Chapter 4c
Mechanical
Properties
Heat Distortion Temperature
•
The maximum temperature at which a polymer can be used in rigid
material applications is called the softening or heat distortion temperature
(HDT).
•
•
A typical test (plastic sheeting) involves application of a static load, and
heating at a rate of 2oC per min. The HDT is defined as the temperature
at which the
elongation becomes 2%.
•
•
•
•
•
•
•
•
A: Rigid poly(vinyl chloride)
50 psi load.
B: Low-density poly(ethylene)
50 psi load.
C: Poly(styrene-co-acrylonitrile)
25 psi load.
D:
Cellulose acetate
(Plasticized) 25 psi load.
Transient Testing: Resilience of Cured
Elastomers 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).
Types of Polymers
Polymer Family Tree
Thermoplastics
Will reform when melted
Thermosets/Elastomers
Will not reform
Not Cross-Linked
90% of market
Cross-linked
10% of market
Polyethylene
Epoxy
33%
Melamine Formaldehyde
Vinyls
Phenolic
16%
Polyester (unsaturated)
Polypropylene
Polyimide
15%
Polyurethane
PMMA
Some are thermoplastic as well.
ABS
Silicone
Nylon
Urea Formaldehyde
Polycarbonate
Saturated Polyester
PEEK
Polyurethane
Some are thermosets as well.
PVC
Ballpark Comparisons
Tensile strengths
Polymers: ~ 10 - 100 MPa
Metals: 100’s - 1000’s MPa
Elongation
Polymers: up to 1000 % in some cases
Metals: < 100%
Moduli (Elastic or Young’s)
Polymers: ~ 10 MPa - 4 GPa
Metals:
~ 50 - 400 GPa
Amorphous v Crystalline Polymers Thermo-mechanical properties
Thermal Expansion
If a part is to be produced within a close dimensional tolerance, careful
consideration of thermal expansion/contraction must be made.
Parts are produced in the melt state, and solidify to amorphous or
semi-crystalline states.
Changes in density must
be taken into account
when designing the mold.
Thermal Expansion
Stress Strain Studies
Anatomy of a Stress Strain Graph
/strain
Elongation = 100% x 

Initial slope is the Young’s Modulus (E’ or sometimes G)
TS = tensile strength
y = yield strength
Toughness = Energy required to break (area under curve)
Compression and Shear vs. Tensile Tests
Stress-strain curves are very dependent on the test method. A modulus
determined under compression is generally higher than one derived
from a tensile experiment, as shown below for polystyrene.
Tensile testing is most sensitive
to material flaws and microscopic
cracks.
Compression tests tend to
be characteristic of the polymer,
while tension tests are more
characteristic of sample flaws.
Note also that flexural and shear
test modes are commonly
employed.
Stress Strain Graphs
Chains in neck align
along elongation
direction:
strengthening

Elongation
by
extension of
neck

Beyond “B”, the yield strength, deformations are plastic
Ductility & Elongation (EL)
Thermosets = strong & brittle
Not Ductile
EL < 5% Brittle
EL > 5% Ductile
Thermolastics = depends on T
Cold Drawing above the Tg
TENSILE RESPONSE:
Stress-strain curves
adapted from Fig. 15.1,
Callister 6e. Inset
figures along elastomer
curve (green) adapted
from Fig. 15.14, Callister
6e. (Fig. 15.14 is from
Z.D. Jastrzebski, The
Nature and Properties of
Engineering Materials,
3rd ed., John Wiley and
Sons, 1987.)
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case)
25
Elastomer Molecules
High entropy
Low energy
Low entropy
High energy
Model of long elastomer molecules, with low degree of cross-linking: (a)
unstretched, and (b) under tensile stress.
YOUNG’S MODULI: COMPARISON
Metals
Alloys
1200
1000
800
600
400
E(GPa)
200
100
80
60
40
109 Pa
Graphite
Ceramics Polymers
Semicond
Diamond
Tungsten
Molybdenum
Steel, Ni
Tantalum
Platinum
Cu alloys
Zinc, Ti
Silver, Gold
Aluminum
Magnesium,
Tin
Si carbide
Al oxide
Si nitride
Carbon fibers only
CFRE(|| fibers)*
<111>
Si crystal
Aramid fibers only
<100>
AFRE(|| fibers)*
Glass-soda
Glass fibers only
GFRE(|| fibers)*
Concrete
GFRE*
20
10
8
6
4
2
1
0.8
0.6
0.4
0.2
Composites
/fibers
CFRE*
GFRE( fibers)*
Graphite
Polyester
PET
PS
PC
CFRE( fibers)*
AFRE( fibers)*
Epoxy only
Based on data in Table B2,
Callister 6e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers.
PP
HDPE
PTFE
LDPE
Wood(
grain)
13
Linear Elasticity: Possion Effect
• Hooke's Law:  = E 
• Poisson's ratio, :
width strain
w /w
L
 


axial strain
l /l

metals:  ~ 0.33
ceramics: ~0.25
polymers: ~0.40
Units:
E: [GPa] or [psi]
: dimensionless
Why does  have minus sign?
Poisson Ratio
• Poisson Ratio has a range –1    1/2
Look at extremes
• No change in aspect ratio: w/w   /
w /w
 
 1
 /

• Volume (V = AL) remains constant:

Hence, V = (L A+A L) = 0.
So,
V =0.
A/A  L/L
In terms of width, A = w2, then A/A = 2 w w/w2 = 2w/w = –L/L.
Hence,
1
2
(  / )
w /w
 
  
 /
 /
 1/2
Incompressible solid.
Water (almost).
Poisson Ratio: materials specific
Metals:Ir
W
0.26
Ni
0.29
Cu
0.31
Al
0.34
Ag
0.34
Au
0.38
0.42
generic value ~ 1/3
Solid Argon: 0.25
Covalent Solids:
Ionic Solids:
MgO
Si
0.27
Ge
0.28
Al2O3
0.23
TiC
0.19
generic value ~ 1/4
0.19
Silica Glass: 0.20
Polymers: Network (Bakelite) 0.49
Elastomer:
Chain (PE) 0.40
Hard Rubber (Ebonite) 0.39
(Natural) 0.49
Example: Poisson Effect
Tensile stress is applied along cylindrical brass rod (10 mm
diameter). Poisson ratio is  = 0.34 and E = 97 GPa.
• Determine load needed for 2.5x10–3 mm change in diameter
if the deformation is entirely elastic?
Width strain: (note reduction in diameter)
x= d/d = –(2.5x10–3 mm)/(10 mm) = –2.5x10–4
Axial strain:
Given Poisson ratio
z= –x/ = –(–2.5x10–4)/0.34 = +7.35x10–4
Axial Stress:
z = Ez = (97x103 MPa)(7.35x10–4) = 71.3 MPa.
Required Load: F = zA0 = (71.3 MPa)(5 mm)2 = 5600 N.
Negtive poisson’s ratio
• foams
Compression
Radial
n = -1.24
Axial
n=0
Lakes, R. S., "No contractile
obligations", Nature, 1992, 358,
713-714.
Anisotropic Materials
1) Compaction of
UHMWPE powder
2) Sintering
3) Extrusion
• Mechanical properties are sensitive to temperature
FIGURE 10.9 Effect of temperature on the stress-strain curve for cellulose acetate, a thermoplastic. Note the
large drop in strength and increase in ductility with a relatively small increase in temperature. Source: After T.S.
Carswell and H.K. Nason. Manufacturing Processes for Engineering Materials, 5th ed. Kalpakjian • Schmid Prentice Hall,
2008.
Poly(methyl methacrylate)
Ceramics
Stress
Metals
Polymers
Strain
•Lower elastic modulus, yield and
ultimate properties
•Greater post-yield deformability
•Greater failure strain
Polymers: Thermal Properties
• In the liquid/melt state enough thermal
energy for random motion (Brownian
motion) of chains
• Motions decrease as the melt is cooled
• Motion ceases at “glass transition
temperature”
• Polymer hard and glassy below Tg,
rubbery above Tg
Polymers: Thermal Properties
log(Modulus)
Tg
Tm
semicrystalline
crosslinked
linear amorphous
Temperature
Polymers: Thermal Properties
Stress
decreasing temperature or increasing
crystallinity
Strain
• Properties depend on amount of cross-linking
Increasing cross-linking
Figure 8.13
M. P. Groover, “Fundamentals of Modern Manufacturing 3/e” John Wiley, 2007