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TRANSCRIPT
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Chapter 8 -
ME 254: Materials Engineering
Chapter 6: Mechanical
Properties of Metals
1st Semester 1435-1436 (Fall 2014)
Dr. Hamad F. Alharbi, [email protected]
November 3, 2014
mailto:[email protected]
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Chapter 8 -
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 does permanent
deformation occur? What materials are most
resistant to permanent deformation?
• Toughness and ductility: What are they and how
do we measure them?
Mechanical Properties of Metals
-
Chapter 8 - 3
Elastic means reversible!
Elastic Deformation
2. Small load
F
δ
bonds
stretch
1. Initial 3. Unload
return to
initial
F
δ
Linear-elastic
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Chapter 8 -
Plastic means permanent!
Plastic Deformation (Metals)
F
δ
linear elastic
linear elastic
δplastic
1. Initial 2. Small load 3. Unload
planesstill sheared
F
δelastic + plastic
bonds stretch & planes shear
δplastic
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Chapter 8 -
Stress has units:
Pa = N/m2
Engineering Stress
• Shear stress, τ:
Area, Ao
Ft
Ft
Fs
F
F
Fs
τ =Fs
Ao
• Tensile stress, σ:
original cross-sectional area
before loading
σ =Ft
Ao m2
N=
Area, Ao
Ft
Ft
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Chapter 8 -
• Simple tension: cable
Common States of Stress
o
σ =F
A
o
τ =Fs
A
σσ
M
M Ao
2R
FsAc
• Torsion (a form of shear): drive shaft
Ao = cross-sectional
area (when unloaded)
FF
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Chapter 8 -
o
σ =F
A
• Simple compression:
Note: compressive
structure member
(σ < 0 here).
OTHER COMMON STRESS STATE
Ao
Balanced Rock, Arches National Park
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Chapter 8 - 8
• Tensile strain: • Lateral strain:
Strain is always
dimensionless.
Engineering Strain
• Shear strain:
θ
90º
90º - θy
x γ = Δx/y = tan θ
e =δ
Lo
δ/2
Lowo
- δeL =
L
wo
δL/2
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Chapter 8 - 9
Linear Elastic Properties
• Modulus of Elasticity, E:(also known as Young's modulus)
• Hooke's Law:
σ = E e σ
Linear-
elastic
E
e
F
Fsimple tension test
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Chapter 8 - 10
Mechanical Properties
Slope of stress strain plot (which is proportional to the
elastic modulus) depends on bond strength of metal
F
d
bonds
stretch
return to
initial
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Chapter 8 -
-
Chapter 8 - 12
Metals
Alloys
Graphite
Ceramics
Semicond
PolymersComposites
/fibers
E(GPa)
Young’s Moduli: Comparison
109 Pa
0.2
8
0.6
1
Magnesium,
Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum
Graphite
Si crystal
Glass -soda
Concrete
Si nitrideAl oxide
PC
Wood( grain)
AFRE( fibers) *
CFRE*
GFRE*
Glass fibers only
Carbon fibers only
Aramid fibers only
Epoxy only
0.4
0.8
2
4
6
10
20
40
6080
100
200
600800
10001200
400
Tin
Cu alloys
Tungsten
Si carbide
Diamond
PTFE
HDPE
LDPE
PP
Polyester
PSPET
CFRE( fibers) *
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
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Chapter 8 -
-
Chapter 8 -
See Example 6.1
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Chapter 8 - 15
• Elastic Shear
modulus, G:
τG
γ
τ = G γ
Other Elastic Properties
simple
torsion
test
M
M
• Special relations for isotropic materials:
2(1 + ν)
EG =
3(1 -2ν)
EK =
• Elastic Bulk
modulus, K: pressuretest: Init.
vol =Vo.
Vol chg.
= ΔV
P
P PP = -K
ΔVVo
P
ΔV
KVo
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Chapter 8 - 16
Poisson's ratio, ν
• Poisson's ratio, ν:
Units:
E: [GPa] or [psi]
ν: dimensionless
eν = - L
e
metals: ν ~ 0.33
ceramics: ν ~ 0.25
polymers: ν ~ 0.40
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Chapter 8 -
See Example 6.2
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Chapter 8 -
Mechanical properties of metals
For Elastic Deformation
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Chapter 8 -
Mechanical properties of metals
Anelasticity
Time-dependent elastic deformation
Viscoelastic deformation
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Chapter 8 - 20
Plastic (Permanent)
Deformation
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Chapter 8 - 21
Plastic (Permanent) Deformation
• Simple tension test:
engineering stress,σ
engineering strain, e
Elastic+Plastic at larger stress
ep
plastic strain
Elastic initially
permanent (plastic) after load is removed
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Chapter 8 -
Mechanical properties of metals
Permanent deformation
Breaking bonds, moving
atoms, & reforming bonds
Elastic strain, ε ~ 0.5 %
(0.005)
Mechanism (metals):Slip
(1) Yield strength σy0.2% strain offset can be
used to find σy
Plastic deformation
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Chapter 8 - 23
• Stress at which noticeable plastic deformation has
occurred.
Yield Strength, σy
y = yield strengthtensile stress, σ
engineering strain, e
σy
ep = 0.002
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Chapter 8 - 24
Values at room
temperature
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Yield Strength : ComparisonGraphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
Yie
ld s
tre
ng
th, σ
y(M
Pa)
PVC
Ha
rd to
me
asu
re,
sin
ce
in t
en
sio
n, fr
actu
re u
su
ally
occu
rs b
efo
re y
ield
.
Nylon 6,6
LDPE
70
20
40
6050
100
10
30
200
300
400
500600700
1000
2000
Tin (pure)
Al (6061) a
Al (6061) ag
Cu (71500) hrTa (pure)Ti (pure) aSteel (1020) hr
Steel (1020) cdSteel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) aW (pure)
Mo (pure)Cu (71500) cw
Ha
rd to
me
asu
re,
in c
era
mic
ma
trix
an
d e
po
xy m
atr
ix c
om
po
sites, sin
ce
in te
nsio
n, fr
actu
re u
su
ally
occu
rs b
efo
re y
ield
.
HDPEPP
humid
dry
PC
PET
¨
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Chapter 8 -
VMSE: Virtual Tensile Testing
25
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Chapter 8 - 26
Tensile Strength, TS
• Metals: occurs when noticeable necking starts.
y
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts
as stress
concentrator
en
gin
ee
rin
g
TSstr
ess
engineering strain
• Maximum stress on engineering stress-strain curve.
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Chapter 8 -
Mechanical properties of metals
(2) Tensile
strength, TS
(3) Fracture
strength
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Chapter 8 - 28
Tensile Strength: Comparison
Si crystal
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
Ten
sile
str
eng
th,
TS
(MP
a)
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) aW (pure)
Cu (71500) cw
LDPE
PP
PC PET
20
3040
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 fibersAramid fib
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Room temperature
values
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Chapter 8 -
Mechanical properties of metals
(4) Ductility: A measure of degree of plastic deformation without fracture
Ductility
measure:
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Chapter 8 - 30
• Plastic tensile strain at failure:
Ductility
• Another ductility measure: 100xA
AARA%
o
fo-
=
x 100L
LLEL%
o
of-
=
LfAo
AfLo
Engineering tensile strain, e
Engineering
tensile
stress, σ
smaller %EL
larger %EL
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Chapter 8 -
Mechanical properties of metals
(5) Toughness
A measure of the ability of a material to absorb energy
up to fractureApproximate by the area under the stress-strain curve
Metals: Tough => High strength + Good ductility
smaller toughness-unreinforcedpolymers
Engineering tensile strain, e
Engineering
tensile
stress, s
smaller toughness (ceramics)
larger toughness(metals, PMCs)
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Chapter 8 - 32
• Energy to break a unit volume of material
Toughness
Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
very small toughness (unreinforced polymers)
Engineering tensile strain, e
Engineering
tensile
stress, σ
small toughness (ceramics)
large toughness (metals)
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Chapter 8 -
Mechanical properties of metals
(6) Resilience:
It is the capacity of a material
to absorb energy when it is
deformed elastically
Modulus of resilience, Ur
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Chapter 8 - 34
Resilience, Ur
• Ability of a material to store energy
– Energy stored best in elastic region
If we assume a linear
stress-strain curve this
simplifies to
yyr2
1U eσ≅
ey
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Chapter 8 - 35
Elastic Strain Recovery
Str
ess
Strain
3. Reapplyload
2. Unload
D
Elastic strain
recovery
1. Load
σyo
σyi
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Chapter 8 -
Hardness
Method:
A small indenter is forced into the
surface of a material to be tested,
under controlled conditions of load
and rate of application. The size of
the resulting indentation is measured,
which in turn is related to a hardness
number.
Softer material >> larger indentation
> lower hardness index number
A measure of a material’s resistance to
localized plastic deformation (e.g., a small
dent or a scratch)
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Chapter 8 - 37
Hardness
• Resistance to permanently indenting the surface.
• Large hardness means:-- resistance to plastic deformation or cracking in
compression.
-- better wear properties.
e.g., 10 mm sphere
apply known force measure size of indent after removing load
dDSmaller indents mean larger hardness.
increasing hardness
most plastics
brasses Al alloys
easy to machine steels file hard
cutting tools
nitrided steels diamond
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Chapter 8 - 38
Hardness: Measurement
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Chapter 8 - 39
Hardness: Measurement
• Rockwell
– No major sample damage
– Each scale runs to 130 but only useful in range
20-100.
– Minor load 10 kg
– Major load 60 (A), 100 (B) & 150 (C) kg
• A = diamond, B = 1/16 in. ball, C = diamond
• HB = Brinell Hardness
– TS (psia) = 500 x HB
– TS (MPa) = 3.45 x HB
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Chapter 8 -
Correlation Between Hardness and Tensile Strength
(empirical)
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Chapter 8 - 41
True Stress and
True Strain
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Chapter 8 -
Mechanical properties of metals
True stress: The load F divided by the instantaneous cross-sectional area
True strain: The natural logarithmof the ratio of instantaneous gauge length to
original gauge length of a specimen
It is obtained by integrating
the incremental strain
Constant volume:
>>>
Valid only to the onset of necking
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Chapter 8 -
Mechanical properties of metals
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Chapter 8 - 44
Hardening
• Curve fit to the stress-strain response:
σT = K eT( )n
“true” stress (F/A) “true” strain: ln(l/lo)
hardening exponent:n = 0.15 (some steels) to n = 0.5 (some coppers)
• An increase in σy due to plastic deformation.σ
e
large hardening
small hardeningσy0
σy1
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Chapter 8 -
Mechanical properties of metals
The region of the true stress–strain curve from the
onset of plastic deformation to the point at which necking
begins may be approximated by
K and n are
constant.
n: strain hardening
exponent
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Chapter 8 -
Mechanical properties of metals
See Example 6.5
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Chapter 8 -
Problems
6.4, 6.8, 6.9, 6.16, 6.21, 6.24,
6.25, 6.26, 6.27, 6.28, 6.30,
6.37, 6.38, 6.39, 6.40, 6.41,
6.44, 6.45