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 do dislocations cause permanent deformation? What materials are most resistant to permanent deformation?
1
• Toughness and ductility: What are they and how do we measure them?
CHAPTER 7: MECHANICAL PROPERTIES
• Ceramic Materials: What special provisions/tests aremade for ceramic materials?
F
bonds stretch
return to initial
2
1. Initial 2. Small load 3. Unload
Elastic means reversible!
F
Linear- elastic
Non-Linear-elastic
ELASTIC 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
PLASTIC DEFORMATION (METALS)
4
• Tensile stress, : • Shear stress, :
Area, A
Ft
Ft
FtAo
original area before loading
Area, A
Ft
Ft
Fs
F
FFs
FsAo
Stress has units:N/m2 or lb/in2
ENGINEERING STRESS
8
• Tensile strain: • Lateral strain:
• Shear strain:/2
/2
/2 -
/2
/2
/2L/2L/2
Lowo
LoL 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
extensometer specimen
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.)
STRESS-STRAIN TESTING
• 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
LINEAR ELASTIC PROPERTIES
• Elastic Shear modulus, G:
12
1G
= G
• Elastic Bulk modulus, K:
P= -KVVo
PV
1-K Vo
• Special relations for isotropic materials:
PP P
M
M
G
E2(1 )
K E
3(1 2)
simpletorsiontest
pressuretest: Init.vol =Vo. Vol chg. = V
OTHER ELASTIC PROPERTIES
130.2
8
0.61
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
406080100
200
6008001000
1200
400
Tin
Cu alloys
Tungsten
<100><111>
Si carbide
Diamond
PTF E
HDPE
LDPE
PP
PolyesterPSPET
CFRE( fibers)*
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
MetalsAlloys
GraphiteCeramicsSemicond
Polymers Composites/fibers
E(GPa)
Eceramics > Emetals >> Epolymers
109 Pa
YOUNG’S MODULI: COMPARISON
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
PLASTIC (PERMANENT) DEFORMATION
16
• Stress at which noticeable plastic deformation has occurred.
when p = 0.002 tensile stress,
engineering strain,
y
p = 0.002
YIELD STRENGTH, y
17
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
Yiel
d st
reng
th,
y (M
Pa)
PVC
Hard
to m
easu
re,
since
in te
nsion
, fra
ctur
e us
ually
occ
urs b
efor
e yie
ld.
Nylon 6,6
LDPE
70
20
40
6050
100
10
30
200300400500600700
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
Hard
to m
easu
re,
in c
eram
ic m
atrix
and
epo
xy m
atrix
com
posit
es, s
ince
in te
nsion
, fra
ctur
e us
ually
occ
urs b
efor
e yie
ld.
HDPEPP
humid
dryPCPET
¨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
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.
TENSILE STRENGTH, TS
strain
eng
inee
ring
stre
ssTS
Typical response of a metal
19
Room T valuesSi crystal
<100>
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
Tens
ile s
treng
th, T
S (M
Pa)
PVCNylon 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
PPPC PET
20
3040
200030005000
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 fibC 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.
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%)
• Another ductility measure: %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.
DUCTILITY, %EL
• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.
21
smaller toughness- unreinforced polymers
Engineering tensile strain,
Engineering tensile stress,
smaller toughness (ceramics)larger toughness (metals, PMCs)
TOUGHNESS
• An increase in y due to plastic deformation.
22
• Curve fit to the stress-strain response:
large hardening
small hardeningun
load
relo
ad
y 0y 1
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)
HARDENING
23
• 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
= midpoint deflection
cross sectionR
bd
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 =
Adapted from Fig. 12.29, Callister 6e.
MEASURING ELASTIC MODULUS
24
• 3-point bend test to measure room T strength.F
L/2 L/2cross section
Rb
d
rect. circ.location of max tension
• Flexural strength:
rect. fs m
fail 1.5FmaxLbd2
FmaxLR3
xFFmax
max
• Typ. values:Material fs(MPa) E(GPa)Si nitrideSi carbideAl oxideglass (soda)
700-1000550-860275-550
69
30043039069
Adapted from Fig. 12.29, Callister 6e.
Data from Table 12.5, Callister 6e.
MEASURING STRENGTH
25
• 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.)
TENSILE RESPONSE: ELASTOMER CASE
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
• Increasing strain rate... --same effects as decreasing T.
Adapted from Fig. 15.3, Callister 6e. (Fig. 15.3 is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.)
20
40
60
80
00 0.1 0.2 0.3
4°C
20°C
40°C
60°C to 1.3
(MPa)
Data for the semicrystalline polymer: PMMA (Plexiglas)
T AND STRAIN RATE: THERMOPLASTICS
27
• Stress relaxation test:
Er(t)
(t)o
--strain to and hold.--observe decrease in stress with time.
• Relaxation modulus:
• Data: Large drop in Er for T > Tg.
(amorphouspolystyrene)
• Sample Tg(C) values:PE (low Mw)PE (high Mw)PVCPSPC
-110- 90+ 87+100+150
103
101
10-1
10-3
105
60 100 140 180
rigid solid (small relax)
viscous liquid (large relax)
transition region
T(°C)Tg
Er(10s) in MPa
Adapted from Fig. 15.7, Callister 6e. (Fig. 15.7 is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.)
Selected values from Table 15.2, Callister 6e.
TIME DEPENDENT DEFORMATION
time
straintensile test
ot( )
• Resistance to permanently indenting the surface.• Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties.
28
e.g., 10mm sphere
apply known force (1 to 1000g) 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
Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Propertiesand Applications of Plastics, p. 202, John Wiley and Sons, 1957.)
HARDNESS
• Design uncertainties mean we do not push the limit.• Factor of safety, N
29
working yN
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 yN
220,000N d2 /4
5
DESIGN OR SAFETY FACTORS
25
Thermal ExpansionMaterials change size when temperature is changed
)(α initialfinalinitial
initialfinal TT
linear coefficient ofthermal expansion (1/K or 1/°C)
Tinitial
Tfinal
initial
final
Tfinal > Tinitial
26
Atomic Perspective: Thermal Expansion
Asymmetric curve: -- increase temperature, -- increase in interatomic separation -- thermal expansion
Symmetric curve: -- increase temperature, -- no increase in interatomic separation -- no thermal expansion
27
Coefficient of Thermal Expansion: Comparison
• Q: Why does
generally decrease with increasing bond energy?
Polypropylene 145-180 Polyethylene 106-198 Polystyrene 90-150 Teflon 126-216
• Polymers
• CeramicsMagnesia (MgO) 13.5Alumina (Al2O3) 7.6Soda-lime glass 9Silica (cryst. SiO2) 0.4
• MetalsAluminum 23.6Steel 12 Tungsten 4.5 Gold 14.2
(10-6/C)at room T
Material
Polymers have larger values because of weak secondary bonds
incr
easi
ng
28
• Occur due to: -- restrained thermal expansion/contraction -- temperature gradients that lead to differential
dimensional changes
Thermal Stresses
E(T0 Tf ) ETThermal stress
• 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.
Note: For materials selection cases related to mechanical behavior, see slides 20-4 to 20-10.
SUMMARY