Presentation on theme: "Introduction to Viscoelasticity"— Presentation transcript:
1 Introduction to Viscoelasticity All viscous liquids deform continuously under the influence of an applied stress – They exhibit viscous behavior.Solids deform under an applied stress, but soon reach a position of equilibrium, in which further deformation ceases. If the stress is removed they recover their original shape – They exhibit elastic behavior.Viscoelastic fluids can exhibit both viscosity and elasticity, depending on the conditions.Viscous fluidViscoelastic fluidElastic solidPolymers display VISCOELASTIC properties
2 A Demonstration of Polymer Viscoelasticity Poly(ethylene oxide) in water
3 “Memory” of Previous State Poly(styrene)Tg ~ 100 °C
4 Chapter 5. Viscoelasticity Is “silly putty” a solid or a liquid?Why do some injection molded parts warp?What is the source of the die swell phenomena that is often observed in extrusion processing?Expansion of a jetof an 8 wt% solution ofpolyisobutylene in decalinPolymers have both Viscous (liquid) and elastic (solid) characteristics
7 Dough Climbing: Weissenberg Effect Other effects:BarusKaye
8 Rheology is the science of flow and deformation of matter What is Rheology?Rheology is the science of flow and deformation of matterRheology Concepts, Methods, & Applications, A.Y. Malkin and A.I. Isayev; ChemTec Publishing, 2006
11 Time dependent processes: Viscoelasticity The response of polymeric liquids, such as melts and solutions, to an imposed stress may resemble the behavior of a solid or a liquid, depending on the situation.•Liquid favored by longer time scales & higher temperatures• Solid favored by short time and lower temperatureDe is large, solid behavior, small-liquid behavior.
15 Network of Entanglements There is a direct analogy between chemical crosslinks in rubbers and “physical” crosslinks that are created by the entanglements.The physical entanglements can support stress (for short periods up to a time tT), creating a “transient” network.
16 Entanglement Molecular Weights, Me, for Various Polymers Me (g/mole)Poly(ethylene) 1,250Poly(butadiene) 1,700Poly(vinyl acetate) 6,900Poly(dimethyl siloxane) 8,100Poly(styrene) 19,000
17 Pitch drop experimentStarted in 1927 by University of Queensland Professor Thomas Parnell.A drop of pitch falls every 9 yearsPitch drop experiment apparatusPitch can be shattered by a hammer
18 Viscoelasticity and Stress Relaxation Whereas steady-shear measurements probe material responses under a steady-state condition, creep and stress relaxation monitor material responses as a function of time.Stress relaxation studies the effect of a step-change in strain on stress.?
19 Physical Meaning of the Relaxation Time Constant strain appliedtimesStress relaxes over time as molecules re-arrangetimeStress relaxation:
20 Static Testing of Rubber Vulcanizates Static tensile tests measure retractive stress at a constant elongation (strain) rate.Both strain rate and temperature influence the resultNote that at common static test conditions, vulcanized elastomers store energy efficiently, with little loss of inputted energy.
21 Dynamic Testing of Rubber Vulcanizates: Resilience Resilience tests reflect the ability of an elastomeric compound to store and return energy at a given frequency and temperature.Change of reboundresilience (h/ho) withtemperature T for:1. cis-poly(isoprene);2. poly(isobutylene);3. poly(chloroprene);4. poly(methyl methacrylate).
22 Mathematical models: Hooke and Newton It is difficult to predict the creep and stress relaxation for polymeric materials.It is easier to predict the behaviour of polymeric materials with the assumption it behaves as linear viscoelastic behaviour.Deformation of polymeric materials can be divided to two components:Elastic component – Hooke’s lawViscous component – Newton’s lawDeformation of polymeric materials combination of Hooke’s law and Newton’s law.
23 Hooke’s law & Newton’s Law The behaviour of linear elastic were given by Hooke’s law:orThe behaviour of linear viscous were given by Newton’s Law:E= Elastic moduluss = Stresse = strainde/dt = strain rateds/dt = stress rate= viscosity** This equation only applicable at low strain
24 Viscoelasticity and Stress Relaxation Stress relaxation can be measured by shearing the polymer melt in a viscometer (for example cone-and-plate or parallel plate). If the rotation is suddenly stopped, ie. g=0, the measured stress will not fall to zero instantaneously, but will decay in an exponential manner..Relaxation is slower for Polymer B than for Polymer A, as a result of greater elasticity.These differences may arise from polymer microstructure (molecular weight, branching).
25 STRESS RELAXATIONCREEPConstant strain is applied the stress relaxes as function of timeConstant stress is applied the strain relaxes as function of time
26 Time-dependent behavior of Polymers The response of polymeric liquids, such as melts and solutions, to an imposed stress may under certain conditions resemble the behavior of a solid or a liquid, depending on the situation.Reiner used the biblical expression that “mountains flowed in front of God” to define the DEBORAH number
28 Static Modulus of Amorphous PS GlassyLeatheryRubberyViscousPolystyreneStress applied at xand removed at y
29 Stress Relaxation Test StrainElasticStressStressViscoelasticStressViscous fluidViscous fluidViscous fluidTime, t
30 Stress relaxation Go (or GNo) is the “plateau modulus”: Stress relaxation after a step strain go is the fundamental way in which we define the relaxation modulus:Go (or GNo) is the “plateau modulus”:where Me is the average mol. weight between entanglementsG(t) is defined for shear flow. We can also define a relaxation modulus for extension:stressstrainviscosityGmodulus
31 Stress relaxation of an uncrosslinked melt perseGlassy behaviorTransition ZoneTerminal Zone(flow region)slope = -1Plateau ZoneMc: critical molecular weight above which entanglements exist3.24
33 Mechanical ModelMethods that used to predict the behaviour of visco-elasticity.They consist of a combination of between elastic behaviour and viscous behaviour.Two basic elements that been used in this model:Elastic spring with modulus which follows Hooke’s lawViscous dashpots with viscosity h which follows Newton’s law.The models are used to explain the phenomena creep and stress relaxation of polymers involved with different combination of this two basic elements.
34 Dynamic Viscosity (dashpot) Shear stressLack of slipperinessResistance to flowInterlayer frictionSI Unit: Pascal-secondShear rate1 centi-Poise = milli Pascal-secondstressstrainviscosityGmodulus
35 Ideal Liquid h= viscosity de/dt = strain rate The viscous response is generally time- and rate-dependent.
39 Polymer is called visco- elastic because: Showing both behaviour elastic & viscous behaviourInstantaneously elastic strain followed by viscous time dependent strainLoad releasedelasticLoad addedviscousviscouselastic
46 Spring Model g = g0⋅sin (ω⋅t) g0 = maximum strain w = angular velocity Since stress, t, ist = Ggt = Gg0sin(wt)And t and g are in phase
47 Whenever the strain in a dashpot is at its maximum, the rate of change of the strain is zero ( g = 0).Whenever the strain changes from positive values to negative ones and then passes through zero, the rate of strain change is highest and this leads to the maximum resulting stress.Dashpot Model
53 DMA Viscoelastic Parameters: The Complex, Elastic, & Viscous Stress The stress in a dynamic experiment is referred to as the complex stress *The complex stress can be separated into two components:1) An elastic stress in phase with the strain. ' = *cos' is the degree to which material behaves like an elastic solid.2) A viscous stress in phase with the strain rate. " = *sin" is the degree to which material behaves like an ideal liquid.Phase angle dComplex Stress, ** = ' + i"Courtesy: TA InstrumentsStrain,
54 DMA Viscoelastic Parameters The Complex Modulus: Measure of materials overall resistance to deformation.G* = Stress*/StrainG* = G’ + iG”The Elastic (Storage) Modulus: Measure of elasticity of material. The ability of the material to store energy.G' = (stress*/strain)cosThe Viscous (loss) Modulus:The ability of the material to dissipate energy. Energy lost as heat.G" = (stress*/strain)sinTan Delta:Measure of material damping - such as vibration or sound damping.Tan = G"/G'Courtesy: TA Instruments
55 DMA Viscoelastic Parameters: Damping, tan Dynamic measurement represented as a vectorIt can be seen here that G* = (G’2 +G”2)1/2G"Phase angle G'The tangent of the phase angle is the ratio of the loss modulus to the storage modulus.tan = G"/G'"TAN DELTA" (tan )is a measure of the damping ability of the material.Courtesy: TA Instruments
56 Frequency Sweep: Material Response TransitionRegionRubbery PlateauRegionTerminal RegionGlassy Regionlog G'and G"12Storage Modulus (E' or G')Loss Modulus (E" or G")log Frequency (rad/s or Hz)Courtesy: TA Instruments
57 Viscoelasticity in Uncrosslinked, Amorphous Polymers Logarithmic plots of G’ and G” against angular frequency for uncrosslinked poly(n-octyl methacrylate) at 100°C (above Tg), molecular weight 3.6x106.
58 Dynamic Characteristics of Rubber Compounds Why do E’ and E” vary with frequency and temperature?The extent to which a polymer chains can store/dissipate energy depends on the rate at which the chain can alter its conformation and its entanglements relative to the frequency of the load.Terminal Zone:Period of oscillation is so long that chains can snake through their entanglement constraints and completely rearrange their conformationsPlateau Zone:Strain is accommodated by entropic changes to polymer segments between entanglements, providing good elastic responseTransition Zone:The period of oscillation is becoming too short to allow for complete rearrangement of chain conformation. Enough mobility is present for substantial friction between chain segments.Glassy Zone:No configurational rearrangements occur within the period of oscillation. Stress response to a given strain is high (glass-like solid) and tand is on the order of 0.1
59 Dynamic Temperature Ramp or Step and Hold: Material Response Glassy RegionTransitionRegionRubbery PlateauRegionTerminal RegionLog G' and G"1Loss Modulus (E" or G")Storage Modulus (E' or G')2TemperatureCourtesy: TA Instruments
68 G’storage modulusG’’loss modulusThese data show the difference between the behaviour of un-aged and aged samples of rubber, and were collected in shear mode on the DMTA at 1 Hz. The aged sample has a lower modulus than the un-aged, and is weaker. The loss peak is also much smaller for the aged sample.
73 Sample is strained (pulled, ) rapidly to pre-determined strain () Stress required to maintain this strain over time is measured at constant TStress decreases with time due to molecular relaxation processesRelaxation modulus defined as:Er(t) also a function of temperatureEr(t) = (t)/e0