2. • Mechanical Properties refers to the behavior of
material when
• external forces are applied
• Stress and strain ⇒ fracture
• For engineering point of view: allows to predict the
ability of a component or a structure to withstand the
forces applied to it
2
For science point of view: what makes
materials strong →helps us to design a
better new one
3. 3
Elastic means reversible!
Elastic Deformation
2. Small load
F
d
bonds
stretch
1. Initial 3. Unload
return to
initial
F
d
Linear-
elastic
Non-Linear-
elastic
Grey iron, concrete,
polymers)
4. 4
Plastic means permanent!
Plastic Deformation (Metals)
F
d
linear
elastic
linear
elastic
dplastic
1. Initial 2. Small load 3. Unload
planes
still
sheared
F
d elastic + plastic
bonds
stretch
& planes
shear
d plastic
5. Direct Stress Examples
Load, P
P
Area
Ao
Lo
L/2
L/2
Direct Stress - Tension
Load, P
P
Area
Ao
Lo
L/2
L/2
Direct Stress - Compression
S
P
Ao
e
L
Lo
Engineering Stress
Engineering Strain
5
6. 6
Stress has units:
N/m2 or lbf /in2
Engineering Stress
• Shear stress, t:
Area, Ao
Ft
Ft
Fs
F
F
Fs
t =
Fs
Ao
• Tensile stress, s:
original area
before loading
s =
Ft
Ao
2
f
2
m
N
or
in
lb
=
Area, Ao
Ft
Ft
7. 7
• Simple tension: cable
Note: t = M/AcR here.
Common States of Stress
o
s
F
A
o
t
Fs
A
s
s
M
M Ao
2R
Fs
Ac
• Torsion (a form of shear): drive shaft Ski lift (photo courtesy
P.M. Anderson)
Ao = cross sectional
area (when unloaded)
F
F
8. 8
(photo courtesy P.M. Anderson)
Canyon Bridge, Los Alamos, NM
o
s
F
A
• Simple compression:
Note: compressive
structure member
(s < 0 here).
(photo courtesy P.M. Anderson)
OTHER COMMON STRESS STATES (i)
Ao
Balanced Rock, Arches
National Park
9. 9
• Bi-axial tension: • Hydrostatic compression:
Pressurized tank
s < 0
h
(photo courtesy
P.M. Anderson)
(photo courtesy
P.M. Anderson)
OTHER COMMON STRESS STATES (ii)
Fish under water
s z > 0
s
q
> 0
10. 10
• Tensile strain: • Lateral strain:
Strain is always
dimensionless.
Engineering Strain
• Shear strain:
q
90º
90º - q
y
x
q
g = x/y = tan
e d
Lo
Adapted from Fig. 6.1(a) and (c), Callister & Rethwisch 8e.
d /2
Lo
wo
-d
eL L
wo
d
L/2
𝛿 = 𝐿-𝐿°
11. 11
Stress-Strain Testing
• Typical tensile test
machine
Adapted from Fig. 6.3, Callister & Rethwisch 8e. (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.)
specimen
extensometer
• Typical tensile
specimen
Adapted from
Fig. 6.2,
Callister &
Rethwisch 8e.
gauge
length
15. 15
Linear Elastic Properties
• Modulus of Elasticity, E:
(also known as Young's modulus)
• Hooke's Law:
s = E e
s
Linear-
elastic
E
e
F
F
simple
tension
test
• Elastic deformation is not permanent; it means that when the load is
removed, the part returns to its original shape and dimensions.
• For most metals, the elastic region is linear. For some materials, including
metals such as cast iron, polymers, and concrete, the elastic region is
non-linear.
17. The elastic modulus is proportional to the slope of the
interatomic force-separation curve at the equilibrium spacing
The
magnitude of
modulus of
elasticity is a
measure of
the resistance
to separation
of adjacent
atoms, that is
interatomic
17
18. Modulus of elasticity- Temperature
18
Values of the modulus of elasticity for
ceramic materials are about the same
as for metals; for polymers they are
lower. These differences are a direct
consequence of the different types of
atomic bonding in the three materials
types.
Furthermore, with increasing
temperature, the modulus of elasticity
diminishes, as
is shown for several metals in Figure.
21. Elastic Properties of Materials
• Poisson’s ratio: When a metal is strained in one
direction, there are corresponding strains in all other
directions.
• For a uniaxial tension strain, the lateral strains
are constrictive.
• Conversely, for a uniaxial compressive strain,
the lateral strains are expansive.
• i.e.; the lateral strains are opposite in sign to
the axial strain.
• The ratio of lateral to axial strains is known as
Poisson’s ratio, n.
21
22. 22
Poisson's ratio, n
• Poisson's ratio, n:
Units:
E: [GPa] or [psi]
n: dimensionless
n > 0.50 density increases
n < 0.50 density decreases
(voids form)
eL
e
-n
e
n - L
e
metals: n ~ 0.33
ceramics: n ~ 0.25
polymers: n ~ 0.40
Ratio of
lateral
and
axial
strains
23. Poisson’s Ratio, n
n -
ex
ez
-
ey
ez
For most metals,
0.25 < n < 0.35
in the elastic range
Furthermore:
)
1
(
2 n
G
E
23
24. 24
• Elastic Shear
modulus, G:
t
G
g
t = G g
Other Elastic Properties
simple
torsion
test
M
M
• Special relations for isotropic materials:
2(1 n)
E
G 3(1 - 2n)
E
K
• Elastic Bulk
modulus, K:
pressure
test: Init.
vol =Vo.
Vol chg.
= V
P
P P
P = -K
V
Vo
P
V
K
Vo
25. 25
(at lower temperatures, i.e. T < Tmelt/3)
Plastic (Permanent) Deformation
• Simple tension test:
engineering stress, s
engineering strain, e
Elastic+Plastic
at larger stress
ep
plastic strain
Elastic
initially
Adapted from Fig. 6.10(a),
Callister & Rethwisch 8e.
permanent (plastic)
after load is removed
27. 27
• Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002
Yield Strength, sy
sy = yield strength
Note: for 2 inch sample
e = 0.002 = l/l
z = 0.004 in
Adapted from Fig. 6.10(a),
Callister & Rethwisch 8e.
tensile stress, s
engineering strain, e
sy
ep = 0.002
28. 28
Room temperature
values
Based on data in Table B.4,
Callister & Rethwisch 8e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Yield Strength : Comparison
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Yield
strength,
s
y
(MPa)
PVC
Hard
to
measure
,
since
in
tension,
fracture
usually
occurs
before
yield.
Nylon 6,6
LDPE
70
20
40
60
50
100
10
30
200
300
400
500
600
700
1000
2000
Tin (pure)
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure)
Ti (pure) a
Steel (1020) hr
Steel (1020) cd
Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a
W (pure)
Mo (pure)
Cu (71500) cw
Hard
to
measure,
in
ceramic
matrix
and
epoxy
matrix
composites,
since
in
tension,
fracture
usually
occurs
before
yield.
HDPE
PP
humid
dry
PC
PET
¨
29. 29
Tensile Strength, TS
• Metals: occurs when noticeable necking starts.
• Polymers: occurs when polymer backbone chains are
aligned and about to break.
Adapted from Fig. 6.11,
Callister & Rethwisch 8e.
sy
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts
as stress
concentrator
engineering
TS
stress
engineering strain
• Maximum stress on engineering stress-strain curve.
30. 30
Tensile Strength: Comparison
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensile
strength,
TS
(MPa)
PVC
Nylon 6,6
10
100
200
300
1000
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure)
Ti (pure) a
Steel (1020)
Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a
W (pure)
Cu (71500) cw
LDPE
PP
PC PET
20
30
40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride
HDPE
wood ( fiber)
wood(|| fiber)
1
GFRE(|| fiber)
GFRE( fiber)
CFRE(|| fiber)
CFRE( fiber)
AFRE(|| fiber)
AFRE( fiber)
E-glass fib
C fibers
Aramid fib
Based on data in Table B.4,
Callister & Rethwisch 8e.
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.
Room temperature
values
31. Microstructural Origins of Plasticity
• Slip, Climb and Slide of atoms in the crystal
structure.
• Slip and Climb occur at Dislocations and Slide
occurs at Grain Boundaries.
t
t
31
32. 32
• Plastic tensile strain at failure:
Ductility
• Another ductility measure:
100
x
A
A
A
RA
%
o
f
o
-
=
x 100
L
L
L
EL
%
o
o
f
-
Lf
Ao
Af
Lo
Adapted from Fig. 6.13,
Callister & Rethwisch 8e.
Engineering tensile strain, e
Engineering
tensile
stress, s
smaller %EL
larger %EL
, ductility is defined by the degree to which a material can
sustain plastic deformation under tensile stress before failure.
33. Ductile Vs Brittle Materials
• Only Ductile materials will exhibit necking.
• Ductile if EL%>8% (approximately)
• Brittle if EL% < 5% (approximately)
Engineering
Stress
Engineering Strain
33
35. 35
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).
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches sy.
38. Problems
38
A cylindrical metal specimen having an original diameter of
12.8 mm (0.505 in.) and gauge length of 50.80 mm (2.000 in.)
is pulled in tension until fracture occurs. The diameter at the
point of fracture is 8.13 mm (0.320 in.), and the fractured
gauge length is 74.17 mm(2.920 in.). Calculate the ductility in
terms of percent reduction in area and percent elongation.
