introduction to aerospace mechanics of materials lecture 2aeweb.tamu.edu/aero214/lecture 2 aero 214...
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Materials for Aerospace Structures
• Aluminum
• Titanium
• Composites: Ceramic Fiber-Reinforced Polymer Matrix Composites
• High Temperature Materials: Superalloys and Ceramics
F
bonds
stretch
return to
initial
2
1. Initial 2. Small load 3. Unload
• Elastic, no remaining deformation upon unloading
• Due to stretching of bonds
Elastic Deformation
F
Linear Elastic
Non-Linear Elastic
• Modulus of Elasticity, E: (also known as Young's modulus)
10
• Hooke's Law:
Linear Elastic Isotropic
s
Linear- elastic
E e
13 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
<100>
<111>
Si carbide
Diamond
PTFE
HDPE
LDPE
PP
Polyester
PSPET
CFRE( fibers)*
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
Metals
Alloys
Graphite
Ceramics
Semicond
Polymers Composites
/fibers
E(GPa)
Based on data in Table B2,
Callister 6e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers.
Comparison of Elastic Moduli
3
1. Initial 2. Small load 3. Unload
• Plastic means permanent! • Permanent set • Proportional/elastic limit • Yielding point
F
linear elastic
linear elastic
plastic
Plastic Deformation in Metals
15
• Simple tension test:
(at lower temperatures, T < Tmelt/3)
Plastic Deformation in Metals
tensile stress, s
engineering strain, e Elastic
initially
Elastic+Plastic at larger stress
permanent (plastic) after load is removed
e p plastic strain
17
Room T values
sy(ceramics)
>>sy(metals)
>> sy(polymers)
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Comparison of Yield Strength Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
Yie
ld s
tren
gth
, s
y (M
Pa)
PVC
Ha
rd t
o m
ea
su
re ,
s
inc
e i
n t
en
sio
n,
fra
ctu
re u
su
all
y o
cc
urs
be
fore
yie
ld.
Nylon 6,6
LDPE
70
20
40
60 50
100
10
30
2 00
3 00
4 00
5 00 6 00 7 00
10 00
2 0 00
Tin (pure)
Al (6061) a
Al (6061) ag
Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) hr
Steel (1020) cd Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a W (pure)
Mo (pure) Cu (71500) cw
Ha
rd t
o m
ea
su
re,
in c
era
mic
ma
trix
an
d e
po
xy
ma
trix
co
mp
os
ite
s,
sin
ce
in t
en
sio
n,
fra
ctu
re u
su
all
y o
cc
urs
be
fore
yie
ld.
H DPE PP
humid
dry
PC
PET
¨
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)
Ductile vs Brittle Failure
Very
Ductile
Moderately
Ductile Brittle
Fracture
behavior:
Large Moderate %AR or %EL Small
Adapted from Fig. 8.1,
Callister 7e.
• Ductile: warning (large plastic deformation) before fracture
• Brittle: No warning
17
• Evolution to failure: Necking is the localization of damage
100 mm
Fracture surface of tire cord wire
loaded in tension. Courtesy of F.
Roehrig, CC Technologies, Dublin,
OH. Used with permission.
Moderately Ductile Failure
necking
s
void nucleation
void growth and linkage
shearing at surface
fracture
Tensile strain at failure, %EL:
20
%AR
Ao A f
Ao
x100
• Note: %AR and %EL are often comparable. crystal slip does not change material volume. %AR > %EL possible if internal voids form in neck.
%EL
L f Lo
Lo
x100
Adapted from Fig. 6.13,
Callister 6e.
Ductility
Reduction in the area at failure, %AL:
• Ability to absorb energy up to fracture
21
smaller toughness- unreinforced polymers
Engineering tensile strain, e
Engineering
tensile
stress, s
smaller toughness (ceramics)
larger toughness (metals, PMCs)
• Usually ductile materials have more toughness than brittle one • Areas below the curves
Toughness
0
f
W de
s e
True Stress & Strain
iT AFs
oiT lne
ee
ess
1ln
1
T
T
• Curve fit to the stress-strain of plastic deformation:
s T K e T n
“true” stress (F/A) “true” strain: ln(L/Lo)
hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers)
22
• Curve fit to the stress-strain response:
True stress & strain
n
TT Kes n = hardening exponent
n = 0.15 (some steels)
n = 0.5 (some copper)
Material
Elastic
Modulus (E)
[GPa]
Strength (S)
[MPa]
%
Elongation
Aluminum
Al 7075-T6 71.7 Yield Strength: 505 11% 2810 25.5 0.18
Titanium
Ti-6Al-4V 113.8 Yield Strength: 830 14% 4430 25.7 0.187
Epoxy 2.41 Tensile Strength: 40 5% 1300 1.85 0.031
Carbon Fiber 230 Tensile Strength: 4000 2% 1780 129.2 2.25
Carbon fiber-Epoxy
Composite
(Vf=60%)
Longitudinal: 220 Tensile Strength: 760 0.3
1700
129.4 0.447
Transverse: 6.9 Tensile Strength: 28 0.4 4.06 0.016
Properties of Common Aerospace Structural Materials
Hardness • Measure of resistance to localized plastic deformation • Simple, non-destructive, not a well-defined material property
1. Scratch hardness: Mohs scale, 2. Indentation hardness: Rockwell, Vickers, Brinell, Shore 3. Rebound (Dynamic) hardness: Leeb, scleroscope
• Larger hardness:
• smaller indent • resistance to plastic deformation or cracking in compression • better wear properties
increasing hardness
most plastics
brasses Al alloys
easy to machine steels file hard
cutting tools
nitrided steels diamond
Brinell Hardness (HB)
10 mm sphere
F= 10,000 N measure size of indent after removing load
d D Smaller indents mean larger hardness.
• D=10 mm hardened steel
• Keep at least 3 indentation diameters away from the edge or previous mark
• Hardness can be related to tensile strength • For steel: TS (MPa) = 3.45 × HB
Stress-Strain Behaviors of Polymers
brittle polymer
Plastic polymer
elastomer
Tensile strength of polymer ca. 10% that of metals
Strains – deformations > 1000% possible (for metals, maximum strain ca. 10% or less)
elastic modulus – less than metal
37
Dislocation Motion Dislocations & plastic deformation
• Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).
• If dislocations don't move,
deformation doesn't occur! Adapted from Fig. 7.1,
Callister 7e.