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ANALYSISOF COMPOSITELAMINATES
ANALYSISOF COMPOSITELAMINATES
TheoriesandTheirApplications
DINGHELI
CollegeofAeronauticalEngineering CivilAviationUniversityofChina Tianjin,China
Elsevier
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Notices
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Dedication
Ihavemanypeopletothank.IamgratefultoProfessorXiongZhangforacademicguidanceduringmydoctoralstudyatTsinghuaUniversityandhisconstructivesuggestions aboutthisbook,whichaidedmeinwritingthetext.IalsoappreciateProfessorJianxin XuandProfessorGuanghuiQingfortheacademicguidanceinmyearlyresearchat theCivilAviationUniversityofChina.IamgratefultoProfessorYanLiuandProfessorXinmingQiufortheiracademicguidanceduringmydoctoralstudyatTsinghua University.IwishtothankthemembersofmyresearchgrouponcomputationalcompositemechanicsattheCivilAviationUniversityofChina.Ireceivedvaluableassistance frommyM.A.studentsincludingRuipengWang,FengZhang,JiuyueYang,DongXu, ZhengguangXiao,WukuiShan,LiangyiLi,ZhengmingWang,ShuoMa,andZhaoxin Yun.IexpressmydeepestappreciationtoZhengmingWangforherassistanceinediting thetext.Finally,Iwishtoexpressmygratitudeandapologiestomyfamily,LiZhang andYinguangLi,forenduringthispastyearwhenmuchofmytimeandenergyshould havebeendevotedtothemratherthantothisbook.
Biography xv
Preface xvii
Acronyms xix
1.Compositeanalysisoverview1
1.1. Introduction 1
1.1.1. Historyofcomposites1
1.1.2. Applicationsofcompositesinaircrafts3
1.2. Compositelaminates5
1.2.1. Definitionandconstituents5
1.2.2. Plies 6
1.2.3. Laminates7
1.3. Analysisschemes9
1.3.1. Basicanalysisschemes9
1.3.2. Basicequations11
1.3.3. Existinganalysistheories14
1.3.4. Challenges16
1.3.5. Futuredevelopments19
1.4. GeneralHooke’slaw20
1.4.1. Hyperelasticmaterials20
1.4.2. Monoclinicmaterials22
1.4.3. Orthotropicmaterials22
1.4.4. Isotropicmaterials24
1.4.5. Planestress-reducedconstitutiverelations24
1.4.6. Transformationofmaterialcoefficients25
1.5. Energyprinciples27
1.5.1. Virtualdisplacementprinciple27
1.5.2. Hamilton’sprinciple30
1.5.3. Mixedvariationalprinciples31 References 33
2.Sheardeformationtheories35
2.1. Introduction35
2.2. Classicallaminatedplatetheory36
2.2.1. Displacementfields36
2.2.2. Kinematicequation38
2.2.3. Constitutiveequations42
2.2.4. Governingequations45
2.3. First-ordersheardeformationtheory47
2.3.1. Displacementfields47
2.3.2. Kinematicequation48
2.3.3. Shearcorrectionfactors50
2.3.4. Constitutiveequations50
2.3.5. Governingequations52
2.4. High-ordersheardeformationtheories53
2.4.1. Second-ordersheardeformationtheory53
2.4.2. Third-ordersheardeformationtheory55
2.4.3. Higher-ordersheardeformationtheories58
2.5. Finiteelementformulations58
2.5.1. CLPT58
2.5.2. FSDT63
2.5.3. TSDT64
2.5.4. Numericalexamples68 References 70
3.Statespacetheory71
3.1. Introduction71
3.2. Hamiltoniancanonicalequationoflaminatedplates72
3.2.1. Hamiltoniancanonicalequationofindividuallayer72
3.2.2. Exactsolutionofsimplysupportsinglelayerplates74
3.2.3. Hamiltoniancanonicalequationoflaminatedplates77
3.3. H-Rvariationalprincipleoflaminatedplates79
3.3.1. H-Rvariationalprincipleinrectangularcoordinatesystem79
3.3.2. H-Rvariationalprincipleincylindricalcoordinatesystem84
3.3.3. Numericalexamples86
3.4. Finiteelementformulationofstatespacetheory87
3.4.1. Hamiltonianisoparametricelement87
3.4.2. Governingequations90
3.4.3. Boundaryconditions91
3.4.4. Precisetime-integration92
3.4.5. Freevibration93
3.4.6. Numericalexamples94
3.5. Meshfreeformulationofstatespacetheory95
3.5.1. Interpolationusingradialbasisfunctions95
3.5.2. Radialbasisfunctions98
3.5.3. Numericalexamples99
3.6. Bondingimperfectionincompositelaminates101
3.6.1. Bondingimperfection101
3.6.2. Statespaceequationofbondingimperfectionproblems102
3.6.3. Numericalexamples104
References 109
4.Layerwisetheories111
4.1. Introduction111
4.2. Integratelayerwisemethods112
4.2.1. Generalizedlaminateplatetheory112
4.2.2. LayerwiseFEM113
4.2.3. OtherILWMs113
4.3. Reddy’slayerwisetheory114
4.3.1. Displacementfields114
4.3.2. Eulerequations116
4.3.3. Constitutiveequations120
4.3.4. Finiteformulations121
4.3.5. Numericalexamples122
4.4. Discretelayerwisetheories127
4.4.1. DevelopmentofDLWM127
4.4.2. Displacement-basedDLWM128
4.4.3. Carrera’sunifiedformulation132
4.4.4. Three-fieldvariablesDLWM134
4.4.5. Multiparticlemodelofmultilayeredmaterials135 References 136
5.Extendedlayerwisemethod139
5.1. Introduction139
5.2. Extendedlayerwisemethodoflaminatedplates140
5.2.1. Displacementsfields140
5.2.2. Descriptionoftransversecrack145
5.2.3. Hamilton’sprincipleandEuler–Lagrangeequations148
5.2.4. Constitutiveequations151
5.2.5. Finiteelementformulations152
5.2.6. Timeintegrations155
5.2.7. Numericalexamples156
5.3. Extendedlayerwisemethodofdoubly-curvedlaminatedshells167
5.3.1. Geometricequationsoflaminatedshells167
5.3.2. Hamilton’sprincipleandEuler–Lagrangeequations170
5.3.3. Constitutiveequations173
5.3.4. Governingequations176
5.3.5. Fullextendedlayerwisemethod179
5.3.6. Numericalexamples182
5.4. Fractureanalysisofcompositelaminates188
5.4.1. Equivalentdomainintegralmethod188
5.4.2. Interactionintegralmethodofisotropicmaterials190
5.4.3. Interactionintegralmethodoforthotropicmaterials191
5.4.4. Interactionintegralmethodofdynamicproblems192
5.4.5. Localremeshingscheme193
5.4.6. Maximumcircumferentialtensilestresscriterion195
5.4.7. VCCTbasedonXLWM196
5.4.8. Determinationofdelaminationfront198
5.4.9. Numericalexamples201
5.5. Fastuniform-griddelaminationscheme208
5.5.1. Thefastuniform-griddelaminationscheme208
5.5.2. Delaminationregionidentification209
5.5.3. Numericalexamples212
5.6. Microfractureanalysisofcompositelaminates220
5.6.1. Force-bearingmechanismsoffibers220
5.6.2. Modelingscheme220
5.6.3. Fibersmodeling222
5.6.4. Governingequations223
5.6.5. Numericalexamples225
References 231
6.Multiphysicalanalysis235
6.1. Introduction235
6.2. Thermomechanicalanalysis236
6.2.1. Variationalprinciplesconsideringtemperatureeffect236
6.2.2. Displacementfields238
6.2.3. Eulerequations239
6.2.4. Constitutiveequations241
6.2.5. Finiteelementformulations243
6.2.6. Timeintegrations245
6.2.7. EvaluationofSIFforthermomechanicaldynamicproblems247
6.2.8. Numericalexamples248
6.3. Piezoelectricanalysis250
6.3.1. Displacementandpotentialfields250
6.3.2. Electromechanicalvariationalprinciple252
6.3.3. Constitutiveequations253
6.3.4. Finiteelementformulation256
6.3.5. Couplingmodelingoflaminatedplateswithpiezoelectricpatch258
6.3.6. Thermo-electromechanicaldynamicanalysis260
6.3.7. Numericalexamples266
6.4. Chemo-thermomechanicalanalysis276
6.4.1. Chemo-thermomechanicalfields276
6.4.2. HamiltonprincipleandEulerequations277
6.4.3. Constitutiveequations279
6.4.4. Finiteelementformulations282
6.4.5. Timesintegration285
6.4.6. Chemomechanicalanalysis286
6.4.7. Numericalexamples287 References 295
7.Analysisofcomplexcomposites297
7.1. Introduction297
7.2. Layerwise/solid-elementmethodofcompositestiffenedshells299
7.2.1. Modelingscheme299
7.2.2. Finiteelementformulationsofthestiffener300
7.2.3. LW/SEmethod301
7.2.4. Numericalexamples302
7.3. Dynamicthermomechanicalanalysisofstiffenedplates307
7.3.1. Dynamicthermomechanicalthree-dimensionalelements307
7.3.2. DynamicthermomechanicalXLW/SE309
7.3.3. Numericalexamples312
7.4. Analysismethodsofsandwichstructures316
7.4.1. DLWMforthesandwichplates316
7.4.2. Layerwise/solid-elementofcompositesandwichplates316
7.4.3. LW/SEofsandwichplateswithmultilayercores321
7.4.4. Modelingofthesandwichstructures323
7.4.5. Numericalexamples324
7.5. Dynamicthermomechanicalanalysisofsandwichplates332
7.5.1. LW/SEmethodofsandwichplateswithsinglecore332
7.5.2. LW/SEmethodofsandwichplateswithmultiplycores337
7.5.3. Numericalexamples341
7.6. Dynamicthermo-chemomechanicalcouplinganalysisonaeroengineturbine346
7.6.1. Three-dimensionalthermo-chemomechanicalformulations346
7.6.2. Transformationofcoordinatesystem349
7.6.3. ModelingofaeroengineturbinewithTBCs351
7.6.4. Numericalexamples357 References 363
8.Progressivefailureanalysis365
8.1. Introduction365
8.2. Continuousdamagemechanicsanalysisframework366
8.2.1. Damageconstitutive366
8.2.2. Damageinitiation367
8.2.3. Damageevolutionlaw372
8.3. Progressivefailureanalysisoflow-velocityimpact373
8.3.1. Mathematicmodelofimpactproblem373
8.3.2. ContactforcebasedonHertz’slaw375
8.3.3. FEMimplementation376
8.3.4. Numericalexamples377
8.4. Progressivefailureanalysisofcomposites382
8.4.1. Discretedamagezonemodel382
8.4.2. DDZM-XLWM384
8.4.3. FatigueanalysisbasedonDDZM-XLWM389
8.4.4. Fatigueparameters393
8.4.5. Numericalexamples397
8.5. ProgressivethermomechanicalDDZM-XLWM408
8.5.1. Problemsdescriptions408
8.5.2. Interfacialheattransfer408
8.5.3. Governingequations410
8.5.4. Numericalexamples414
References 421
9.Multiscaleanalysis423
9.1. Introduction423
9.2. Layerwisemultiscaleanalysismethod424
9.2.1. MultiscaleanalysisbasedonEST424
9.2.2. Homogenizationmethod425
9.2.3. Layerwisemultiscaleanalysismethod428
9.2.4. Implementation431
9.2.5. Numericalexamples432
9.3. Two-scale C 2 ofalaminatedcurvedbeams434
9.3.1. TSDTofcurvedbeams434
9.3.2. Displacementdecomposition438
9.3.3. Finiteelementformulations440
9.3.4. Nonlocalquadrature443
9.4. Three-scale C 2 oflaminatedcurvedbeams444
9.4.1. Displacementdecomposition444
9.4.2. Finiteelementformulations446
9.4.3. Numericalexamples452
9.5. C 2 oflaminatedplates455
9.5.1. Frameworkof C 2 forlaminatedplates455
9.5.2. Two-scaleanalysisoflaminatedplates459
9.5.3. Three-scaleanalysisoflaminatedplates462
References 467
10.Sensitivityanalysis471
10.1. Introduction471
10.2. SensitivityanalysisbasedonFEM472
10.2.1. Staticresponses472
10.2.2. Frequencyandmodeshape473
10.3. Evaluationmethods475
10.3.1. AM476
10.3.2. FDM476
10.3.3. SAM477
10.3.4. StepsizesofSAMandFDM477
10.4. SensitivityanalysisbasedonSST482
10.4.1. Hybridgoverningequations482
10.4.2. Hybridgoverningequationofbondingimperfectionproblems484
10.4.3. Implementofsensitivityanalysis486
10.4.4. Numericalexamples488
References 493
11.Analysiscodes495
11.1. Overallframework495
11.2. Datastructuresandpre/postprocess496
11.2.1. Matrixstorageformats496
11.2.2. Preprocess497
11.2.3. Post-processtool500
11.3. Solvermodels502
11.3.1. Solver sdt
11.3.2. Solver sst
11.3.3. Solver rlw
11.3.4. Solver xlw
Biography
Dr.LiisaProfessorandVicePresidentattheCollegeofAeronauticalEngineering, CivilAviationUniversityofChina,andhasbeenfeaturedamongtheWorld’sTop2% ScientistsListcreatedbyStanfordUniversity.HefinishedhisMScattheCivilAviation UniversityofChinaonthesensitivityanalysisofcompositestructuresinthestatespace framework,andgraduatedoneyearaheadofschedule.HisPhDwasdevotedtothe impactdamageanalysisandrefinedtheoriesofthecompositestructures.Hewasthe firstdoctortograduatein2.5yearsintheSchoolofAerospaceEngineering,Tsinghua University.HehasworkedwithProfessorJacobFishonmultiscaleanalysisproblems ofcompositelaminatesatColumbiaUniversityinNewYorkCity.Dr.Lifocusedon solvingthebasicmechanicalproblemsinthecompositeengineeringstructures,involvingthehigh-precisionlaminatedplateandshellanalysistheories,advancednumerical method,fractureanddamagemechanicsofanisotropicmaterial,multiphysicalfieldand multiscaleanalysistheoriesofcompositestructures.In2015,Dr.Liwasselectedasthe secondlevelcandidateoftheTianjin“131”innovativetalenttrainingprojectandthe “YouthBlueSky”scholaroftheCivilAviationUniversityofChina.In2019,hewas selectedasthehigh-leveltalentsupportplanoftheCivilAviationUniversityofChina. Dr.Liistheauthorofnearly60journalpapers.Hehasobtainedtwosoftwarecopyrightsandwrittenonebook(Compositerepairofaircraftstructures:theory,design,and applications).Dr.Liisayoungeditorialboardmemberof AviationScienceandTechnology andaspeciallyinvitedreviewerofthe JournalofComputationalMechanics.
Acronyms
AM analyticalmethod
C2 computationalcontinua
CLPT classicallaminatedplatetheory
CCC carbon-carboncomposite(carbonmatrix)
CDM continuumdamagemechanics
CTDM centraldifferencemethod
CFRP carbonfiberreinforcedplates
CMC ceramicmatrixcomposite
CUF Carrera’sunifiedformulation
CUC computationalunitcell
DCB doublecantileverbeam
DDZM discretedamagezonemodel
DLWM discretelayerwisemethods
DNS directnumericalsimulation
DOF degree-of-freedom
EST equivalentsingle-layertheory
IIM interactionintegralmethod
ILWM integratedlayerwisemethods
LMAM layerwisemultiscaleanalysismethod
LSM levelsetmethod
LWT layerwisetheory
LW/SE laywise/solid-element
FDM finitedifferencemethod
FWDM forwarddifferencemethod
Full-XLWM fullextendedlayerwisemethod
FSDT first-ordersheardeformationtheory
FEM finiteelementmethod
HSDT high-ordersheardeformationtheory
HrSDT higher-ordersheardeformationtheory
GLPT generalizedlaminateplatetheory
GFRP glassfiberreinforcedplates
PMC polymermatrixcomposite
MMC metalmatrixcomposite
MCEP minimumcomplementaryenergyprinciple
MCTSC maximumcircumferentialtensilestresscriterion
MPEP minimumpotentialenergyprinciple
MQ modifiedmultiquadrics
RBF radialbasisfunctions
RLWT Reddy’slayerwisetheory
RPIM radialpointinterpolationmethod
SAM semianalyticalmethod
SDT sheardeformationtheories
SIF stressintensityfactor
SERR strainenergyreleaserate
SSDT second-ordersheardeformationtheory
SST statespacetheory
TPS thinplatespline
TSDT third-ordersheardeformationtheory
ZZT zig-zagtheory
XLWM extendedlayerwisemethod
XLW/SE extendedlayerwise/solid-element
XFEM extendedfiniteelementmethod
VCCT virtualcrackclosuretechnique
VDP virtualdisplacementprinciple
Preface
Nowadayscompositematerialsplayaveryimportantroleinalltypesofengineering structures,suchasaerospace,automotive,underwaterstructures,medicalproductions, electronic,andsportsequipments.Computationalmechanicanalysisisthebaseofthe dramaticdevelopmentofcompositematerials.Compositestructurescanbestudied byusingtwobasicanalysisschemes:micromechanicalmethodsandmacromechanical methods.Ingeneral,micro-mechanicalanalysisisaimedatpredictingandunderstanding theaveragepropertiesintermsofthedetailedmicroscopicbehaviorofthematerial,ratherthangeneratingaccuratedesigndata;whilemacromechanicalanalysisdraws mainlyontheresultsobtainedfromphysicalandmechanicaltestingofunidirectional composites.Ifweneedtoanalyzethemacroandmicroresponsesimultaneously,multiscaleanalysismethodsarenecessary.Thisbookisfocusedonthemacromechanical analysisandmultiscaleanalysisofcompositeengineeringstructures.Intheearlydays oflaminatedcomposites,thetechniqueusedforanalyzingconventionalplateswasextendedtoanalyzethesenewstructures.Thezig-zageffectsand C 0 z -Requirementsposes aseriouschallengetotheearlytraditionalanalyticalmethods.Althoughthecompositeanalysistheorieshavemadegreatprogress,therearestillmanychallengesbecause ofthecomplexcharacteristicsandwideapplicationsofcomposites:theircomplexintegratedmoldingprocess,complexanisotropicconstitutiverelations,complexdamage mechanism,complexmultiphysicalloading,andcomplexmultiscaleeffective,namely C 5 challenges.Unfortunately,itisalmostimpossibletoaccuratelyconsiderallthechallengesusingtheexistingrefinedanalysismethods.
Theauthorandhisresearchteamhavefocusedonsolvingthebasicmechanicalproblemsincompositeengineeringstructures,especiallythetheoriesofcompositelaminated beams,plates,andshells;theyarecalledthecompositelaminatedtheoriesinthisbook. Theresearchteamhasdevelopedacompositestructureanalysissoftwaresystem,with atotalcodeofmorethan200,000lines.Thesoftwaresystemhasalargenumberof solversbasedonsheardeformationtheories,statespacetheory,thelayerwisemethod, extendedlayerwisemethod,computationalcontinua,multipointmultilevelgridrefinementmethod,andtakingthefracture,damage,multiscaleandmultiphysicsanalysis problemsasitsadvantages.Analysisobjectsofthissoftwaresysteminclude:beams, plates,shells,stiffenedplatesandshells,sandwichplatesandshells,andmultilayersandwichplatesandshells.Loadingtypesinclude:mechanic,thermal,electric,chemical,and theircouplingloading.Thesoftwaresystemadoptsadvancedstorageandsolutiontechnologies,andrequireslessmemoryandharddiskthancommercialsoftware.Forsome specificchallengingengineeringproblems,theefficiencyandaccuracyoftheproposed softwarearebetterthantheseofthecommercialsoftwareaswell.
Asthereisadramaticincreaseintheuseofcompositematerials,thenumberof studentstakingcoursesincompositemechanicshassteadilyincreasedinrecentyears, andthestudentsaredrawntothesecoursesfromavarietyofdisciplines.Thecourses offeredatuniversitiesandthebookspublishedoncompositematerialsareofthreetypes: materialscience,mechanics,anddesign.Thepresentbookbelongstothemechanics category.Themotivationforthepresentbookhascomefrommanyyearsoftheauthor’s researchinlaminatedcompositestructuresandfromthefacttheredoesnotexistabook thatcontainsadetailedcoverageofvariouslaminatetheories,analyticalsolutions,finite elementmodels,andtheirapplicationsinstructuralengineeringproblems.Thebookis largelybasedontheauthor’soriginalworkonrefinedtheoriesoflaminatedcomposite platesandshells,andtheanalyticalandfiniteelementsolutionsheandhiscollaborators havedevelopedoverthelasttwodecades.Thenoveltyofthisbookisthattheexisting mostimportantanalysismethodsandtheircodesareintroduced,andmainlyfocuson fractureanddamageanalysis,togetherwithmultiscaleanalysisandmultiphysicsanalysis. Thistextbookisuniqueinthreerespects:
• Theoryandimplementation.Thetextprovidesadetailedexpositionofthestate-ofthe-artcompositeanalysistheoriesandtheirinsertionintoengineeringapplications oftypicalstructureformsandproblems;
• Hands-onexperience.Includedwiththistextbookisanacademicversionofthe compositeanalysiscodes,whichincludesmorethan200,000linesofcode;
• Engineeringproblems.Manystructuralengineeringproblemsarestudiednumerically.Alotofbenchmarkexamplesaredesignedanddetailednumericalresultsare presented.
Duetoabroadspectrumofapplicationareas,thiscourseisintendedtobeofinterest andusedtoavariedaudience,including:
• Graduatestudentsandresearchersinacademiaandgovernmentlaboratorieswho areinterestedinacquiringfundamentalskillsthatwillenablethemtoadvancethe state-of-the-artinthefield;
• Practitionersincivil,aerospace,andautomotiveindustrieswhoareengagedinanalysis,design,andoptimizationofcompositestructures;
• Commercialsoftwarevendorswhoareinterestedinextendingtheirproductportfoliosandtappingintonewmarkets.
DingheLi Tianjin
CHAPTER1
Compositeanalysisoverview
1.1.Introduction
1.1.1Historyofcomposites
Thehistoryofcompositematerialscanbetracedbacktoancienttimes.Straworwheat strawreinforcedclayandreinforcedconcrete,whichhavebeenusedformanyyears, arecomposedoftwodifferentmaterials.Theycanberegardedasthetypicalcomposite materials.However,themoderncompositematerialshavebeendevelopedforabout80 years.In1940s,inordertoimprovethedesignofmilitaryvehicles,suchasairplanes, helicopters,androckets,thehighstrengthandlightweightmaterialswereatapremium comparedwiththetraditionalmetal.Sincethepolymerindustrieswerequicklydeveloping,thelightweightpolymersprovidedapossiblesolutionforthischallenge.Onthe otherhand,theextremelyhightheoreticalstrengthofglassfiberswasdiscovered,but howtouseithasbecometheobstacleforthestructuralengineeringproblems.Based onabovetwodrivingforces,themoderncompositematerialsmadeupbytwoormore differentphases,wereinventedandbeingextensivelyadoptedinvariousstructuralengineeringfields,includingaerospace,automotive,andcivilengineeringjustnameafew. Ingeneral,thedevelopingprocessofmoderncompositematerialscanbedividedinto fourgenerationsorstagesfor80years.
Thefirstgenerationistheglassfiberreinforcedmaterials.Inthe1940s,theglass fiberswereimmersedintolightweightandlowerstrengthpolymers,andastrongernew materialwasobtained.Thepolymerisregardedasamatrixandprotectsthefibersfrom scratchesthatmightresultintofractureunderlowstresslevel.Thefibersareregarded asreinforcementandimprovethestrengthoffragilepolymersbyshoulderingmostof thestresstransferredfromthepolymerthroughthefiber/matrixinterface.Thefibers cansignificantlystopthepropagationofmicrocracksinthematrixduetothebridge effect.Thefirstglassfiberlaminatedstructurewasproducedin1942.Theearliestapplicationsofglassfiberreinforcedplates(GFRP)wereinthemarineindustrytoreplace thetraditionalwoodormetalcomponents.ThelightweightandstrongGFRPwasnot subjectedtorottingorrustingoftheirmetalcounterparts,andeasytomaintain.Until now,theGFRPcontinuestobeamajorcomponentofboatsandships;furthermore,it comprisesabout90% ofthecomposites’market.
Thesecondgenerationisthehighperformancecompositematerials.TheGFRP technologieswasrapidlyappliedintomanyengineeringfieldsduringthe1950s,butthe newdemandsfrommilitaryspaceprogramspromptedageneralnotionofcomposite materials.SpacecraftrequiresevenlighterandstrongercomponentsthanGFRP.The AnalysisofCompositeLaminates https://doi.org/10.1016/B978-0-32-390804-7.00009-1
heatgeneratedduringthereentryofaspacecraftcouldexceed1500◦ C,whichisbeyond thetemperaturelimitsofanymonolithicorcompositematerial,especiallylow-melting pointpolymers.In1956,anasbestosfiberwasaddedintoaphenolicresinasapossible reentrynoseconematerial,andthecompositesofmetalmatrixwasalsoregardedasa solution.Inthesecompositematerials,theinorganic,ceramicfiber,orparticulatephase wereemployedtoimprovetheheatresistanceoflightweightmetalsandtolowertheir thermalexpansioncoefficient.Thespaceraceprovidedanimpetusforthedevelopment ofcarbonandboronfibersaswell.Theyweredevelopedaroundthesametime,but thecarbontooktheleadinthe1960sduetoitssuperiorprocessingcapabilitiesand lowercost.Thegraphitefiberswereofuseonlyinpolymermatricesatthistime. Becauseofthereactivityofcarbonwithaluminumandmagnesium,theuseofgraphite fibersasreinforcementformetalmatriceswasnotpossible.Thestrengthofboronfibers exceededthatofcarbonfibers,anditismoresuitabletomilitaryapplicationswherethe costwasnoconcern,andmadenoextensionintootherindustries.Thecompoundof aramidfiberswasdevelopedin1964.Aramidsbelongtothenylonfamilyofpolymers; thekeystructuralfeatureisaromaticringslinkedbyamidegroups.
Thethirdstageissearchingfornewapplicationfieldsandsynergyofproperties, whereasthespacecraftandaircraftdemandspromptednewhighmodulusfibersinthe 1960s.Thecompositesmadewiththeaforementionedexpensivefibershadtofindcivil applicationsinthe1970swhenthespaceandmilitarydemandsdeclined.Thesportsand automobileindustriesbecamemoreimportantmarkets.Atthesametime,theanalysis anddesignmethodsbasedonthecomputationalcompositemechanicsdrovefurther applications,suchasthecivilianandmilitaryaircraft.Thecarbonfiberswereusedextensivelyinsportingproductsbeginninginthe1970s,withgraphitetennisracketsand golfclubsreplacingthewoodenandsteelmaterials.Duringthesameperiod,thecompositesofaceramicmatrixwasdevelopedandapplied.Itmustbereinforcedbyhigh temperaturefibers,suchasSiC,becauselow-meltingfiberswouldbedestroyedatthe highprocessingtemperaturesrequiredforceramicsintering.Ontheotherhand,the brittleceramicsneedareinforcingphasetoimprovethetoughness.
Thefourthgenerationisthehybridmaterials,nanocomposites,andbiocomposites (green-composites).Inthe1990s,bothacademicandindustrialresearchersstartedto extendthecompositeparadigmintosmallerandsmallerscales.Fromthemacroscopic scaletothemolecularscale,itresultsintohybridmaterials.Theyareanintentional andcomplimentingcombinationoftwoormorematerialswithnewproperties.Accordingtotheircriterion,thedifferencebetweenhybridmaterialsandcompositesis theirfunctionsand/orproperties.Towardthenanoscale,itresultsintonanocomposites. Nanocompositesaresolidmaterialsthathavemultiplephasedomainsandatleastoneof thesedomainshasananoscalestructure.Abiocompositeisamaterialcomposedoftwo ormoredistinctconstituentmaterials(onebeingnaturallyderived),whicharecombinedtoyieldanewmaterialwithimprovedperformanceoverindividualconstituent
materials,namely,thenaturalfiber-reinforcedbiopolymers.Thesecompositematerials havebeendevelopedasanalternativetoconventionalmaterialsthatmaybenonrenewable,recalcitrant,ormanufacturedbypollutionemittingprocesses.Becausethese compositematerialsarenotstudiedinthisbook,moredetailedinformationwillnot presented.
1.1.2Applicationsofcompositesinaircrafts
Theapplicationsofcompositesincivilianandmilitaryaircraftfollowedthetypical stagesofeverynewtechnology.Inthebeginning,thelimitedapplicationonsecondary structureminimizedriskandimprovedunderstandingbyscientificresearchandservice experience.Thislimitedusagewasfollowedbywiderapplicationsfirstinsmalland militaryaircrafts.Morerecently,withtheincreasedrequirementonefficiencyandlow operationcosts,thecompositematerialswerebeingappliedwidelyinlargercivilian aircraft.
Intheaircraftindustry,thehelicopterdesignengineerswereamongthefirsttorecognizethepotentialofcompositematerialsandusethemonprimarystructures.From theseatsandenginebaydoortothefuselageandtailplane,anintegralpartofhelicopters wasmadefromthecompositematerials.However,therotorbladehasperhapsbenefited mostsignificantlyfromtheuseofcompositematerials.Themostcriticalproblemsof traditionalwood,steel,oraluminumbladecanbehugelyreducedbythecompositematerials,togetherwithmanyotherdesigndrawbacks.Inaddition,thestrength-to-density ratioofcompositesmaterialsisfourtosixtimesgreaterthanthoseofsteeloraluminum, leadingtocompositebladesthatareupto45% lighterthanmetalones.
Inthe1970s,withthecompositesapplicationsonsailplanesandhelicoptersincreasing,thefirstall-compositeplanesappeared,buttheseweresmallrecreationalor aerobaticplanes,andjustcocuredandbondedconstructionswithverylimitednumbersoffasteners.Inthe1970sandearly1980s,thefirstall-compositeairplaneoflarger sizebeganwiththeLearFan2100andsoughtFAAcertification(FAR,Part23).The guidelinesoftheAdvisoryCircularoncompositestructurewereobservedthroughout thisprogram,andAdvisoryCircular20–107wasusedasaguideforthecertification procedures.
Withfuelpricesrising,thecompositematerialsbecameaveryattractivealternativeforthelargecivilaircraftstoreducedweightcomparedwiththetraditionalmetal structure.Applicationsinthelargeciviliantransportcategorystartedintheearly1980s withthesandwichhorizontalstabilizerofB737.Meanwhile,thehorizontalandvertical stabilizersoftheA320weremadeofcompositematerialsaswell.Thenextsignificant applicationofcompositematerialsonaprimaryaircraftstructurewastheB777in1990s, theempennage,controlsurfaces,andmainfloorbeamsweremadefromcompositematerials.However,thecostofcompositestructureswasnotattractiveenoughtoleadto anevenwildlyapplicationatthattime.
Withdecadesofdevelopment,thecompositematerialshavebeencalledtheshape ofaerospace’sfuture.Inthecivilaviationindustry,A380,A350,andB787representthe applicationofcompositematerials.TheA380isthefirstaircraftthathasacentralwing boxwithcarbonfiberreinforcedplates(CFRP),representingaweightsavinguptoone andahalftonnescomparedtothemostadvancedaluminumalloys.Themainchallenge isthewingrootjoint,wherecompositecomponentscouldbeupto45mmthick. Forthisspecificapplication,AirbusreapsalargebenefitfromtheA340-600CFRP keelbeams(16meterslongand23mmthick),eachofwhichcarriesaforceof450 tonnes.AmonolithicCFRPdesignhasalsobeenadoptedforthefinboxandrudder, aswellasthehorizontalstabilizerandelevators.ThesizeoftheCFRPhorizontal tailplaneisclosetothesizeofwingsoftheA320,sothemainchallengebecomes thesizeofthecomponents.Asforthecenterwingbox,thesizeofthecomponents justifiestheintensiveuseofautomatedtape-layingtechnology.Furthermore,theupper deckfloorbeamsandtherearpressurebulkheadismadeoftheCFRP.Theadvanced glass/aluminumcompositeswasusedontheupperportionoffuselage,anditiscalled theglarelaminate.Theglarelaminateisafibermetallaminatecomposedofseveralvery thinaluminumlayersinterspersedwithglassfiberprepreglayers,andtheyarebonded togetherwithamatrixsuchasepoxy.Thisnewaerostructurematerialiswidelyused infatiguedpartsduetoitsoutstandingfeaturesinanticrackingandtension.
BoeingwasthefirsttocommittoacompositefuselageandwingfortheB787.Such extendedapplicationsofcompositematerials(about50% ofthestructure)wouldgive theefficiencyimprovementneededbytheairlineoperators,suchasabout20% more fuelefficientand20% feweremissions.TheB787isthefirstmajorcommercialairplane tohaveacompositefuselage,wings,andmostotherairframecomponents.EachB787 containsapproximately35metrictonsofCFRP,madewith23metrictonsofcarbon fiber.Thefuselageisconstructedintubularsegments,whicharethenjoinedtogether duringthefinalassembly.TheapplicationsofcompositesintheB787saves50,000rivets perplane;andeachrivetsitewouldhaverequiredmaintenancecheckingasapotential failurelocation.Otheradvantagesofusingcompositematerialsisthatatypicalbonded repaironthestandardaluminumairframesometimesrequiresmorethan24hoursof downtime,butBoeinghascreatedanewwayofrepairingcompositematerialsinless thananhour.Thisleadstoquickerturnaroundsandofferstheopportunityforaquick in-and-outforminordamagethatmightmakeanaluminumairplaneunabletofly.
TheA350isthefirstAirbusairplanewithbothfuselageandwingstructuresmade primarilyoftheCFRP.TheA350alsohasaslightlyhigherproportionofcomposites (about52% ofthestructure)initsconstructionthanthatoftheB787.Mostpartsofthe aircraftareamixtureofcompositeandalloy.Inthewings,themainmetalcomponents areintersparribs(thesparsbeingthesupportingstructuresandrunningalongthewing fromtiptoroot;theribsrunningacrossthewidthofthestructure).Inthefuselage,the outerskinpanelsareconstructedbyCFRP,andtheframeincludesaluminumstripsto ensurethatlightningstrikescanbedissipated.
1.2.Compositelaminates
1.2.1Definitionandconstituents
Acompositematerialisamaterialmadefromtwoormoreconstituentmaterialsata macroscopicscale,andtheseconstituentmaterialshavesignificantlydifferentphysicalor chemicalproperties.Thiscombinationproducesanewmaterialwithmoreusefulcharacteristicsthantheindividualcomponents.Theindividualcomponentsremainseparate anddistinctwithinthefinishedstructure.Intypicalcomposites,thematrixsurrounds thefibers,andtheyaremustbeproperlybondedtogetherasasinglematerialsystem [1].Thereforethefiber,matrix,andinterfacearethecontrolledfactors.
Accordingtotheformoffiber,thecompositematerialscanbedividedintotwo categories:continuousanddiscontinuousfibercomposites.Thelongcontinuousfibers areconsideredtobehighperformancesincetheirmechanicalpropertiesaremaximized, thisformisthemostcommontypeforaircraftstructures.Thediscontinuousfibershave reducedpropertiesbecausetheloadpathofthefiberisdisrupted.Theyarenotusually suitableforprimaryaircraftstructures,thoughthereareexceptions,theymayalsobe consideredforsomesecondarystructures.Thecompositematerialsalsocanbeclassified bythetypeofmatrixaspolymermatrixcomposites(PMC),ceramicmatrixcomposites (CMC),metalmatrixcomposites(MMC),andcarbon-carboncomposites(CCC).
Ingeneral,thematerialinfiberformhassuperiorpropertiescomparedtothebulk form.Theamountandseverityofdetrimentalimperfectionsdecreaseasthediameteroffiberisreduced,andfibercanberapidlycooled;sotherearefewerdefectsin fiberform.Thefiberscanbestretchedalongtheiraxisduringprocessingtoincrease itsstrengthaswell.Forexample,thesuddenfractureofglasssheetscanresultfroma smallflaworlowenergyimpact,buttheglassfibercompositesarelesssusceptibleto theimpactdamage;thisistrueforcarbonfibersandcarbonfibercomposites.Therefore thecompositionoffibersandmatrixissuperiortoabulkmaterial.Inthecomposites,thematrixcantransfertheloadtotheadjacentfibersifanindividualfiberfails. Amatrixcanalsoresistthedamageintroducedbyimpactsandotherthreatsduetothe reinforcementoffibers,sothecompositeisnotexcessivelybrittle.Ingeneral,thefiber isthemajorloadcarryingcomponent,andcanbemadefrommaterialssuchascarbon, graphite,glass,boron,aramid,orquartz.Eachofthesefibershasitsownadvantagesand disadvantages.Stiffness,staticstrength,impactstrength,fatigueperformance,electrical conductivity,electricalpermeability,andthermalpropertiesareamongtheproperties thatareconsideredforselectingafiber.
Comparedwiththefiber,thematrixissofterandoflowerstrength,andholdthe fiberstogetheranddistributetheloads;whilethefunctionoffibrousreinforcementisto carrytheexternalloads.Thematrixallowsthecompositestobearcompressionloading andprotectsthefibersfromphysicalandenvironmentalthreats.Exceptfortheaforementionedloadingtransfer,thematrixalsoprovidesanenergy-absorbingmechanism; thiscanimproveimpactdamageresistanceandalsosoftenthestressconcentrations.
Thefiber/matrixinterfaceisknownastheinterphase.Thepropertiesofmatrixand thebondoffiber/matrixinterfacedominatethemechanicalpropertiesofcomposite materials.Thematrixandmatrix/fiberinteractionalsohaveasignificanteffectonthe crackpropagationofthecompositematerials.Ifthematrixshearstrengthandmodulus andthefiber/matrixbondstrengtharetoohigh,acrackmaypropagatethroughthe fiberandmatrixwithoutturning,sothecompositematerialswillbehaveasabrittle materialandshowcleanfracturesurfaces.Ifthebondstrengthistoolow,thematrix willactasafiberbundleandthecompositematerialswillbeweak.Fortheintermediate bondstrength,thecrackspropagatinginresinorfiberwouldturnatthematrix/fiber interfaceandextendalongthefiber.Thecompositematerialsthatfailedinthismode willshowconsiderablefiberpull-outandthefracturesurfacewillbeveryrough.This resultsinconsiderableenergyabsorption.
Iftheintactfibersareavailablebehindthecracktipsandconnectatthecrackfaces, thecrackbridgingmechanismisoperative.Hence,theloadwouldbesharedbythe bridgingfibersandcracktips,andthestressintensityfactor(SIF)onthecracktipwould bereducedsignificantly.AhigheramountofbridgingfibersleadstothelowerSIFon thecracktip,andtheresistancetocrackgrowthincreaseswithcracklengthincreasing. Theextensionofatransversecrackbridgedbytheintactfibersleadstothedebonding andfiberspull-out.Thiswillincreasethefracturetoughnessofcompositematerials. Thestrengthandfracturetoughnessoffiberreinforcedcompositesisdeterminedbythe interplaybetweenthedamageprocessesindifferentelementsofcompositematerials. Thereforethefiberbridgingeffectoftransversecrackanddelaminationisaveryimportantandchallengingproblemtounderstandthedamagemechanismofcomposite materials,andmanyanalyticmethodshavebeenestablished[2,3].
1.2.2Plies
Aply,whichconsistsoffibersandmatrixandalsoknownasalaminaorlayer,isshown inFig. 1.1.Thecontinuousfibersinthepliescanbeorientedinasingledirection, ormultipledirectionsforthewovencomposites.Intheaircraftstructures,theplies canbeinaprepregformordryfabricform.Theprepregisacommonform.Itis preimpregnatedbythefibersandaresininasemicuredstate,wherethefibersandresin arecombinedbutarestillflexibleenoughtobelaidintooling.Thelaminateisfully curedprepreglayers,andthenthecuredresinisreferredtoasthematrixmentioned inprevioussection.Theprepregformsalsoinclude:tape,slittape,fabric,sheet,and tow/roving.Theprepregsarecommonusedforlargeaircraftstructuresandcanconsist ofdryfabriclayersthatareimpregnatedwithanuncuredandlowviscosityresin.This isknownasawetlayup,asitmaybeconsideredforrepairsbutarenotcommonlyused fortheoriginalstructuresinlargeaircraft.
Foraunidirectionalindividualply,thefibersareallalignedinasingledirection.In tapeform,itmayalsobecalledaunitapeoratapeply.Fabricsmaybeinprepregordry
