Cohesive Zone Model for Facesheet-Core Interface Delamination in Honeycomb FRP Sandwich Panels by Weiqiao Wang Dissertation submitted to the College of Engineering and Mineral Resources at West Virginia University in partial fulfillment of the requirementsfor the degree of Doctor of Philosophy in Civil Engineering Approved by Julio F. Davalos, Ph.D., Chair Jacky C. Prucz, Ph.D. Bruce Kang, Ph.D. Pizhong Qiao, Ph.D. Indrajit Ray, Ph.D. Department of Civil and Environmental Engineering Morgantown, West Virginia 2004 Keywords: Delamination, Fracture, Sandwich Structure, Cohesive Zone Model Copyright 2004 Weiqiao Wang iiCohesive Zone Model for Facesheet-Core Interface Delamination in Honeycomb FRP Sandwich Panels Weiqiao Wang Advisor: Dr. Julio F. Davalos Abstract: Thefocusofthisdissertationisondevelopingefficientmodelingtechniquesto studyfacesheet-coreinterfacedelaminationinhoneycombfiber-reinforcedpolymer (HFRP)sandwichpanels.Delaminationproblemsareusuallytreatedfromafracture mechanicspointofview.However,interfacedelaminationisgenerallyverycomplexin natureanddifficulttosolve,becauseitinvolvesnotonlygeometricandmaterial discontinuities,butalsotheinherentlycoupledModeI,IIandIIIfractureinlayered materialsystemsattributedtothewell-knownoscillatorysingularitynatureofthestress and displacement field in the vicinity of the delamination crack tip. One of the key issues in this research is to determine the best way to characterize interface delamination within the framework of continuum mechanics rather than using ad hoc methods just to facilitate numerical implementations, such as springs across a crack in the finite element method. Theusualrequirementofdefininganinitialcrackandassumingself-similar progressionofacrack,maketraditionalfracturemechanicsapproachesinefficientfor modelinginterfacedelamination.Tocircumventthesedifficulties,fivemostrelevant nonlinearcrackmodelsarereviewedandcompared.Itisconcludedthatbyunifying strength-basedcrackinitiationandfracture-basedcrackprogression,thecohesivecrack modeling approach has distinct advantages compared to other global methods.Inthisstudy,acohesivezonemodel(CZM)withlinear-exponentialirreversible softeningtraction-separationlaw,satisfyingempiricalmixed-modefracturecriteria,is proposedtorepresentprogressivedamageoccurringwithintheinterfaceduringthe fractureprocess.TheCZMisimplementedasacohesiveinterfaceelementthrougha user-definedelementsubroutinewithinthegeneralpurposefiniteelementcode ABAQUS. The framework and formulation of a three dimensional interface element are presented. Two sets of parameters are required for application of the developed interface element, namely, interfacial strength and fracture toughness. The initiation of fracture is determined by the interfacial strength and the progression of fracture is determined by the interface fracture toughness. The surface-like interface element consists of an upper and a lowerfacewithinitiallyzerothicknessintheundeformedconfiguration.Inthefinite elementmodeling,theseinterfaceelementsarepositionedwithintheinterfacewhere potentialdelaminationpropagationisexpected.Acontact-typeinterfaceelementisalso developed to simulate contact behavior in the delaminated region. iiiVerificationexamplesapplyingthedevelopedinterfaceelementarepresented withnumericalsimulationsofstandardfracturetestconfigurations,namelydouble cantileverbeam(DCB)andmixed-modebending(MMB)specimens,underModeI, ModeII,ormixed-modeloadingconditions.Forallthesimulations,thepresentfinite element solutions are in good agreement with either the linear elastic fracture mechanics analyticalsolutionsorexperimentaldataavailableintheliterature.Non-self-similar delaminationgrowthoracurveddelaminationfrontduetoanticlasticbendingeffectin theDCBspecimeniscapturednumerically.TotesttherobustnessoftheCZMin simulating delamination coupled with highly nonlinear structural response, delamination bucklingofalaminatedcompositeplateunderin-planecompressionissimulated;in order to lessen the burden of using a fine mesh, a slight modification of the formulation of the interface element was made resulting in a more brittle fracture behavior within the interface. Delaminationincompositesandwichstructuresisanimportantfailuremode. Although the problem of a facesheet delaminated from a solid core has been extensively investigated,thefailuremechanismofdelaminationofafacesheetfromahoneycomb coreisfarfromfullyunderstood.ApplicationoftheCZMtostudyfacesheet-core interface delamination of honeycomb sandwich structures is rare. In this study, facesheet delaminationinHFRPsandwichpanelsisaddressedwiththedevelopedcohesive interface element.The interfacial properties of strength and fracture toughness are obtained through a systematic experimental program. The effects of such parameters as facesheet bonding layersandcore-wallthicknessareinvestigated,andalthoughmoretestsareneeded beforeadefiniteconclusioncanbedrawnfromthecurrentexperimentaldata,some preliminaryobservationsareprovidedregardingtheireffectsoninterfacefracture response. It is shown that the response of the HFRP sandwich panel involving facesheet-coreinterfacedelaminationpropagationismainlycontrolledbytheinterfacefracture toughness,whiletheinterfacialstrengthhasarelativelysmalleffect.Assuch,the interfacial strength value need not be measured precisely. Simulationofthecontoureddoublecantileverbeam(CDCB)specimenwith verticalcoreelements,usedtoobtainfracturetoughnessvalues,issuccessfully performed with the measured interfacial properties. It is verified that in this test the Mode IIcontributionisnegligible,showingthevalidityofusingtheCDCBspecimenfor measurementofModeIinterfacefracturetoughness.Apeelingdelaminationtestofan HFRP sandwich panel is successfully modeled, demonstrating the predictive capability of the developed CZM to simulate the facesheet-core interface delamination propagation in actualHFRPsandwichpanelswithsinusoidalwavecoreconfiguration.Finally,a simulationofafour-pointbendingtestof an actual HFRP sandwich panel is conducted, and without assuming an initial delamination, the cohesive zone modeling approach with thepresentinterfaceelementsuccessfullypredictedthedelaminatedregionobservedin the experiment. ivAcknowledgments IwouldliketoexpressmygratitudeandappreciationtomyadvisorDr.JulioF. Davalos, for his continuing assistance, support and encouragement through the inspiring guidance of this research. Special thanks to the committee members, Dr.J. Prucz, Dr. B. Kang,Dr.P.QiaoandDr.I.Rayfortheiracademiccollaborationandvaluable suggestions for this dissertation. ThanksarealsoowedtoKansasStructuralCompositesInc.forgenerously providing all the test samples. Laboratory assistance of Mr. Raabal El-Amine, Mr. Justin Robinson and Mr. Avinash Vantaram should be acknowledged.I also want to thank my colleagues Mr. An Chen and Mr. Chuanyu Feng for helpful discussions. At last but not least, I want to express deepest thanks to my lovely and beautiful wifeJiemingforherendlesssupportandforbearancethroughoutmyacademiccareer.I also must thank my parents and family for their everlasting support and blessings in my life. This research is supported by NSF Partnerships for Innovation program. v Table of Contents Abstract ............................................................................................................................. ii Acknowledgements......................................................................................................... iv List of Figures ................................................................................................................. viii List of Tables.................................................................................................................... xi Nomenclature.................................................................................................................. xii Chapter 1 ........................................................................................................................... 1 Introduction....................................................................................................................... 1 1.1 Sandwich Structures.................................................................................................. 1 1.2 HFRP sandwich panels ............................................................................................. 3 1.2.1 Delamination: An Important Failure Mode ....................................................... 5 1.3 Objective and Scope ................................................................................................. 6 1.4 Organization of the Dissertation............................................................................... 8 Chapter 2 ......................................................................................................................... 10 Fracture Mechanics and Nonlinear Crack Models...................................................... 10 2.1 Linear Elastic Fracture Mechanics (LEFM) ........................................................... 11 2.2 Elastic-Plastic Fracture Mechanics (EPFM)........................................................... 14 2.3 Bi-material Interface Fracture Mechanics (BIFM) ................................................. 18 2.4 Nonlinear Crack Models for Nonmetallic Materials .............................................. 23 2.4.1 Damage Crack Model ...................................................................................... 23 2.4.2 Cohesive Crack Model..................................................................................... 25 2.4.3 Crack Band Model ........................................................................................... 33 2.4.4 Bridged Crack Model....................................................................................... 35 2.4.5 Microcrack Interacting Model ......................................................................