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Introduction to Viscoelasticity

Introduction to Viscoelasticity. All viscous liquids deform continuously under the influence of an applied stress – They exhibit viscous behavior.

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Introduction to Viscoelasticity

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  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 fluid Polymers display VISCOELASTIC properties Viscoelastic fluid Elastic solid

  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 jet of an 8 wt% solution of polyisobutylene in decalin Polymers have both Viscous (liquid) and elastic (solid) characteristics

  5. Measurements of Shear Viscosity • Melt Flow Index • Capillary Rheometer • Coaxial Cylinder Viscometer (Couette) • Cone and Plate Viscometer (Weissenberg rheogoniometer) • Disk-Plate (or parallel plate) viscometer

  6. Weissenberg Effect

  7. Dough Climbing: Weissenberg Effect Other effects: Barus Kaye

  8. What is Rheology? Rheology is the science of flow and deformation of matter Rheology Concepts, Methods, & Applications, A.Y. Malkin and A.I. Isayev; ChemTec Publishing, 2006

  9. 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 temperature De is large, solid behavior, small-liquid behavior.

  10. increasing loading rate Stress Strain

  11. Time and temperature

  12. 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.

  13. Entanglement Molecular Weights, Me, for Various Polymers Me (g/mole) Poly(ethylene) 1,250 Poly(butadiene) 1,700 Poly(vinyl acetate) 6,900 Poly(dimethyl siloxane) 8,100 Poly(styrene) 19,000

  14. Pitch drop experiment • Started in 1927 by University of Queensland Professor Thomas Parnell. • A drop of pitch falls every 9 years Pitch drop experiment apparatus Pitch can be shattered by a hammer

  15. ? 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.

  16. g Constant strain applied s Stress relaxes over time as molecules re-arrange time Stress relaxation: Physical Meaning of the Relaxation Time time

  17. Static Testing of Rubber Vulcanizates • Static tensile tests measure retractive stress at a constant elongation (strain) rate. • Both strain rate and temperature influence the result Note that at common static test conditions, vulcanized elastomers store energy efficiently, with little loss of inputted energy.

  18. 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 rebound • resilience (h/ho) with • temperature T for: • 1. cis-poly(isoprene); • 2. poly(isobutylene); • 3. poly(chloroprene); • 4. poly(methyl methacrylate).

  19. 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 law • Viscous component – Newton’s law • Deformation of polymeric materials  combination of Hooke’s law and Newton’s law.

  20. Hooke’s law & Newton’s Law • The behaviour of linear elastic were given by Hooke’s law: or • The behaviour of linear viscous were given by Newton’s Law: E= Elastic modulus s= Stress e =strain de/dt = strain rate ds/dt = stress rate = viscosity ** This equation only applicable at low strain

  21. 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).

  22. STRESS RELAXATION CREEP Constant strain is applied  the stress relaxes as function of time Constant stress is applied  the strain relaxes as function of time

  23. 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

  24. metal elastomer Viscous liquid

  25. Glassy Leathery Rubbery Viscous Static Modulus of Amorphous PS Polystyrene Stress applied at x and removed at y

  26. Stress Relaxation Test Strain Elastic Viscoelastic Stress Stress Stress Viscous fluid Viscous fluid Viscous fluid 0 Time, t

  27. 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: where Me is the average mol. weight between entanglements • G(t) is defined for shear flow. We can also define a relaxation modulus for extension: stress strain viscosity Gmodulus

  28. Glassy behavior Transition Zone Plateau Zone Terminal Zone (flow region) slope = -1 perse Stress relaxation of an uncrosslinked melt Mc: critical molecular weight above which entanglements exist 3.24

  29. Mechanical Model • Methods 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 law • Viscous 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.

  30. Dynamic Viscosity (dashpot) Shear stress • Lack of slipperiness • Resistance to flow • Interlayer friction SI Unit: Pascal-second Shear rate 1 centi-Poise = milli Pascal-second stress strain viscosity Gmodulus

  31. Ideal Liquid h= viscosity de/dt = strain rate The viscous response is generally time- and rate-dependent.

  32. Ideal Liquid

  33. Ideal (elastic) Solid Hooks Law response is independent of time and the deformation is dependent on the spring constant.

  34. Ideal Solid

  35. Polymer is called visco- elastic because: • Showing both behaviour elastic & viscous behaviour • Instantaneously elastic strain followed by viscous time dependent strain Load released elastic Load added viscous viscous elastic

  36. stress strain viscosity Gmodulus

  37. Maxwell Model

  38. Kelvin Voigt Model

  39. Burger Model

  40. Glassy Leathery Rubbery Viscous Static Modulus of Amorphous PS Polystyrene Stress applied at x and removed at y

  41. Dynamic Mechanical Analysis

  42. Spring Model • g = g0⋅sin (ω⋅t) g0 = maximum strain w = angular velocity Since stress, t, is t = Gg t = Gg0sin(wt) And t and g are in phase

  43. 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

  44. Kelvin-Voigt Model

  45. Courtesy: Dr. Osvaldo Campanella

  46. Purely Viscous Response (Newtonian Liquid) Purely Elastic Response (Hookean Solid) Dynamic Mechanical Testing Response for Classical Extremes  = 90°  = 0° Stress Stress Strain Strain Courtesy: TA Instruments

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