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Chapter 8. Flow and mechanical properties of polymers. Concepts, coefficients, definitions. Fluid shear: the shear stress on a fluid element is related to the viscosity gradient by

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chapter 8

Chapter 8

Flow and mechanical properties of polymers

chapter 8

concepts coefficients definitions
Concepts, coefficients, definitions
  • Fluid shear: the shear stress on a fluid element is related to the viscosity gradient by
  • Volume change on deformation: some fluids (constant density under shear) and solids (cross-linked elastomers) deform isochorically. Poisson’s ratio, 0 < n < 0.5.
  • Modulus of elasticity (Young’s modulus). The strain in a solid is related to the load by the modulus of elasticity.

chapter 8

concepts coefficients definitions cont d
Concepts, coefficients, definitions, cont’d.
  • Shear modulus: the shear stress of a solid is related to the strain by
  • The elastic and shear moduli are related using the bulk modulus (measures how the solid volume changes with pressure) and Poisson’s ratio. When Poisson’s ratio = 0.5 (perfect elasticity), the tensile modulus is three times the shear modulus.
  • Compliance: the inverse of the elastic modulus.

chapter 8

concepts coefficients definitions cont d1
Concepts, coefficients, definitions, cont’d.
  • Dynamic measurements of solids and fluids yield two coefficients (Young’s modulus used as the example)
  • The dynamic modulus contains a storage (or elastic) component and a loss (or damping) component

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rheology

Rheology

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fluid element under simple shear
Fluid element under simple shear

Newtonian fluid: the coefficient linking shear stress to shear rate is constant over the entire range of the variable. Molecular relaxations are much faster than the time scale of the shear force or shear rate. Steady flows – velocity profile is constant; oscillating flows – fluid responds instantly to forcing function.

chapter 8

non newtonian fluid
Non-Newtonian fluid

Viscosity changes with shear rate. Apparent viscosity is always defined by the relationship between shear stress and shear rate.

Many polymeric fluids are shear-thinning, i.e., their viscosities decrease with shear rate or shear stress.

chapter 8

generalized oswald fluid
Generalized Oswald fluid

Pseudoplastic: shear thinning.

Shear thickening: viscosity increases with shear stress.

Dilatant: shear thickening fluids that contain suspended solids. Solids can become close packed under shear.

Time-dependent: in many polymeric fluids, the response time of the material may be longer than response time of the measurement system, so the viscosity will change with time. Thixotropic: shear thinning with time; antithixotropic: shear thickening with time. Rheopectic: thixotropic materials that can recover original viscosity under low shear.

chapter 8

generalized oswald fluid1
Generalized Oswald fluid
  • Shear rate vs. shear stress with high and low stress limits on viscosity
  • Viscosity vs. shear rate. Zero shear rate, m0, and infinite shear rate, m∞, viscosities.
  • Pseudoplastic: shear thinning.
  • Shear thickening: viscosity increases with shear stress.
  • Dilatant: shear thickening fluids that contain suspended solids

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pseudoplastics
Pseudoplastics

Flow of pseudoplastics is consistent with the random coil model of polymer solutions and melts. At low stress, flow occurs by random coils moving past each other w/o coil deformation. At moderate stress, the coils are deformed and slip past each other more easily. At high stress, the coils are distorted as much as possible and offer low resistance to flow. Entanglements between chains and the reptation model also are consistent with the observed viscosity changes.

chapter 8

viscometers
Viscometers

In order to get meaningful (universal) values for the viscosity, we need to use geometries that give the viscosity as a scalar invariant of the shear stress or shear rate. Generalized Newtonian models are good for these steady flows: tubular, axial annular, tangential annular, helical annular, parallel plates, rotating disks and cone-and-plate flows. Capillary, Couette and cone-and-plate viscometers are common.

chapter 8

ballpoint pen ink
Ballpoint pen ink

László Bíró, a Hungarian newspaper editor, was frustrated by the amount of time that he wasted in filling up fountain pens and cleaning up smudged pages, and the sharp tip of his fountain pen often tore the paper. Bíró had noticed that inks used in newspaper printing dried quickly, leaving the paper dry and smudge free. He decided to create a pen using the same type of ink. Since, when tried, this viscous ink would not flow into a regular fountain pen nib, Bíró, with the help of his brother George, a chemist, began to work on designing new types of pens. Bíró fitted this pen with a tiny ball in its tip that was free to turn in a socket. As the pen moved along the paper, the ball rotated, picking up ink from the ink cartridge and leaving it on the paper. Bíró filed a British patent on 15 June 1938.[5]

Earlier pens leaked or clogged because of incorrect viscosity of the ink, and depended on gravity to deliver the ink to the ball. Depending on gravity caused difficulties with the flow and required that the pen be held nearly vertically. The original Biro pen used capillary action and a piston that pressurised the ink column, solving the ink delivery flow problems. Later Biro pens had a spring that kept pressure on the piston, and still later the Biro pens used just gravity and capillary action.[6]

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slide16

Disposable pens are chiefly made of plastic throughout and discarded when the ink is consumed; refillable pens are metal and some plastic and tend to be much higher in price. The refill replaces the entire internal ink reservoir and ball point unit rather than actually refilling it with ink, as it takes special high-speed centrifugation to properly fill a ball point reservoir with the viscous ink. The simplest types of ball point pens have a cap to cover the tip when the pen is not in use, while others have a mechanism for retracting the tip. This mechanism is usually controlled by a button at the top and powered by a spring within the pen body, but other possibilities include a pair of buttons, a screw, or a slide.

Rollerball pens combine the ballpoint design with the use of liquid ink and flow systems from fountain pens;

Space Pens, developed by Fisher in the United States, combine a more than normally viscous ballpoint pen ink with a gas-pressured piston which forces the ink toward the point. This design allows the pen to write even upside down or in zero gravity environments.[8] A graphite pencil can also be used in this way but produces graphite dust, requires sharpening, and is erasable, making it undesirable or unsuitable for use in some situations.

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slide17

The earliest fabric softeners were developed during early 20th century to counteract the harsh feel which the drying methods imparted to cotton. The cotton softeners were typically based on water emulsion of soap and olive oil, corn oil, or tallow oil.

Contemporary fabric softeners tend to be based on quaternary ammonium salts with one or two long alkyl chains, a typical compound being dipalmitoylethyl hydroxyethylmonium methosulfate.[3] Other cationic compounds can be derived from imidazolium, substituted amine salts, or quaternary alkoxy ammonium salts. One of the most common compounds of the early formulations was dihydrogenated tallow dimethyl ammonium chloride (DHTDMAC).

Anionic softeners and antistatic agents can be, for example, salts of monoesters and diesters of phosphoric acid and the fatty alcohols. These are often used together with the conventional cationic softeners. Cationic softeners are incompatible with anionic surfactants used in the bulk of surfactants used in detergents, with which they form a solid precipitate. Therefore, they have to be added during the rinse cycle instead. Anionic softeners can be combined with anionic surfactants directly. Other anionic softeners can be based on smectite clays. Some compounds, such as ethoxylated phosphate esters, have softening, anti-static, and surfactant properties.[4]

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slide18

The softening compounds differ in affinity to different materials. Some are better for cellulose-based fibers, others have higher affinity to hydrophobic materials like nylon, polyethylene terephthalate, polyacrylonitrile, etc.

Silicone-based compounds such as polydimethylsiloxane comprise the new softeners which work by lubricating the fibers. Derivatives with amine- or amide-containing functional groups are used as well. These groups help the softeners bind better to fabrics.

As the softeners themselves are often of hydrophobic nature, they are commonly occurring in the form of an emulsion. In the early formulations, soaps were used as emulsifiers. The emulsions are usually opaque, milky fluids. However there are also microemulsions where the droplets of the hydrophobic phase are substantially smaller[not specific enough to verify]. The advantage of microemulsions is in the increased ability of the smaller particles to penetrate into the fibers. A mixture of cationic and non-ionic surfactants is often used as an emulsifier. Another approach is using a polymeric network, an emulsion polymer.

Other compounds are included to provide additional functions; acids or bases for maintaining the optimal pH for adsorption to the fabric, electrolytes, carriers (usually water, sometimes water-alcohol mixture), and others, eg. silicone-based anti-foaming agents, emulsion stabilizers, fragrances, and colors.[5] A relatively recent form on the market are the ultra-concentrates, where the amount of carriers and some other chemicals is substantially lower and much smaller volumes are used.

In recent years, the importance of delivering perfume onto the clothes has possibly exceeded that of softening.[citation needed] The perfume levels in fabric softeners has gradually increased, requiring high-shear mixing technology to be used to incorporate greater amounts of perfumes within the emulsions. Long term release of perfume on the fabric is a key technology now being utilized. Each country tends to have different perfume requirements and brands may have different softener/perfume ratio depending on the country.

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molten chocolate
Molten chocolate

Follows Bingham plastic behavior

chapter 8

applications
applications
  • Dilatant: all wheel drive systems with viscous coupling unit for power transmission
  • Pseudoplastic: paint flows readily off the brush but should not drip excessively
  • Bingham plastic: finite yield stress before flow; drilling mud, toothpaste, mayonnaise, chocolate, mustard; at rest, these fluid surfaces can hold peaks
  • Rheopectic:

chapter 8

home video assignments
Home video assignments

Oobleck

  • An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch (e.g. cornstarch) in water, sometimes called "oobleck" or "ooze" (1 part of water to 1.5–2 parts of corn starch).[7][8] Uncooked imitation custard, being a suspension of primarily cornflour, has the same properties. The name "oobleck" is derived from the children's book Bartholomew and the Oobleck.

Flubber

  • Flubber is a non-Newtonian fluid, easily made from polyvinyl alcohol based glues and borax, that flows under low stresses, but breaks under higher stresses and pressures. This combination of fluid-like and solid-like properties makes it a Maxwell solid. Its behaviour can also be described as being viscoplastic or gelatinous.[9]

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slide23

Chilled caramel topping

  • Another example of this is chilled caramel ice cream topping. The sudden application of force—for example by stabbing the surface with a finger, or rapidly inverting the container holding it—leads to the fluid behaving like a solid rather than a liquid. This is the "shear thickening" property of this non-Newtonian fluid. More gentle treatment, such as slowly inserting a spoon, will leave it in its liquid state. Trying to jerk the spoon back out again, however, will trigger the return of the temporary solid state. A person moving quickly and applying sufficient force with their feet can literally walk across such a liquid.

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slide24

Silly Putty

  • Silly Putty is a silicone polymer based suspension which will flow, bounce, or break depending on strain rate.

Ketchup

  • Ketchup is a shear thinning fluid.[3] Shear thinning means that the fluid viscosity decreases with increasing shear stress. In other words, fluid motion is initially difficult at slow rates of deformation, but will flow more freely at high rates.

chapter 8

assignments
assignments

chapter 8

generalized newtonian models
Generalized Newtonian models

Power law model

Ellis model

chapter 8

example 8 2
Example 8.2

chapter 8

dependence of viscosity on molecular weight
Dependence of viscosity on molecular weight

Branched polymers have different rheology. Melt viscosities of LMW materials are lower than those of linear polymers because the volume occupied by a branch unit is smaller than that of a chain element.

Melt viscosities of high molecular weight materials have the reverse trend. Branched polymers have a higher zero shear viscosity. Usually, linear polymers are preferred for processing.

chapter 8

effects of variables on polymer viscosity
Effects of variables on polymer viscosity

The Arrhenius equation can be used to scale the viscosity. This can be applied to constant shear rate or constant shear stress values over moderate ranges of temperature.

Plasticizers tend to reduce melt viscosities while fillers tend to increase melt viscosity.

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molecular weight effects
Molecular weight effects

For M < Mc; m = k * M

For M > Mc; m = k * M3.4

The critical molecular weight is the point at which molecular entanglements restrict the movement of polymer molecules relative to each other.

chapter 8

shift factors
Shift factors

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modulus vs t
Modulus vs. t

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sheet die
Sheet die

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elastic state

Elastic State

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unique conditions of polymer elasticity
Unique conditions of polymer elasticity
  • Elastomers are used above Tg; the temperature range for elastic performance increases with molecular weight
  • At low stress, there is no visible elongation of the elastomer
  • Crystallization can occur in the stretched state, and increases the tensile strength
  • Deformation of elastomers (noncrystalline segments) stores energy in changed conformations (entropic), meaning that the modulus increases with temperature

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volume vs p and t
Volume vs. P and T
  • Total derivative of volume
  • Fractional volume change
  • Term for temperature derivative is the volume expansivity, b, and that for the pressure derivative is the isothermal compressibility, k. These coefficients are relatively independent of temperature and pressure for moderate ranges.

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elongation vs t f
elongation vs. T & F
  • Total derivative of length
  • Fractional length change
  • Term for temperature derivative is linear expansivity, a, and that for the force derivative is the Young’s modulus, E.
  • The fractional change in length is:
  • This is a mechanical equation of state for elastomers

chapter 8

in class exercise
In-class exercise
  • A butyl rubber part is being used to suspend a motor. As the motor is used, the temperature of the part increases by 25 C. Estimate the change in force exerted by the butyl rubber mount when this occurs.

chapter 8

in class exercise solution
In-class exercise: solution
  • A butyl rubber part is being used to suspend a motor. As the motor is used, the temperature of the part increases by 25 C. Estimate the change in force exerted by the butyl rubber mount when this occurs.

Suppose that the elongation does not change so e ~ 0.

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tensile test
Tensile test
  • A0 – initial cross-sectional area
  • L0 – initial length
  • F – force, L – length, A – cross-sectional area
  • Elastic deformation, a constant volume process for small deformations
  • seng = engineering stress = load/initial area
  • eeng = engineering strain = length change/initial length

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definition of yield
Definition of yield

Test equipment has some “slack” in it.

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additional definitions
Additional definitions
  • True stress and strain
  • At high strains, many polymers crystallize so that DV is not zero and this analysis is not correct
  • True stress and true strain are always larger than the engineering values
  • When the volume is constant on strain:

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additional definitions1
Additional definitions
  • When a material is deformed, it absorbs energy as the force acts over the distance, L-L0.
  • Ductility – the amount of permanent strain prior to fracture failure
  • Toughness – amount of energy absorbed by the material during fracture failure, i.e., the area under the stress-strain curve.
  • Initial yield – stress/strain to which deformations are elastic
  • Maximum tensile strength – highest load the material can take prior to fracture
  • Resiliency – amount of energy absorbed elastically and completely recoverable. Resilience = ½*smax*emax.
  • At higher stresses, the sample has permanent strain.

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other notes
Other notes
  • Cold drawing of fibers: stress above the yield point crystallizes the material.
  • Product failure can occur at the yield point as the original dimensions are not recovered.
  • In some cases, product failure occurs when the part breaks
  • Toughness is a measure of energy needed to break the part.

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summary table
Summary table

chapter 8

failure mechanisms

Failure mechanisms

polymers

chapter 8

failure mechanisms1
Failure mechanisms
  • Elastic deformation
  • Brittle fracture initiated by shear banding or crazing
  • Plasticity terminating in ductile fracture
  • Cold drawing
  • Rubbery and viscous flow
  • Adiabatic heating

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brittle fracture t 0 8 t g
Brittle fracture,T< 0.8 Tg
  • Material fails by brittle fracture; stress-strain is nearly linear to break point. Fracture may be initiated by shear yielding or crazing.
  • Elongation may be less than 5%
  • Brittle fracture can also occur in ductile materials if the strain rate is very high (projectile speeds)
  • Failure in tension is initiated at cracks or flaws in the sample. Polymers have a limiting critical flaw size, below which fracture stress is independent of the flaws (fillers?)
  • PMMA critical flaw size is 0.05 mm.

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compression
Compression
  • Failure strength in compression may be an order of magnitude greater than that in tension
  • Crack growth is more difficult in compression – perhaps failure occurs by plastic flow

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crazing t 0 8t g
Crazing, T~0.8Tg
  • Crazes are cracks that fill in with oriented, load-bearing material
  • Usually initiated at free surfaces
  • Crazing is thought to be a microdrawing process that results in fibrillation of the polymer in the craze
  • Crazes may thicken by pulling more material into the fibrils
  • The thickening process stops when the local stress decreases due to deformation

chapter 8

plasticity ductile failure t 0 8t g
Plasticity/ductile failure, T> 0.8Tg
  • Shear banding is observed as “kink bands” – local changes in orientation often at an angle to the tensile or compressive force
  • Shear yielding modes are common under compression

chapter 8

cold drawing
Cold drawing
  • Non-crystalline polymers – yield point followed by constant stress region and then break
  • Semi-crystalline polymers – yield point, load drop, high elongation with material necking and crystallization in this region. The neck has a nearly constant cross-sectional area and pulls in material from each end. The chain alignment gives materials with much higher tensile strength than the original sample.

chapter 8

viscous flow
Viscous flow
  • T > 1.1 Tg
  • WLF equation
  • Polymer deform via viscous flow
  • Upper temperature limit is usually determined by degradation

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adiabatic heating
Adiabatic heating
  • At high deformation rates, the heat generated in deformation may not have time to be conducted away, and the local temperature can increase significantly.
  • Heating usually occurs in the craze and shear banding regions
  • As the temperature increases, the local elastic modulus decreases and the material can undergo strain softening.
  • Necking then occurs

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other factors
Other factors
  • T
  • P
  • Strain rate
  • Annealing
  • Cold drawing

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time to failure
Time to failure

HDPE water pipes at 4 temperatures. Failure modes: 1) ductile failure, 2) creep crazing.

chapter 8

composites
Composites

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composites1
Composites

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impact failure
Impact failure

Izod test

chapter 8