CHAPTER 7:
MECHANICAL PROPERTIES
ISSUES TO ADDRESS...
• Stress and strain: What are they and why are
they used instead of load and deformation?
• Elastic behavior: When loads are small, how much
deformation occurs? What materials deform least?
• Plastic behavior: At what point do dislocations
cause permanent deformation? What materials are
most resistant to permanent deformation?
• Toughness and ductility: What are they and how
do we measure them?
• Ceramic Materials: What special provisions/tests are
made for ceramic materials?
1
ELASTIC DEFORMATION
1. Initial
2. Small load
3. Unload
bonds
stretch
return to
initial

F
Elastic means reversible!
2
PLASTIC DEFORMATION
(METALS)
1. Initial
2. Small load
3. Unload
F
Plastic means permanent!
linear
elastic
linear
elastic
plastic

3
ENGINEERING STRESS
• Tensile stress, s:
• Shear stress, t:
Ft
s
Ao
original area
before loading
Stress has units:
N/m2 or lb/in2
4
ENGINEERING STRAIN
• Tensile strain:
• Lateral strain:
/2
wo
• Shear strain:
L/2
Lo
/2
L/2
/2
 = tan 
/2 - 
/2
Strain is always
dimensionless.
/2
8
STRESS-STRAIN TESTING
• Typical tensile specimen
• Typical tensile
test machine
Adapted from Fig. 6.2,
Callister 6e.
• Other types of tests:
--compression: brittle
materials (e.g., concrete)
--torsion: cylindrical tubes,
shafts.
Adapted from Fig. 6.3, Callister 6e.
(Fig. 6.3 is taken from H.W. Hayden,
W.G. Moffatt, and J. Wulff, The
Structure and Properties of
Materials, Vol. III, Mechanical
Behavior, p. 2, John Wiley and Sons,
New York, 1965.)
9
LINEAR ELASTIC PROPERTIES
• Modulus of Elasticity, E:
(also known as Young's modulus)
• Hooke's Law:
s=Ee
• Poisson's ratio, n:
metals: n ~ 0.33
ceramics: ~0.25
polymers: ~0.40
Units:
E: [GPa] or [psi]
n: dimensionless
10
OTHER ELASTIC PROPERTIES
• Elastic Shear
modulus, G:
t=G
M
t
G
1
simple
torsion
test

M
• Elastic Bulk
modulus, K:
P
P
• Special relations for isotropic materials:
E
E
G
K
2(1  n)
3(1  2n)
P
pressure
test: Init.
vol =Vo.
Vol chg.
= DV
12
YOUNG’S MODULI:
COMPARISON
Metals
Alloys
1200
1000
800
600
400
E(GPa)
200
100
80
60
40
109 Pa
Graphite
Composites
Ceramics Polymers
/fibers
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
CFRE*
GFRE( fibers)*
Graphite
Polyester
PET
PS
PC
CFRE( fibers)*
AFRE( fibers)*
Epoxy only
PP
HDPE
PTFE
LDPE
Wood( grain)
13
PLASTIC (PERMANENT)
DEFORMATION
(at lower temperatures, T < Tmelt/3)
• Simple tension test:
15
YIELD STRENGTH, sy
• Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002
tensile stress, s
sy
engineering strain, e
ep = 0.002
16
YIELD STRENGTH: COMPARISON
sy(ceramics)
>>sy(metals)
>> sy(polymers)
Room T values
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
17
TENSILE STRENGTH, TS
• Maximum possible engineering stress in tension.
Adapted from Fig. 6.11,
Callister 6e.
• Metals: occurs when noticeable necking starts.
• Ceramics: occurs when crack propagation starts.
• Polymers: occurs when polymer backbones are
aligned and about to break.
18
TENSILE STRENGTH:
COMPARISON
TS(ceram)
~TS(met)
~ TS(comp)
>> TS(poly)
Room T values
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers.
19
DUCTILITY, %EL
L f  Lo
x100
• Plastic tensile strain at failure: %EL 
Lo
Adapted from Fig. 6.13,
Callister 6e.
Ao  A f
• Another ductility measure: %AR 
x100
Ao
• Note: %AR and %EL are often comparable.
--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck.
20
TOUGHNESS
• Energy to break a unit volume of material
• Approximate by the area under the stress-strain
curve.
Engineering
tensile
stress, s
smaller toughness (ceramics)
larger toughness
(metals, PMCs)
smaller toughnessunreinforced
polymers
Engineering tensile strain, e
21
HARDENING
• An increase in sy due to plastic deformation.
• Curve fit to the stress-strain response:
22
MEASURING ELASTIC MODULUS
• Room T behavior is usually elastic, with brittle failure.
• 3-Point Bend Testing often used.
--tensile tests are difficult for brittle materials.
Adapted from Fig.
12.29, Callister 6e.
• Determine elastic modulus according to:
E
F
L3

4bd3
rect.
cross
section

F
L3
 12R 4
circ.
cross
section
23
MEASURING STRENGTH
• 3-point bend test to measure room T strength.
cross section
d
b
rect.
L/2
F
L/2
Adapted from Fig.
12.29, Callister 6e.
R
circ.
location of max tension
• Typ. values:
• Flexural strength:
fail
s fs  s m

1.5FmaxL
bd2
rect.

FmaxL
R3
sfs(MPa)
Si nitride
700-1000
Si carbide
550-860
Al oxide
275-550
glass (soda)
69
Material
E(GPa)
300
430
390
69
Data from Table 12.5, Callister 6e.
24
TENSILE RESPONSE: ELASTOMER
CASE
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
T AND STRAIN RATE:
THERMOPLASTICS
• Decreasing T...
--increases E
--increases TS
--decreases %EL
• Increasing
strain rate...
--same effects
as decreasing T.
Adapted from Fig. 15.3, Callister 6e. (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.)
26
TIME DEPENDENT
DEFORMATION
• Stress relaxation test:
--strain to eo and hold.
--observe decrease in
stress with time.
• Data: Large drop in Er
for T > Tg.
(amorphous
polystyrene)
Adapted from Fig.
15.7, Callister 6e.
(Fig. 15.7 is from
A.V. Tobolsky,
Properties and
Structures of
Polymers, John
Wiley and Sons,
Inc., 1960.)
• Relaxation modulus:
s(t )
Er (t ) 
eo
• Sample Tg(C) values:
PE (low Mw)
PE (high Mw)
PVC
PS
PC
-110
- 90
+ 87
+100
+150
Selected values
from Table 15.2,
Callister 6e.
27
HARDNESS
• Resistance to permanently indenting the surface.
• Large hardness means:
--resistance to plastic deformation or cracking in
compression.
--better wear properties.
Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Properties
and Applications of Plastics, p. 202, John Wiley and Sons, 1957.)
28
DESIGN OR SAFETY FACTORS
• Design uncertainties mean we do not push the limit.
• Factor of safety, N
Often N is
between
sy
s working 
1.2 and 4
N
• Ex: Calculate a diameter, d, to ensure that yield does
not occur in the 1045 carbon steel rod below. Use a
factor of safety of 5.
s working 
220,000N


2

 d / 4 


sy
N
5
29
Thermal Expansion
Materials change size when temperature
is changed
 initial
 final
Tinitial
Tfinal
Tfinal > Tinitial
 final   initial
 α (Tfinal  Tinitial )
 initial
linear coefficient of
thermal expansion (1/K or 1/°C)
25
Atomic Perspective: Thermal Expansion
Asymmetric curve:
-- increase temperature,
-- increase in interatomic
separation
-- thermal expansion
Symmetric curve:
-- increase temperature,
-- no increase in interatomic
separation
-- no thermal expansion
26
Coefficient of Thermal Expansion: Comparison
Material
increasing a
• Polymers
Polypropylene
Polyethylene
Polystyrene
Teflon
• Metals
Aluminum
Steel
Tungsten
Gold
• Ceramics
Magnesia (MgO)
Alumina (Al2O3)
Soda-lime glass
Silica (cryst. SiO2)
a (10-6/C)
at room T
145-180
106-198
90-150
126-216
23.6
12
4.5
14.2
Polymers have larger
a values because of
weak secondary bonds
• Q: Why does a
generally decrease
with increasing
bond energy?
13.5
7.6
9
0.4
27
Thermal Stresses
• Occur due to:
-- restrained thermal expansion/contraction
-- temperature gradients that lead to differential
dimensional changes
Thermal stress s
 Ea (T0 Tf )  Ea DT

28
SUMMARY
• Stress and strain: These are size-independent
measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often
shows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E or G).
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches sy.
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.
Note: For materials selection cases related to
mechanical behavior, see slides 20-4 to 20-10.
30