流变学基础及应用课件

流变学基础及应用

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Welcome使用牙膏时挤出要容易，挤出后要求挺括，在牙刷上不能下陷，刷牙时又要轻松，这就是要求牙膏遇剪切时粘度迅速下降，而静止时又要具备一定的屈服应力，以保持坚挺。牙膏—一个典型的流变学问题提纲I.流变学基础 1．流变学定义及发展历史 2.粘度计及流变仪简介 3.稳态流变学 4.动态流变学 4.1弹性行为及剪切模量 4.2粘弹性行为 4.3蠕变测试 4.4弛豫测试 4.5振荡测试II.PhysicaMCR300流变仪简介III.PhysicaMCR300流变仪应用演示I.流变学基础Thepersoninthepicture:ThomasG.Mezger,RheologistofAnton-Paar1流变学及其发展历史

什么是流变学？

流变学：研究物质流动和变形的科学

Rheology=thescienceofdeformationandflowofmatter(SocietyOfRheology,SOR)希腊语:rheos=toflow，流动流动行为变形行为古代“万物皆流”

1676虎克定律：弹性固体（形变与受力成正比）1687牛顿定律：粘性液体（流动阻力与流动速度成正比）1905爱因斯坦：悬浮液粘度方程（h=hs(1+2.5f)）1920宾汉（Bingham）提出“流变学”概念1945首台旋转粘度计面世（Brookfield）1951首台旋转流变仪Rheogoniometer（Weissenberg）自1970年开始，流动曲线测试代替以前的单点测试自1980年开始，大规模使用数控和计算机，流变学得到较大发展

流变学的发展历史

中国的流变学“我国流变学的应用研究起步较晚，20世纪60年代还只有个别自发研究，目前的应用研究领域较少，甚至连流变学赖以发展的聚合物加工行业也知之不多。以塑料制品为例，塑料厂引进的模具‘吃’进口的聚合物粒子时，制品光滑、美观，可以和国外的同类产品相媲美，而一旦换成国产原料粒子时，产品质量就下降。这是因为所使用的模具是按国外原料的流变性能设计的，而国产原料的流变性与进口原料并不完全相同，所以制品质量下降。尽管生产厂对模具进行完善修改，但也只是凭经验做机械上的改动，并未考虑到粒子的流变性。”

—

江体乾流变学（Rheology）

研究物质的流动及变形行为粘性（viscous）弹性（elastic）粘弹性（viscoelastic）流体（流动行为）Newton定律固体（变形行为）Hooke定律粘弹性流体（流动行为）Maxwell定律粘弹性固体（变形行为）Kelvin/Voigt定律

流变学的研究内容

流变学的研究范围及方法液体固体(理想)粘性流体行为粘弹性流动行为粘弹性变形行为(弹性)变形行为Newton定律Maxwell定律Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验弛豫实验振荡实验物质状态性能表现依据原理研究方法稳态流变学动态流变学SimpleTestMethods铲刀试验（troweltest）

-高粘流体：“稠”

-低粘流体：“稀”手指试验（fingertest）

-粘稠：“长”

-稀薄：“短”2流变行为的研究工具—粘度计及流变仪定性！

简单测试Bostwick稠度计（Consistometer）1samplecontainer,max.100ml2gate,tobeopenedbyaspring3scaledflowpath测定流体（如番茄酱等）在一定时间内流过的长度schematicpresentationofa

BOSTWICK-constistometer

粘度计Falling-BallViscometersDIN53015

ISO12058measuringtube

includingtheballstandthermometerjacket,

fortemp.control

落球粘度计HAAKEGENEQe.g.forpastesand

paste-likeprintinginksweightprintinginkfallingrodfallingrodviscometer

(Laray)Falling-RodViscometers

落杆粘度计accordingtoASTMD803andD1545checkmarkGasbubblerisesafter

turningthetube.

Viscosityevaluation

bycomparison

toasetoftubes

气泡粘度计BubbleViscometersWater-Clock(Klepsýdra)

fortimemeasurements

since3500yearsinEgypt

e.g.5lcorrespondsto6minflowtime

流杯FlowCupsmeasurementofthe

flowtime

determinationofthe

kinematicviscosity

流杯FlowCupsISO

DIN

Ford(ASTM)Zahn

Engler

ShellDINISO

流杯CapillaryViscometers

玻璃毛细管粘度计

Stormer粘度计Preset:

constanttorque

(shearstress)appliedbyafree

fallingweight(ingrams)Result:rotationalspeed

ofthemeasuringsystemKrebsmeasuringsystem("Paddle")

asarelativemeasuringsystem

designationinKrebsUnits,KU

Brookfield

粘度计spindlesas

relativemeasuringsystems:cylindersdiskspinsT-bar

旋转流变仪—绝对测量系统圆筒状转子（Cylinder）notrecommended

forpastes

(airbubbles)锥板转子（Cone-Plate）withdispersions

onlyusefulfor

particles

under5

m平行板（Parallel-plates）usefulfor

gelsandpastes旋转及振荡流变仪（rotationalandoscillatoryrheometers）

accordingtoDIN53019andISO3219

HAAKE旋转流变仪HAAKEExtenCaBer1HAAKERheoScopeHAAKERheoStress1HAAKERheoStress600HAAKERotoVisco1

TA旋转流变仪AR500AR1000AR2000ARESARES-1sARES-rdaARES-rfs

Bohlin旋转流变仪BohlinCVOBohlinC-VORBohlinGeminiBohlinV88

Physica旋转流变仪RheolabMC1SmartPaveMCR300、500MCR301、501ACS16/32

毛细管流变仪Poiseuille-Hagen定律毛细管流变学的基础!DP2R

毛细管流变仪HAAKERheoCapS20HAAKERheoCapT1000RH7D&RH10DRH2100/2200

毛细管流变仪的功能在聚合物工业中，无论旋转流变仪还是毛细管流变仪，其作用都是：模仿聚合物加工过程中的流动和变形行为！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

聚合物加工过程对应的剪切速率Log

Log

POWER-LAWPROCESSINGRANGE103s-1101s-1旋转流变仪毛细管流变仪3稳态流变学—流动行为液体固体(理想)粘性流动行为粘弹性流动行为Newton定律Maxwell定律粘弹性变形行为(理想)

弹性变形行为Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验、弛豫实验、振荡实验

基本概念：剪切应力、剪切速率、粘度……牛顿流体的流动行为

非牛顿流体（剪切依赖型）的流动行为：剪切稀释、剪切增稠、屈服值……

时间依赖型：触变性、震凝性温度依赖型ShearstressShearrate

剪切应力及剪切速率剪切应力单位面积所受的作用力剪切速率[]1ss1msmhvD-=úûùêëé=úûùêëé×==g)(&Strain应变单位长度的伸长constantmmhv=úûùêëé=g=dgdt单位时间的应变，也称为“剪切梯度”、“速度梯度”、“应变率”、“变形率”）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以前所用单位：厘泊1cP=1mPa

s(1643–1727)

粘度的定义[]Pa

s1/sPa=úûùêëé=γτη&牛顿流体（NewtonianFluid）:粘度不受剪切速率的影响，为恒定值。如，水、矿物油等

非牛顿流体（Non-NewtonianFluid）：粘度随时间的变化而变化。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受控剪切应力

理想粘性流动行为（IdealviscousFlowBehavior）或称：Newtonian流动行为（牛顿流体）flowcurves（流动曲线）viscositycurves（粘度曲线）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)（牛顿流体）2shear-thinning(pseudoplastic)（非牛顿流体：剪切稀释型）3shear-thickening(dilatant)（非牛顿流体：胀凝型）4withoutyieldpoint（非牛顿流体：不具有屈服值）5withyieldpoint（非牛顿流体：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（剪切稀释）

pseudoplastic（假塑性）

剪切稀释（Shear-Thinning）流动行为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）流动行为Shear-ThickeningFlowBehaviorflowcurveviscositycurve

-shear-thickening（剪切增稠）

-dilatant（胀凝型）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）也称：屈服点(Yieldpoint)屈服应力(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

时间依赖流动行为（Time-DependentFlowBehavior

）StepTest:Thixotropy（触变性）presettingmeasuringresultasrotationaltestwith3intervalslow-shearconditionshigh-shearconditionslow-shearconditionsstateofreststructuredecompositionstructureregeneration触变性用来描述材料的结构的破坏与恢复的过程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

温度依赖流动行为（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动态流变学—变形行为液体固体(理想)粘性流动行为粘弹性流动行为Newton定律Maxwell定律粘弹性变形行为(理想)弹性变形行为Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验、弛豫实验、振荡实验液体固体(理想)粘性流动行为粘弹性流动行为Newton定律Maxwell定律粘弹性变形行为(理想)弹性变形行为Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验、弛豫实验、振荡实验4.1弹性行为(Elasticbehavior)

剪切形变(ShearDeformation)或应变(ShearStrain)

ShearStressShearDeformation

orShearStrain

RobertHooke(1635to1703)Shearmodulus

1GPa=1000MPa=106kPa=109PaEmodulus

orYoung'smodulusForTensileTestsapplies:s

=tensilestresse

=elongation

withPoisson'sratio

弹性行为及剪切模量(Elasticbehavior&Shearmodulus)剪切模量及刚性模量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:液体固体(理想)粘性流动行为粘弹性流动行为Newton定律Maxwell定律粘弹性变形行为(理想)弹性变形行为Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验、弛豫实验、振荡实验4.2粘弹性行为(Viscoelasticbehavior)tack(showinglongstrings)

e.g.mouthsensationstirringprocess:Weissenbergeffect

("rodclimbingeffect")

poormixingresultextrusion:extrudateswelling

e.g.dimensionstabilityresult:Inmanycasesthemeasurementofviscosityonlyisnotsufficient

becauseelasticeffectsareoccuring,resultinginviscoelasticbehavior.粘弹性行为(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粘弹性模型MaxwellModel

forViscoelasticLiquidsafteraloadcycle,

thesampleremains

partlydeformedKelvin/VoigtModel

forViscoelasticSolidsafteraloadcycle,

thesampleshowsdelayed

butcompletere-formation

法向应力(NormalStress)粘弹性材料运动或形变时，不仅在其形变方向产生应力，而且通常会出现三维形变！可用三维张量描述：

X方向：txx，txy，txz Y方向：tyx，tyy，tyz Z方向：tzx，tzy，tzz第一法向应力差：N1[Pa]=txx–tyy，是剪切速率的函数：N1(g).第二法向应力差：N2[Pa]=tyy–tzz，是剪切速率的函数：N2(g)

.

第一法向应力系数：Y1[Pas2]=N1/g2，是剪切速率的函数：Y1

(g)

利用第一零法向应力系数Y1,0[Pas2]=lim(g0)Y1(g)=常数，在双对数坐标上可以发现一个平台值....

第二法向应力系数：Y2[Pas2]=N2/g2，是剪切速率的函数：Y2

(g)

利用第一零法向应力系数Y2,0[Pas2]=lim(g0)Y2(g)=常数，在双对数坐标上也可以发现一个平台值...........ViscoelasticBehavior

DifferentialEquationsidealviscosbehavior

(viscositylawofNewton):idealelasticbehavior

(elasticitylawofHooke):behaviorofaviscoelasticsolid

(Kelvin/Voigtmodel:thetotalshearstressisdistributed

onbothmodelcomponents)behaviorofaviscoelasticliquid

(Maxwellmodel:thedeformationsorshearrates,resp.

areoccuringforeachindividualmodelcomponent)液体固体(理想)粘性流动行为粘弹性流动行为Newton定律Maxwell定律粘弹性变形行为(理想)弹性变形行为Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验、弛豫实验、振荡实验shearstressstep

withcreepintimeintervalt0tot2

creeprecoveryintimeintervalt2tot4

elasticreformation

remainingdeformation(viscousportion)4.3蠕变实验(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液体固体(理想)粘性流动行为粘弹性流动行为Newton定律Maxwell定律粘弹性变形行为(理想)弹性变形行为Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验、弛豫实验、振荡实验shearstrainstep(sheardeformationstep)

with

stressrelaxation

intimeintervalt2tot3

4.4弛豫实验(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液体固体(理想)粘性流动行为粘弹性流动行为Newton定律Maxwell定律粘弹性变形行为(理想)弹性变形行为Kelvin/Voigt定律Hook定律流动/粘度曲线蠕变实验、弛豫实验、振荡实验OscillatoryTests:Basics(1)

Two-Plate-ModelIdealelasticBehaviorofatotallystiffsample

(e.g.stone,orsteel)noshiftbetween

thesinecurvesof

shearstressandsheardeformation:thecurvesofand

areinphase4.5振荡实验(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（衰减或损耗因子）

asquotientoftheviscousandelasticportionsOscillatoryTests:Basics(3)VectordiagramG*[Pa]

complexshearmodulus

复（数）剪切模量elasticitylawofHooke(foroscillation):G‘[Pa]storagemodulus,elasticportion

储能模量弹性模量G''[Pa]lossmodulus,viscousportion

耗能模量粘性模量

oftheviscoelasticbehaviorOscillatoryTests:Basics(4)Vectordiagramh*[Pas]

complexshearviscosity

复（数）剪切粘度h‘[Pas