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## Flow and mechanical properties of polymers

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Title: Flow and mechanical properties of polymers

1
Chapter 8
• Flow and mechanical properties of polymers

2
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.
Poissons ratio, 0 lt n lt 0.5.
• Modulus of elasticity (Youngs modulus). The
strain in a solid is related to the load by the
modulus of elasticity.

3
Concepts, coefficients, definitions, contd.
• 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 Poissons ratio. When
Poissons ratio 0.5 (perfect elasticity), the
tensile modulus is three times the shear modulus.
• Compliance the inverse of the elastic modulus.

4
Concepts, coefficients, definitions, contd.
• Dynamic measurements of solids and fluids yield
two coefficients (Youngs modulus used as the
example)
• The dynamic modulus contains a storage (or
elastic) component and a loss (or damping)
component

5
Rheology
6
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.
7
Defining relationship
8
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.
9
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.
10
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, m8, viscosities.
• Pseudoplastic shear thinning.
• Shear thickening viscosity increases with shear
stress.
• Dilatant shear thickening fluids that contain
suspended solids

11
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.
12
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.
13
Power law parameters
Material k, Pa-sn n Shear rate range, s-1
Ball point pen ink 10 0.85 1 1000
Fabric conditioner 10 0.6 1-100
Polymer melt 10000 0.6 100-10,000
Molten chocolate 50 0.5 0.1 10
Synovial fluid 0.5 0.4 0.1 100
Toothpaste 300 0.3 1- 1000
Skin cream 250 0.1 1 100
Lubricating grease 1000 0.1 0.1 - 100
14
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15
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
16
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.
17
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
18
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 smallernot
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.
19
Molten chocolate
Follows Bingham plastic behavior
20
Non-Newtonian fluids
Type Name Behavior example
Viscoelastic Kelvin material Elastic viscous
Anelastic Material returns to a well-defined rest shape
Time-independent Shear thinning pseudoplastic Viscosity decreases w/ increasing shear Latex paint, blood, paper pulp suspension
Shear thickening dilatant Viscosity increases w/ increasing shear Corn starch in water, sand in water
Generalized Newtonian fluids Viscosity is constant Blood plasma, custard
Time-dependent Rheopectic Viscosity increases w/stress length/time Some lubricants, whipped cream
Thixotropic Viscosity decreases w/stress length/time Clays, drilling muds, paints, synovial fluids
21
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

22
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 1.52
parts of corn starch).78 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

23
• Chilled caramel topping
• Another example of this is chilled caramel ice
cream topping. The sudden application of
forcefor example by stabbing the surface with a
finger, or rapidly inverting the container
holding itleads 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.

24
• 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.

25
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26
assignments
Team Video assignment Viscosity model example
Dirty ½ dozen oobleck Syrup I
polymerization flubber Syrup II
isomers Chilled caramel topping SC 0.020
Dipole moment Silly putty SC 0.025
Ramrod ketchup SP 0.025
27
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28
Generalized Newtonian models
Power law model
Ellis model
29
Example 8.2
30
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.
31
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.
32
Molecular weight effects
For M lt Mc m k M For M gt 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.
33
Free volume model
34
Shift factors
35
Modulus vs. t
36
Failure pressure scaled with t, T
37
Extensional flow geometry
38
Normal stress
39
Elongational, extensional, shear-free flows
40
Sheet die
41
Elastic State
42
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

43
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.

44
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 Youngs modulus, E.
• The fractional change in length is
• This is a mechanical equation of state for
elastomers

45
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.

46
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.
47
Mechanical performance
48
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

49
Definition of yield
Test equipment has some slack in it.
50
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

51
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 ½smaxemax.
• At higher stresses, the sample has permanent
strain.

52
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.

53
Effect of T on stress-strain curves
54
Summary table
55
End-use properties
56
Failure mechanisms
• polymers

57
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

58
Brittle fracture, Tlt 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.

59
Internal defect
60
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

61
Crazing, T0.8Tg
• 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

62
Plasticity/ductile failure, Tgt 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

63
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.

64
Viscous flow
• T gt 1.1 Tg
• WLF equation
• Polymer deform via viscous flow
• Upper temperature limit is usually determined by
degradation

65
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

66
Other factors
• T
• P
• Strain rate
• Annealing
• Cold drawing

67
Time to failure
HDPE water pipes at 4 temperatures. Failure
modes 1) ductile failure, 2) creep crazing.
68
Composites
69
Composites
70
Impact failure
Izod test
71
Notch tip radius, material effects
72
Impact speed effects
73
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74
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