流变学基础及应用

1、SMZHUHHWelcome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。 牙膏牙膏一个典型的流变学问题提提 纲纲I. 流变学基础1流变学定义及发展历史流变学定义及发展历史2. 粘度计及流变仪简介粘度计及流变仪简介3. 稳态流变学稳态流变学4. 动态流变学动态流变学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. Physica MCR300流变仪简介III. Physica MCR300流变仪应用演示I. 流变学基础流变学基础The pe

2、rson in the picture: Thomas G. Mezger, Rheologist of Anton-Paar1 流变学及其发展历史流变学及其发展历史 什么是流变学？ 流变学：研究物质流动流动和变形的科学 Rheology = the science of deformation and flow of matter (Society Of Rheology, SOR)流流 动动 行行 为为www.physica.de变变 形形 行行 为为古代 “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

3、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 流变学的发展历史流变学的发展历史 中国的中国的流变学流变学 “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

4、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。” 江体乾江体乾粘性（viscous）弹性（elastic）粘弹性（viscoelastic）流体（流动行为）固体（变形行为）粘弹性流体（流动行为）粘弹性固体（变形行为） 流变学的研究内容流变学的研究内容 流变学的研究范围及方法流变学的研究范围及方法液液 体体固固 体体(理想理想)粘性流体行为粘性流体行为 粘弹性流动行为粘弹

5、性流动行为粘弹性变形行为粘弹性变形行为(弹性弹性)变形行为变形行为Newton定律定律Maxwell定律定律Kelvin/Voigt定律定律Hook定律定律流动流动/粘度曲线粘度曲线蠕变实验蠕变实验 弛豫实验弛豫实验 振荡实验振荡实验物质状态物质状态性能表现性能表现依据原理依据原理研究方法研究方法稳态流变学稳态流变学动态流变学动态流变学Simple Test Methods铲刀试验（铲刀试验（trowel test） - 高粘流体：“稠” - 低粘流体：“稀”手指试验（手指试验（finger testfinger test） - 粘稠：“长” - 稀薄：“短”2 流变行为的研究工具流变行为的研

6、究工具粘度计及流变仪粘度计及流变仪定性！定性！ 简单测试简单测试Bostwick稠度计稠度计（Consistometer）1 sample container, max. 100 ml2 gate, to be opened by a spring3 scaled flow path测定流体（如番茄酱等）在一定时间内流过的长度测定流体（如番茄酱等）在一定时间内流过的长度schematic presentation of a BOSTWICK-constistometer 粘度计粘度计Falling-Ball ViscometersDIN 53015ISO 12058measuring tube

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

8、sity evaluationby comparison to a set of tubes 气泡气泡粘度计粘度计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 玻璃玻璃毛细管粘度计毛细管粘度计 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 旋转流变仪旋转流变仪绝对测量系统绝对测量系统圆筒状转子（Cylinder）not recommendedfor pastes(air bubbles)锥板转子（Cone-Plate）with dispersionsonly useful forparticlesunder 5m平行板（Parallel-plates）useful for gels and pastes旋转及振荡流变仪（rotational and oscillatory rheometers）according to DIN

11、 53019 and ISO 3219 HAAKE旋转流变仪旋转流变仪HAAKE Exten CaBer1HAAKE RheoScopeHAAKE RheoStress1HAAKE RheoStress600HAAKE RotoVisco1 TA旋转流变仪旋转流变仪AR500AR1000AR2000ARESARES-1sARES-rdaARES-rfs Bohlin旋转流变仪旋转流变仪BohlinCVOBohlinC-VORBohlinGeminiBohlinV88 Physica旋转流变仪旋转流变仪RheolabMC1SmartPaveMCR300、500MCR301、501ACS16/32

12、 毛细管流变仪毛细管流变仪LrPr234rQrQPLrrr83hPoiseuille-Hagen定律毛细管流变学的基础!P2R 毛细管流变仪毛细管流变仪HAAKE RheoCap S20HAAKE RheoCap T1000RH7D & RH10DRH2100/2200 毛细管流变仪的功能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！.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

13、(Pa.s)RelaxationCoatingFree surfaceMixingExtrusion Injection moulding 聚合物加工过程对应的剪切速率聚合物加工过程对应的剪切速率Log hLog POWER-LAWPROCESSINGRANGE103 s-1101 s-1旋转流变仪毛细管流变仪3 稳态流变学稳态流变学流动行为流动行为液液 体体固 体( (理想理想) )粘性流动行为粘性流动行为粘弹性流动行为粘弹性流动行为Newton定律定律Maxwell 定律定律粘弹性变形行为粘弹性变形行为( (理想理想) ) 弹性变形行弹性变形行为为Kelvin/Voigt 定律定律Hook

14、 定律定律流动流动/ /粘度曲线粘度曲线蠕变实验、弛豫实验、振荡实验蠕变实验、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Shear stressPamNAF2 Shear rate 剪切应力及剪切速率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- - )(Strain应变单位长度的伸长constantmmhv d dt单位时间的应变，也称为“剪切梯度”、“速度梯度”、“应变率”、“变形率”）Typical Shear Rate

15、RangesProcessShear 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:

16、 Sedimentation 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 seal

17、ing PVC 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 cy

18、linder1 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 以前所用单位：厘泊1 cP = 1 mPas(1643 1727) 粘度的定义粘度的定义Pas 1/sPa 牛顿流体（Newtonian Fluid）:粘度不受剪切速率的影响，为恒定值。如，水、矿物油等

19、 非牛顿流体（Non-Newtonian Fluid）：粘度随时间的变化而变化。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 ra

20、tes of 10 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受控剪切应

21、力 理想粘性流动行为（理想粘性流动行为（Idealviscous Flow Behavior）或称：Newtonian 流动行为（牛顿流体）flow curves（流动曲线）viscosity curves（粘度曲线）Rotation CSRTest presettingResultraw dataspeed n 1/mintorque M mNmrheological parametersshear rate 1/sshear stress PaRotation CSSTest settingResultraw datatorque M mNmspeed n 1/minrheological

22、 parametersshear 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/mi

23、ndeflection angle , , rad viscosity shear modulusPaG/G Pas/ h h h h Flow Behavior (linear scales)flow curves viscosity curvesyield point1 idealviscous (Newtonian)（牛顿流体）2 shear-thinning (pseudoplastic)（非牛顿流体：剪切稀释型）3 shear-thickening (dilatant)（非牛顿流体：胀凝型）4 without yield point（非牛顿流体：不具有屈服值）5 with yield

24、 point（非牛顿流体：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 h01

25、0203040506080Pa 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 h10-510-410-310-2100

26、Pa 1001011021/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（剪切稀释）- pseudoplastic（假塑性） 剪切稀释剪切稀释（Shear-Thinning）流动行为流动行为flo

27、w curveviscosity 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

28、 Decrease 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

29、 particles. 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 Be

30、haviorEmulsionThe 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

31、)(aqueous 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 h0501001502002

32、50300Pa 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 Flo

33、w Behavior 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

34、 10-1100Pash 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 visco

35、elastic 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 Po

36、lymerslow-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 methylc

37、ellulose 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

38、 shear load: the rod inclines solidification of the slowly liquid due to shear-thickening flow behavior 剪切增稠剪切增稠（Shear-Thichening）流动行为流动行为Shear-Thickening Flow Behaviorflow curve viscosity curve - shear-thickening（剪切增稠） - dilatant（胀凝型）Shear-Thickening Flow BehaviorSuspensionc . solid concentrationsh

39、ear-thickening 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 susp

40、ensions(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 to

41、o low softener amounthViscositylinear scales logarithmic scalesyield point as limiting value of the shear stress 屈服值（屈服值（Yield Value）也称：屈服点(Yield point)屈服应力(Yield stress)Flow curve with Yield Point (lin/lin)0500 1000 1500 2000 2500 3000Pa 02004006001,0001/sShear Rate .ketchupShear StressFlow curve w

42、ith Yield 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-Bu

43、lkleytau0 = 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

44、and Viscosity 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 viscosit

45、yhViscosityFlow 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-thinnin

46、g)3: range of the infinite-shear viscosity 0h h h hSometimes cats are very curiousSometimes cats are very stupid 时间依赖流动行为（时间依赖流动行为（ Time-Dependent Flow Behavior ）Step Test: Thixotropy（触变性）（触变性）presettingmeasuring resultas rotational test with 3 intervalslow-shear conditionshigh-shear conditionslow-s

47、hear conditionsstate of reststructure decompositionstructure regeneration触变性用来描述材料的结构的破坏与恢复的过程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 tcoati

48、ng 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 are

49、a 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 steadi

50、ly decreasing or increasing viscosity, respectivelygel formation and curingpresetting: constant shear conditions (shear rate or shear stress)result: viscosity / temperature-curve showing a viscosity minimum 温度依赖流动行为（温度依赖流动行为（ Temperature-Dependent Flow Behavior ）Temperature Curve 0.1110100Pash h-100

51、-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 h0,00310,00320,00330,00340,00350,

52、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 50ChViscositymineral oi

53、l at 80ChViscosity3-dimensional diagram4 动态流变学动态流变学变形行为变形行为液液 体体固固 体体( (理想理想) )粘性流动行为粘性流动行为粘弹性流动行为粘弹性流动行为Newton定律定律Maxwell 定律定律粘弹性变形行为粘弹性变形行为( (理想理想) )弹性变形行为弹性变形行为Kelvin/Voigt 定律定律Hook 定律定律流动流动/ /粘度曲线粘度曲线蠕变实验、弛豫实验、振荡实验蠕变实验、弛豫实验、振荡实验液液 体体固固 体体( (理想理想) )粘性流动行为粘性流动行为粘弹性流动行为粘弹性流动行为Newton定律定律Maxwell 定律定律

54、粘弹性变形行为粘弹性变形行为( (理想理想) )弹性变形行为弹性变形行为Kelvin/Voigt 定律定律Hook 定律定律流动流动/ /粘度曲线粘度曲线蠕变实验、弛豫实验、振荡实验蠕变实验、弛豫实验、振荡实验4.1 弹性行为弹性行为(Elastic behavior) 剪切形变剪切形变(Shear Deformation)或应变或应变(Shear Strain) Shear Stress PamNAF2 Shear Deformationor Shear Strain %hs1001mm Robert Hooke (1635 to 1703)Shear modulus 1 GPa = 100

55、0 MPa = 106 kPa = 109 PaE modulus or Youngs modulusPa1PaEFor Tensile Tests applies: = tensile stress = elongation with Poissons ratio 11G2EPa1PaG 弹性行为及剪切模量弹性行为及剪切模量(Elastic behavior & Shear modulus)剪切模量及刚性模量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 体体固固 体体( (理想理想) )粘性流动行为粘性流动行为粘弹性流动行为粘弹性流动行为Newton定律定律Maxwell 定律定律粘弹性变形行为粘弹性变形行为( (理想理想) )弹性变形行为弹性变形行为Kelvin/Voigt 定律定律Hook 定律定律流动流动/ /粘度曲线粘度曲线蠕变实验、弛豫实验、振荡实验蠕变实验、弛豫实验、振荡实验4.2 粘弹性行为粘弹性行为(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. 粘弹性行为粘弹性行为(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 ( / - Diagram)te