流變學(xué)基礎(chǔ)及應(yīng)用課件

流變學(xué)基礎(chǔ)及應(yīng)用

SMZHUHH

Welcome使用牙膏時(shí)擠出要容易，擠出后要求挺括，在牙刷上不能下陷，刷牙時(shí)又要輕松，這就是要求牙膏遇剪切時(shí)粘度迅速下降，而靜止時(shí)又要具備一定的屈服應(yīng)力，以保持堅(jiān)挺。牙膏—一個(gè)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(jì)及流變儀簡介 3.穩(wěn)態(tài)流變學(xué) 4.動(dòng)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(cè)試 4.4弛豫測(cè)試 4.5振蕩測(cè)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(dòng)和變形的科學(xué)

Rheology=thescienceofdeformationandflowofmatter(SocietyOfRheology,SOR)希臘語:rheos=toflow，流動(dòng)流動(dòng)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(dòng)阻力與流動(dòng)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(tái)旋轉(zhuǎn)粘度計(jì)面世（Brookfield）1951首臺(tái)旋轉(zhuǎn)流變儀Rheogoniometer（Weissenberg）自1970年開始，流動(dòng)曲線測(cè)試代替以前的單點(diǎn)測(cè)試自1980年開始，大規(guī)模使用數(shù)控和計(jì)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(gè)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(shí)，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(shí)，產(chǎn)品質(zhì)量就下降。這是因?yàn)樗褂玫哪＞呤前磭庠系牧髯冃阅茉O(shè)計(jì)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(duì)模具進(jìn)行完善修改，但也只是憑經(jīng)驗(yàn)做機(jī)械上的改動(dòng)，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(dòng)及變形行為粘性（viscous）彈性（elastic）粘彈性（viscoelastic）流體（流動(dòng)行為）Newton定律固體（變形行為）Hooke定律粘彈性流體（流動(dòng)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(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)弛豫實(shí)驗(yàn)振蕩實(shí)驗(yàn)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(dòng)態(tài)流變學(xué)SimpleTestMethods鏟刀試驗(yàn)（troweltest）

-高粘流體：“稠”

-低粘流體：“稀”手指試驗(yàn)（fingertest）

-粘稠：“長”

-稀薄：“短”2流變行為的研究工具—粘度計(jì)及流變儀定性！

簡單測(cè)試Bostwick稠度計(jì)（Consistometer）1samplecontainer,max.100ml2gate,tobeopenedbyaspring3scaledflowpath測(cè)定流體（如番茄醬等）在一定時(shí)間內(nèi)流過的長度schematicpresentationofa

BOSTWICK-constistometer

粘度計(jì)Falling-BallViscometersDIN53015

ISO12058measuringtube

includingtheballstandthermometerjacket,

fortemp.control

落球粘度計(jì)HAAKEGENEQe.g.forpastesand

paste-likeprintinginksweightprintinginkfallingrodfallingrodviscometer

(Laray)Falling-RodViscometers

落桿粘度計(jì)accordingtoASTMD803andD1545checkmarkGasbubblerisesafter

turningthetube.

Viscosityevaluation

bycomparison

toasetoftubes

氣泡粘度計(jì)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(jì)

Stormer粘度計(jì)Preset:

constanttorque

(shearstress)appliedbyafree

fallingweight(ingrams)Result:rotationalspeed

ofthemeasuringsystemKrebsmeasuringsystem("Paddle")

asarelativemeasuringsystem

designationinKrebsUnits,KU

Brookfield

粘度計(jì)spindlesas

relativemeasuringsystems:cylindersdiskspinsT-bar

旋轉(zhuǎn)流變儀—絕對(duì)測(cè)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(dòng)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(duì)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(dòng)行為液體固體(理想)粘性流動(dòng)行為粘彈性流動(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)

基本概念：剪切應(yīng)力、剪切速率、粘度……牛頓流體的流動(dòng)行為

非牛頓流體（剪切依賴型）的流動(dòng)行為：剪切稀釋、剪切增稠、屈服值……

時(shí)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(shí)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(shí)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(dòng)行為（IdealviscousFlowBehavior）或稱：Newtonian流動(dòng)行為（牛頓流體）flowcurves（流動(dòng)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(dòng)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(dòng)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(diǎn)(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(shí)間依賴流動(dòng)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(dòng)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(dòng)態(tài)流變學(xué)—變形行為液體固體(理想)粘性流動(dòng)行為粘彈性流動(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)液體固體(理想)粘性流動(dòng)行為粘彈性流動(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)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(dòng)行為粘彈性流動(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)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(yùn)動(dòng)或形變時(shí)，不僅在其形變方向產(chǎn)生應(yīng)力，而且通常會(huì)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(duì)數(shù)坐標(biāo)上可以發(fā)現(xiàn)一個(gè)平臺(tái)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(duì)數(shù)坐標(biāo)上也可以發(fā)現(xiàn)一個(gè)平臺(tái)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(dòng)行為粘彈性流動(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)shearstressstep

withcreepintimeintervalt0tot2

creeprecoveryintimeintervalt2tot4

elasticreformation

remainingdeformation(viscousportion)4.3蠕變實(shí)驗(yàn)(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(dòng)行為粘彈性流動(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)shearstrainstep(sheardeformationstep)

with

stressrelaxation

intimeintervalt2tot3

4.4弛豫實(shí)驗(yàn)(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(dòng)行為粘彈性流動(dòng)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(dòng)/粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)OscillatoryTests:Basics(1)

Two-Plate-ModelIdealelasticBehaviorofatotallystiffsample

(e.g.stone,orsteel)noshiftbetween

thesinecurvesof

shearstressandsheardeformation:thecurvesofand

areinphase4.5振蕩實(shí)驗(yàn)(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(chǔ)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