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1、Modeling of CNT based composites: Numerical IssuesN. Chandra and C. Shet FAMU-FSUCollegeofEngineering,FloridaStateUniversity,Tallahassee,FL32310AMMLObjectiveTodevelopananalyticalmodelthatcanpredictthemechanicalpropertiesofshort-fibercompositeswithimperfectinterfaces.Tostudytheeffectofinterfacebondst
2、rengthoncriticalbondlengthlcTostudytheeffectofbondstrengthonmechanicalpropertiesofcomposites.ApproachTomodeltheinterfaceascohesivezones,whichfacilitatestointroducearangeofinterfacepropertiesvaryingfromzerobindingtoperfectbindingAMMLFig.Shearlagmodelforalignedshortfibercomposites.(a)representativesho
3、rtfiber(b)unitcellforanalysis(a)(b)ShearLagModel*Prelude1ThegoverningDEWhosesolutionisgivenbyWhereDisadvantages TheinterfacestiffnessisdependentonYoungsmodulusofmatrixandfiber,henceitmaynotrepresentexactinterfaceproperty.kremainsinvariantwithdeformationCannotmodelimperfectinterfaces*Originalmodeldev
4、elopedbyCox1andKelly21Cox,H.L.,J.Appl.Phys.1952;Vol.3:p.722Kelly, A., Strong Soilids, 2nd Ed., Oxford UniversityPress, 1973,Chap.5.AMMLPrelude2CohesiveZoneModelCZMisrepresentedbytraction-displacementjumpcurvestomodeltheseparatingsurfacesAdvantagesCZM can create new surfaces. Maintains continuity con
5、ditions mathematically, despite the physical separation. CZM represents physics of the fracture process at the atomic scale.Eliminates singularity of stress and limits it to the cohesive strength of the the material.It is an ideal framework to model strength, stiffness and failure in an integrated m
6、anner.AMMLModifiedShearlagModelThegoverningDEIftheinterfacebetweenfiberandmatrixisrepresentedbycohesivezone,thenEvaluatingconstantsbyusingboundaryconditions,stressesinfiberisgivenbyAMMLComparisonbetweenOriginalandModifiedShearLagModelVariationofstress-strainresponseintheelasticlimitwithrespecttopara
7、meterbTheparameterb definedbydefinestheinterfacestrengthintwomodelsthroughvariablek.InoriginalmodelInmodifiedmodelinterfacestiffnessisgivenbyslopeoftraction-displacementcurvegivenbyInoriginalmodelkisinvariantwithloadinganditcannotbevariedInmodifiedmodelkcanbevariedtorepresentarangeofvaluesfromperfec
8、ttozerobondingAMMLComparisonwithExperimentalResultTheaveragestressinfiberandmatrixfaraappliedstraineisgivenbyThenbyruleofmixturethestressincompositescanbeobtainedasFig.Atypicaltraction-displacementcurveusedforinterfacebetweenSiCfiberand6061-AlmatrixForSiC-6061-T6-AlcompositeinterfaceismodeledbyCZMmo
9、delgivenbyWithN=5,andk0=1,k1=10,k2=-36,k3=72,k4=-59,k5=12.Taking smax=1.8 sy,wheresyisyieldstressofmatrixanddmax=0.06dcAMMLFig. Comparison of experimental 1 stress-strain curve for Sic/6061-T6-Alcompositewithstress-straincurvespredictedfromoriginalshearlagmodelandCZMbasedShearlagmodel.1Dunn,M.L.andL
10、edbetter,H.,Elastic-plasticbehavioroftexturedshort-fibercomposites,Actamater.1997;45(8):3327-3340Theconstitutivebehaviorof6061-T6Almatrix21canberepresentedbyComparison(contd.)yieldstress =250MPa,andhardeningparametersh =173MPa,n=0.46.Youngsmodulusofmatrixis76.4GPa.YoungsmodulusofSiCfiberisEf of423GP
11、aResultcomparisonExperimental1Youngsmodulusis105GPaandfailurestrengthisaround515MPaEc115104.41540522(GPa)FailureStrength(MPa)VariableOriginalModifiedAMMLFEAModelThe CNT is modeled as a hollow tube with a length of 200 , outer radius of 6.98 and thickness of 0.4 . CNT modeled using 1596 axi-symmetric
12、 elements. Matrix modeled using 11379 axi-symmetric elements.Interface modeled using 399 4 node axisymmetric CZ elements with zero thicknessComparisonwithNumericalResultsFig.(a)Finiteelementmeshofaquarterportionofunitmodel(b)aenlargedportionofthemeshnearthecurvedcapofCNTAMMLLongitudinalStressinfiber
13、atdifferentstrainlevelInterfacestrength=5000MPaInterfacestrength=50MPaAMMLShearStressinfiberatdifferentstrainlevelInterfacestrength=5000MPaInterfacestrength=50MPaAMMLCriticalBondLengthl/2Table1.Criticalbondlengthsforshortfibersoflength200andfordifferentinterfacestrengthsandinterfacedisplacementparam
14、eterdmax1value0.15.AMMLCriticalbondlengthvarieswithinterfaceproperty(Cohesivezoneparameters(smax,dmax1)Whentheexternaldiameterofasolidfiberisthesameasthatofahollowfiber,then,foranygivenlengththeloadcarriedbysolidfiberismorethanthatofhollowfiber.Thus,itrequiresalongercriticalbondlengthtotransferthelo
15、adAthigherdmax1thelongitudinalfiberstresswhenthematrixbeginstoyieldislower,hencecriticalbondlengthreducesForsolidcylindricalfibers,atlowinterfacestrengthof50MPa,whenthefiberlengthis600andabove,thecriticalbondlengthoneachendofthefiberexceedssemi-fiberlengthforsomevaluesdmax1tendingthefiberineffective
16、intransferringtheloadinterfacestrengthis5000MPaVariationofCriticalBondLengthwithinterfacepropertyinterfacestrengthis50MPaAMMLTable:VariationofYoungsmodulusofthecompositewithmatrixyoungsmodulus,volumefractionandinterfacestrengthEffectofinterfacestrengthonstiffnessofCompositesYoungsModulus(stiffness)o
17、fthecompositenotonlyincreaseswithmatrixstiffnessandfibervolumefraction,butalsowithinterfacestrengthAMMLEffectofinterfacestrengthonstrengthofCompositesTableYieldstrength(inMPa)ofcompositesfordifferentvolumefractionandinterfacestrengthFibervolumefraction=0.02Fibervolumefraction=0.05Yieldstrength(whenm
18、atrixyields)ofthecompositeincreaseswithfibervolumefraction(andmatrixstiffness)butalsowithinterfacestrengthWithhigherinterfacestrengthhardeningmodulusandpostyieldstrengthincreasesconsiderablyAMMLEffectofinterfacedisplacementparameterdmax1onstrengthandstiffnessFig.Variationofstiffnessofcompositemateri
19、alwithinterfacedisplacementparameterdmax1fordifferentinterfacestrengths.Fig.Variationofyieldstrengthofthecompositematerialwithinterfacedisplacementparameterdmax1fordifferentinterfacestrengths.AstheslopeofT-d curvedecreases(withincreaseindmax1),theoverallinterfacepropertyisweakenedandhencethestiffnes
20、sandstrengthreduceswithincreasingvaluesofdmax1.Whentheinterfacestrengthis50MPaandfiberlengthissmalltheyoungsmodulusandyieldstrengthofthecompositematerialreachesalimitingvalueofthatofmatrixmaterial.AMMLEffectoflengthofthefiberonstrengthandstiffnessFig.Variationofyieldstrengthofthecompositematerialwit
21、hdifferentfiberlengthsanddifferentinterfacestrengthsFig.VariationofYoungsmodulusofthecompositematerialwithdifferentfiberlengthsandfordifferentinterfacestrengthsForagivenvolumefractionthecompositematerialcanattainoptimumvaluesformechanicalpropertiesirrespectiveofinterfacestrength.Forcompositeswithstr
22、ongerinterfacetheoptimumpossiblevaluescanbeobtainedwithsmallerfiberlengthWithlowinterfacestrengthlongerfiberlengthsarerequiredtoobtainhighercompositeproperties.DuringprocessingitisdifficulttomaintainlongerCNTfiberstraigth.AMMLConclusion1.Thecriticalbondlengthorineffectivefiberlengthisaffectedbyinter
23、face strength. Lower the interface strength higher is theineffectivelength.2.In addition to volume fraction and matrix stiffness, interfaceproperty, length and diameter of the fiber also affects elasticmodulusofcomposites.3.Stiffness and yield strength of the composite increases withincreaseininterfacestrength.4.Inordertoexploitthesuperiorpropertiesofthefiberindevelopingsuperstrongcomposites,interfacesneedtobeengineeredtohavehigherinterfacestrength.AMML
