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Transcript of Special Assignment Add figures/graphics to all slides Use bullets instead of short sentences For...
Special Assignment
Add figures/graphics to all slides
Use bullets instead of short sentences
For the 15’ presentations use fonts 18 or bigger; however, for the 50’, font sizes 10, 12, 14 are fine. You may use 16 or 18 for titles.
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CHAPTER 7: MECHANICAL PROPERTIES
CHAPTER 7: MECHANICAL PROPERTIES
ISSUES TO ADDRESS...
• Stress and strain
• Elastic behavior
• Plastic behavior
• Toughness and ductility
• Ceramic Materials
StressStrainElasticityStrengthTensileElongationDuctileFractureTensionFlexuralPlasticity
4
• Tensile stress, : • Shear stress, :
Area, A
Ft
Ft
FtAo
original area before loading
Area, A
Ft
Ft
Fs
F
F
Fs
FsAo
Stress has units:N/m2 or lb/in2
7.2 STRESS & STRAIN
Tensile loadCompressive load
Shear strain = tan
Torsional deformationangle of twist,
o
FA
Stress () for tension and compression
Lo
Strain () for tension and compression
Shear stress
o
FsA
5
• Simple tension: cable
o
FA
• Simple shear: drive shaft
Ao = cross sectional Area (when unloaded)
FF
o
FsA
Note: = M/Ac
Ski lift (photo courtesy P.M. Anderson)
7.2 COMMON STATES OF STRESS
M
M Ao
2R
FsAc
Canyon Bridge, Los Alamos, NM
6
• Simple compression:
Ao
Balanced Rock, Arches National Park o
FA
Note: compressivestructure member( < 0 here).
(photo courtesy P.M. Anderson)
(photo courtesy P.M. Anderson)
OTHER COMMON STRESS STATES
7
• Bi-axial tension: • Hydrostatic compression:
Fish under waterPressurized tank
z > 0
> 0
< 0h
(photo courtesyP.M. Anderson)
(photo courtesyP.M. Anderson)
OTHER COMMON STRESS STATES
8
• Tensile strain: • Lateral strain:
• Shear strain:/2
/2
/2 -
/2
/2
/2
L/2L/2
Lowo
Lo
L L
wo
= tan Strain is alwaysdimensionless.
ENGINEERING STRAIN
• Typical tensile specimen
9
• Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts.
gauge length
(portion of sample with reduced cross section)=
• Typical tensile test machine
load cell
extensometerspecimen
moving cross head
Adapted from Fig. 6.2, Callister 6e.
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.)
7.2 STRESS-STRAIN TESTING
Normal and shear stresses on an arbitrary plane
Stress is a function of the orientation
On plane p-p’ the stress is not pure tensile
There are two componentsTensile or normal stress ’ (normal to the pp’ plane)Shear stress ’ (parallel to the pp’ plane)
• Modulus of Elasticity, E: (also known as Young's modulus)
10
• Hooke's Law:
= E • Poisson's ratio, :
metals: ~ 0.33 ceramics: ~0.25 polymers: ~0.40
L
L
1-
F
Fsimple tension test
Linear- elastic
1E
Units:E: [GPa] or [psi]: dimensionless
ELASTIC DEFORMATIONS7.3 Stress-strain behavior
11
• Elastic modulus, E
Energy ~ curvature at ro
cross sectional area Ao
L
length, Lo
F
undeformed
deformed
L F Ao
= E Lo
Elastic modulus
r
larger Elastic Modulus
smaller Elastic Modulus
Energy
ro unstretched length
E is larger if Eo is larger.
PROPERTIES FROM BONDING: E
c07f08
c07tf01
7.4 ANESLATICITY
Assumed:Time-independent elastic deformationApplied stress produces instantaneous elastic strainRemains constant while elasticity stress is appliedAt release of load, strain is recovered
In real life:Time-dependent elastic strain component: AnelasticityTime-dependent microscopic and atomistic processesFor metals is smallSignificant for polymeric materials: Viscoelastic behavior
7.5 ELASTIC PROPERTIES OF MATERIALS
Poisson’s ratio = -x/z = -y/z
G
E2(1 )
For isotropic materials
130.2
8
0.6
1
Magnesium,Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, NiMolybdenum
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
46
10
20
406080
100
200
600800
10001200
400
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTF E
HDPE
LDPE
PP
Polyester
PSPET
CFRE( fibers)*
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
MetalsAlloys
GraphiteCeramicsSemicond
PolymersComposites
/fibers
E(GPa)
Eceramics > Emetals >> Epolymers
109 Pa
Based on data in Table B2,Callister 6e.Composite data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE)fibers.
YOUNG’S MODULI: COMPARISON
II. MECHANICAL BEHAVIOR—METALS
F
bonds stretch
return to initial
2
1. Initial 2. Small load 3. Unload
Elastic means reversible!
F
Linear- elastic
Non-Linear-elastic
II. ELASTIC DEFORMATION
15
• Simple tension test:
(at lower temperatures, T < Tmelt/3)
tensile stress,
engineering strain,
Elastic initially
Elastic+Plastic at larger stress
permanent (plastic) after load is removed
pplastic strain
II. PLASTIC (PERMANENT) DEFORMATION
3
1. Initial 2. Small load 3. Unload
Plastic means permanent!
F
linear elastic
linear elastic
plastic
planes still sheared
F
elastic + plastic
bonds stretch & planes shear
plastic
II. PLASTIC DEFORMATION (METALS)
16
• YIELD STRENGTH, y
Stress at which noticeable plastic deformation has occurred.
when p = 0.002 tensile stress,
engineering strain,
y
p = 0.002
7.6 Tensile properties
17
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
Yield
str
en
gth
, y (M
Pa)
PVC
Ha
rd t
o m
ea
sure,
si
nce in
ten
sion
, fr
actu
re u
sually
occu
rs b
efo
re y
ield
.
Nylon 6,6
LDPE
70
20
40
6050
100
10
30
200
300
400500600700
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 t
o m
ea
sure
, in
cera
mic
matr
ix a
nd
ep
oxy m
atr
ix c
om
posi
tes,
sin
ce
in
ten
sion
, fr
actu
re u
sually
occu
rs b
efo
re y
ield
.HDPEPP
humid
dryPC
PET
¨
Room T values
y(ceramics) >>y(metals) >> y(polymers)
Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered
7.6 YIELD STRENGTH: COMPARISON
18
Maximum possible engineering stress in tension
• Metals: occurs when noticeable necking starts.• Ceramics: occurs when crack propagation starts.• Polymers: occurs when polymer backbones are aligned and about to break.
Adapted from Fig. 6.11, Callister 6e.
7.6 TENSILE STRENGTH, TS
strain
en
gin
eeri
ng
s
tress
TS
Typical response of a metal
19
Room T valuesSi crystal
<100>
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
Ten
sile
str
en
gth
, TS
(MPa
)
PVC
Nylon 6,6
10
100
200300
1000
Al (6061)a
Al (6061)agCu (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
20003000
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 TS(ceram)
~TS(met)
~ TS(comp) >> TS(poly)
Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%fibers.
7.6 TENSILE STRENGTH: COMPARISON
• Plastic tensile strain at failure:
20
Engineering tensile strain,
Engineering tensile stress,
smaller %EL (brittle if %EL<5%)
larger %EL (ductile if %EL>5%)
ductility as percent reduction in area
%AR
Ao A fAo
x100
• Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck.
Lo LfAo Af
%EL
L f LoLo
x100
Adapted from Fig. 6.13, Callister 6e.
7.6 DUCTILITY, %ELDegree of plastic deformation at fracture
Brittle, when very little plastic deformation
c07tf02
c07f14
Stress-strain of iron at several temperatures
RESILIENCE
Capacity to absorb energy when deformed elastically and then upon unloadign, to have this energy recovered
Modulus of Resilience
For a linear elastic region:
y
dU r
0
yyrU 2
1
• Ability to absorb energy up to fracture
21
smaller toughness- unreinforced polymers
Engineering tensile strain,
Engineering tensile stress,
smaller toughness (ceramics)
larger toughness (metals, PMCs)
7.6 TOUGHNESS
Usually ductile materials are tougher than brittle onesAreas below the curves
7.7 True stress & strain
Decline in stress necessary to continue deformation past MLooks like metal become weakerActually, it is increasing in strengthCross sectional area decreases rapidly within the neck regionReduction in the load-bearing capacity of the specimenStress should consider deformation
HARDENING: An increase in y due to plastic deformation.
22
• Curve fit to the stress-strain response:
large hardening
small hardeningunlo
ad
relo
ad
y 0
y 1
7.7 True stress & strain
nTT K n = hardening exponent
n = 0.15 (some steels)n = 0.5 (some copper)
c07tf04
7.8 Elastic Recovery After Plastic Deformation
7.9 Compressive, Shear, and Torsional Deformation
Similar to tensile counterpart
No maximum for compression
Necking does not occur
Mode of fracture different from that of tension
III. MECHANICAL BEHAVIOR—CERAMICSLimited applicability, catastrophic fracture in a brittle manner, little energy absorption
7.10 FLEXURAL STRENGTH
Tensile tests are difficultdifficult to prepare geometryeasy to fractureceramics fail at 0.1% strainbending stressrod specimen is usedthree of four point loading techniqueflexure test
7.10 MEASURING STRENGTH• Flexural strength= modulus of rupture= fracture strength = bend strength
• Type values:Material fs(MPa) E(GPa)
Si nitrideSi carbideAl oxideglass (soda)
700-1000550-860275-550
69
30043039069
Data from Table 12.5, Callister 6e.
22
3
bd
LFffs
3R
LFffs
7.11 Elastic Behavior (for ceramics)
Similar to tensile test for metals
Linear stress-strain
Moduli of elasticity for ceramics are slightly higher than for metals
No plastic deformation priorto fracture
7.12 INFLUENCE OF POROSITY ON THE MECHANICAL PROPERTIES OF CERAMICS
Powder as precursorCompaction to desire shapePores or voids elimination incompleteResidual porosity remainsDeleterious influence on elasticity and strengthVolume fraction porosity P
Eo = modulus of elasticity of the non porous material-Pores reduce the area -Pores are stress concentrators-tensile stress doubles in an isolated spherical pore
Aluminum oxideE = Eo(1 – 1.9P + 0.9P2)
Aluminum oxide
fs = oe-nP
• Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case)
Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig. 15.14, Callister 6e. (Fig. 15.14 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)
IV MECHANICAL BEHAVIOR—POLYMERS
7.13 STRESS—STRAIN BEHAVIOR
initial: amorphous chains are kinked, heavily cross-linked.
final: chains are straight,
still cross-linked
0
20
40
60
0 2 4 6
(MPa)
8
x
x
x
elastomer
plastic failure
brittle failure
Deformation is reversible!
26
• Decreasing T... --increases E --increases TS --decreases %EL
7.13 T & STRAIN RATE: THERMOPLASTICS
• Increasing strain rate... --same effects as decreasing T.
c07f25
7.14 Macroscopic Deformation
Semicrystaline polymer
7.15 Viscoelasticity Deformation
Amorphous polymer:Glass at low TViscous liquid at higher TSmall deformation at low T may be elastic Hooke’s lawRubbery solid at intermediate TA combination of glass and viscous/liquidViscoelasticityElastic deformation is instantaneousUpon release, deformation is totally recovered
c07f26
7.15 Viscoelasticity Deformation
Totally elastic
Viscoelastic
Viscous
Load
Relaxation Modulus for viscoelastic polymers:
or
ttE
)(
)(
Amorphous polystyreneA viscoelastic polymer
Polystyrene configurations
amorphous
Lightly crosslinked atactic
Almost totally crystalline isotactic
Viscoelastic creepCreep modulus Ec(t)
)()(
ttE o
c
V. Hardness & Other Mechanical Property Considerations
7.16 Hardness
Measure of material resistance to localized plastic deformationEarly tests: Mohs scale 1 for talc and 10 for diamond
Depth or size of an indentation
Tests:Mohs HardnessRockwell HardnessBrinell HardnessKnoop & Vickers Microindentation Hardness
c07tf05
c07tf06a
c07tf06b
Hardness Conversion
Correlation between Hardness and Tensile Strength
Tensile strength and Hardness measure metal resistance to plastic deformation
For example:
TS(Mpa) = 3.45 × HB
or
TS(psi) = 500 × HB
c07tf07
7.17 Hardness of Ceramic Materials
7.18 Tear Strength & Hardness of Polymers
Thin films in packagingTear Strength: Energy required to tear apart a cut specimen of a standard geometry
VI. Property Variability and Design/Safety Factors
7.19 Variability of Material Properties: Average and standard deviation
• Design uncertainties mean we do not push the limit.• Factor of safety, N
29
working
y
N
Often N isbetween1.2 and 4
• 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.
1045 plain carbon steel: y=310MPa TS=565MPa
F = 220,000N
d
Lo working
y
N
220,000N
d2 /4
5
7.20 DESIGN/SAFETY FACTORS
d = 47.5 mm
• 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 y.
30
• Toughness: The energy needed to break a unit volume of material.• Ductility: The plastic strain at failure.
SUMMARY