ch-9 [compatibility mode]
TRANSCRIPT
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Chapter: 9
Mechanical Properties
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ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS... Stress and strain: What are they and why are
they used instead of load and deformation?
MECHANICAL PROPERTIES
Elastic behavior: When loads are small, how muchdeformation 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?
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Introduction
To know the characteristics of material
To design the member To avoid the failure
To concern to variety of parties
To study distributions
To study the requirement
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bondsstretch
return toinitial
1. Initial 2. Small load 3. UnloadELASTIC DEFORMATION
F
Elastic means reversible!
F
Linear-
elasticNon-Linear-elastic
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1. Initial 2. Small load 3. Unload
planes
stillsheared
bondsstretch
& planesshear
PLASTIC DEFORMATION (METALS)
Plastic means permanent!
F
linearelastic
linearelastic
plastic
F
elastic + plastic plastic
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Tensile stress, : Shear stress, :
Area, A
Ft
Area, A
Ft
Fs
F
ENGINEERING STRESS
Ft =
FtA
ooriginal areabefore loading
FtF
Fs
=Fs
AoStress has units:
N/m2 or lb/in2
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Simple tension: cable
=F
Ao = cross sectionalArea (when unloaded)
FF
COMMON STATES OF STRESS
o
Simple shear: drive shaft
o =
Fs
A
Note: = M/AcR here.
Ski lift (photo courtesy P.M. Anderson)
M
M Ao
2R
Fs
Ac
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Simple compression:
Ao
OTHER COMMON STRESS STATES (1)
Canyon Bridge, Los Alamos, NM
Balanced Rock, ArchesNational Park o =
F
A
Note: compressive
structure member( < 0 here).
(photo courtesy P.M. Anderson)
(photo courtesy P.M. Anderson)
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Bi-axial tension: Hydrostatic compression:
OTHER COMMON STRESS STATES (2)
Fish under waterPressurized tank
z > 0
> 0
< 0h
(photo courtesy
P.M. Anderson)
(photo courtesy
P.M. Anderson)
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Tensile strain: Lateral strain:
/2
/2
Lowo =
Lo L =
L
wo
ENGINEERING STRAIN
Shear strain:/2
/2
/2 -
/2
LL
= tan Strain is always
dimensionless.
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Typical tensile specimen Typical tensile
test machineload cell
extensometerspecimen
Adapted from Fig. 6.2,
Callister 6e.
STRESS-STRAIN TESTING
Other types of tests:--compression: brittle
materials (e.g., concrete)
--torsion: cylindrical tubes,
shafts.
gaugelength
(portion of sample withreduced cross section)
=
moving cross head
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.)
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Shear test
Shear and flexural test are performed bythree-point or four point beam
tested is subjected to a concentrated load
The experiment may be conducted on UTM
and Tensometer using suitable attachments,or on a machine specially meant for it.
M/I=E/R=f/y =VQ/bIzz
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Torsion tests
T
Ability of material to resist twisting
moment is determine by a torsion test
G/L=T/J=/r
= 16T/d3
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Geometric Considerations of the Stress
State
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Geometric Consideration of the Stress
State
CED
2
2'
)
2
21('
SinCosSinSin
BE
BEBCSinBE
CosCos
BE
BCCosBCBE
====
+===
AB
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Modulus of Elasticity, E:(also known as Young's modulus)
Hooke's Law: = E
Poisson's ratio, : L
F
Linear-elastic
1
E
LINEAR ELASTIC PROPERTIES
metals: ~ 0.33
ceramics: ~0.25
polymers: ~0.40
= L
1-
Fsimpletension
testUnits:
E: [GPa] or [psi]
: dimensionless
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Non-linear and Interatomic relation ME
temp
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Force versus interatomic separation
Fc or Ft=-F=dP/dr where P= - A/rn+B/rm
Hence A,B, m and n are constant in whichm>n
E-dF/dr=d2P/dr2
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Linear Strain and shear strain
,2
1)
1(
2
1)
2
1)(
2
1(
451'1)1(
=
=
AB
BB
AB
BB
BD
CosBB
BD
BB
BD
BDDBd
B1 B C1C
q
B
( )
)1(2
1
.221
+=
+=
+=
==
GE
Eqd
E
q
E
qd
Gqd
AD
q
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ANELASTICITY
Time dependent elastic behavior is knownas anelasticity
Time dependent microscopic and atomstic
processes that are attendant to thedeformation
For metal normally small and is often
neglected however for some polymericmaterials its magnitude is significant
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Elastic Shear
modulus, G:
1
G
= G
M
M
simple
torsion
test
OTHER ELASTIC PROPERTIES
modulus, K:
P= -KVVo
V
1-K
Vo
Special relations for isotropic materials:
P P
G =
E
2(1+ ) K =
E
3(1 2)
pressure
test: Init.
vol =Vo.Vol chg.
= V
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Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum
Si crystal
Si nitrideAl oxide Carbon fibers only
Aramid fibers only
80100
200
600
80010001200
400
Cu alloys
Tungsten
Si carbide
Diamond
AFRE fibers *
CFRE(|| fibers)*
Metals
Alloys
Graphite
Ceramics
Semicond
PolymersComposites
/fibers
E(GPa)
Eceramics
> Emetals>> Epolymers
YOUNGS MODULI: COMPARISON
0.2
8
0.6
1
Magnesium,
um num
Graphite
-
Concrete
PC
Wood( grain)
AFRE( fibers)*
CFRE*
GFRE*
Glass fibers only
Epoxy only
0.4
0.8
2
4
6
10
20
40
60
Tin
PTFE
HDPE
LDPE
PP
Polyester
PSPET
CFRE( fibers)*
GFRE( fibers)*
GFRE(|| fibers)*
109 Pa
,
Callister 6e.Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers.
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Simple tension:
= FLoEA
o
L
= FwoEA
o
/2
F
Ao
Simple torsion:
M=moment =angle of twist
=2MLoro
4G
USEFUL LINEAR ELASTIC RELATIONS
/2
L/2
L/2
Lowo
2ro
Lo
Material, geometric, and loading parameters all
contribute to deflection.
Larger elastic moduli minimize elastic deflection.
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Simple tension test:
(at lower temperatures, T < Tmelt/3)
tensile stress,
Elastic+Plastic
at larger stress
PLASTIC (PERMANENT) DEFORMATION
engineering strain,
initiallypermanent (plastic)after load is removed
p
plastic strain
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Stress at which noticeableplastic deformation has
occurred.
when p = 0.002tensile stress,
y
YIELD STRENGTH, y
engineering strain,
p = 0.002
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Graphite/Ceramics/Semicond
Metals/Alloys
Composites/fibers
Polymers
y(MPa
)
cursbeforeyield.
400
500600700
1000
2000
Steel (1020)cdSteel (4140)a
Steel (4140)qt
Ti (5Al-2.5Sn)aW (pure)
Mo (pure)Cu (71500)cw
,
composites,si
nce
rsbeforeyield.
y(ceramics)
>>y(metals)
>> y(polymers)
YIELD STRENGTH: COMPARISON
Yieldstrength,
PVC
Hardtomeasu
re
sinceintensio
n,
fractureusually
oc
Nylon 6,6
LDPE
70
20
40
60
50
100
10
30
200
Tin (pure)
Al (6061)a
Al (6061)ag
Cu (71500)hrTa (pure)Ti (pure)aSteel (1020)hr
Hardtomeas
ur
inceramicmatrixandepoxyma
trix
intension,
fractureusuallyo
cc
HDPEPP
humid
dry
PC
PET
oom va ues
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawncw = cold worked
qt = quenched & tempered
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Maximum possible engineering stress in tension.
Adapted from Fig. 6.11,
Callister 6e.
TENSILE STRENGTH, TS
eering
ess
TS
Metals: occurs when noticeable necking starts.
Ceramics: occurs when crack propagation starts.
Polymers: occurs when polymer backbones are
aligned and about to break.
strain
engin
st
Typical response of a metal
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Graphite/Ceramics/Semicond
Metals/Alloys
Composites/fibers
Polymers
TS(MP
a)
300
1000
Al (6061)ag
Cu (71500)hr
Ti (pure)a
Steel (1020)
Steel (4140)a
Steel (4140)qt
Ti (5Al-2.5Sn)aW (pure)
Cu (71500)cw
2000
3000
5000
Al oxide
Diamond
Si nitride
GFRE(|| fiber)CFRE(|| fiber)
AFRE(|| fiber)
E-glass fib
C fibersAramid fib TS(ceram)
~TS(met)
~ TS(comp)
>> TS(poly)
TENSILE STRENGTH: COMPARISON
Si crystal
Tensilestrength
,
PVC
Nylon 6,6
10
100 Al (6061)a
a pure
LDPE
PP
PC PET
20
3040
Graphite
Concrete
Glass-soda
HDPE
wood( fiber)
wood(|| fiber)
1
GFRE( fiber)CFRE( fiber)AFRE( fiber)
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold workedqt = 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:
Engineeringtensilestress,
smaller %EL
(brittle if %EL5%)
Another ductility measure:
%AR =
Ao A f
Aox100
Note: %AR and %EL are often comparable.--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck.
Adapted from Fig. 6.13,
Callister 6e.
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Resilience
Capacity of material to absorbenergy when it is deformed
elastically and then, upon
un oa ng, to ave t s energy
recovered.
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Energy to break a unit volume of material
Approximate by the area under the stress-strain
curve.
Engineeringtensile
smaller toughness (ceramics)
larger toughness
TOUGHNESS
smaller toughness-unreinforcedpolymers
Engineering tensile strain,
, ,
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Resistance to permanently indenting the surface.
Large hardness means:--resistance to plastic deformation or cracking in
compression.--better wear properties.
e.g.,apply known force(1 to 1000g)
measure sizeof indent after
HARDNESS
mm sp ere
removing load
dDSmaller indentsmean largerhardness.
increasing hardness
mostplastics
brassesAl alloys
easy to machinesteels file hard
cuttingtools
nitridedsteels diamond
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.)
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An increase in y due to plastic deformation.
large hardening
small hardening
ad
ad
y0
y1
HARDENING
Curve fit to the stress-strain response:
u
nl
re
lo
T = C T( )
n
true stress (F/A) true strain: ln(L/Lo)
hardening exponent:n=0.15 (some steels)to n=0.5 (some copper)
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Design uncertainties mean we do not push the limit.
Factor of safety, N
working=
y
N
Often N is
between
1.2 and 4
Ex: Calculate a diameter, d, to ensure that yield does
DESIGN OR SAFETY FACTORS
.
factor of safety of 5.
1045 plaincarbon steel:
y=310MPa
TS=565MPa
F = 220,000N
d
Loworking =
y
N
220,000N d2/ 4
5
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Stress and strain: These are size-independent
measures of load and displacement, respectively.
Elastic behavior: This reversible behavior oftenshows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E or G).
SUMMARY
Plastic behavior: This permanent deformationbehavior occurs when the tensile (or compressive)
uniaxial stress reaches y.
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.
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Room T behavior is usually elastic, with brittle failure.
3-Point Bend Testing often used.--tensile tests are difficult for brittle materials.
FL/2 L/2
cross section
Rd
Adapted from Fig.
12.29, Callister 6e.
MEASURING ELASTIC MODULUS
9
deflection
rect. circ.
Determine elastic modulus according to:
E =F
L3
4bd3
=F
L3
12R4rect.cross
section
circ.cross
section
Fx
linear-elastic behavior
F
slope =
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3-point bend test to measure room T strength.
FL/2 L/2
cross section
Rb
d
rect. circ.
Adapted from Fig.
12.29, Callister 6e.
MEASURING STRENGTH
10
Flexural strength:
rect.
fs = mfail =
1.5FmaxL
bd
2=
FmaxL
R
3
xF
Fmax
max
Typ. values:Material fs(MPa) E(GPa)
Si nitride
Si carbideAl oxide
glass (soda)
700-1000
550-860275-550
69
300
430390
69Data from Table 12.5, Callister 6e.
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Elevated Temperature Tensile Test (T > 0.4 Tmelt).
creep test
x
slope = ss = steady-state creep rate.
MEASURING ELEVATED T RESPONSE
11
Generally,
time
ssceramics < ss
metals
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Ceramic materials have mostly covalent & someionic bonding.
Structures are based on:
--charge neutrality--maximizing # of nearest oppositely charged neighbors.
Structures may be predicted based on:
SUMMARY
12
-- .
Defects--must preserve charge neutrality
--have a concentration that varies exponentially w/T.
Room T mechanical response is elastic, but fracture
brittle, with negligible ductility. Elevated T creep properties are generally superior to
those of metals (and polymers).