一份关于压缩板中筋板对其屈服过程中抗扭刚度影响的一次实验调查.doc

KSMEInternationalJournal,VoL16,No.5,pp.599-608,2002599CharacterizationofFractureBehaviorinRepairedSkin/StiffenerStructurewithanInclinedCentralCrackKi-HyunChung,Won-HoYang,Sung-Pi!HeoDepartmentofMechanicalEngineering,SungkyunkwanUniversity,300Chunchun-Dong,Jangan-Ku,Suwon,Kyunggirdo440-746,KoreaFiniteelementanalysisforthestressintensityfactortSfF)attheskin/stiffenerstructurewithinclinedcentralcrackrepairedbycompositestiffenedpanelsisdeveloped.Anumericalinvestigationwasconductedtocharacterizethefracturebehaviorandcrackgrowthbehaviorattheinclinedcrack.Inordertoinvestigatethecrackgrowthdirection,maximumtangentialstress(MTS)criterionareused.Also,thispaperistostudytheperformanceoftheeffectivebondedcompositepatchrepairofaplatecontaininganinclinedcentralthrough-crack.Themainobjectiveofthisresearchisthevalidationoftheinclinedcrackpatchingdesign.Inthispaper,thereductionofstressintensityfactorsatthecrack-tipandpredictionofcrackgrowthdirectionaredeterminedtoevaluatetheeffectsofvariousnon-dimensionaldesignparameterincluding;compositepatchthicknessandstiffenerdistance.Wereporttheresultsoffiniteelementanalysisonthestiffenerlocationsandcrackslantanglesanddiscusstheminthispaper.Theresearchoncrackedstructuresubjectedtomixedmodeloadingisaccomplishedandconcludesthatmoreworkusingadifferentapproachesisnecessary.Theauthorshopethepresentstudywillaidthosewhoareresponsiblefortherepairofdamagedaircraftstructuresandalsoprovidegeneralrepairguidelines.KeyWords:FractureMechanicsAnalysis,Skin/Stiffener,MaximumTangentialStress(MTS),CrackGrowthDirection,ReductionofStressIntensityFactor1.IntroductionDuetotherapiddevelopmentofaerospaceindustry,manyinvestigatorshavestudiedthecrackedstructuresbytherequestofsafety.Intheviewofincreasingtheservicelifeandreducingtherepaircost,theproperrepairmethodshavebeensuggested.Asasimpleandhandymethod,compositebondedpatches,whichnowarewidelyusedforcrackedstructures,canbeusedtorepairorreinforceaerospacestructuresbymodifyingtheirloaddistributionandbypassingdefectsorCorrespondingAuthor,E-mail:chungkhnature.skku.ac.krTEL:+82-31-290-7496;FAX:+82-31-290-5849DepartmentofMechanicalEngineering,Sungkyun-kwanUniversity,300Chunchun-Dong,Jangan-Ku,Suwon,Kyunggi-do440-746,Korea.(ManuscriptRe-ceivedNovember30,2000;RevisedMarch2,2002)cracks.Inviewoftherapidlyincreasinguseofhighstrength,stiffnessandlowweight,fiber-reinforcedcompositematerialinadvancedengi-neeringstructuressuchashigh-performanceair-craftisdevelopedandused.Damagetolerancedesignandreliabilityofthecompositestructureshavebeenofsignificantconcernandhavealsobroughtarenewedinterestinthetheoreticalanalysis.Skin/stiffenerstructuresarecommonfeaturesofairframes(e.g.fuselages)andwingsarefrequentlymadefromstiffenedsheets.Crackscanoccurinsuchstructuresinthevicinityofthestiffener.BakerandJones(1988)expressedthemanyadvantagesofemployingcompositematerialpatchesforthebondedrepairofcrackedanddamagedmetallicstructures.Bondedrepairsarelight-weight,eliminateunnecessaryfastenerholesinanalreadyweakenedanddamagedstructure,600Ki-HyunChung,Won-HoYangandSung-Pi!Heoenableloadtransfermoreevenlyandoverlargearea,thusenhancingthefatiguelifeoftherepairedstructure.Theprimaryadvantageofcompositerepairstocrackedstructuresistoimprovethedamagetoleranceoftherepairedstructure.Tothisaim,itisessentialtodemon-stratebyfractureanalysisandtestthattherepaircanretainthecrackpropagationanddamagetolerancerequirements.But,thismethodisverydifficulttoexactlyinvestigatethecrackbehavior.So,theexperimentalinvestigationandnumericalmethod(FiniteElementMethodandBoundaryElementMethodetc.)arecontinuouslyaccom-plishedtoproblemssuchashowtodistributestressorhowtorestrainthecrack,andhowtopredictthecrackpropagationdirection.However,forasuccessfulimplementationofthisrepairtechnique,athoroughunderstandingoftheeffectofvariousdesignparametersofrepaironthecrack-tipstressintensityfactorsisneces-sary.loneandCallinan(1979,1983)studiedthecrackedpatchingusingthefiniteelementmethod.ChuandKo(1989)proposedamethodusingcollapsedisoparametricelementtopreservethesingularstresscharacteristicatthecracktip.Butthismethodrequireslargenumberofnodaldegreesoffreedom.Toovercomethisproblem,Atluri(1992)suggestedthefiniteelementalternatingmethod(FEAM)inwhichthemeshneedsnotbeveryrefinedintheregionofcracks.ChungandYang(2000)studiedthepatchsefficiencyinviewoffracturemechanicsanddebonding.Andtheysuggestedtheoptimalpatchshapeonthereductionofstressintensityfactor.Aseriesofpreviouslyreportedresultshavesomelimitationonthehypothesisthatthestructureissubjecteduniaxialloading,butmostofthestruc-turalcomponentsaresubjectedtobiaxialloading.Asthecrackdoesnotalignwithoneoftheprincipaldirections,themixedmodebehaviorwillhaveasignificanteffectonthecrackgrowthandfracturemechanics(Chue,etal.,1994).Inthispaper,theanalysisofrepairedskin/stiffenerstructurewithaninclinedcentralcrackisreported.Thefracturemechanicsanalysisatthecracktipisperformedandexpectationofthecrackpropagationdirectionistobesuggested.2.MethodofAnalysisAschematicdiagramoftheskin/stiffenerstructuretobestudiedisshowninFig.1.Analuminumrectangularskinandl-rypestiffenerpossessacentrallylocatedhorizontalthrough-thicknessinclinedcrack.Topreventthepropaga-tionofcrack,anontapered0/90.boron/epoxycompositepatchisconsidered.FromthestudybyChungetal.(2000)consideringbothfracturemechanicsanddebonding,taperedpatchshapeismoreeffectivethannontaperedpatch.Skin/stiffenerandskin/patcharebondedwithepoxy.Thethicknessesplate,adhesivelayerandpatchare3mm,O.lmmand3mm.TheotherdimensionsandthematerialpropertiesaregiveninFig.2andTableI,respectively.Itisassumedthattheskin/stiffenersupportsanuniformtensilestress(00)of10MPainthey-Fig.1Configurationofskin/stiffenerplateFig.2Geometryofskin/stiffenerplatewithinclinedcentralcrack(unit:mrn)CharacterizationofFractureBehaviorinRepairedSkin/StiffenerStructurewithanInclinedCentral-601Table1Materialpropertiesofthealuminum,theboron/epoxypatch,andtheadhesivelayerYoungsmoduliShearmoduliPoissonsratio(OPa)(OPa)E1E2E3G12G13G23)12)13V23Al-plate71.02-0.32-IPatch40.16770.16770.Q35Adhesive2.2-0.32-where(Jistheappliedload,aisthehalf-cracklength,andaistheanglebetweenthecracklineandthetensileaxis.Thestressintensityfactorcanalsobeobtainedbyconsideringthedisplacementoverthequar-ter-pointcrack-tipelementsshowninFig.3(a)2.1StressintensityfactorThefractureparameterforthecrackedstructureisoftengivenintermsofthestressintensityfactor.Thestressintensityfactorforacentralslantcrackoflength2ainaninfinitesheetsubjectedtoaremoteuniformuniaxialtensilestressisgivenby(Smith,1988)direction.Owingtosomeofthelimitationsofanalysis,thispaperisbasedonthefollowingsimplifiedassumptions.(l)Thecurvatureofthepanelisneglectedandisidealizedasaflatpanel.(2)Thebondingofthepatchandstiffenerisperfectwithoutdebonding.Thealuminumskin/stiffener,theboron/epoxycompositepatchandepoxylayermustremainlinearelastic.(3)Theadhesivelayerthicknessisrelativelythincom-paredtotheplate/patchthickness,sothatageneralizedplanestressconditionisconsidered.Andtheshearstressbetweenplateandpatchistreatedasabodyforce.Theunpatchplatewithaninclinedcentralcracksituationisconsideredfirstforvalidityofthefiniteelementanalysis.Thisanalysisismadetoevaluatethestressintensityfactorsandcrackpropagationdirectionoftheplateunderserviceloadsintheabsenceofthepatchandstiffener.Theinvestigationofthepatchefficiency,bothofwithoutpatchandwithpatchareconsidered.Kr=(Jfiiisin2aKrr=(Jfiiisinacosa(1)(2)(Cooketal.,1989):KI=K1fIf-(4VB2-Vd-(4VBI-VC1)(3a)K=KIfIf-(4uB2-ud-(4UBI-UC1)(3b)where,u=E/2(1+II)istheshearmodulusofelasticity,Kisequalto(3-411)forplanestrainand(3-1I)/(1+v)forplanestress,andu.,ViareX-,y-componentsofthecrackopeningdisplacementCOD)atthecollapsedcracktipelements.IngraffaandManu(1980)proposedthecalcu-lationofstressintensityfactorforthethree-dimensionalquarter-pointcrack-tipelementsshowninFig.3(b).s,4(1V2)j211(2VB-VC+2VE-VF-2vB+vc,-2vE1+vp-VD)+217(-4VB+VC(4a)+4VE-vF+4v8-vc,-4vE+vp)+i-7l(VF+VC-2VD-vp-vc,+2vD)x,4(11I2)!211(2U8-UC+2UE-UF-2uB+Uc,-2uE1+up-UD)+217(-4U8+UC(4b)+4UE-UF+4uB-Uc-4uE+up)+7l(UF+Uc-2uD-up-uc+2uD)where,EandIIaretheYoungsmodulusandthePoissonsratio,L1isthelengthofquarter-pointelementand17isthelocalcoordinateatthecrackfront,respectively.602Ki-HyunChung,Won-HoYangandSung-PilHeoIY.l11+-1-9C2:=_-4ix.uCl(a)(b)Fig.3Arrangementofquarter-pointwedgeelementalongsegmentofcrackfront(6a)(6b)2.2ReductionofstressintensityfactorForthemeasureofthefracturemechanicssafe-tyandpatchingefficiencycriteriaattherepairedcrack,thenondimensionalizedreductionofstressintensityfactorcanbeusedsuchthat(5)where,Ku,Kparethestressintensityfactorsfortheunpatchedandpatchedcrackplates.Thereductionofstressintensityfactorsisveryimportanttodesignofrepairedcrackedplatebecausethisvalueimpliesthepatchefficiency.AsK*increasesthecrackpropagationde-creases,ontheotherhand,asK*decreasesthepossibilityoffractureincreases.(1963)isoneoftheearliesttheoriesdealingwithstablemixed-modecrackgrowthdirectionunderstaticloading.Itpostulatesthatthecrackwillpropagationinthedirectiongovernedbythemaximumvalueofstressnormaltotheradiallinefromthecracktip.Therefore,thiscriterionassumesamodeIcrackgrowthmechanism.Mathematically,conditionforthecrackgrowthdirectioncanbeexpressedas:aa8=0.(fa80sin28-0.92sin8+4Rk(cos28-cos8)+R/(0.92sin8-3sin8)=0where,RioistheratioKJ!K.3.FiniteElementAnalysis(11)(12)Theconditionforcrackgrowthdirectioncanbeexpressedas:(a)(c)Thebasicgeometryofcrackedskin/stiffenerstructureconsideredinthisstudyisshownin(b)Distance(s=80mm)(d)Fig.4Finiteelementmodelingaroundcrack,inclineddegree(0)(a):0,(b):45,(c):90,(d):wholemodelingofS/a=8604Ki-HyunChung,Won-HoYangandSung-PitHeoFig.1.Considerathinelasticaluminumsheet240X360X3mmwithancentralcrackoflengthaandIrtypealuminumstiffener.Thebasicrepairconfigurationisa40X80X3mmboron/epoxycompositepatchbondedby0.3mmthickfilm-epoxyadhesive.Onceanefficientmodelisestablished,wewouldinvestigateasetofthisbasicconfigurationtostudytheeffectofstiffenerdistanceandcrackslantangle.Theslantcrackedsheetissubjectedtoaremoteuniaxialtensileloadof10MPa.Sincetheprob-lemhasnoplaneofsymmetry,itisnecessarytomodelthewholestructurebyusingthree-dimen-sional20-nodeisoparametricbrickelements.Theregionadjacenttothecrackfrontismodelledwiththesingularcrackelements.Inthesingularelementthemid-sidenodesareshiftedtothequar-ter-pointpositiontoinducetherequired(1/r)1/2stresssingularity(Fig.4).Togetbetterresults,thesingularelementsizesarekeptwithin10%ofthecracklength.FiniteelementanalysisisdoneusingacommercialABAQUScode(version5.8-8).Figure4showsthefiniteelementmodelingforthestiffenerdistance80mmandthedetailconfig-urationofthecrackpartwithrespecttocrackangle.4.ResultsandDiscussionTable2Comparisonofstressintensityfactorforinclinedcrackedrectangularplates(00=10MPa,unit:MPavffiffi)InclinedSmithPresentCrackModeIiModenModeIModenAngleC)SIFsiSIFsSIFsSIFs056.06!0i60.380II1054.36I9.60I58.6010.912049.5018.02I53.3420.463042.0424.27I45.3227.594032.9027.60I35.5031.41I4528.0328.03I30.2331.88I5023.1627.60i25.0231.436014.0124.2715.1327.63706.56I18.02I7.0820.52801.699.601.8210.9190000080r-r=;t7010o-=901530456075Inclinedcrackangle,8()-=_Nopateh-_hplhs-0.167._hplhs-0.333.-.-_hplhs=O.SOO_.-._-_.=:=:.i3.Smithinfinite)oL-koHInclinedcrackangle,IJ()7080r:=-r=:=)lFig.6ModenSIFwithrespecttoinclinedcrackangle(00=IOMPa)Fig.5ModeISIFwithrespecttoinclinedcrackangle(00=10MPa)4.1RepairofinclinedcrackinunstiffenedpanelsFigures5-6showthestressintensityfactorswithrespecttotheinclinedcrackangle.Thestressintensityfactorsareobtainedintheaveragesensethroughthethickness.Toinvestigatethevalidityoftheresultsobtained,wecomparethosewithotheravailableresults.AscanbeseeninTable2andFigs.5-6,theresultsareingoodagreementwithin7-10%withthoseobtainedbySmith(1988).Theseerrorsmaybecausedbythefactthatthepresentstudyconsidersthefinitemodel,butSmithsstudyconsideredtheinfinitemodel.Figures7-8showthenondimensionalreductionofSIFwithrespecttovariousinclinedcrackangles.Fromtheresult,thepatchisveryefficienttorestrainthecrackgrowth.Ascom-paredwithunpatchedplate,themodeISIFsCharacterizationofFractureBehaviorinRepairedSkin/StiffenerStructurewithanInclinedCentral605ofpatchedplatearereducedabout20-30%.ModeISIFsofthickpatcharerapidlyde-creasedastheanglebetweenloadingdirectionandinclinedcrackisdecreased.Oppositely,whenthecrackedinclinedangleisover75,modeISIFsareincreasedasthethicknessofpatchincreases.Especially,modeISIFisnotzeroat90ofpatchedplate.Thisphenomenonisduetothepresenceofout-of-planebendingdeformationwhichcausesthenonlinearbehaviorofmaterialandgeometry.ModenSIFsofpatchedplatearereducedabyabout30-45%.ThereductionofmodenSIFsisabout0.3-0.4,andwhihisindependentofinclinedangle.Ascanbeconcluded,theeffectofthickerpatchbecomesevenstronger,buttheSIFdoesnotgrowinfinitelyasthepatchthicknessincreasesbecauseoftheout-of-planebendingdeformation.And4.3RepairofinclinedcrackinstiffenedpanelsTheinfluenceofthedistanceofthestiffenertheeffectofpatchtothemodenbehaviorismoresignificantthanthemodeIbehavior.4.2PredictionofcrackgrowthdirectioninunstiffenedpanelsMostofthestudiesofcrackgrowthundermixedmodeIandnloadingshavebeenconductedusingaplatewithaninclinedcentralcrackundertension.Topredictofcrackgrowthdirection,themaximumtangentialstresscriterionisexamined.Figure9showsthecrackgrowthdirectionattheunrepairedandrepairedplateswithaninclinedcentralcrack.Ascanbeseen,thepatcheffecttothecrackgrowthdirectionisrelativelyslight.Togetherwiththepatchthicknessincrease,thecrackgrowthdirectionhasatendencytogrowtowardthemodeIdirection.Asinclinedcrackangle(8lapproachesabout50-60,whichtherangeisequalmodeISIFwithmodenSIF,thecrackgrowthdirectionoftheplaterepairedbycompositepatchbecomesperpendiculartotheapplyloadingdirection.Whentheinclinedangleapproachestheload-ingdirection,thedifferencebetweenthepredictedcrackgrowthdirectionoftheoreticalanalysisandpredicteddirectionofpresentanalysisbecomeslanger.So,thecrackgrowthdirectionisunstable.bplhr-O.167_hplbs-O.333-+-hplbs=0.500-e-bplbs-O.667-e-hplbs=O.8334530151=-._-O.8,.;-0.69075304560Inclinedcrackangle,8()150:.-o-+-Nopatch_hplbs=O.167_hplhs-o.333_hPlbS=O.SOO-e-bpibs-Q.667I.-=:t;J;=.-jhplbs-O.833I-3.Theoretical90.hpihr-Q.167_hplbs-O.333-+-hpihs=O.500-e-hplbs=O.667-e-hplbs-O.83330456075Inclinedcrackangle,8()15oL-.-or.o.0.4.,;0.2.=0.8=O.6Fig.8ReductionofmodenSIFwithrespecttoinclinedcrackangleFig.9Predictionofcrackgrowthdirectionfortherepairedplate606Ki-HyunChung,Won-HoYangandSung-Pi/HeoInclinedcrackangle,J()Fig.12ReductionofmodeISIFwithrespecttoinclinedcrackangle90_S16.Suapalb).S18.0uupalb)_S1a-9.Suupa:b).S1a-605pa:b).-0.S1.S.0pateb).-0.S1a=9.5(teb)oo8070:;30Cil20IS30456075Inclinedcrackangle,J()Fig.10ModeISIFwithrespecttoinclinedcrackangle(10=IOMPa)_S1a-605_S1.-S.0.51.-95).Unstiffenede0)-0-.&.&.e)0HaInclinedcrackangle,J()ReductionofmodeIISIFwithrespecttoinclinedcrackangleooFig.13-.0.8.lei.:.;0.6=e:0.4e.oSg0.2_S1a-605uupa:b)-1.S1a-S.Ouupaleb)_S1a-905(uupateb).S16.Spa:b).-0.S1S.Dpa:b)-1-OS1a_9.S(pa:b)HaDInclinedcrackangle,8()Mode.IISIFwithrespecttoinclinedcrackangle(oo=lOMPa)o-.-.:.;o70_60e50loo!401-lei30f-Cil20Fig,111080(S=65mm,80mmand95mm)onthepredictedSIFandreductionofSIFisillustratedinFigs.10-13.Ascanbeseen,thestiffenerlocationhaslessinfluenceontheSIF.But,whenthecracksizeincreases,thedistanceofstiffenerlocationmightbeplayingthemoreimportantroleinthecrackrestraintandcrackgrowthdirection.TheSIFofpatchedskin/stiffenerstructureisdecreasedabout1.5to2timesasmuchasunpatchedskin/stiffenerstructures.Wheninclinedcrackanglereached90,thestressintensityfactorofmodeIdoesnotvanish.Inthosefigures,thestressintensityfactorsobtainedarethemaximumvalu