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流變學(xué)基礎(chǔ)及應(yīng)用
SMZHUHH
Welcome使用牙膏時擠出要容易,擠出后要求挺括,在牙刷上不能下陷,刷牙時又要輕松,這就是要求牙膏遇剪切時粘度迅速下降,而靜止時又要具備一定的屈服應(yīng)力,以保持堅挺。牙膏—一個典型的流變學(xué)問題提綱I.流變學(xué)基礎(chǔ) 1.流變學(xué)定義及發(fā)展歷史 2.粘度計及流變儀簡介 3.穩(wěn)態(tài)流變學(xué) 4.動態(tài)流變學(xué) 4.1彈性行為及剪切模量 4.2粘彈性行為 4.3蠕變測試 4.4弛豫測試 4.5振蕩測試II.PhysicaMCR300流變儀簡介III.PhysicaMCR300流變儀應(yīng)用演示I.流變學(xué)基礎(chǔ)Thepersoninthepicture:ThomasG.Mezger,RheologistofAnton-Paar1流變學(xué)及其發(fā)展歷史
什么是流變學(xué)?
流變學(xué):研究物質(zhì)流動和變形的科學(xué)
Rheology=thescienceofdeformationandflowofmatter(SocietyOfRheology,SOR)希臘語:rheos=toflow,流動流動行為變形行為古代“萬物皆流”
1676虎克定律:彈性固體(形變與受力成正比)1687牛頓定律:粘性液體(流動阻力與流動速度成正比)1905愛因斯坦:懸浮液粘度方程(h=hs(1+2.5f))1920賓漢(Bingham)提出“流變學(xué)”概念1945首臺旋轉(zhuǎn)粘度計面世(Brookfield)1951首臺旋轉(zhuǎn)流變儀Rheogoniometer(Weissenberg)自1970年開始,流動曲線測試代替以前的單點測試自1980年開始,大規(guī)模使用數(shù)控和計算機(jī),流變學(xué)得到較大發(fā)展
流變學(xué)的發(fā)展歷史
中國的流變學(xué)“我國流變學(xué)的應(yīng)用研究起步較晚,20世紀(jì)60年代還只有個別自發(fā)研究,目前的應(yīng)用研究領(lǐng)域較少,甚至連流變學(xué)賴以發(fā)展的聚合物加工行業(yè)也知之不多。以塑料制品為例,塑料廠引進(jìn)的模具‘吃’進(jìn)口的聚合物粒子時,制品光滑、美觀,可以和國外的同類產(chǎn)品相媲美,而一旦換成國產(chǎn)原料粒子時,產(chǎn)品質(zhì)量就下降。這是因為所使用的模具是按國外原料的流變性能設(shè)計的,而國產(chǎn)原料的流變性與進(jìn)口原料并不完全相同,所以制品質(zhì)量下降。盡管生產(chǎn)廠對模具進(jìn)行完善修改,但也只是憑經(jīng)驗做機(jī)械上的改動,并未考慮到粒子的流變性?!?/p>
—
江體乾流變學(xué)(Rheology)
研究物質(zhì)的流動及變形行為粘性(viscous)彈性(elastic)粘彈性(viscoelastic)流體(流動行為)Newton定律固體(變形行為)Hooke定律粘彈性流體(流動行為)Maxwell定律粘彈性固體(變形行為)Kelvin/Voigt定律
流變學(xué)的研究內(nèi)容
流變學(xué)的研究范圍及方法液體固體(理想)粘性流體行為粘彈性流動行為粘彈性變形行為(彈性)變形行為Newton定律Maxwell定律Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗弛豫實驗振蕩實驗物質(zhì)狀態(tài)性能表現(xiàn)依據(jù)原理研究方法穩(wěn)態(tài)流變學(xué)動態(tài)流變學(xué)SimpleTestMethods鏟刀試驗(troweltest)
-高粘流體:“稠”
-低粘流體:“稀”手指試驗(fingertest)
-粘稠:“長”
-稀薄:“短”2流變行為的研究工具—粘度計及流變儀定性!
簡單測試Bostwick稠度計(Consistometer)1samplecontainer,max.100ml2gate,tobeopenedbyaspring3scaledflowpath測定流體(如番茄醬等)在一定時間內(nèi)流過的長度schematicpresentationofa
BOSTWICK-constistometer
粘度計Falling-BallViscometersDIN53015
ISO12058measuringtube
includingtheballstandthermometerjacket,
fortemp.control
落球粘度計HAAKEGENEQe.g.forpastesand
paste-likeprintinginksweightprintinginkfallingrodfallingrodviscometer
(Laray)Falling-RodViscometers
落桿粘度計accordingtoASTMD803andD1545checkmarkGasbubblerisesafter
turningthetube.
Viscosityevaluation
bycomparison
toasetoftubes
氣泡粘度計BubbleViscometersWater-Clock(Klepsydra)
fortimemeasurements
since3500yearsinEgypt
e.g.5lcorrespondsto6minflowtime
流杯FlowCupsmeasurementofthe
flowtime
determinationofthe
kinematicviscosity
流杯FlowCupsISO
DIN
Ford(ASTM)Zahn
Engler
ShellDINISO
流杯CapillaryViscometers
玻璃毛細(xì)管粘度計
Stormer粘度計Preset:
constanttorque
(shearstress)appliedbyafree
fallingweight(ingrams)Result:rotationalspeed
ofthemeasuringsystemKrebsmeasuringsystem("Paddle")
asarelativemeasuringsystem
designationinKrebsUnits,KU
Brookfield
粘度計spindlesas
relativemeasuringsystems:cylindersdiskspinsT-bar
旋轉(zhuǎn)流變儀—絕對測量系統(tǒng)圓筒狀轉(zhuǎn)子(Cylinder)notrecommended
forpastes
(airbubbles)錐板轉(zhuǎn)子(Cone-Plate)withdispersions
onlyusefulfor
particles
under5
m平行板(Parallel-plates)usefulfor
gelsandpastes旋轉(zhuǎn)及振蕩流變儀(rotationalandoscillatoryrheometers)
accordingtoDIN53019andISO3219
HAAKE旋轉(zhuǎn)流變儀HAAKEExtenCaBer1HAAKERheoScopeHAAKERheoStress1HAAKERheoStress600HAAKERotoVisco1
TA旋轉(zhuǎn)流變儀AR500AR1000AR2000ARESARES-1sARES-rdaARES-rfs
Bohlin旋轉(zhuǎn)流變儀BohlinCVOBohlinC-VORBohlinGeminiBohlinV88
Physica旋轉(zhuǎn)流變儀RheolabMC1SmartPaveMCR300、500MCR301、501ACS16/32
毛細(xì)管流變儀Poiseuille-Hagen定律毛細(xì)管流變學(xué)的基礎(chǔ)!DP2R
毛細(xì)管流變儀HAAKERheoCapS20HAAKERheoCapT1000RH7D&RH10DRH2100/2200
毛細(xì)管流變儀的功能在聚合物工業(yè)中,無論旋轉(zhuǎn)流變儀還是毛細(xì)管流變儀,其作用都是:模仿聚合物加工過程中的流動和變形行為!log/s-1DMAOsc.
/Rot.rheometerHighpressurecapillaryrheometerViscosities:(low-),middle-tohigh-viscousQuantities:Shear-andextensionalviscosity,wallslip
relaxation,PVT,Flowinstabilities10-110-3Levelling104101Extrusion,InjectionMoulding100102Mixing103106RollCoating,SprayingViscosities:lowviscoustosolid-likeQuantities:Shearviscosity,yield,viscoelasticproperties,relaxationetc.Non-destructiveOscillaroryshear
rot.rheometer:structural/lowshearmeasurements
high-pressurecapillary:processingflowbehaviour.RelaxationCoatingFreesurfaceMixingExtrusionInjectionmoulding
聚合物加工過程對應(yīng)的剪切速率Log
Log
POWER-LAWPROCESSINGRANGE103s-1101s-1旋轉(zhuǎn)流變儀毛細(xì)管流變儀3穩(wěn)態(tài)流變學(xué)—流動行為液體固體(理想)粘性流動行為粘彈性流動行為Newton定律Maxwell定律粘彈性變形行為(理想)
彈性變形行為Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗、弛豫實驗、振蕩實驗
基本概念:剪切應(yīng)力、剪切速率、粘度……牛頓流體的流動行為
非牛頓流體(剪切依賴型)的流動行為:剪切稀釋、剪切增稠、屈服值……
時間依賴型:觸變性、震凝性溫度依賴型ShearstressShearrate
剪切應(yīng)力及剪切速率剪切應(yīng)力單位面積所受的作用力剪切速率[]1ss1msmhvD-=ú?ùê?é=ú?ùê?é×==g)(&Strain應(yīng)變單位長度的伸長constantmmhv=ú?ùê?é=g=dgdt單位時間的應(yīng)變,也稱為“剪切梯度”、“速度梯度”、“應(yīng)變率”、“變形率”)TypicalShearRateRangesProcessShearRate(1/s)sedimentation<0,001to0,01surfacelevelling0,01to0,1sagging0,01to1dipcoating1to100pipeflow,pumping,fillingintocontainers1to10000coating,painting,brushing100to10000spraying1000to10000(high-speed)coating,bladecoating100000to1mio.Application:
SedimentationofDispersionsinthebeginningherbsinsaladdressingafter15minApplication:LevellingandSagging
ofaCoating200μm0.5m/sCalculationoftheshearrateApplication:Coating,Painting,BrushingApplication:AutomotiveCoatingscarbodydegreasing&phosphatizingelectrodipcoatingPVCseamsealingPVCunderbodysprayingprimerandfillertopcoatandclearcoatcavityconservation
a)Plastisols:seamsealing,underbodyspraying,cavityconservation
b)Primer
c)Coatings:filler,basecoat,topcoat,clearcoatApplication:OffsetPrintingInksink
containerplatecylinderrubbercylinderrubbercylinder1ductor
2filmroller
3transferroller
4rubber
5cylindertoapply
thepaint
6
7clammyductor
8clammyrubber
9paperweb(剪切)粘度((shear)viscosity):
1Pa
s=1000mPa
s1MPa
s=1000kPa
s=1Mio.Pa
s以前所用單位:厘泊1cP=1mPa
s(1643–1727)
粘度的定義[]Pa
s1/sPa=ú?ùê?é=γτη&牛頓流體(NewtonianFluid):粘度不受剪切速率的影響,為恒定值。如,水、礦物油等
非牛頓流體(Non-NewtonianFluid):粘度隨時間的變化而變化。如,聚合物溶液等ViscosityValuesMaterialsShearviscosity
Gases/air0,01to0,02/0,018mPa
sWaterat20°C/at0°C/at40°C1,00/1,79/0,65mPa
sMilk,coffeecream2to10mPa
sOliveoilapprox.100mPa
sGlycerine1480mPa
sPolymermelts(T=+100to+200°C
andatshearratesof10to10001/s)10to10000Pa
sPolymermelts(zero-shearviscosity)1kPasto1MPa
sBitumen(T=+80/+60/+40/
+20/+0°C)200Pa
s/1kPa
s/20kPa
s/
0,5MPa
s/1MPa
sPresettingsforFlowCurvesshearrateramp
CSR:controlledshearrate受控剪切速率shearstressramp
CSS:controlledshearstress受控剪切應(yīng)力
理想粘性流動行為(IdealviscousFlowBehavior)或稱:Newtonian流動行為(牛頓流體)flowcurves(流動曲線)viscositycurves(粘度曲線)RotationCSRTestpresettingResultrawdataspeedn[1/min]torqueM[mNm]rheologicalparametersshearrate[1/s]shearstress
[Pa]RotationCSSTestsettingResultrawdatatorqueM[mNm]speedn[1/min]rheologicalparametersshearstress
[Pa]shearrate[1/s]RawDataandRheologicalParameters
Summary:MeasuringParametersPhysicalParametersrawdata,dependentonthemeasuringsystemRheologicalParameterscalculatedvalues,independentofthemeasuringsystemshearstress
shearratesheardeformationtorqueM[Nm]rotationalspeedn[1/min]deflectionangle[°],[rad]viscosity shearmodulusFlowBehavior(linearscales)flowcurvesviscositycurvesyieldpoint1idealviscous(Newtonian)(牛頓流體)2shear-thinning(pseudoplastic)(非牛頓流體:剪切稀釋型)3shear-thickening(dilatant)(非牛頓流體:脹凝型)4withoutyieldpoint(非牛頓流體:不具有屈服值)5withyieldpoint(非牛頓流體:具有屈服值)FlowBehavior(log.scales)1idealviscous(Newtonian)2shear-thinning(pseudoplastic)3shear-thickening(dilatant)4withzero-shearviscosity5withoutzero-shearviscosityflowcurvesviscositycurveszero-shearviscosityyieldpointIdealviscousFlowBehavior010203040506080mPash010203040506080Pat020040060010001/sShearRate
g.mineraloilat50°CCC27hViscositytShearStressIdealviscousFlowBehavior100101Pash10-310-210-1100101103Pat10-310-210-11001011021/sShearRate
g.siliconeoilMK23(50mm,2°)hViscositytShearStressIdealviscousFlowBehavior10-410-310-2Pash10-510-410-310-2100Pat1001011021/sShearRate
g.waterDG42hViscositytShearStressComparisonofIdealviscousand
Shear-ThinningFlowBehavior00.511.52Pash01002003004005001/sShearRate
g.idealviscoushViscosityshear-thinninghViscosity
shear-thinning(剪切稀釋)
pseudoplastic(假塑性)
剪切稀釋(Shear-Thinning)流動行為flowcurveviscositycurveShear-ThinningFlowBehaviorpolymermoleculesstateatrest:
coiled,
entangledstateunderhighshearload:
deformationinsheardirection
disentangled,
consequence:
shear-thinningflowbehaviorShear-ThinningFlowBehaviorMaterialAtRest:DuringShearing:
HighViscosityDecreaseinViscositySuspensionwith
needle-shapedor
platelet-shaped
particlesTheparticlesareTheparticlesare
suspendedrandomlyorientated.
(ifthereareno
interactionforces).Agglomerated
ParticlesThesmallprimaryTheagglomeratesare
particlesformdisintegratedintoprimary
agglomerates(intheparticles.Thedispersion
formoflargersecondaryliquidisnolongerbound
particles).Theyalsoandagainfreetoflow.
surroundapartofthe
dispersionliquidand
immobilizeit.Shear-ThinningFlowBehaviorMaterialAtRest:DuringShearing:
HighViscosityDecreaseinViscosityShear-thinningFlowBehaviorEmulsionThedisperseddropletsThedropletsaredeformed
showtheshapeofandtakeontheshapeof
spheres.ellipses.MaterialAtRest:DuringShearing:
HighViscosityDecreaseinViscosityShear-ThinningFlowBehavior0.10.20.30.40.50.6Pash050100150200Pat02004006001,0001/swallpaperpaste(lin)(aqueousmethylcellulosesolution)hViscositytShearStressShearRate
g.Shear-ThinningFlowBehavior0.20.30.40.50.60.70.81Pash050100150200250300Pat020040060010001/sShearRate
g.O/WemulsionhViscositytShearStressO/Wemulsionwith10%waterhViscositytShearStressShear-ThinningFlowBehavior00.050.10.150.20.250.3Pash020040060010001/sShearRate
g.gravureprintingink,binder1hViscositygravureprintingink,binder2hViscositygravureprintingink,binder3hViscosityAllthreesampleshavethesame
pigmentconcentrationandshow
thesameflowcuptime.Shear-ThinningFlowBehavior10-1100Pash10-310-210-1100101102103Pat10-310-210-11001011021031/sShearRate
g.wallpaperpaste(log)(aqueousmethylcellulosesolution)hViscositytShearStressh0Shear-thinning1)Orientationofthemacromolecules
undershearload
disentanglements
here,thevaluedecreases
2)Re-coilingsdueto
viscoelasticbehaviorre-entanglements
here,thevalueincreasesExplanationoftheZero-ShearViscosity(零剪切粘度)
ofPolymersSuperpositionoftwoprocesses:Result:Inthelow-shearrangethereisno
changeinthetotalviscosityvalue,
whichisreferredtoasthevalue.ViscosityFunctionofPolymers"low-shearrange""flowrange""high-shearrange"
withshear-thinning
zero-shearviscosity:flowbehavior:infinite-shearviscosity:Shear-ThinningFlowBehavior10-210-1100101Pash10-210-11001021/sShearRate
g.mineraloilhViscositywallpaperpaste(log)(aqueousmethylcellulosesolution)hViscositypolymersolutionhViscosityDependenceofviscosityonconcentrationwithdiluted(c<c*)andhighlyconcentratedpolymersolutions(c>c*).Zero–ShearViscositylowshear
viscosityZero-ShearViscosityviscosityincreaseofpolymersolutions
withincreasingmolarmassincreasingmolarmass
ofapolymeratlowshearload:athighshearload:
therodinclinessolidificationofthe
slowlyliquiddueto
shear-thickening
flowbehavior
剪切增稠(Shear-Thichening)流動行為Shear-ThickeningFlowBehaviorflowcurveviscositycurve
-shear-thickening(剪切增稠)
-dilatant(脹凝型)Shear-ThickeningFlowBehaviorSuspensionc...solidconcentration
shear-thickeningofhighlyconcentratedsuspensions
underhighshearloadcShear-ThickeningFlowBehavior00.050.10.150.20.250.30.4Pash050100150200250300400Pat020040060010001/sShearRate
g.ceramicsuspensionhViscositytShearStressShear-ThickeningFlowBehaviorcomparisonofaqueouschalkstonesuspensions(1)cube-shapedparticles(2)sphericalparticles
Withbothsuspensionshavingthesamesolidconcentration
for(2)shear-thickeningflowbehavioroccursathighershearrates.Shear-ThickeningFlowBehavior0500
1000
1500
2000
2500
3000
4000Pash01002003004005001/sShearRate
g.plastisol
withtoolowsofteneramounthViscositylinearscaleslogarithmicscalesyieldpointaslimitingvalueoftheshearstress
屈服值(YieldValue)也稱:屈服點(Yieldpoint)屈服應(yīng)力(Yieldstress)FlowcurvewithYieldPoint(lin/lin)0500
1000
1500
2000
2500
3000Pat02004006001,0001/sShearRate
g.ketchuptShearStressFlowcurvewithYieldPoint(log/log)101102103104Pat1001011021031/sShearRate
g.ketchuptShearStressFlowcurveswithYieldPoint(lin/lin)ShearRate
g.02004006008001,200Pat0501001/scream1tShearStresscream2tShearStresscream1Herschel-BulkleyYieldPoint:705.0PatShearStresscream2Herschel-BulkleyYieldPoint:31.2PatShearStressanalysisusinganapproximationfunctionforflowcurvesFlowandViscosityCurves(log/log)100101102103Pash10-310-210-1100101103Pat10-210-11001011021/sShearRate
g.primerhViscositytShearStresstopcoatinghViscositytShearStressViscosityCurves(log/log)100101102Pash10-210-11001011021/sShearRate
g.withoutzero-shearviscosityhViscositywithzero-shearviscosityhViscosityFlowandViscosityCurves1:idealviscous(Newtonian)2:shear-thinning(pseudoplastic)3:shear-thickening(dilatant)SummaryFlowandViscositycurves4:withoutyieldpoint5:withyieldpointSummaryviscosityfunctionofpolymers
1:rangeofthe
zero-shearviscosity
2:flowrange(shear-thinning)
3:rangeofthe
infinite-shearviscositySometimescatsareverycuriousSometimescatsareverystupid
時間依賴流動行為(Time-DependentFlowBehavior
)StepTest:Thixotropy(觸變性)presettingmeasuringresultasrotationaltestwith3intervalslow-shearconditionshigh-shearconditionslow-shearconditionsstateofreststructuredecompositionstructureregeneration觸變性用來描述材料的結(jié)構(gòu)的破壞與恢復(fù)的過程testconditions:1.interval:=0.11/s2.interval:=1001/s3.interval:=0.11/sTime-DependentStructureDecomposition
andRegeneration(lin/log)
g.
g.
g.10-1100101102Pash0100200300400500600700sTime
tcoatingKhViscositycoatingMhViscosityTime-DependentFlowBehaviorpresetting:shearrateprofiletestin3intervals:upwardramp,holdtime,downwardrampanalysis:hysteresisareadisadvantages:testinginanon-stationarystate,
nomeasurementofthestructureregenerationevaluationofthehysteresisarea
inbetweentheflowcurves
asameasureofthe
structuredecomposition
duringtheholdingtimeThixotropyTest,conventionalsofteningandmelting,
orsolidificationandcrystallizationpresetting:constantshearconditions
(shearrateorshearstress)
result:viscosity/temperature-curve
withsteadilydecreasingorincreasing
viscosity,respectivelygelformationandcuringpresetting:constantshearconditions
(shearrateorshearstress)
result:viscosity/temperature-curve
showingaviscosityminimum
溫度依賴流動行為(Temperature-DependentFlowBehavior
)TemperatureCurve0.1110100Pash-100-50050100°CTemperature
TsiliconeoilhViscosityTemperatureCurveand
AnalysisaccordingtoArrhenius10100mPash10152025303540°CTemperature
TcrudeoilArrheniusAnalysishighTArrheniusAnalysislowTTemperatureCurveand
AnalysisaccordingtoArrhenius(1/T)10100mPash0,00310,00320,00330,00340,00350,00361/K1/Temperature
1/TcrudeoilArrheniusAnalysishighTArrheniusAnalysislowTTemperatureCurve0246810Pash2025303540°CTemperature
TchocolatehViscosityTemperature-DependentViscosityCurves(3D)00.10.2Pash05001,0001/sg.050100°CTmineraloilat23°ChViscositymineraloilat50°ChViscositymineraloilat80°ChViscosity3-dimensionaldiagram4動態(tài)流變學(xué)—變形行為液體固體(理想)粘性流動行為粘彈性流動行為Newton定律Maxwell定律粘彈性變形行為(理想)彈性變形行為Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗、弛豫實驗、振蕩實驗液體固體(理想)粘性流動行為粘彈性流動行為Newton定律Maxwell定律粘彈性變形行為(理想)彈性變形行為Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗、弛豫實驗、振蕩實驗4.1彈性行為(Elasticbehavior)
剪切形變(ShearDeformation)或應(yīng)變(ShearStrain)
ShearStressShearDeformation
orShearStrain
RobertHooke(1635to1703)Shearmodulus
1GPa=1000MPa=106kPa=109PaEmodulus
orYoung'smodulusForTensileTestsapplies:s
=tensilestresse
=elongation
withPoisson'sratio
彈性行為及剪切模量(Elasticbehavior&Shearmodulus)剪切模量及剛性模量TensileTestTensileTestatthebeginningandaftertheelongationl=l–l0,
TensileStress/ElongationDiagramofsteel,yieldstressSandyieldstrengthS,breakingstressBandelongationatbreakBPoisson'sratio:l...lengthofthespecimend...thicknessofthespecimenclampspecimenforceFlinearelasticdeformation
=E?plasticdeformation,
latticedislocationof
crystalsTensileTestTensileTestofamorphous,unlinkedor
sparselycross-linkedpolymersorcoatingfilmsTg...glasstransition
temperaturebrittlefractureatT<TgcoldflowatTg-30°CtoTgrubber-elasticatT>TgDefinitionofShearRatea)
shearrateastime-dependentrateofdeformationorstrainrateb)
shearrateasvelocitygradientexplanation:液體固體(理想)粘性流動行為粘彈性流動行為Newton定律Maxwell定律粘彈性變形行為(理想)彈性變形行為Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗、弛豫實驗、振蕩實驗4.2粘彈性行為(Viscoelasticbehavior)tack(showinglongstrings)
e.g.mouthsensationstirringprocess:Weissenbergeffect
("rodclimbingeffect")
poormixingresultextrusion:extrudateswelling
e.g.dimensionstabilityresult:Inmanycasesthemeasurementofviscosityonlyisnotsufficient
becauseelasticeffectsareoccuring,resultinginviscoelasticbehavior.粘彈性行為(Viscoelasticbehavior)ViscoelasticBehaviorof
Polyisobutylene(PIB)dieswellwhenflowingoutWeissenbergeffectduringa
ofacapillarystirringprocessViscoelasticBehaviorextrusionofapolystyrene:viscoelasticbehavior(extrudateswelling)
andmeltfracture
testtemperatureT=190°C
diegeometryL/R=24,R=1mmYieldPoint(/-Diagram)testwithpresettingoftheshearstress:yieldpointaslimitingvalue
oftheshearstressdeterminationoftheyieldpoint
y
usingthetangentintheelastic
deformationrangedeterminationoftheyieldpoint
y
usingthetangentcrossovermethodThesamplestartstoflow
notbeforetheexternal
forcesareexceedingthe
internalforcesofthe
structure.
BelowtheyieldpointThereiselasticdeformation.YieldPoint(/-Diagram)10-210-1100101102103104106%g0.11101001,000PaShearStress
twithoutbindergwithbindergyieldpointwithoutbindertau_0=13,5Pagyieldpointwithbindertau_0=114PagComparisonoftwoKetchupsYieldPoint(FlowCurve)0100200300400500600Pat0204060801001/sShearRate
g.PrimertTopCoatingt0.010.11101001,000Pat0.0010.010.11101001/sShearRate
g.PrimertTopCoatingtComparisonoftwoCoatingslinearscaleslogarithmic
scalesYieldPoint
(/-Diagram)10-1100101102103104106%g0.010.1110100PaShearStress
tPrimergTopCoatinggYieldPointTopCoating(for5%bandwidth)tau_0=7.02PagComparisonoftwoCoatingsViscoelasticSolidKelvin/VoigtModel
parallelconnection
ofspringanddashpotViscoelasticLiquidMaxwellModel
serialconnection
ofspringanddashpot粘彈性模型MaxwellModel
forViscoelasticLiquidsafteraloadcycle,
thesampleremains
partlydeformedKelvin/VoigtModel
forViscoelasticSolidsafteraloadcycle,
thesampleshowsdelayed
butcompletere-formation
法向應(yīng)力(NormalStress)粘彈性材料運動或形變時,不僅在其形變方向產(chǎn)生應(yīng)力,而且通常會出現(xiàn)三維形變!可用三維張量描述:
X方向:txx,txy,txz Y方向:tyx,tyy,tyz Z方向:tzx,tzy,tzz第一法向應(yīng)力差:N1[Pa]=txx–tyy,是剪切速率的函數(shù):N1(g).第二法向應(yīng)力差:N2[Pa]=tyy–tzz,是剪切速率的函數(shù):N2(g)
.
第一法向應(yīng)力系數(shù):Y1[Pas2]=N1/g2,是剪切速率的函數(shù):Y1
(g)
利用第一零法向應(yīng)力系數(shù)Y1,0[Pas2]=lim(g0)Y1(g)=常數(shù),在雙對數(shù)坐標(biāo)上可以發(fā)現(xiàn)一個平臺值....
第二法向應(yīng)力系數(shù):Y2[Pas2]=N2/g2,是剪切速率的函數(shù):Y2
(g)
利用第一零法向應(yīng)力系數(shù)Y2,0[Pas2]=lim(g0)Y2(g)=常數(shù),在雙對數(shù)坐標(biāo)上也可以發(fā)現(xiàn)一個平臺值...........ViscoelasticBehavior
DifferentialEquationsidealviscosbehavior
(viscositylawofNewton):idealelasticbehavior
(elasticitylawofHooke):behaviorofaviscoelasticsolid
(Kelvin/Voigtmodel:thetotalshearstressisdistributed
onbothmodelcomponents)behaviorofaviscoelasticliquid
(Maxwellmodel:thedeformationsorshearrates,resp.
areoccuringforeachindividualmodelcomponent)液體固體(理想)粘性流動行為粘彈性流動行為Newton定律Maxwell定律粘彈性變形行為(理想)彈性變形行為Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗、弛豫實驗、振蕩實驗shearstressstep
withcreepintimeintervalt0tot2
creeprecoveryintimeintervalt2tot4
elasticreformation
remainingdeformation(viscousportion)4.3蠕變實驗(CreepTest)CreepTest:AnalysisBurgersmodelCreepTest:Analysisa)intheLVErange
b)outsideoftheLVErangecreepcomplianceCreepTest
0246812%g0100200300400sTime
tPDMS2PaPDMS5PaPDMS10PaPDMS20PaPDMS40PaCreepCompliance
00.00050.0010.00150.0020.00250.0030.0041/PaJ(t)020406080100120sTime
tPDMS2PaPDMS5PaPDMS10PaPDMS20PaPDMS40PaCreepTest00.10.20.30.40.5%g0100200300400500600sTime
tgel1Pa液體固體(理想)粘性流動行為粘彈性流動行為Newton定律Maxwell定律粘彈性變形行為(理想)彈性變形行為Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗、弛豫實驗、振蕩實驗shearstrainstep(sheardeformationstep)
with
stressrelaxation
intimeintervalt2tot3
4.4弛豫實驗(RelaxationTest)RelaxationTest:Analysisrelaxationmodulus
withtheplateauvalueG0
RelaxationTimeSpectrumand
RetardationTimeSpectrumgeneralizedgeneralized
MaxwellmodelKelvin/Voigtmodelrelaxationtimespectrummolarmassdistribution(MMD)
1...narrowMMD;2...wideMMDw[%]
rel.amount
M[g/mol]
molarmassRelaxationTest10-1100101102%g00.20.40.60.81sTime
tPDMS1%PDMS25%PDMS50%RelaxationTest
05,00010,00015,00020,00030,000Pat00.20.40.60.81sTime
tPDMS1%PDMS25%PDMS50%RelaxationModulus
101102103104106PaG(t)10-210-1100101102sTime
tPDMS1%PDMS25%PDMS50%RelaxationTimeSpectrum
10-210-1100101102103104106PaH(l)10-410-310-210-1100101102103104sRelaxationTime
lPDMS50%Cont.EPRRelax.SpectrumRelaxationTimeSpectrum
01,0002,0003,0004,0005,0006,0007,0008,000PasH(l)l10-410-310-210-1100101102103104sRelaxationTime
lPDMS50%Cont.EPRRelax.SpectrumMolarMassDistribution
05,00010,00015,00020,00025,00030,00035,00040,00045,00050,00060,000g/molMiwi104105106g/molMolarMass
MiPDMS50%MMDThimm-Kermel液體固體(理想)粘性流動行為粘彈性流動行為Newton定律Maxwell定律粘彈性變形行為(理想)彈性變形行為Kelvin/Voigt定律Hook定律流動/粘度曲線蠕變實驗、弛豫實驗、振蕩實驗OscillatoryTests:Basics(1)
Two-Plate-ModelIdealelasticBehaviorofatotallystiffsample
(e.g.stone,orsteel)noshiftbetween
thesinecurvesof
shearstressandsheardeformation:thecurvesofand
areinphase4.5振蕩實驗(OscillatoryTest)OscillatoryTests:Basics(2)Presetting:constantfrequencyand
constantamplitude,
here:withthestrain(deformation)amplitudeResult:Inmostcasesthesamplesshow
viscoelasticbehaviorwiththephaseshift
betweenthesinecurvesof
presettingandresult.
physically:
G‘forthestroredand
G''forthelost(dissipated)deformationenergytand[1]=G‘’/G‘dampingorlossfactor(衰減或損耗因子)
asquotientoftheviscousandelasticportionsOscillatoryTests:Basics(3)VectordiagramG*[Pa]
complexshearmodulus
復(fù)(數(shù))剪切模量elasticitylawofHooke(foroscillation):G‘[Pa]storagemodulus,elasticportion
儲能模量彈性模量G''[Pa]lossmodulus,viscousportion
耗能模量粘性模量
oftheviscoelasticbehaviorOscillatoryTests:Basics(4)Vectordiagramh*[Pas]
complexshearviscosity
復(fù)(數(shù))剪切粘度h‘[Pas
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