The document discusses mechanical properties and mechanical testing. It addresses key concepts like stress, strain, elastic behavior, plastic behavior, toughness, ductility, stress-strain curves, yield strength, tensile strength and the effects of temperature. Specifically, it explains that yield strength and tensile strength decrease with increasing temperature while ductility increases with temperature. Brittle materials have low ductility and toughness while ductile metals can absorb more energy due to plastic deformation.

1. Chapter 6 - 1
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 does permanent
deformation occur? What materials are most
resistant to permanent deformation?
• Toughness and ductility: What are they and how
do we measure them?
Chapter 6:
Mechanical Properties

2. Chapter 6 - 2
Mechanical Loads and Deformation
• Loads
– Tension and Compression
– Shear and Torsion
– Stress = Force / area
– What force ? Which Area ?
• Deformation
- Change in the shape of a specimen.
- Strain – relative change in its dimension
- Which dimension ?
• Stress-Strain Behavior  Property ?
• Which in What ?
– Forces  Statics
– Stresses  Strength of Materials
– Property-Structure  Material Science

3. Chapter 6 - 3
Engineering Stress-Definition
• Shear stress, τ:
Area, A
Ft
Ft
Fs
F
F
Fs
τ =
Fs
Ao
• Tensile stress, σ:
With original area (before loading)  Engineering Stress
With Ai (instantaneous area)  True Stress σT
σ =
Ft
Ao
2
f
2
m
N
or
in
lb
=
F
Area, A
Ft
t

4. Chapter 6 - 4
• Simple tension: cable
τ
Note: τ = M/AcR here.
Real Systems of Stress
Ao
FF
o
σ =
F
A
o
τ =
Fs
A
σσ
M
M Ao
2R
Fs
Ac
• Torsion (a form of shear): drive shaft

5. Chapter 6 - 5
• Simple compressioncompression:
Note: This is Compressive Stress (σ < 0)
Other Applications-STRESS
o
σ =
F
A
Ao

6. Chapter 6 - 6
• Bi-axial tension: • Hydrostatic compression:
Pressurized tank
σ < 0h
Other Applications-STRESS
Fish under water
σz > 0
σθ > 0

7. Chapter 6 - 7
• Tensile strain:
Engineering Strain-Definition
ε = δ (or ∆L)
Lo
δ/2
Lo
Where ∆L = L– Lo
* Note:
With L (instantaneous): integrate with variable L  True Strain  ε = Ln(1+ε)
At any instant AL = AoLo initial; (Constant Volume)
dε = dL
L
With Lo (constant)  Engineering Strain*
Integrate to get ε, from Lo to any
L
define
L

8. Chapter 6 - 8
Stress-Strain Testing
Typical tensile test machine
specimenextensometer
Typical tensile specimen
gauge
length

9. Chapter 6 - 9
Stress-Strain General Behavior
• True stress
• True Strain
iT AF=σ
( )oiT ln=ε
( )
( )ε+=ε
ε+σ=σ
1ln
1
T
T

10. Chapter 6 - 10
Stress Strain Behavior
Two behaviors: low loads versus large loads
Elastic Range
Initially, stress and strain are directly proportional to each other
Why: atoms can be thought of as masses connected to each other
through a network of springs (Imagine)
According to Hooke’s law:
the extension of a spring, x, and the applied force, F,
are related by the spring constant, k:
F = - kx
Thus, Stress (F/A) must be linear with strain
This is Stretching of bonds
Plastic Range
Non-Linear relation of stress with strain
 breaking of bonds and forming new bonds

11. Chapter 6 - 11
Linear Elastic Properties
• Modulus of Elasticity, E:
(also known as Young's modulus)
• Hooke's Law:
σ = E ε
F
Fsimple
tension
test
At low levels of stress: the shape is recoverable
The deformation is reversible
Linearity for Tension
Linearity for other types of stresses ? (later)
σ
Linear-
elastic
E
ε

12. Chapter 6 - 12
Elastic means reversible!
For some materials: it is non-linear
e.g. gray cast iron and concrete
Elastic Deformation
1. Initial 2. Small load 3. Unload
F
δ
bonds
stretch
return to
initial
F
δ
Linear-
elastic
Non-Linear-
elastic
Anelasticity: e = f (time); the specimen continue to deform

13. Chapter 6 - 13
Structure-Property Relationship
• Elastic modulus (E: slope of σ verus ε) depends on bond strength of
metal
• Remember curves Energy (E) versus interatomic spacing (r),
• Now interatomic force F versus r ?
E ~
dF
dr
roA
B
Which is more stiff ?

14. Chapter 6 - 14
Metals
Alloys
Graphite
Ceramics
Semicond
Polymers
Composites
/fibers
E(GPa)
Young’s Moduli: Comparison
109
Pa
0.2
8
0.6
1
Magnesium,
Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum
Graphite
Si crystal
Glass -soda
Concrete
Si nitride
Al 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
60
80
100
200
600
800
1000
1200
400
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTFE
HDPE
LDPE
PP
Polyester
PS
PET
CFRE( fibers) *
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*

15. Chapter 6 - 15
Poisson's ratio, ν
Upon Elongation in one direction (z) i.e. εz is +ve
 contraction occurs in the other two directions (εx and εy)
Theoretically, ν = ¼ , νmax = 0.5
Practically:
For metals: ν ~ 0.33
For ceramics: ν ~ 0.25
For polymers: ν ~ 0.40
ε
ν = − x
εz
ε
=− y
εz
Define Poisson's ratio, ν: : how much strain occurs in the lateral
directions (x& y) when strained in the (z) direction:
Note: For uniaxial stresses εx = εy

16. Chapter 6 - 16
Shear Strain-Definition
Remember: Strain is always dimensionless.
θ
90º
y
∆xθγ = ∆x/y = tanDefine
Elastic Shear modulus, G:
τ = G γ
Special relations for isotropic materials:
2(1+ ν)
E
G =
τ
G
γ
Units:
E abd G: [GPa] or [psi]
ν: dimensionless
Approximation: For most metals G ≅ 0.4 E (show ?)

17. Chapter 6 - 17
From Elastic to Plastic Behavior
What happens if we continue to apply tensile loading beyond the
elastic limit? (i.e., stretching atomic bonds to the point of breaking)
Plastic deformation:
• stress and strain are not proportional
• the deformation is not reversible
• deformation occurs by breaking and re-arrangement
of atomic bonds (in
Proportional Limit or elastic limit, is the point where
The stress and strain values at this point are known as the proportional-limit
stress and strain, respectively.
This is the point beyond which Hooke's law can no longer be used – no spring

18. Chapter 6 - 18
Plastic means permanent!
Not recoverable - irreversible
Plastic Deformation (Metals)
F
δ
linear
elastic
linear
elastic
δplastic
1. Initial 2. Small load 3. Unload
planes
still
sheared
F
δelastic + plastic
bonds
stretch
& planes
shear
δplastic

19. Chapter 6 - 19
(at lower temperatures, i.e. T < Tmelt/3)
Plastic (Permanent) Deformation
• Simple tension test:
engineering stress, σ
engineering strain, ε
Elastic+Plastic
at larger stress
permanent (plastic)
after load is removed
εp
plastic strain
Elastic
initially

20. Chapter 6 - 20
• Stress at which noticeable plastic deformation has occurred.
when εp = 0.002
Yield Strength, σy
σy = yield strength
tensile stress, σ
engineering strain, ε
σy
εp = 0.002
Proportionality Limit (P)
Initial deviation from linearity
Hard to determine  use yield strength
Why do we need σy ?
For design (to prevent plastic deformation)

21. Chapter 6 - 21
Yield Strength – Clear Case
For a low-carbon steel
• The stress vs. strain curve includes both an upper and lower yield point.
• The yield strength is defined in this case as
the average stress at the lower yield point

22. Chapter 6 - 22
Room T values
Yield Strength : Comparison
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Yieldstrength,σy(MPa)
PVC
Hardtomeasure,
sinceintension,fractureusuallyoccursbeforeyield.
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
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
Hardtomeasure,
inceramicmatrixandepoxymatrixcomposites,since
intension,fractureusuallyoccursbeforeyield.
HDPE
PP
humid
dry
PC
PET
¨

23. Chapter 6 - 23
Tensile Strength, TS
For Metals: TS occurs when noticeable necking starts.
σy
Typical response of a metal
F = fracture or
ultimate strength
Neck – acts as stress
concentrator
Later: types of fracture
engineering
TS
stress
engineering strain
• Maximum stress on engineering stress-strain curve.

24. Chapter 6 - 24
Tensile Strength : Comparison
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensilestrength,TS(MPa)
PVC
Nylon 6,6
10
100
200
300
1000
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure)
Ti (pure) a
Steel (1020)
Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a
W (pure)
Cu (71500) cw
LDPE
PP
PC PET
20
30
40
2000
3000
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 fibers
Aramid fib
Room Temp. values
Based on data in Table B4,
Callister 7e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worke
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers.

25. Chapter 6 - 25
Types of Failure (from Ch.8)
Ductile fracture is usually desirable!
Details in Chapter 8
Very
Ductile
Moderately
Ductile
Brittle
Fracture
behavior:
Large ModerateElongation: Small
Ductile:
warning before fracture
Brittle:
No warning

26. Chapter 6 - 26
• Evolution to failure:
Resulting fracture surfaces (steel)
50 mm
particles
serve as void
nucleation
sites.
50 mm
100 mm
Moderately Ductile Failure
necking
σ
void
nucleation
void growth
and linkage
shearing
at surface
fracture

27. Chapter 6 - 27
Ductile vs. Brittle Failure
cup-and-cone fracture brittle fracture

28. Chapter 6 - 28
Ductility
2- Percentage Area Reduction 100x
A
AA
RA%
o
fo
-
=
Percentage tensile strain at failure: x 100
L
LL
EL%
o
of
−
=
ε
σ smaller %EL
larger %EL
Lf
Ao
Af
Lo
Distinguish Behavior ? ductile versus brittle ?
Define a parameter - ductility: measures the amount of plastic deformation
that a material goes through by the time it breaks.
1- Elongation:
Ductility increases with temperature

29. Chapter 6 - 29
Energy absorbed by material up to fracture per unit volume
(Energy to break a unit volume of material at low strain rate)
• Approximation: the area under the stress-strain curve.
Toughness
Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
very small toughness
(unreinforced polymers)
ε
σ
small toughness (ceramics)
large toughness (metals)

30. Chapter 6 - 30
Effect of Testing Temperature on Mechanical Behavior
The yield and tensile strengths ………… with increasing temperature.
Ductility ……………. with temperature.
Stiffness …….. with temperature
Toughness …….. with temperature

31. Chapter 6 - 31
Resilience, Ur
Ability of a material to store energy and (release it upon unloading)
– Energy stored best in elastic region
If we assume a linear stress-strain curve:
yyr
2
1
U εσ≅
∫
ε
εσ= y
dUr 0
Units: J/m3
Show that
For springs: better to absorb large energy i.e.
Ur should be large
This needs large σy and low E

32. Chapter 6 - 32
Example
a) Modulus of elasticity
b) Yield strength
c) Tensile Strength
d) Fractural Strength
e) Ductility (% Elongation)
f) Resilience
g) Toughness
From the tensile σ - ε behavior for a specimen of brass shown in the figure, determine the
following:

33. Chapter 6 - 33
Hardness
Material Resistance to localized plastic deformation
Resistance to surface indentation (surface property)
Historically; the ability of material to scratch another
Large hardness means:
- resistance to plastic deformation or cracking in compression.
- better wear properties.
e.g., 10 mm sphere
(1) apply known force
(2) measure size of indent
after removing load
D
Smaller indents mean larger hardness
d
How: indenter with a load and a specimen
The indenter must be harder than the specimen, otherwise  flattening
Hardness is related to the size (depth) of the indentation
Specimen: smooth surface

34. Chapter 6 - 34
Hardness
increasing hardness
most
plastics
brasses
Al alloys
easy to machine
steels file hard
cutting
tools
nitrided
steels diamond
Importance of Hardness Test
• Easy
• Nondestructive
• Can be used to get other data (e.g. T.S.)
(both are resistance to plastic deformation)
There are different scales for hardness- they vary in:
Shape of indenter: (1) ball, (2) conical diamond and (3) square based diamond
Load : 100 kg, 150 kg …etc/
Rockwell: uses indenter (1) and (2) - for rapid and routine tests
Brinell: uses indenter (1) for materials with moderate hardness
Vickers: uses indenter (3) for all ranges – more accurate
HB = Brinell Hardness
TS (psia) = 500 x HB
TS (MPa) = 3.45 x HB

35. Chapter 6 - 35
Hardness: Measurement
Table 6.5

36. Chapter 6 - 36
Hardening
• Curve fit to the stress-strain response:
σT = K εT( )n
“true” stress (F/A) “true” strain: ln(L/Lo)
hardening exponent:
n = 0.15 (some steels)
to n = 0.5 (some coppers)
• An increase in σy due to plastic deformation.
σ
ε
large hardening
small hardeningσy0
σy
1

37. Chapter 6 - 37
• Design uncertainties mean we do not push the limit.
• Factor of safety, N
N
y
working
σ
=σ
Often N is
between
1.2 and 4
Example: 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.
Data for Design - Safety Factors
( )4
000220
2
/d
N,
π
5
N
y
working
σ
=σ 1045 plain
carbon steel:
σy = 310 MPa
TS = 565 MPa
F = 220,000N
d
Lo
d = 0.067 m = 6.7 cm

38. Chapter 6 - 38
• 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).
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.
Summary
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches σy.

39. Chapter 6 - 39
• Impact Test – Rapid loading
• Fatigue Test – Cyclic loading
• Creep Test – Effect of time
Other Tests from Chapter 8

40. Chapter 6 - 40
Impact Testing
final height initial height
(Charpy)
•Measures Toughness
•“energy absorbed by a specimen up to fracture”
•Upon Rapid loading
Energy absorbed =
change in potential energy of the hammer

41. Chapter 6 - 41
Note: Loading Rate
• Increased loading rate...
-- increases σy and TS
-- decreases %EL
• Why? An increased rate
gives less time for
dislocations to move past
obstacles.σ
ε
σy
σy
TS
TS
larger
ε
smaller
ε

42. Chapter 6 - 42
• Increasing temperature...
--increases %EL and Kc
• Ductile-to-Brittle Transition Temperature (DBTT)...
Impact Results and Effect of Temperature
BCC metals (e.g., iron at T < 914°C)
ImpactEnergy
Temperature
High strength materials (σ y > E/150)
polymers
More DuctileBrittle
Ductile-to-brittle
transition temperature
FCC metals (e.g., Cu, Ni)
Adapted from Fig. 8.15,
Callister 7e.

43. Chapter 6 - 43
• Pre-WWII: The Titanic • WWII: Liberty ships
• Problem: Used a type of steel with a DBTT ~ Room temp.
Design Strategy:
Stay Above The DBTT!
Ship-cyclic loading
from waves.
Large Impact

44. Chapter 6 - 44
Fatigue
• Fatigue = failure under cyclic stress.
causes ~ 90% of mechanical engineering failures
• Stress varies with time.
key parameters are S, σm, and frequency
σmax
σmin
σ
time
σm
S
tension on bottom
compression on top
countermotor
flex coupling
specimen
bearing bearing
Count number of cycles to failure
Stress amplitude S or σa
σa= σmax+(-σmin)
2

45. Chapter 6 - 45
Fatigue limit, Sfat:
no fatigue if S < Sfat
Fatigue limit OR
Endurance limit ≅ T.S./2
Fatigue Results and Design Parameters
Sfat
case for
steel (typ.)
N = Cycles to failure
10
3
10
5
10
7
10
9
unsafe
safe
S = stress amplitude
Sometimes, the fatigue limit is zero!
case for
Al (typ.)
N = Cycles to failure
10
3
10
5
10
7
10
9
unsafe
safe
S = stress amplitude
Ferrous alloysFerrous alloys
Nonferrous alloysNonferrous alloys

46. Chapter 6 - 46
Creep
Time-dependent deformation
Sample deformation at a constant stress (σ) vs. time
Important at elevated temperature
i.e. at T > 40% of Tmelting
σ
σ,ε
0 t
How ?
• Subject the specimen to constant load
• Measure Length as f(time)
• Then get ε = (L-Lo)/Lo = f(time)
• Plot the curve

47. Chapter 6 - 47
Results of Creep
Primary Creep: slope (creep rate) decreases with time.
Secondary Creep: steady-state i.e., constant slope.
Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate.

48. Chapter 6 - 48
• Occurs at elevated temperature, T > 0.4 Tm
Effect of Temperature on Creep
elastic
primary
secondary
tertiary