Chapter 6

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CHAPTER 6:
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?
Chapter 6- 1
ELASTIC DEFORMATION
1. Initial
2. Small load
3. Unload
bonds
stretch
return to
initial

F
Elastic means reversible!
Chapter 6- 2
PLASTIC DEFORMATION (METALS)
1. Initial
2. Small load
3. Unload
F
Plastic means permanent!
linear
elastic
linear
elastic
plastic

Chapter 6- 3
ENGINEERING STRESS
• Tensile stress, s:
• Shear stress, t:
Ft
s
Ao
original area
before loading
Stress has units:
N/m2 or lb/in2
Chapter 6- 4
COMMON STATES OF STRESS
• Simple tension: cable
F
s
Ao
• Simple shear: drive shaft
Ski lift
(photo courtesy P.M. Anderson)
Fs
t 
Ao
Note: t = M/AcR here.
Chapter 6- 5
OTHER COMMON STRESS STATES (1)
• Simple compression:
Ao
Canyon Bridge, Los Alamos, NM
(photo courtesy P.M. Anderson)
Balanced Rock, Arches
National Park
(photo courtesy P.M. Anderson)
Note: compressive
structure member
(s < 0 here).
Chapter 6- 6
OTHER COMMON STRESS STATES (2)
• Bi-axial tension:
Pressurized tank
(photo courtesy
P.M. Anderson)
• Hydrostatic compression:
Fish under water
s > 0
sz > 0
(photo courtesy
P.M. Anderson)
s h< 0
Chapter 6- 7
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
Chapter 6- 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.)
Chapter 6- 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
Chapter 6- 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
Chapter 6- 11
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
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)
Chapter 6- 12
USEFUL LINEAR ELASTIC RELATIONS
• Simple tension:
• Simple torsion:
M=moment
 =angle of twist
Lo
2ro
• Material, geometric, and loading parameters all
contribute to deflection.
• Larger elastic moduli minimize elastic deflection.
Chapter 6- 13
PLASTIC (PERMANENT) DEFORMATION
(at lower temperatures, T < Tmelt/3)
• Simple tension test:
Chapter 6- 14
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
Chapter 6- 15
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
Chapter 6- 16
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.
Chapter 6- 17
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.
Chapter 6- 18
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.
Chapter 6- 19
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
Chapter 6- 20
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.)
Chapter 6- 21
HARDENING
• An increase in sy due to plastic deformation.
• Curve fit to the stress-strain response:
Chapter 6- 22
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


 d2 / 4 


sy
N
5
Chapter 6- 23
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 22-4 to 22-10.
Chapter 6- 24

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