Post on 05-Apr-2018
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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?
LECTURE 6
Mechanical Properties
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Elastic means reversible!
Elastic Deformation
1. Initial 2. Small load 3. Unload
F
bonds
stretch
return toinitial
F Linear-elastic
Non-Linear-elastic
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Plastic means permanent!
Plastic Deformation (Metals)
F
linearelastic
linearelastic
plastic
1. Initial 2. Small load 3. Unload
planesstillsheared
F
elastic + plastic
bondsstretch& planesshear
plastic
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Stress has units:
N/m2 or lbf/in2
Engineering Stress
Shearstress, :
Area, A
Ft
Ft
Fs
F
F
Fs
=Fs
Ao
Tensile stress, :
original area
before loading
Area, A
Ft
Ft
= FtAo
2f
2mNor
inlb=
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Simple tension: cable
Note: = M/AcRhere.
Common States of Stress
Ao = cross sectional
area (when unloaded)
FF
o
FA
o
Fs
AM
M Ao
2R
FsAc
Torsion (a form of shear): drive shaftSki lift (photo courtesyP.M. Anderson)
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(photo courtesy P.M. Anderson)Canyon Bridge, Los Alamos, NM
oF
A
Simple compression:
Note: compressivestructure member
( < 0 here).(photo courtesy P.M. Anderson)
OTHER COMMON STRESS STATES (1)
Ao
Balanced Rock, ArchesNational Park
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Bi-axial tension: Hydrostatic compression:
Pressurized tank
< 0h
(photo courtesyP.M. Anderson)
(photo courtesy
P.M. Anderson)
OTHER COMMON STRESS STATES (2)
Fish under water
z > 0
> 0
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Tensile strain: Lateral strain:
Shearstrain:
Strain is always
dimensionless.
Engineering Strain
90
90 -y
x = x/y= tan
LoL
L
wo
Adapted from Fig. 6.1 (a) and (c), Callister 7e.
/2
L/2
Lowo
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Stress-Strain Testing
Typical tensile testmachine
Adapted from Fig. 6.3, Callister 7e. (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.)
specimenextensometer
Typical tensilespecimen
Adapted from
Fig. 6.2,Callister 7e.
gauge
length
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Linear Elastic Properties
Modulus of Elasticity, E:(also known as Young's modulus)
Hooke's Law:
= E
Linear-elastic
EF
Fsimpletensiontest
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Poisson's ratio,
Poisson's ratio, :
Units:
E: [GPa] or [psi]
: dimensionless
> 0.50 density increases
< 0.50 density decreases(voids form)
L
-
L
metals: ~ 0.33
ceramics: ~ 0.25
polymers: ~ 0.40
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Mechanical Properties
Slope of stress strain plot (which isproportional to the elastic modulus) depends
on bond strength of metal
Adapted from Fig. 6.7,
Callister 7e.
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MetalsAlloys
GraphiteCeramics
Semicond
PolymersComposites
/fibers
E(GPa)
Based on data in Table B2,
Callister 7e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)fibers.
Youngs 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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(at lower temperatures, i.e. T< Tmelt/3)
Plastic (Permanent) Deformation
Simple tension test:
engineering stress,
engineering strain,
Elastic+Plasticat larger stress
permanent (plastic)after load is removed
p
plastic strain
Elasticinitially
Adapted from Fig. 6.10 (a),
Callister 7e.
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Stress at which noticeable plastic deformation hasoccurred.
when p = 0.002
Yield Strength, y
y= yield strength
Note: for 2 inch sample
= 0.002 = z/z
z= 0.004 in
Adapted from Fig. 6.10 (a),
Callister 7e.
tensile stress,
engineering strain,
y
p = 0.002
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Room Tvalues
Based on data in Table B4,
Callister 7e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Yield Strength : ComparisonGraphite/Ceramics/Semicond
Metals/
Alloys
Composites/
fibersPolymers
Yieldstrength,
y(MPa)
PVC
H
ardtomeasure
,
sinceintension,fractureusuallyoccursbeforeyield.
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
Hardtomeasure,
inceramicmatrix
andepoxymatrixcomposites,since
intension,frac
tureusuallyoccursbefore
yield.
HDPEPP
humid
dry
PCPET
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Tensile Strength, TS
Metals: occurs when noticeable necking starts.
Polymers: occurs when polymer backbone chains arealigned and about to break.
Adapted from Fig. 6.11,
Callister 7e.
y
strain
Typical response of a metal
F= fracture or
ultimate
strength
Neck acts
as stress
concentratorengineering
TS
stress
engineering strain
Maximum stress on engineering stress-strain curve.
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Tensile Strength : Comparison
Si crystal
Graphite/Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensilestrength,
TS
(MPa)
PVC
Nylon 6,6
10
100
200
300
1000
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure)Ti (pure) aSteel (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
Room Temp. valuesBased on data in Table B4,
Callister 7e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawncw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers.
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Plastic tensile strain at failure:
Adapted from Fig. 6.13,
Callister 7e.
Ductility
Another ductility measure: 100xA
AARA%
o
fo-
=
x 100L
LLEL%o
of
Engineering tensile strain,
Engineering
tensile
stress,
smaller %EL
larger %ELLf
AoAfLo
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Energy to break a unit volume of material Approximate by the area under the stress-strain
curve.
Toughness
Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
very small toughness(unreinforced polymers)
Engineering tensile strain,
Engineering
tensile
stress,
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 6.13,
Callister 7e.
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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
Adapted from Fig. 6.15,
Callister 7e.
yyr2
1U
y dU
r 0
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Elastic Strain Recovery
Adapted from Fig. 6.17,
Callister 7e.
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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 sizeof indent afterremoving load
dDSmaller indentsmean largerhardness.
increasing hardness
mostplastics
brassesAl alloys
easy to machinesteels file hard
cuttingtools
nitridedsteels diamond
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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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Hardness: MeasurementTable 6.5
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True Stress & Strain
Note: S.A. changes when sample stretched
True stress
True Strain
iT AF
oiT ln
1ln
1
T
T
Adapted from Fig. 6.16,
Callister 7e.
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Hardening
Curve fit to the stress-strain response:
T K Tn
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 ydue to plastic deformation.
large hardening
small hardeningy0
y1
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Design uncertainties mean we do not push the limit.
Factor of safety, N
N
y
working
Often Nis
between
1.2 and 4
Example: Calculate a diameter, d, to ensure that yield doesnot occur in the 1045 carbon steel rod below. Use a
factor of safety of 5.
Design or Safety Factors
4000220
2 /d
N,
5
N
y
working
1045 plain
carbon steel:
y= 310 MPaTS = 565 MPa
F= 220,000N
d
Lo
d= 0.067 m = 6.7 cm
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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 (EorG).
Toughness: The energy needed to break a unit
volume of material.
Ductility: The plastic strain at failure.
Summary
Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches y.