributionpatternisfound un-derhigherloadingrates.

4) ThecumulativeenergyofAEactivityintherangeof100–200kHz waslinearlycorrelatedtothedensityoftransversematrixcracks. Thisobservationpavesapromisingwayforthereal-time quantiﬁ-cationofcrackevolutionbasedsolelyontheAEactivity.

5) Narrowstripsofstrainconcentrationoccurredattheexterior0°_ply

oncetransversmatrixcracksinitiatedandacorrelationbetweenthe numberofstripsandthenumberofcrackswasfound.Thestrips,at alaterstage,expandedorconnectedwithoneanothertoformwide concentrationregions.Thelargeststrainconcentrationregionwas presentedatthelowestrate(0.019kN/s)wherelocalcrackdensity ishighenoughtoinducetheexpansionsandconnectionsofnarrow stripsofstrainconcentration.

6) Spatialconsistencewasobservedbetweentransversematrixcracks atedgesandstressconcentrationsattheexterior0°_ply_from_DIC._The

peaksofaxialstrainwerelocatedeithernearthenewestdeveloped cracksorattheplacewiththeminimumcrackspacing.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinﬂuence theworkreportedinthispaper.

Acknowledgments

Theauthors would like tothank theﬁnancial supports of China ScholarshipCouncil(No.201706290028).

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