1. Chapter 7:機械性質(Mechanical Properties)
Tensile & Hardness Testing;
Macroscopic Behavior;
Elastic Deformation;
Elastic Modulus;
Proportional Limit;
Poisson's Ratio;
Plastic deformation;
Yielding and Yielding Strength;
Tensile Strength;
Fracture Strength;
Ductility;
Resilience;
Toughness
Property Variability;
Design Safety Factors. 1 1

2. 7.2 應力和應變(Stress and Strain)的觀念
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3. 拉力試驗
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4. Common States of Stress
• Simple tension: cable A o
= cross sectional
area (when unloaded) F o s = F A s
• Torsion (a form of shear): drive shaft M A o 2R F s c o t = F s A
Note: R × t ×Ac= M here. 4 4

5. OTHER COMMON STRESS STATES (i)
• Simple compression: A o
Balanced Rock, Arches
National Park
(photo courtesy P.M. Anderson)
Canyon Bridge, Los Alamos, NM o s = F A
Note: compressive
structure member
(s < 0 here).
(photo courtesy P.M. Anderson) 5 5

6. OTHER COMMON STRESS STATES (ii)
• Bi-axial tension:
• Hydrostatic compression:
Fish under water
Pressurized tank
(photo courtesy
P.M. Anderson)
(photo courtesy
P.M. Anderson) s z
> 0 q
s < 0 h 6 6

7. Engineering Stress s = F A F t s = A m N or in lb • Tensile stress, s:
original area
before loading s = F t A o 2 f m N or in lb
Area, Ao
• Shear stress, t:
Area, Ao F t s = A o
 Stress has units: N/m2 or lbf /in2 7 7

8. Engineering Strain L w e = d L - d e = w q g = Dx/y = tan
• Tensile strain: d /2 L o w
• Lateral strain: e = d L o - d e L = w o d L /2
• Shear strain: q
90º
90º - q y x
g = Dx/y = tan
Strain is always
dimensionless.
Adapted from Fig. 7.1 (a) and (c), Callister & Rethwisch 3e. 8 8

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10. 彈性變形(Elastic Deformation) 7.3 應力-應變行為(Stress-Strain behavior)
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11. Elastic Deformation d F F d 1. Initial 2. Small load 3. Unload
bonds
stretch
3. Unload
return to
initial F
Linear-
elastic
Elastic means reversible!
Non-Linear-
elastic d 11 11

12. Linear Elastic Properties
• Modulus of Elasticity, E:
(also known as Young's modulus)
• Hooke's Law:
s = E e s
Linear-
elastic E e F
simple
tension
test 12 12

13. Plastic Deformation (Metals)
1. Initial
2. Small load
3. Unload
planes
still
sheared F d
elastic + plastic
bonds
stretch
& planes
shear
plastic F d
linear
elastic
plastic
Plastic means permanent! 13 13

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15. c07f07
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16. Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal
Adapted from Fig. 7.7,
Callister & Rethwisch 3e. 16 16

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19. Young’s Moduli: Comparison
Graphite
Ceramics
Semicond
Metals
Alloys
Composites
/fibers
Polymers
0.2 8
0.6 1
Magnesium,
Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum G
raphite
Si crystal
Glass -
soda
Concrete
Si nitride
Al oxide PC
Wood( grain)
AFRE( fibers) *
CFRE
GFRE*
Glass fibers only
Carbon
fibers only A
ramid fibers only
Epoxy only
0.4
0.8 2 4 6 10 00
1200
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTF E
HDP
LDPE PP
Polyester PS
PET C
FRE( fibers)
FRE( fibers)*
FRE(|| fibers)*
E(GPa)
Based on data in Table B.2,
Callister & Rethwisch 3e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers.
109 Pa 19 19

20. 7.4 滯彈性(Anelasticity)
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21. 7.5 材料的彈性性質(Poission’s Ratio)
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22. Poisson's Ratio, n eL e -n e n = - • Poisson's ratio, n: Units:
metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40
Units:
E: [GPa] or [psi]
n: Dimensionless
 > density increases
 < density decreases (voids form) 22 22

23. Other Elastic Properties
simple
torsion
test M t G g
• Elastic Shear
modulus, G:
t = G g
• Elastic Bulk
modulus, K:
pressure
test: Init.
vol =Vo.
Vol chg.
= DV P
P = - K D V o
• Special relations for isotropic materials:
2(1 + n) E G =
3(1 - 2n) K 23 23

24. c07prob
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25. c07f10ab 7.6 拉力性質(塑性變形) Mechanical Properties: Macroscopic Behavior;
Elastic Deformation;
Elastic Modulus;
Proportional Limit;
Poisson's Ratio;
Plastic deformation;
Yielding and Yielding Strength;
Tensile Strength;
Fracture Strength;
Ductility;
Resilience;
Toughness.
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26. Plastic (Permanent) Deformation
(at lower temperatures, i.e. T < Tmelt/3)
• Simple tension test:
Elastic+Plastic
at larger stress
engineering stress, s
Elastic
initially
permanent (plastic)
after load is removed ep
plastic strain
engineering strain, e
Adapted from Fig (a),
Callister & Rethwisch 3e. 26 26

27. Yielding and Yield Strength, y
• Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002
tensile stress, s
engineering strain, e sy p
= 0.002
y = yield strength
Note: for 2 inch sample
 = = z/z
 z = in
Adapted from Fig (a),
Callister & Rethwisch 3e. 27 27

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29. Tensile Strength, TS TS engineering stress strain engineering strain
• Maximum stress on engineering stress-strain curve. y
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts as stress concentrator
engineering TS
stress
engineering strain
Adapted from Fig. 7.11, Callister & Rethwisch 3e.
• Metals: occurs when noticeable necking starts.
• Polymers: occurs when polymer backbone chains are
aligned and about to break. 29 29

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31. Yield Strength : Comparison
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Yield strength, s y
(MPa)
PVC
Hard to measure ,
since in tension, fracture usually occurs before yield.
Nylon 6,6
LDPE 70 20 40 60 50
100 10 30
200
300
400
500
600
700
1000
2000
Tin (pure) Al
(6061) a ag Cu
(71500) hr Ta
(pure) Ti
Steel
(1020) cd
(4140) qt
(5Al-2.5Sn) W
Mo (pure) cw
Hard to measure,
in ceramic matrix and epoxy matrix composites, since
in tension, fracture usually occurs before yield. H
DPE PP
humid
dry PC
PET
Room temperature values
Based on data in Table B.4,
Callister & Rethwisch 3e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered 31 31

32. Tensile Strength: Comparison
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensile
strength, TS
(MPa)
PVC
Nylon 6,6 10
100
200
300
1000 Al
(6061) a ag Cu
(71500) hr Ta
(pure) Ti
Steel
(1020)
(4140) qt
(5Al-2.5Sn) W cw L
DPE PP PC
PET 20 30 40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride H
wood
( fiber)
wood(|| fiber) 1
GFRE
(|| fiber)
( fiber) C
FRE A
FRE( fiber)
E-glass fib
Aramid
fib
Room temperature values
Based on data in Table B4,
Callister & Rethwisch 3e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers. 32 32

33. Ductility(延性)
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34. Ductility x 100 L EL % - = • Plastic tensile strain at failure: Lf Ao
Adapted from Fig. 7.13, Callister & Rethwisch 3e.
Engineering tensile strain, e E
ngineering
tensile
stress, s
smaller %EL
larger %EL Lf Ao Af Lo
• Another ductility measure:
100 x A RA % o f - = 34 34

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37. Resilience(彈性能, 回彈性), Ur
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38. Resilience, Ur 2 1 U e s @ Ability of a material to store energy
Energy stored best in elastic region
If we assume a linear stress-strain curve this simplifies to y r 2 1 U e s @
Adapted from Fig. 7.15, Callister & Rethwisch 3e. 38 38

39. Toughness(韌性) • Energy to break a unit volume of material
• Approximate by the area under the stress-strain curve.
very small toughness
(unreinforced polymers)
Engineering tensile strain, e E
ngineering
tensile
stress, s
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 7.13, Callister & Rethwisch 3e.
Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy 39 39

40. 7.7 真應力與真應變
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42. 7.8 塑性變形期間之彈性回復
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43. Elastic Strain Recovery
syi D
syo
Elastic strain
recovery
2. Unload
Stress
1. Load
3. Reapply
load
Strain
Adapted from Fig. 7.17, Callister & Rethwisch 3e. 43 43

44. 7.10 Fexural Strength of Ceramics)
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45. Mechanical Properties of Ceramics
Ceramic materials are more brittle than metals. Why is this so?
Consider mechanism of deformation
In crystalline, by dislocation motion
In highly ionic solids, dislocation motion is difficult
few slip systems
resistance to motion of ions of like charge (e.g., anions) past one another 45 45

46. Flexural Tests – Measurement of Elastic Modulus
• Room T behavior is usually elastic, with brittle failure.
• 3-Point Bend Testing often used.
-- tensile tests are difficult for brittle materials. F
L/2
d = midpoint
deflection
cross section R b d
rect.
circ.
Adapted from Fig. 7.18, Callister & Rethwisch 3e.
• Determine elastic modulus according to: F x
linear-elastic behavior d
slope =
(rect. cross section)
(circ. cross section) 46 46

47. Flexural Tests – Measurement of Flexural Strength
• 3-point bend test to measure room-T flexural strength. F
L/2
d = midpoint
deflection
cross section R b d
rect.
circ.
location of max tension
Adapted from Fig. 7.18, Callister & Rethwisch 3e.
• Flexural strength:
• Typical values:
Data from Table 7.2, Callister & Rethwisch 3e.
Si nitride
Si carbide
Al oxide
glass (soda-lime) 69
304
345
393
Material s fs
(MPa) E(GPa)
(rect. cross section)
(circ. cross section) 47 47

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51. 7.16 硬度(Hardness)與硬度試驗
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56. 7.19 Property Variability and Design Safety Factors
Elastic modulus is material property
Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability.
Statistics
Mean
Standard Deviation
All samples have same value
Because of large variability must have safety margin in engineering specifications 56
where n is the number of data points 56

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58. Summary • 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 sy.
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure. 58 58