Day 29: Mechanical Behavior of Polymers Review How are

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Day 29 Mechanical Behavior of Polymers

• Review
• How are Properties Defined
• Introduction to Viscoelasticity
• Simple Material Models
• Strain Rate and Temperature Effects

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Review

• Basic definitions thermoplastic, thermoset,
  elastomer.
• Lets talk about the kind of mechanical behavior
  seen in polymers.
• Stiffness, E
• Strength
• Ductility
• Factors which can determine the strength of a
  polymer.

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Lets remember some particular polymers

• Importance of fiber. What does it take for a
  polymer to form fiber?

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Different Types of Mechanical Behaviors in
Polymers
Focus on this one today
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Mechanical Properties

• i.e. stress-strain behavior of polymers

brittle polymer
?FS of polymer ca. 10 that of metals
plastic
elastomer
elastic modulus less than metal
Adapted from Fig. 15.1, Callister 7e.
Strains deformations gt 1000 possible
(for metals, maximum strain ca. 10 or less)
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Tensile Properties for Polymers
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T and Strain Rate Thermoplastics
s
(MPa)
Decreasing T... -- increases E --
increases TS -- decreases EL Increasing
strain rate... -- same effects
as decreasing T.
Data for the
4C
semicrystalline
polymer PMMA
20C
(Plexiglas)
40C
to 1.3
60C
0
e
0
0.1
0.2
0.3
Adapted from Fig. 15.3, Callister 7e. (Fig. 15.3
is from T.S. Carswell and J.K. Nason, 'Effect of
Environmental Conditions on the Mechanical
Properties of Organic Plastics", Symposium on
Plastics, American Society for Testing and
Materials, Philadelphia, PA, 1944.)
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Effects of Strain Rate and Temperature
stress
Increasing strain rate
Increasing temp
strain
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Time Temp for Delrin (Strain Rate)
http//www2.dupont.com/Plastics/en_US/assets/downl
oads/design/230323c.pdf
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Time Temp for Delrin (Strain Rate and Temp)
http//www2.dupont.com/Plastics/en_US/assets/downl
oads/design/230323c.pdf
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Time Temp Dependence

• Plastic deformation of polymers involves chain
  uncoiling and chain sliding
• Increasing temperature increases relative space
  between chains and makes uncoiling easier.
• Slowing the strain rate means there is more time
  for chain reconfiguration.

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Introduction to Viscoelasticity

• Some features that are observed in polymeric
  materials that do not seem to be noticeable in
  metals or ceramics
• Mechanical properties depend on Temperature
• Mechanical properties depend on Strain Rate
• Creep (noticed in metals at high temperatures)
• Stress Relaxation
• Hysteresis

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Creep

• Take a tension specimen made from a polymer and
  and put on a series of constant stresses on it.
• We observe

Creep Progressive strain (deformation) over time
at constant stress (load), usually at high
temperatures
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Creep Test

• We instantly load with constant stress for a
  certain time, and instantly unload.

• Note that both linear elastic and viscous fluid
  behaviors are present.
• Note that there seems to be some residual strain
  at the end, i.e. the material does not completely
  recover. There is both elasticity and
  plasticity.

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Creep of PEEK
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Write down two examples of parts that see
constant tensile or bending load.
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Stress Relaxation

• Think of a polymer specimen loaded with a
  constant strain.

• Note that both linear elastic and viscous fluid
  behaviors are present.
• Note that there seems to be some residual stress
  at the end, i.e. the material does not completely
  recover. There is both elasticity and
  plasticity.

Stress Relaxation Progressive loss of stress
(load) over time under constant strain
(deformation), usually at high temperatures
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Stress Relaxation of Delrin
http//www2.dupont.com/Plastics/en_US/assets/downl
oads/design/230323c.pdf
19
Write down two examples of parts that see
constant strain.
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Time Dependent Deformation
Stress relaxation test
-- strain to eo and hold. -- observe decrease in
stress with time.
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Effect of Temperature Glass Transition
Temperature Or why does Garden Hose behave the
way it does?
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Melting vs. Glass Transition Temp.

• What factors affect Tm and Tg?
• Both Tm and Tg increase with increasing chain
  stiffness
• Chain stiffness increased by
• Bulky sidegroups
• Polar groups or sidegroups
• Double bonds or aromatic chain groups
• Regularity effects Tm only

Adapted from Fig. 15.18, Callister 7e.
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Tg and Tm
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Hysteresis

• Polymers often dont load and unload on the same
  line on the stress-strain curve.
• The difference in areas under those curves
  represents energy loss (often to heat).
• This means that polymers can have inherent energy
  damping.
• This means plastic springs may not be as good an
  idea as plastic dampers.

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Sinusoidal Response Tests

• We have a polymer specimen experiencing a
  sinusoidal loading.

Note that there is a phase shift, and that there
is also hysteresis indicating that energy is
being dissipated cyclically. This all suggests
some simple material models.
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Load-Unload Cycle in Nylon
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Hysteresis in Delrin
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Takeaways

• Yield and Ultimate Strength are defined
  differently for polymers.
• Polymers have time and temperature dependent
  properties (viscoelasticity)
• Creep
• Stress Relaxation
• Tg, Tm
• Hysteresis

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Maxwell Model

• Here is an alternative to the simple spring model
  of linear elasticity. Add a damper. This gives
  what is called as the Maxwell model.

In the limit, its a fluid!
strain
stress
Stress relaxation is not bad
Creep not too good!
time
time
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Kelvin-Voigt Model

• Try putting the spring and damper in series!
  This gives the Kelvin-Voigt model.

In the limit, its a solid!
strain
stress
Doesnt really show stress relaxation!
time
time
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Standard Linear Solid

• Further improvement is possible.

Shows both creep and stress relaxation!
stress
strain
time
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Stress Strain Relationships

• We can get stress from strain history and strain
  form stress history through the following
  heriditary relationships.

K is creep modulus, and F is the relaxation
modulus.
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Examples of These Time Dependent Moduli
H(t) is the unit step function. d(t) is the
Dirac delta function
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More on the material models

• Testing needs to be done to fit the parameters of
  the model to the behavior of an actual material.
• Note the fact that the history of the material
  must be recorded to be able to complete the
  calculations.
• Some additional complexity. The parameters in
  the creep modulus and relaxation modulus are
• Temperature Dependent
• Strain Rate Dependent

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Summary

• Very complex behavior!
• Difficult to model.
• Great sensitivity to temperature.
• Great sensitivity to strain rate.

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Tensile Response Brittle Plastic
s
(MPa)
brittle failure
x
onset of
necking
plastic failure
x
unload/reload
e
Stress-strain curves adapted from Fig. 15.1,
Callister 7e. Inset figures along plastic
response curve adapted from Figs. 15.12 15.13,
Callister 7e. (Figs. 15.12 15.13 are from J.M.
Schultz, Polymer Materials Science,
Prentice-Hall, Inc., 1974, pp. 500-501.)
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Tensile Response Elastomer Case
s
(MPa)
brittle failure
x
Stress-strain curves adapted from Fig. 15.1,
Callister 7e. Inset figures along elastomer
curve (green) adapted from Fig. 15.15, Callister
7e. (Fig. 15.15 is from Z.D. Jastrzebski, The
Nature and Properties of Engineering Materials,
3rd ed., John Wiley and Sons, 1987.)
plastic failure
x
x
elastomer
e
Compare to responses of other polymers --
brittle response (aligned, crosslinked
networked polymer) -- plastic response
(semi-crystalline polymers)
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Thermoplastics vs. Thermosets
Thermoplastics -- little crosslinking
-- ductile -- soften w/heating --
polyethylene polypropylene
polycarbonate polystyrene
Thermosets -- large crosslinking
(10 to 50 of mers) -- hard and brittle
-- do NOT soften w/heating -- vulcanized
rubber, epoxies, polyester resin,
phenolic resin
Adapted from Fig. 15.19, Callister 7e. (Fig.
15.19 is from F.W. Billmeyer, Jr., Textbook of
Polymer Science, 3rd ed., John Wiley and Sons,
Inc., 1984.)
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Predeformation by Drawing
Drawing(ex monofilament fishline) --
stretches the polymer prior to use -- aligns
chains in the stretching direction Results of
drawing -- increases the elastic modulus (E)
in the stretching direction --
increases the tensile strength (TS) in the
stretching direction -- decreases ductility
(EL) Annealing after drawing... --
decreases alignment -- reverses effects of
drawing. Compare to cold working in metals!
Adapted from Fig. 15.13, Callister 7e. (Fig.
15.13 is from J.M. Schultz, Polymer Materials
Science, Prentice-Hall, Inc., 1974, pp. 500-501.)