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1、PartIFundamentalRelationshipsFundamentalRelationships¾¾1.BasicConcepts1.BasicConcepts¾¾2.Modeling2.Modeling¾¾3.FractureBehavior3.FractureBehavior12.ModelingTomodelthephysicalandmechanicalbehaviorsofmulticomponentpolymersmodulus,viscosity,phasemodulus,viscosity,phasecontinuity,cont
2、inuity,…………2.1TakayanagimodelsÎE2.2KernerequationÎG2.3Phasecontinuityandinversion2.4Polymer-polymermiscibility2ReviewReview¾Maxwellmodel¾Voigt-Kelvinmodel¾Burger’smodel3MaxwellmodelConsistsofanelasticspringanelasticspringεε1andaviscousdashpotaviscousdashpotcoupledinseries.εε2Strai
3、nStrainεε==εε11++εε22==σσ00/E+t/E+tσσ00//ηη4Voigt-KelvinmodelConsistsofanelasticspringanelasticspringσσ1σσ2andaviscousdashpotaviscousdashpotcoupledinparallel.StressStressσσ==σσ11++σσ22==EEεε++ηηddεε/dt/dt5Burger’smodelεε1CombiningMaxwellMaxwellandVoigtVoigt--KelvinKelvinεε2element
4、sinseries.StrainStrainεε==εε11++εε22++εε33εε3==σσ/E/E++σσ/E/E(1(1--ee-t/τ)+t)+tσσ//ηη001100110036ModelingModeling2.1TakayanagiModels1963Tomodeltwoseparatedphases,suchaspolymerblends,blocks,grafts,orIPNs.ModelingYoungModelingYoung’’smodulussmodulus((E)7TakayanagiModelsFortwoseparat
5、edphasestwoseparatedphases,R(rubber)R(rubber)andP(plastic)P(plastic)suchaspolymerblends,blocks,grafts,orIPNs.8TwosimplephasesSimpleparallelmodelSimpleseriesmodelλandφ:representingthevolumefractionsoftherubberphase.9Simpleparallelmodelσσ==σσRR++σσP==ε(ε(EERR+E+EPP))Young’smodulus,E
6、=(1−λ)E+λEPRExample:Bothphasesarecontinuousphases,e.g.,alongfibercomposites,multilayeredfilm.10Simpleseriesmodelεε==εεRR++εεPPYoung’smodulus,-1E=[φ/ER+(1−φ)/EP]Example:Neitherphaseiscontinuousinspace.11TwocomplexphasesExample:*acontinuousplasticphaseandadiscontinuousrubberphase;*c
7、omposites.1213ExamplecalculationsExamplecalculationsPolymerblendsPolymerblendsPS:E=3x109Pa(3GPa)plasticphasePB:E=2x106Pa(2MPa)rubberphasePS/PB50/50WhatrangesofitsYoung’smodulusmightbe?14Ε=(1−λ)E+λESimpleparallelmodelPR=0.5x3x109Pa+0.5x2x106Pa≈1.5x109Pa(1.5GPa)Approximatelyhalfofth
8、eplasticmodulusApproximatelyhalfo
