流變學(xué)基礎(chǔ)及應(yīng)用

1、SMZHUHHWelcome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。 牙膏牙膏一個(gè)典型的流變學(xué)問題提提 綱綱I. 流變學(xué)基礎(chǔ)1流變學(xué)定義及發(fā)展歷史流變學(xué)定義及發(fā)展歷史2. 粘度計(jì)及流變儀簡介粘度計(jì)及流變儀簡介3. 穩(wěn)態(tài)流變學(xué)穩(wěn)態(tài)流變學(xué)4. 動態(tài)流變學(xué)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. Physica MCR300流變儀簡介III. Physica MCR300流變儀應(yīng)用演示I. 流變學(xué)基礎(chǔ)流變學(xué)基礎(chǔ)The pe

2、rson in the picture: Thomas G. Mezger, Rheologist of Anton-Paar1 流變學(xué)及其發(fā)展歷史流變學(xué)及其發(fā)展歷史 什么是流變學(xué)？ 流變學(xué)：研究物質(zhì)流動流動和變形的科學(xué) Rheology = the science of deformation and flow of matter (Society Of Rheology, SOR)流流 動動 行行 為為www.physica.de變變 形形 行行 為為古代 “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

3、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(jì)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(diǎn)測試自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)展歷史流變學(xué)的發(fā)展歷史 中國的中國的流變學(xué)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

4、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，并未考慮到粒子的流變性?！?江體乾江體乾粘性（viscous）彈性（elastic）粘彈性（viscoelastic）流體（流動行為）固體（變形行為）粘彈性流體（流動行為）粘彈性固體（變形行為） 流變學(xué)的研究內(nèi)容流變學(xué)的研究內(nèi)容 流變學(xué)的研究范圍及方法流變學(xué)的研究范圍及方法液液 體體固固 體體(理想理想)粘性流體行為粘性流體行為 粘彈性流動行為粘彈

5、性流動行為粘彈性變形行為粘彈性變形行為(彈性彈性)變形行為變形行為Newton定律定律Maxwell定律定律Kelvin/Voigt定律定律Hook定律定律流動流動/粘度曲線粘度曲線蠕變實(shí)驗(yàn)蠕變實(shí)驗(yàn) 弛豫實(shí)驗(yàn)弛豫實(shí)驗(yàn) 振蕩實(shí)驗(yàn)振蕩實(shí)驗(yàn)物質(zhì)狀態(tài)物質(zhì)狀態(tài)性能表現(xiàn)性能表現(xiàn)依據(jù)原理依據(jù)原理研究方法研究方法穩(wěn)態(tài)流變學(xué)穩(wěn)態(tài)流變學(xué)動態(tài)流變學(xué)動態(tài)流變學(xué)Simple Test Methods鏟刀試驗(yàn)（鏟刀試驗(yàn)（trowel test） - 高粘流體：“稠” - 低粘流體：“稀”手指試驗(yàn)（手指試驗(yàn)（finger testfinger test） - 粘稠：“長” - 稀?。骸岸獭? 流變行為的研究工具流變行為的研

6、究工具粘度計(jì)及流變儀粘度計(jì)及流變儀定性！定性！ 簡單測試簡單測試Bostwick稠度計(jì)稠度計(jì)（Consistometer）1 sample container, max. 100 ml2 gate, to be opened by a spring3 scaled flow path測定流體（如番茄醬等）在一定時(shí)間內(nèi)流過的長度測定流體（如番茄醬等）在一定時(shí)間內(nèi)流過的長度schematic presentation of a BOSTWICK-constistometer 粘度計(jì)粘度計(jì)Falling-Ball ViscometersDIN 53015ISO 12058measuring tube

7、including the ballstandthermometerjacket,for temp. control 落球落球粘度計(jì)粘度計(jì)HAAKEGENEQe.g. for pastes andpaste-like printing inksweightprinting inkfalling rodfalling rod viscometer(Laray)Falling-Rod Viscometers 落桿落桿粘度計(jì)粘度計(jì)according to ASTM D803 and D1545check markGas bubble rises afterturning the tube.Visco

8、sity evaluationby comparison to a set of tubes 氣泡氣泡粘度計(jì)粘度計(jì)Bubble ViscometersWater-Clock (Klepsdra)for time measurements since 3500 years in Egypt e.g. 5 l corresponds to 6 min flow time 流杯流杯Flow Cupsmeasurement of theflow time determination of the kinematic viscosity 流杯流杯Flow CupsISODINFord (ASTM)Zah

9、nEnglerShellDINISO 流杯流杯Capillary Viscometers 玻璃玻璃毛細(xì)管粘度計(jì)毛細(xì)管粘度計(jì) Preset: constant torque(shear stress) applied by a freefalling weight (in grams)Result:rotational speed of the measuring systemKrebs measuring system (Paddle)as a relative measuring systemdesignation in Krebs Units, KU spindles as relativ

10、e measuring systems:- cylinders- disks- pins- T-bar 旋轉(zhuǎn)流變儀旋轉(zhuǎn)流變儀絕對測量系統(tǒng)絕對測量系統(tǒng)圓筒狀轉(zhuǎn)子（Cylinder）not recommendedfor pastes(air bubbles)錐板轉(zhuǎn)子（Cone-Plate）with dispersionsonly useful forparticlesunder 5m平行板（Parallel-plates）useful for gels and pastes旋轉(zhuǎn)及振蕩流變儀（rotational and oscillatory rheometers）according to DIN

11、 53019 and ISO 3219 HAAKE旋轉(zhuǎn)流變儀旋轉(zhuǎn)流變儀HAAKE Exten CaBer1HAAKE RheoScopeHAAKE RheoStress1HAAKE RheoStress600HAAKE RotoVisco1 TA旋轉(zhuǎn)流變儀旋轉(zhuǎn)流變儀AR500AR1000AR2000ARESARES-1sARES-rdaARES-rfs Bohlin旋轉(zhuǎn)流變儀旋轉(zhuǎn)流變儀BohlinCVOBohlinC-VORBohlinGeminiBohlinV88 Physica旋轉(zhuǎn)流變儀旋轉(zhuǎn)流變儀RheolabMC1SmartPaveMCR300、500MCR301、501ACS16/32

12、 毛細(xì)管流變儀毛細(xì)管流變儀LrPr234rQrQPLrrr83hPoiseuille-Hagen定律毛細(xì)管流變學(xué)的基礎(chǔ)!P2R 毛細(xì)管流變儀毛細(xì)管流變儀HAAKE RheoCap S20HAAKE RheoCap T1000RH7D & RH10DRH2100/2200 毛細(xì)管流變儀的功能毛細(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！.1.E+001.E+021.E+041.E+061.E+081.E-051.E-031.E-011.E+011.E+031.E+05Shear rate (s-1)Viscosity (Pa.

13、s)RelaxationCoatingFree surfaceMixingExtrusion Injection moulding 聚合物加工過程對應(yīng)的剪切速率聚合物加工過程對應(yīng)的剪切速率Log hLog POWER-LAWPROCESSINGRANGE103 s-1101 s-1旋轉(zhuǎn)流變儀毛細(xì)管流變儀3 穩(wěn)態(tài)流變學(xué)穩(wěn)態(tài)流變學(xué)流動行為流動行為液液 體體固 體( (理想理想) )粘性流動行為粘性流動行為粘彈性流動行為粘彈性流動行為Newton定律定律Maxwell 定律定律粘彈性變形行為粘彈性變形行為( (理想理想) ) 彈性變形行彈性變形行為為Kelvin/Voigt 定律定律Hook 定律定

14、律流動流動/ /粘度曲線粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)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(shí)間依賴型：觸變性、震凝性 溫度依賴型Shear stressPamNAF2 Shear rate 剪切應(yīng)力及剪切速率剪切應(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- - )(Strain應(yīng)變單位長度的伸長constantmmhv d dt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”）Typical Shear Rate Rang

15、esProcessShear Rate (1/s)sedimentation 0,001 to 0,01surface levelling0,01 to 0,1sagging0,01 to 1dip coating1 to 100pipe flow, pumping, filling into containers1 to 10 000coating, painting, brushing100 to 10 000spraying1 000 to 10 000(high-speed) coating, blade coating100 000 to 1 mio.Application: Sed

16、imentation of Dispersionsin the beginningherbs in salad dressingafter 15minApplication: Levelling and Saggingof a Coating200 m0.5 m/s14s 2500sm102m5 . 0hv-Calculation of the shear rateApplication: Coating, Painting, Brushingcar body degreasing & phosphatizing electro dip coatingPVC seam sealing PVC

17、underbody sprayingprimer and filler top coat and clear coat cavity conservationa) Plastisols: seam sealing, under body spraying, cavity conservationb) Primerc) Coatings: filler, base coat, top coat, clear coatApplication: Offset Printing Inksinkcontainerplate cylinderrubber cylinderrubber cylinder1

18、ductor2 film roller3 transfer roller4 rubber5 cylinder to apply the paint6 7 clammy ductor8 clammy rubber9 paper web（剪切）粘度（(shear) viscosity）：1 Pas = 1000 mPas1 MPas = 1000 kPas = 1 Mio. Pas 以前所用單位：厘泊1 cP = 1 mPas(1643 1727) 粘度的定義粘度的定義Pas 1/sPa 牛頓流體（Newtonian Fluid）: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（N

19、on-Newtonian Fluid）：粘度隨時(shí)間的變化而變化。如，聚合物溶液等Viscosity ValuesMaterialsShear viscosity h h Gases / air0,01 to 0,02 / 0,018 mPasWater at 20C / at 0C / at 40C1,00 / 1,79 / 0,65 mPasMilk, coffee cream2 to 10 mPasOlive oilapprox. 100 mPasGlycerine1480 mPasPolymer melts (T=+100 to +200C and at shear rates of 1

20、0 to 1000 1/s)10 to 10 000 PasPolymer melts (zero-shear viscosity)1 kPas to 1MPasBitumen (T = +80 / +60 / +40 / +20 / +0C)200 Pas / 1 kPas / 20 kPas / 0,5 MPas / 1 MPasPresettings for Flow Curvesshear rate rampCSR: controlled shear rate受控剪切速率shear stress rampCSS: controlled shear stress受控剪切應(yīng)力 理想粘性流動

21、行為（理想粘性流動行為（Idealviscous Flow Behavior）或稱：Newtonian 流動行為（牛頓流體）flow curves（流動曲線）viscosity curves（粘度曲線）Rotation CSRTest presettingResultraw dataspeed n 1/mintorque M mNmrheological parametersshear rate 1/sshear stress PaRotation CSSTest settingResultraw datatorque M mNmspeed n 1/minrheological paramet

22、ersshear stress Pashear rate 1/sRaw Data and Rheological Parameters Summary: Measuring Parametersraw data, dependent on the measuring systemcalculated values,independent of the measuring systemshear stress shear rate shear deformation PaMCSS s/nCSR1 %orCSD1 torque M Nmrotational speed n 1/mindeflect

23、ion angle , , rad viscosity shear modulusPaG/G Pas/ h h h h Flow Behavior (linear scales)flow curves viscosity curvesyield point1 idealviscous (Newtonian)（牛頓流體）2 shear-thinning (pseudoplastic)（非牛頓流體：剪切稀釋型）3 shear-thickening (dilatant)（非牛頓流體：脹凝型）4 without yield point（非牛頓流體：不具有屈服值）5 with yield point（非

24、牛頓流體：具有屈服值）Flow Behavior (log. scales)1 idealviscous (Newtonian)2 shear-thinning (pseudoplastic)3 shear-thickening (dilatant)4 with zero-shear viscosity5 without zero-shear viscosity flow curvesviscosity curveszero-shear viscosityyield pointIdealviscous Flow Behavior 010203040506080mPash h0102030405

25、06080Pa 020040060010001/sShear Rate .mineral oil at 50CCC 27hViscosityShear StressIdealviscous Flow Behavior 100101Pash h10-310-210-1100101103Pa 10-310-210-11001011021/sShear Rate .silicone oilMK 23 (50mm,2)hViscosityShear StressIdealviscous Flow Behavior10-410-310-2Pash h10-510-410-310-2100Pa 10010

26、11021/sShear Rate .waterDG 42hViscosityShear StressComparison of Idealviscous and Shear-Thinning Flow Behavior00.511.52Pash h01002003004005001/sShear Rate .idealviscoushViscosityshear-thinninghViscosity1 1h h2 2h h- shear-thinning（剪切稀釋）- pseudoplastic（假塑性） 剪切稀釋剪切稀釋（Shear-Thinning）流動行為流動行為flow curvev

27、iscosity curve 2211 h h h hShear-Thinning Flow Behaviorpolymer moleculesstate at rest:coiled, entangledstate under high shear load:deformation in shear directiondisentangled,consequence: shear-thinning flow behaviorShear-Thinning Flow BehaviorMaterial At Rest: During Shearing: High Viscosity Decreas

28、e in ViscositySuspension withneedle-shaped orplatelet-shapedparticlesThe particles are The particles are suspended randomly orientated.(if there are no interaction forces).AgglomeratedParticlesThe small primary The agglomerates areparticles form disintegrated into primaryagglomerates (in the particl

29、es. The dispersionform of larger secondary liquid is no longer boundparticles). They also and again free to flow.surround a part of thedispersion liquid and immobilize it.Shear-Thinning Flow BehaviorMaterial At Rest: During Shearing: High Viscosity Decrease in ViscosityShear-thinning Flow BehaviorEm

30、ulsionThe dispersed droplets The droplets are deformedshow the shape of and take on the shape ofspheres. ellipses.Material At Rest: During Shearing: High Viscosity Decrease in ViscosityShear-Thinning Flow Behavior Pash h050100150200Pa 02004006001,0001/swall paper paste (lin)(aqueou

31、s methylcellulose solution)hViscosityShear StressShear Rate .Shear-Thinning Flow Behavior0.81Pash h050100150200250300Pa 02004006001,0001/sShear Rate .O/W EmulsionhViscosityShear StressO/W Emulsion with 10% waterhViscosityShear Stress0.81Pash h050100150200250300Pa

32、02004006001,0001/sShear Rate .O/W EmulsionhViscosityShear StressO/W Emulsion with 10% waterhViscosityShear Stress0.81Pash h050100150200250300Pa 020040060010001/sShear Rate .O/W emulsionhViscosityShear StressO/W emulsion with 10% waterhViscosityShear StressShear-Thinning Flow Behavi

33、or 00.00.250.3Pash h020040060010001/sShear Rate .gravure printing ink, binder 1hViscositygravure printing ink, binder 2hViscositygravure printing ink, binder 3hViscosityAll three samples have the samepigment concentration and showthe same flow cup time.Shear-Thinning Flow Behavior 10-1100

34、Pash h10-310-210-1100101102103Pa 10-310-210-11001011021031/sShear Rate .wall paper paste (log)(aqueous methylcellulose solution)hViscosityShear Stressh0Shear-thinning1) Orientation of the macromolecules under shear load disentanglements here, the h value decreases 2) Re-coilings due to viscoelastic

35、behavior re-entanglements here, the h value increases Explanation of the Zero-Shear Viscosity （零剪切粘度）（零剪切粘度）of PolymersSuperposition of two processes:Result: In the low-shear range there is no change in the total viscosity value, which is referred to as the value.0h hViscosity Function of Polymerslo

36、w-shear range flow range high-shear range with shear-thinning zero-shear viscosity: flow behavior: infinite-shear viscosity: h hh h 00lim h hh h h hh h limShear-Thinning Flow Behavior 10-210-1100101Pash h10-210-11001021/sShear Rate .mineral oilhViscositywall paper paste (log)(aqueous methylcellulose

37、 solution)hViscositypolymer solutionhViscosityDependence of viscosity on concentration with diluted (c c*).Zero Shear Viscositylow shearviscosityZero - Shear Viscosityviscosity increase of polymer solutions with increasing molar massincreasing molar massof a polymerat low shear load: at high shear l

38、oad: the rod inclines solidification of the slowly liquid due to shear-thickening flow behavior 剪切增稠剪切增稠（Shear-Thichening）流動行為流動行為Shear-Thickening Flow Behaviorflow curve viscosity curve - shear-thickening（剪切增稠） - dilatant（脹凝型）Shear-Thickening Flow BehaviorSuspensionc . solid concentrationshear-thic

39、kening of highly concentrated suspensionsunder high shear load 1s- - cShear-Thickening Flow Behavior 00.0Pash h050100150200250300400Pa 020040060010001/sShear Rate .ceramic suspensionhViscosityShear StressShear-Thickening Flow Behaviorcomparison of aqueous chalkstone suspensions(

40、1) cube-shaped particles (2) spherical particlesWith both suspensions having the same solid concentration for (2) shear-thickening flow behavior occurs at higher shear rates.Shear-Thickening Flow Behavior 0500 1000 1500 2000 2500 3000 4000Pash h01002003004005001/sShear Rate .plastisolwith too low so

41、ftener amounthViscositylinear scales logarithmic scalesyield point as limiting value of the shear stress 屈服值（屈服值（Yield Value）也稱：屈服點(diǎn)(Yield point)屈服應(yīng)力(Yield stress)Flow curve with Yield Point (lin/lin)0500 1000 1500 2000 2500 3000Pa 02004006001,0001/sShear Rate .ketchupShear StressFlow curve with Yiel

42、d Point (log/log)101102103104Pa 1001011021031/sShear Rate .ketchupShear StressFlow curves with Yield Point (lin/lin)Shear Rate .02004006008001,200Pa 0501001/sCream 1Shear StressCream 2Shear StressCream 1 Herschel-Bulkleytau0 = 705.01 Pa; b = 11.503; p = 0.84742Shear StressCream 2 Herschel-Bulkleytau

43、0 = 31.224 Pa; b = 4.7648; p = 0.94538Shear Stress02004006008001,200Pa 0501001/scream 1Shear Stresscream 2Shear Stresscream 1 Herschel-BulkleyYield Point: 705.0 PaShear Stresscream 2 Herschel-BulkleyYield Point: 31.2 PaShear Stressanalysis using an approximation function for flow curvesFlow and Visc

44、osity Curves (log/log)100101102103Pash h10-310-210-1100101103Pa 10-210-11001011021/sShear Rate .primerhViscosityShear Stresstop coatinghViscosityShear StressViscosity Curves (log/log)100101102Pash h10-210-11001011021/sShear Rate .without zero-shear viscosityhViscositywith zero-shear viscosityhViscos

45、ityFlow and Viscosity Curves1: idealviscous (Newtonian)2: shear-thinning (pseudoplastic)3: shear-thickening (dilatant)SummaryFlow and Viscosity curves4: without yield point5: with yield pointSummaryviscosity function of polymers1: range of the zero-shear viscosity2: flow range (shear-thinning)3: ran

46、ge of the infinite-shear viscosity 0h h h hSometimes cats are very curiousSometimes cats are very stupid 時(shí)間依賴流動行為（時(shí)間依賴流動行為（ Time-Dependent Flow Behavior ）Step Test: Thixotropy（觸變性）（觸變性）presettingmeasuring resultas rotational test with 3 intervals1.low-shear conditions2.high-shear conditions3.low-she

47、ar conditions1.state of rest2.structure decomposition3.structure regeneration觸變性用來描述材料的結(jié)構(gòu)的破壞與恢復(fù)的過程test conditions:1. interval: = 0.1 1/s2. interval: = 100 1/s3. interval: = 0.1 1/sTime-Dependent Structure Decomposition and Regeneration (lin/log) . . .10-1100101102Pash h0100200300400500600700sTime tc

48、oating KhViscositycoating MhViscosityTime-Dependent Flow Behaviorpresetting: shear rate profiletest in 3 intervals: upward ramp, hold time, downward rampanalysis: hysteresis areadisadvantages: testing in a non-stationary state, no measurement of the structure regenerationevaluation of the hysteresis

49、 area in between the flow curves as a measure of the structure decomposition during the holding timeThixotropy Test, conventionalsoftening and melting, or solidification and crystallizationpresetting: constant shear conditions (shear rate or shear stress)result: viscosity / temperature-curve with st

50、eadily decreasing or increasing viscosity, respectivelygel formation and curingpresetting: constant shear conditions (shear rate or shear stress)result: viscosity / temperature-curve showing a viscosity minimum 溫度依賴流動行為（溫度依賴流動行為（ Temperature-Dependent Flow Behavior ）Temperature Curve 0.1110100Pash h

51、-100-50050100CTemperature Tsilicone oilhViscosityTemperature Curve and Analysis according to Arrhenius 10100mPash h10152025303540CTemperature Tcrude oilArrhenius Analysis high TArrhenius Analysis low TTemperature Curve and Analysis according to Arrhenius (1/T)10100mPash h0,00310,00320,00330,00340,00

52、350,00361/K1/Temperature 1/Tcrude oilArrhenius Analysis high TArrhenius Analysis low TTemperature Curve 0246810Pash h2025303540CTemperature TchocolatehViscosityTemperature-Dependent Viscosity Curves (3D)00.10.2Pash h05001,0001/s .050100CTmineral oil at 23ChViscositymineral oil at 50ChViscosityminera

53、l oil at 80ChViscosity3-dimensional diagram4 動態(tài)流變學(xué)動態(tài)流變學(xué)變形行為變形行為液液 體體固固 體體( (理想理想) )粘性流動行為粘性流動行為粘彈性流動行為粘彈性流動行為Newton定律定律Maxwell 定律定律粘彈性變形行為粘彈性變形行為( (理想理想) )彈性變形行為彈性變形行為Kelvin/Voigt 定律定律Hook 定律定律流動流動/ /粘度曲線粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)液液 體體固固 體體( (理想理想) )粘性流動行為粘性流動行為粘彈性流動行為粘彈性流動行為Newton定律定律Maxwell

54、定律定律粘彈性變形行為粘彈性變形行為( (理想理想) )彈性變形行為彈性變形行為Kelvin/Voigt 定律定律Hook 定律定律流動流動/ /粘度曲線粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)4.1 彈性行為彈性行為(Elastic behavior) 剪切形變剪切形變(Shear Deformation)或應(yīng)變或應(yīng)變(Shear Strain) Shear Stress PamNAF2 Shear Deformationor Shear Strain %hs1001mm Robert Hooke (1635 to 1703)Shear modulus 1 GPa =

55、 1000 MPa = 106 kPa = 109 PaE modulus or Youngs modulusPa1PaEFor Tensile Tests applies: = tensile stress = elongation with Poissons ratio 11G2EPa1PaG 彈性行為及剪切模量彈性行為及剪切模量(Elastic behavior & Shear modulus)剪切模量及剛性模量Tensile TestTensile Test at the beginning and after the elongation l = l l0, Tensile Stre

56、ss / Elongation Diagram of steel, yield stress S and yield strength S, breaking stress B and elongation at break BPoissons ratio: l.length of the specimend.thickness of the specimenldld00clampspecimenforce Flinear elastic deformation = E plastic deformation,lattice dislocation of crystalsTensile Tes

57、tTensile Test of amorphous, unlinked orsparsely cross-linked polymers or coating filmsTg.glass transition temperaturebrittle fracture at TTgDefinition of Shear Ratea) -dtdttt0101shear rate as time-dependent rate of deformation or strain rate b) dhdv shear rate as velocity gradientexplanation:dtddtdh

58、dsdhdtdsdhdtdsdhdv液液 體體固固 體體( (理想理想) )粘性流動行為粘性流動行為粘彈性流動行為粘彈性流動行為Newton定律定律Maxwell 定律定律粘彈性變形行為粘彈性變形行為( (理想理想) )彈性變形行為彈性變形行為Kelvin/Voigt 定律定律Hook 定律定律流動流動/ /粘度曲線粘度曲線蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)蠕變實(shí)驗(yàn)、弛豫實(shí)驗(yàn)、振蕩實(shí)驗(yàn)4.2 粘彈性行為粘彈性行為(Viscoelastic behavior)tack (showing long strings)e.g. mouth sensationstirring process: Weissen

59、berg effect (rod climbing effect) poor mixing resultextrusion: extrudate swelling e.g. dimension stabilityresult: In many cases the measurement of viscosity only is not sufficient because elastic effects are occuring, resulting in viscoelastic behavior. 粘彈性行為粘彈性行為(Viscoelastic behavior)Viscoelastic

60、Behavior of Polyisobutylene (PIB)die swell when flowing out Weissenberg effect during aof a capillary stirring processViscoelastic Behaviorextrusion of a polystyrene:viscoelastic behavior (extrudate swelling)and melt fracture test temperature T = 190Cdie geometry L/R = 24, R = 1 mmYield Point ( / -