Low velocity impact behavior of composite sandwich panels

夹心板的低速冲击

Composites:PartA36(2005)1389–1396

/locate/compositesa

Lowvelocityimpactbehaviorofcompositesandwichpanels

PatrickM.Schubel*,Jyi-JiinLuo,IsaacM.Daniel

RobertR.McCormickSchoolofEngineeringandAppliedScience,CenterforIntelligentProcessingofComposites,

NorthwesternUniversity,2137TechDrive,Evanston,IL60208,USA

Received24June2004;revised23October2004;accepted22November2004

ThispaperissubmittedinhonorofProfessorJackR.VinsonoftheUniversityofDelaware.ThisisatributerecognizingProf.Vinson’soutstandingandenduringcontributionstothe eldofcompositematerialsingeneralandmorespeci callytostructuralapplicationsofcompositesandcompositesandwich

structures.Inaddition,oneoftheauthors(Daniel)feelsprivilegedandthankfultoProfessorVinsonforhispersonalfriendship.

Abstract

Compositesandwichstructuresaresusceptibletolowvelocityimpactdamageandthoroughcharacterizationoftheloadinganddamageprocessduringimpactisimportant.Theobjectiveofthisworkistostudyexperimentallythelowvelocityimpactbehaviorofsandwichpanelsconsistingofwovencarbon/epoxyfacesheetsandaPVCfoamcore.Instrumentedpanelswereimpactedwithadropmasssetupandtheload,strain,andde ectionhistorieswererecorded.Damagewascharacterizedandquanti edafterthetest.Resultswerecomparedwiththoseofanequivalentstaticloadingandshowedthatlowvelocityimpactwasgenerallyquasi-staticinnatureexceptforlocalizeddamage.Astraightforwardpeakimpactloadestimationmethodgavegoodagreementwithexperimentalresults.Acontactforce–indentationrelationshipwasalsoinvestigatedforthestaticloadingcase.Experimentalresultswerecomparedwithanalyticaland niteelementmodelanalysistodeterminetheireffectivenessinpredictingtheindentationbehaviorofthesandwichpanel.q2005ElsevierLtd.Allrightsreserved.

Keywords:A.Carbon bercomposite;B.Impactbehavior;D.MechanicalTesting;Sandwichpanels

1.Introduction

Theuseofcompositesandwichstructuresisexpandingintheaerospaceandmarineindustries,aswellasinotherareaswherealightweightmaterialwithhighin-planeand exuralstiffnessisneeded[1].Theconceptbehindthesestructuresistheseparationofrelativelystiff,strongandthinfacesheetsbyalightweightandthicker exiblecore.Theproperdesignandapplicationofsandwichconstructiondependsonathoroughcharacterizationandunderstandingofnotonlythesandwichconstituentmaterials(facesheets,core,andadhesive),butalsoofthestructureasawholeunderquasi-staticanddynamicloadings.Sandwichstructuresareknowntobesusceptibletoimpactdamagebyforeignobjects[2,3].Thistypeofdamageandmorespeci cally,theresponseofcompositesandwichpanelsunderlowvelocity

*Correspondingauthor.Tel.:C18474917961.

E-mailaddress:p-schubel@northwestern.edu(P.M.Schubel).

1359-835X/$-seefrontmatterq2005ElsevierLtd.Allrightsreserved.doi:10.1016/positesa.2004.11.014

impact,isthefocusofthisstudy.Althoughtheinduceddamagemaynotbereadilyapparent,itseffectsonthestrengthandreliabilityofthestructurecanbequitedetrimental.Severalcommonfailuremodeshavebeenidenti ed,includingcoreindentation/cracking,facesheetbuckling,delaminationwithinthefacesheet,anddebondingbetweenthefacesheetandcore[4–6].

Becauseofitscomplexnature,positesandwichbeamshavebeenstudiedtocharac-terizefailureprocessesanddamage[7–11].Thistwo-dimensionalapproachsomewhatsimpli esanalysisandgivesacross-sectionalviewofthedamage.However,asandwichpanelcanprovideamorecompletedeformationanddamageresponse.Mostofthepreviousimpactresearchconductedonpanelshasfocusedontheanalysisofimpactdynamics,thecharacterizationofimpactdamage,andthedeterminationofthepost-impactmechanicalpropertiesofthecompositestructure[2].Awiderangeofmaterials,geometries,andfacesheetlayupshavebeenused[12–17]

.

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1390P.M.Schubeletal./Composites:PartA36(2005)1389–1396

Inthisstudy,simplysupportedsandwichpanelsconsistingofwoven-carbon/epoxyfacesheetsandPVCfoamcorewereloadedundercentralpointimpactinadropweightapparatus.Identicalsandwichpanelswerealsotestedundercentralpointquasi-staticloadingforcom-parison.Thelowvelocityimpactresponseofthecurrentsandwichpanelwasdeterminedbymeansofadetailedload–strainanalysisanddamagecharacterization.Becauseoftherelativelydensecoreandwovencarbonfacesheets,thecontactforces,alongwiththeimpactenergyrequiredtoproducedamage,arequitehighcomparedtothe ndingsinthereferencedworksabove.Althoughmuchresearchalreadyexistsonthestudyoflowvelocityimpactofcompositestructures,newcon gurationsarecontinuallybeingdevelopedandneedtobecharacterized.Thecontactforce–indentationrelationshipforsandwichpanelsisanareathatrequiresadditionalinvestigationaswell.Analyticalmodelsanda niteelementanalysiswerecomparedwithexperimentalresultsonindentationforthestaticloadingcase.

2.Experimental

2.1.Constituentmaterialsandfabrication

Thefacesheetsofthesandwichpanelwerewoven-carbonfabric/epoxylaminates(AGP370-5H/3501-6S).ThisAS4-basedcarbonfabricwasa ve-harnesssatinweavewiththesametowcountinthewarpand lldirections.Thematrixisanamine-curedepoxyresin.Thefacesheetswerelaminatesmadeoffourpliesofprepreg,resultinginacuredplatewithathicknessof1.37mmanda bervolumeratioof0.62.Table1listsmeasuredmechanicalpropertiesofthiswovencarboncomposite.

Thecoreusedforthesandwichpanelwasaclosed-cellPVCfoam(DivinycellH250obtainedfromDIAB).Thisfoamisrelativelydensecomparedtoothercommonlyusedfoamsforcorematerials.Thecorewas25.4mmthick.Table2listsselectedmechanicalpropertiesofDivinycellH250.

Table1

In-planemechanicalpropertiesofcarbonfabric/epoxycompositeusedforsandwichfacesheets[18]Property

ValueDensity,r(kg/m3)

1600

Fibervolumeratio,Vf(%)62Warpmodulus,E1t(GPa)77Fillmodulus,E2t(GPa)75MajorPoisson’sratio,n12

0.07In-planeshearmodulus,G12(GPa)6.5Out-of-planeshearmodulus,G31(GPa)5.1Out-of-planeshearmodulus,G32(GPa)4.1Warptensilestrength,F1t(MPa)963Ultimatewarp, lltensilestrain,3ult1t;2t(%)

1.3

Table2

Selectedmechanicalpropertiesofsandwichcorematerial:DivinycellH250Property

ValueDensity,r(kg/m3)

250In-planemodulus,E1(MPa)240Out-of-planemodulus,E3(MPa)

403Transverseshearmodulus,G13(MPa)115In-planecompressivestrength,F1c(MPa)4.6Transverseshearstrength,F13(MPa)

5

ThesandwichpanelwasfabricatedbybondingthecuredfacesheetstothecorematerialwithHysol9430adhesive,aroomtemperaturecuringepoxyresin.Thefacesheetsandcorewerebondedtogetherandcuredundervacuum.The nalsandwichpanelwasasquareplateof27.9!27.9cmdimensionswithanoverallthicknessof2.82cmandamassof0.83kg(Fig.1).Threeplateswerefabricatedforthisstudy,oneforquasi-statictestingandtwoforimpacttesting.2.2.Quasi-statictesting

Todeterminetheleveltowhichdynamicprocessesshouldbeconsideredinlowvelocityimpacttesting,asandwichpanelwas rsttestedunderaquasi-staticloadingforsubsequentcomparisonwiththeimpactloadingcase.Thecomparisoninvolvescorrelatingloadandstrainlevelsbetweenthetwotypesoftests.Inbothloadingsituations,thesandwichpanelwassimplysupportedonrollersalongtwoparalleledges.Thesupportsweresteelbarsof25.4mmdiameterandwere rgelocalstrainscausedbyindentationcaninduceearlyfailureofthesandwichfacesheet[19].

Thepanelwasinstrumentedwith16straingagesatvariouslocationsonthetopandbottomfacesheets.SelectedstraingagelocationsareshowninFig.2.Thede ectionofthesandwichplateattheloadpointwasrecordedbythestrokeoftheInstronservo-hydraulicmachine,whichalso

Fig.1.Photographof nishedcompositesandwichpanel.

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P.M.Schubeletal./Composites:PartA36(2005)1389–13961391

Fig.2.Diagramshowingpaneldimensionsandselectedstraingagelocations.

recordedtheloadlevelsduringthetest.Thedisplacementofthebottomfacesheetdirectlybelowtheloadpointwasrecordedwithanextensometersetup.Theplatewasloadedslowlyuntilthe rstindicationofdamageinitiationandthencarefullyunloaded.2.3.Impacttesting

Adroptowerapparatuswithafree-fallingmasswasusedtoimpactthesandwichplates.Theimpactor(tup)surfacewassphericalwitharadiusof12.7cmandthetotalmassofthedroppedcarriagewas6.22kg.Thesupportconditionswereidenticaltothoseofthestatictestingcase.Thepanelsweresubjectedtoimpactwithincreasingheightsofmassdropuntildamagewasinduced.Thiscorrespondstoanimpactenergyrangeof7.8–108J.Impactvelocitiesrangedfrom1.6to5m/s.Aftertheinitialcontact,thedropmasswasheldmanuallytopreventrepeatedimpacts.

Impactloadswereacquiredwithapiezoelectricforcetransducerlocatedbetweentheimpactorandthecarriage.Thepositionofthemasswasrecordedduringtheimpacteventwithanon-contactlineardisplacementsensorthatdetectsametaltargetthroughinductivetechnology.Bydifferentiatingthedisplacement–timecurve,thevelocityofthedropmasswasdeterminedjustbefore,during,andjustafterimpact.Theplatewasinstrumentedwithstraingagesonitsupperandlowerfacesheets,atidenticallocationsasinthequasi-statictest.Thedynamicload,positionandstrainhistoriesoftheimpacteventwerecapturedwithdigitizingoscilloscopes.

3.Resultsanddiscussion3.1.Quasi-staticloading

Loadvs.displacementcurvesforthestaticloadingtestareshowninFig.3.Thedisplacementsofboththetopandbottomfacesheetsatthepanelcenteraregiven.Thedifferencebetweenthetopandbottomfacesheetde ectionsisduetoindentationofthefacesheetwithcorecrushing.Thetopde ectionincreasesatanearlylinearrateandaportionisrecovereduponunloading.Theportionthatisnotrecoveredisduetopermanentindentation.Facesheetdamagewasinitiatedataloadof17.3kN.Thetotalindentationcanbeobtainedbysubtractingthebottomfacesheetde ectionfromtheupperde ection,andwillbediscussedinafollowingsection.

Eightstrainreadingsweretakenontheupperfacesheetandeightonthelowerone.Asthesandwichpanelunderwentdeformation,thesestrainscouldbemonitoredto ndwherethehigheststrainsoccurred.Ingeneral,thereadingswereclassi edastwotypes,near-andfar- eld.Thenear- eldstrainswererecordedsuf cientlyclosetotheloadpointatthecenterofthetopfacesheet.Far- eldstrainswerethoserecordedonthebottomfacesheetandsuf cientlyfarfromtheloadpoint.Fig.4showsloadvs.strainplotsforthreelocationsonthetopandbottomfacesheets.Thetensilereadingonthebottomfacesheetdirectlybelowtheloadpoint(gagenumber3inFig.2)isfar- eldandincreasesinagenerallinearmannerwiththeload.Thisisalsothecaseforthecompressivefar- eldstrainonthetopfacesheet,measured50.8mmfromthecenterpointoftheplateandalignedperpendiculartothesupports(gage2inFig.2),althoughthestrainlevelsweresomewhatlower.However,thetensilenear- eldstraingage,located25.4mmfromthecenterpointandalignedperpendiculartothesupports(gage1inFig.2)ishighlynon-linearandreachesstrainlevelsabovethoseinthefar- eldrange.Thesereadingsoffercluesaboutthedeformationpro leofthepanelasitisloaded.Aplatewiththecurrentsupportandloading

)

Nk( daoLDisplacement (mm)

Fig.3.Loadvs.displacementcurvesforupperandlowerfacesheetsofsandwichpanelunderquasi-staticloading.

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1392P.M.Schubeletal./Composites:PartA36(2005)1389–1396

)

Nk( daoLStrain (%)

Fig.4.Load–strainresponseatnear-andfar- eldlocationsofsandwichpanelinquasi-static

test.

conditionswillexhibitaglobalin-planecompressivestrainonitstopsurface.Neartheloadpoint,localeffectsbecomeapparentandtensilestrainsareproducedduetoindentation.Onthebottomfacesheet,globalbendingeffectsdominateandtensilestrainsonlyarepresent.Afterthestatictest,damageintheplatewasevaluated.Permanentindentationwasvisiblyapparentandmeasured1.3mmindepthatthepanelcenter.Theupperfacesheetwasultrasonicallyscannedtodeterminetheextentofdamageinthecompositeandbondwiththecore.Damageresultsarepresentedinafollowingsection.3.2.Impacttesting

Fig.5showsthestrainhistoriesforthestraingagelocationcorrespondingtogage1inFig.2forvariousimpactenergies.Thepeaktensilestrainincreasedwithincreasingimpactenergyand,excludingthehighestenergyimpact,thestrainpulsedurationwasconsistent.Forthehigherenergydrops,somepermanentstrainwasapparentaftertheimpact,

)

%( niartSTime (ms)

Fig.5.Impactstrainhistoriesatnear- eldgagelocation1.

)

Nk( ecroFTime (ms)

Fig.6.Impactloadhistoriesshowingpeakimpactloadandpulseduration.

whichwouldindicateonsetofdamage.Alsoofimportanceinthe108Jimpact,thepeakstrainof1.25%isquiteclosetothematerialultimatetensilefailurestrainof1.3%[18].Theloadhistoryofeachimpacteventwasacquiredandthepeakforceateachimpactenergylevelwasobtained(Fig.6).Forlowimpactenergies,theloadpulseissinusoidalandathigherenergiesthesinusoidalnatureofthepulseispreservedwithsome uctuationspossiblyindicatingfacesheetdamage.Thepulsedurationwasrelativelyconstantforallevents.Becauseoftheassumedsinusoidalpulse,arelativelystraightforwardloadhistoryestimationmethodcanbeusedtopredictthemaximumloadforagivenimpactenergy.Theloadpulsecanberepresentedasahalf-sinewavefðtÞZP

2pt

0sinT

(1)

whereP0isthemaximumload.Tistwicethepulseduration(period)andstaysconstant.Themaximumloadwasobtainedbycomputingthedifferenceofmomentofmomentumbyintegratingf(t)from0toT/4asP2pmv0Z

T

(2)

wheremisthemassoftheimpactorandvisthevelocityoftheimpactorjustbeforeimpactwhichcanbefoundbydirectmeasurementorenergybalance.TheincomingvelocitycanalsobeexpressedintermsofimpactenergytogivethemaximumloadasafunctionofimpactenergyP0Z

2pp

2mE(3)

whereEistheimpactenergyforaspeci cimpactevent.Thepulsedurationcanbedeterminedbydirectexaminationoftheloadhistory,orbymakingtheassumptionthattheforce–de ectionresponseislinearunderlowvelocityimpact.

夹心板的低速冲击

P.M.Schubeletal./Composites:PartA36(2005)1389–13961393

30)

N25Calculated T = 9.2 ms

k( ec20roF tc15apmI k10aExperimentaleP5Load History

Estimation Method

25

50

75

100

125

Impact Energy (J)

Fig.7.Predictedandexperimentalpeakimpactloadvs.impactenergy.LoadestimationscalculatedwiththeoreticalT(9.2ms).

Then,Tcanbeestimatedby

TZ2p

r m

k

(4)

wherethepanelstiffnessk(2.87MN/m)canbefoundfromtheinitialslopeofthestaticloadvs.de ectioncurveoftheupperfacesheet(Fig.3).Inthecurrentstudy,theaimwastopredicttheloadresponseusingtheoreticalmethodstodetermineboththeimpactorvelocityandthepulseduration.However,themeasuredTfromFig.6(8.8ms)isclosetothetheoreticalvalueof9.2ms.ThepredictedmaximumloadsshowninFig.7asafunctionofimpactenergyareingoodagreementwiththeexperimentalresults.Thismethodisadvantageousbecause,byrunningonequasi-staticloadingtest,parisonofquasi-staticandimpacttests

Incomparingthequasi-staticandimpactloadingresponseofcompositesandwichpanels,theload–straincharacteristicsatcorrespondinglocationswereused.Fortheimpactcase,thepeakloadandstrainsforeachimpacteventwereusedintheanalysis.Iftheloadsarethesameatidenticalfacesheetlocationsandstrainlevels,then,thelowvelocityimpactbehaviorofthesandwichplateisverysimilartothequasi-staticcase.However,anyobserveddifferencescanbeexplained.

Fig.8showsacomparison,atgagelocation1onthetopfacesheet,ofthestaticload–strainresponseandthepeakimpactloadvs.strainbehavior.Atequivalentstrains,theimpactloadisconsistentlyhigher.Asthestrainlevelsincrease,thestaticandimpactresponsesdivergefurther.Thenon-linearupturnattheendofthestaticload–strainresponseisnotseenintheimpactdata.Thisdivergencecouldsuggestthatthedeformationpro leofthetopfacesheetinthestatictestismoresevere,meaningthatthestrainsaroundthecontactareaarehigher.Additional

30

25

20)

Nk( da15

oL10

IMPACT

5

QUASI-STATIC

00.5

11.5

Strain (%)

parisonofload–strainresponseofnear- eldgagelocation1.

near- eldstrainreadingsontheupperfacesheetcon rmthiseffectaswell.

Atadistancesuf cientlyfarfromtheloadingarea,thestrainsarenotin uencedbythelocalizeddeformationpro lecausedbytheindenter/impactorcontactarea.Fig.9showsthecomparisonoftheload–strainresponseofthesandwichpanelatgageposition2.Thebehaviorisquiteconsistent.Far- eldstrainreadingstakenfromthebottomfacesheetalsocorrelatewellforstaticandimpactloadings.Thefar- eldstrainsareoutsidetheregionaffectedbythelocalizedindentationandtheload–straincurvesincreaserelativelylinearly,unlikethenear- eldcurveswhicharenon-linearathigherloads.Thus,staticandlowvelocityimpactloadingsproducesimilardeformationbehaviorin

30

IMPACT25

QUASI-STATIC

20)

Nk( da15

oL10

5

00.050.10.150.20.250.3

Compressive Strain (%)

parisonofload–strainresponseoffar- eldgagelocation2.

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1394P.M.Schubeletal./Composites:PartA36(2005)1389–1396

theplateexceptforthelocaleffectsproducedbytheindenter/impactor.

3.4.Posttestdamagecharacterization

Thestaticandimpact-loadedpanelswereinspectedandultrasonicallyscannedafterthetestsfordamage.Bothplatesshoweddelaminationdamagearoundthecontactareaoftheindenter/impactor.Fig.10showsultrasonicC-scanimagesforthetwoloadingconditions.Thedarkareasatthepanelcenterindicatefacesheetdamage,whichB-scanscon rmedtobedelaminationswithintheupperfacesheet.ThelighterareasontheC-scanofthestaticallyloadedpanelsignifyadhesivenon-uniformityinthefacesheet-corebondbutdonotaffectitsresponse.Uponvisualinspection,apronouncedindentationcouldbeseenatthecenteroftheimpactedpanelwhichmeasured0.9mmindepth.Alldamageinbothloadingcaseswaslocalizedandthedelaminatedareaswereroughlythesameinsize.Althoughthepeakloadlevelintheimpacttestswashigherthanthatinthequasi-statictest,noincreaseinthelevelofdamagewasapparent.Acomparablelevelofdelaminationdamagewasinitiatedinthestaticpanelatalowerload.Therefore,thestatictestingeneralismoreconservativewhenconsideringlocalizedstrainanddamagelevels,whichhasbeenconcludedinothersandwichimpactstudies[20].

Alongwiththeloadhistoryestimationmethod,astraightforwarddamagepredictionmodelcanbedeveloped.Runningaquasi-statictestonacompositesandwichpanelyieldsthepanelstiffnessaswellasadamageinitiationload.Foragivenimpactenergy,thepeakimpactforcecanbeestimated.Bycomparingthispeakimpactforcewiththedamageinitiationloadfromthequasi-statictest,aquickdamagepredictioncanbemade.Ifthepredictedpeakimpactforceexceedsthatofthestaticdamageinitiation,damageispossibleinthepanelforthegivenimpactenergy.

3.5.Indentationbehaviorofsandwichpanels

Describingthebehaviorofacompositesandwichpanelalsoinvolvesunderstandingitsindentationbehaviorasitisloaded.Indentationincludeslocalfacesheetdeformationandcorecrushing,ofteninteractinginacomplexway.Analysisofindentationismorestraightforwardinasandwichbeamcon gurationandtheoreticalcontactlawshavebeensuccessfullyestablishedwithgoodagreementwithexperimentalresults[19,21].However,quasi-staticindentationonasandwichpanelwitharigidspherepresentsadditionalanalyticaldif culties.Sburlati[22]addressedtheproblemwithamathematicalmodelbasedonelasticplatetheorywithsomesuccess,butthemodeldidnotextendpasttheinitiallinearload–indentationrelationship,afterwhichcoreyieldingeffectsarepresent.ThesameistruefortheworkbyAndersonandMadenci[23],whereathree-dimensionalanalyticalmodelbasedonlaminatetheorydevelopscompletestressanddisplacement eldsandcomputesthecontactarea.Thesemodelsdonotcapturethecorecrushingdamageprocessesandnon-linearindentationbehavior.

OlssonandMcManus[24]developedamethodtoincorporateindentationdamageeffectsintothesandwichpanelbehavior.Inthismodel,apoint-loadisassumedandmustbecorrectedduringcalculation.A‘membranesolution’isdescribedwherepastthelinearregionofthecontactload–indentationcurve,largede ectionsinthefacesheetcauseittobedominatedbymembranestresses.Theregionaffectedbycorecrushingismodeledasamembrane,whiletherestofthesandwichpanelismodeledasaplateonanelasticfoundation.Thistheoryresultsinaload–indentationcurvewithaninitiallinearregion,asofteninguponcoreyieldingfollowedbyastiffeningasthemembranestressbecomesdominant.Themodelseemstodescribeapproximatelytheindentationprocesses

observed

Fig.10.UltrasonicC-scanimagesofsandwichpanelsshowingposttestdelaminationdamage:(a)staticallyloadedpanel;(b)impactloadedpanel(108J).

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P.M.Schubeletal./Composites:PartA36(2005)1389–1396

1395

)

Nk( ecroF tcatnoC0

1

2

3

Indentation (mm)

Fig.11.Staticloadingindentationresponsecomparingexperiment,analyticalmodelsandFEanalysis.

inthecurrentstudy.However,whenappliedtothecurrentsandwichpanelcon gurationandstaticloadingsituation,thestiffeningeffectwaspresentbutthemodelunder-estimatedtheindentationandthecorrelationbetweenthemembranesolutionandexperimentalresultswasnotclose.A niteelementmodelwasdevelopedtosimulatetheload–de ectionbehaviorofthetopandbottomfacesheetsinthestaticloadingcase.Withthisinformation,amodeloftheindentationofthesandwichpanelwasobtained.ThemodelwasconstructedwithABAQUS,withthefacesheetsmodeledasorthotropiclaminaeandthecoreasanisotropicelasticmaterialuntilyielding.Aftercoreyielding,thecorewasmodeledasaplasticallyyieldingmaterial(crushablefoam).Theindenterwasrigidandcontactwasassumedfrictionless.Theuniformmeshwasthree-dimensional,withsimplysupportedboundaryconditionsalongtwoedges,identicaltotheexperimentalsetup.Fig.11showstheexperimentalcontactforce–indentationcurvealongwiththeFEanalysisresults.TheFEmodelmatchesquitewelltheexperimentalresultsandcapturesthestiffeningbehavior.Forcomparison,themembranesolutionisalsoplottedwhichshowsthepooragreementwithexperimentaldata.Additionally,aplateonanelasticfoundationsolutionforsmallde ectionsisshown[25].Thelinearplatesolutioncorrelateswellwiththebehavioratsmallindentationspriortocoreyielding.

4.Conclusions

Besidesthelocalizedeffectscausedbyloadcontactcharacteristics,thequasi-staticandlowvelocityimpactbehaviorofcompositesandwichpanelscomposedofwovencarbonfabric/epoxyfacesheetsandaPVCfoamcoreinvestigatedinthecurrentstudyarequitesimilar.Inthisrespect,thelowvelocityimpactresponseofplatescanbecharacterizedasquasi-staticinnature.Thisconclusionis

basedonthecomparisonofaquasi-statictestandmultipleimpacttestsonsandwichpanelsandananalysisoftheload–strainresponse,aswellasathoroughdamageevaluationofpanelsunderbothtypesofloading.Therefore,aquasi-statictest,whichiseasiertoperformandanalyze,canbeusedtopredictrelatedimpactresponse.Localizedeffectsdealmainlywiththecontactcharacteristicsbetweentheindenter/impactorandtheupperfacesheet.Astatictestproducesamorepronounceddeformationpro leanddamageprocessesareinitiatedearlier.Thecurrentresultssuggestthatthequasi-statictestisingeneralmoresevereintermsofthedeformationandstrainlevelsinducedintheloadedfacesheet.

Additionally,aloadhistoryestimationmethod,basedonthesinusoidalshapeoftheimpactloadpulse,wasemployedtopredictthepeakimpactforceasafunctionofimpactenergy.Assumingalinearload–de ectionrelationship,thepulseperiodcanbecalculatedfromaquasi-statictest.Thepredictedpeakloadsagreedquitewellwiththeexperimen-talresults,meaninglowvelocityimpactbehaviorcanbepredictedwithoutrunningasingleimpacttest.Astraight-forwarddamagepredictionmethodwasalsoputforthwhichcouldbeusedtopredictimpactdamageinthecompositesandwichpanelbycomparingthepeakimpactloadtothestaticdamageinitiationload.

Thecontactforce–indentationrelationshipforsandwichpanelswasalsoinvestigatedforthestaticloadingcase.Someanalyticalmodelswerestudiedfortheirapplica-bilitytothecurrentsandwichsetup.Two[22,23]werefoundtobelimitedintheirscopebecausetheydidnotmodelthepanelbehaviorbeyondcoreyielding.Anothermodel[24]didaccountforcoreyieldingandfacesheetstiffeningbutunderestimatedtheindentationresponseforthecurrentcon guration.Aneedexistsforananalyticalindentationmodelthatcanaccountforthecomplexinteractionsthatgovernthebehaviorofthestructurefromsmallcontactarealoading,leadingtocoreyieldingandultimatelyincludingthestiffeningeffectobservedinsandwichplates.Theinitiallinearindentationbehavioruntilcoreyieldingmatchedwellthatofasimpleplateonanelasticfoundationmodel.A niteelementmodelwasimplementedtocapturethefullresponseofthepanelindentationandwasabletomatchthestiffeningbehaviorseenintheexperimentsquitewell.

Acknowledgements

ThisresearchwassponsoredbytheOf ceofNavalResearch(ONR).WearegratefultoDrY.D.S.RajapakseofONRforhisencouragementandcooperation.WealsoacknowledgetheeffortsofDrJ.W.YoofordevelopingandimplementingtheABAQUS niteelementmodelforthispaper.

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1396P.M.Schubeletal./Composites:PartA36(2005)1389–1396

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