1. Day 29: Mechanical Behavior of Polymers
Review
How are Properties Defined
Introduction to Viscoelasticity
Simple Material Models
Strain Rate and Temperature Effects

2. Review Basic definitions: thermoplastic, thermoset, elastomer.
Let’s talk about the kind of mechanical behavior seen in polymers.
Stiffness, E
Strength
Ductility
Factors which can determine the strength of a polymer.

3. Let’s remember some particular polymers
Plus
Delta PE PC PS
Teflon PP PI
PVC PB
Nylon
SBS
Kevlar
ABS
PMMA
Epoxy
Importance of fiber. What does it take for a polymer to form fiber?

4. Different Types of Mechanical Behaviors in Polymers
A=brittle
B=elastic/plastic
C=elastomeric
Focus on this one today

5. 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 > 1000% possible (for metals, maximum strain ca. 10% or less)

6. Tensile Properties for Polymers

7. T and Strain Rate: Thermoplastics
(MPa)
• Decreasing T...
-- increases E
-- increases TS
-- decreases %EL
• Increasing
strain rate...
-- same effects
as decreasing T. 20 4 6 8
Data for the
4°C
semicrystalline
polymer: PMMA
20°C
(Plexiglas)
40°C
to 1.3
60°C e
0.1
0.2
0.3
Adapted from Fig. 15.3, Callister 7e. (Fig 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.)

8. Effects of Strain Rate and Temperature
stress
Increasing strain rate
Increasing temp
strain

9. Time Temp for Delrin (Strain Rate)

10. Time Temp for Delrin (Strain Rate and Temp)

11. 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.

12. 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

13. 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

14. 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.

15. Creep of PEEK

16. Write down two examples of parts that see constant tensile or bending load.

17. 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

18. Stress Relaxation of Delrin

19. Write down two examples of parts that see constant strain.

20. Time Dependent Deformation
• Stress relaxation test:
• Data: Large drop in Er
for T > Tg.
(amorphous
polystyrene)
Adapted from Fig. 15.7, Callister 7e. (Fig is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) 10 3 1 -1 -3 5 60
100
140
180
rigid solid
(small relax)
transition
region
T(°C) Tg
Er (10s)
in MPa
viscous liquid
(large relax)
-- strain to eo and hold.
-- observe decrease in
stress with time.
time
strain
tensile test eo
s(t)
• Relaxation modulus:
• Sample Tg(C) values:
PE (low density)
PE (high density)
PVC PS PC
- 110
- 90
+ 87
+100
+150
Selected values from Table 15.2, Callister 7e.

21. Effect of Temperature: Glass Transition Temperature
Or why does Garden Hose behave the way it does?

22. 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 , Callister 7e.

23. Tg and Tm

24. Hysteresis
Polymers often don’t 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.

25. 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.

26. Load-Unload Cycle in Nylon

27. Hysteresis in Delrin

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

29. 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, it’s a fluid!
strain
stress
Stress relaxation is not bad
Creep not too good!
time
time

30. Kelvin-Voigt Model
Try putting the spring and damper in series! This gives the Kelvin-Voigt model.
In the limit, it’s a solid!
strain
stress
Doesn’t really show stress relaxation!
time
time

31. Shows both creep and stress relaxation!
Standard Linear Solid
Further improvement is possible.
Shows both creep and stress relaxation!
stress
strain
time

32. 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.

33. Examples of These Time Dependent Moduli
Material
Creep Modulus
Relaxation Modulus
Maxwell
Kelvin Voigt
Standard Linear Solid
H(t) is the unit step function. d(t) is the Dirac delta function

34. 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

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

36. Tensile Response: Brittle & Plastic
(MPa)
fibrillar structure
near
failure
Initial
Near Failure x
brittle failure
onset of
crystalline
regions align
necking
plastic failure x
crystalline
regions
slide
amorphous
regions
elongate
aligned,
cross-
linked
case
networked
unload/reload e
semi-
crystalline
case
Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along plastic response curve adapted from Figs & 15.13, Callister 7e. (Figs & are from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp )

37. Tensile Response: Elastomer Case
(MPa)
final: chains
are straight,
still
cross-linked x
brittle failure
Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along elastomer curve (green) adapted from Fig , Callister 7e. (Fig is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)
plastic failure x x
elastomer
initial: amorphous chains are
kinked, cross-linked.
Deformation
is reversible! e
• Compare to responses of other polymers:
-- brittle response (aligned, crosslinked & networked polymer)
-- plastic response (semi-crystalline polymers)

38. Thermoplastics vs. Thermosets
Callister,
Fig. 16.9 T
Molecular weight Tg Tm
mobile
liquid
viscous
rubber
tough
plastic
partially
crystalline
solid
• 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 , Callister 7e. (Fig is from F.W. Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.)

39. 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
-- decreases ductility (%EL)
• Annealing after drawing...
-- decreases alignment
-- reverses effects of drawing.
• Compare to cold working in metals!
Adapted from Fig , Callister 7e. (Fig is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp )