Chapter 1:

Mechanical Properties
Mechanical properties?
The response or deformation of materials to an applied
load or force.

Chapter 6 -
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 - 2
 Introduction
To understand and describe how materials deform (elongate,
compress, twist) or break as a function of applied load, time,
temperature, and other conditions we need first to discuss standard
test methods and standard language for mechanical properties of
materials.

extensometer specimen

Chapter 6 - 3
Chapter 6 - 4
Chapter 6 - 5
 What is the unit of Engineering Stress?
• Tensile stress, s: • Shear stress, t:
Ft Ft F

Area, A Area, A Fs

Fs
Ft
Fs Ft
Ft N t= F
s= = 2
Ao
Ao m
original area
before loading
 Stress has units:
N/m2
Chapter 6 - 6
What is the unit of Engineering Strain?

Chapter 6 - 7
 Unit of Engineering Strain
• Tensile strain: • Lateral strain:
d/2
-dL
e = d eL =
Lo Lo wo
wo

dL /2
• Shear strain:
q
x g = x/y = tan q

y 90º - q
Strain is always
90º dimensionless.
Chapter 6 - 8
 Real Example of Stress
• Simple tension: cable
F F
A o = cross sectional
area (when unloaded)
F
s= s s
Ao
Ski lift
• Torsion (a form of shear): drive shaft
M Fs Ao
Ac
Fs
t =
Ao
M
2R
Chapter 6 -
 Real Example of Stress
• Simple compression:

Ao

Canyon Bridge, Los Alamos, NM

F
s=
Note: compressive
Balanced Rock, Arches structure member
National Park Ao (s < 0 here).

Chapter 6 - 10
Real Example of Stress (Other Type )
• Bi-axial tension: • Hydrostatic compression:

Pressurized tank Fish under water

sq > 0

sz > 0 sh< 0

Chapter 6 - 11
extensometer specimen

Chapter 6 - 12
What is actually happened: Elastic Deformation
1. Initial 2. Small load 3. Unload

bonds
stretch

return to
initial
d
F
F Linear-
elastic
Elastic means reversible! Non-Linear-
elastic
d
Chapter 6 - 13
What is actually happened: Plastic Deformation (Metals)

1. Initial 2. Small High load 3. Unload

bonds
stretch p lanes
& planes still
shear sheared

dplastic
delastic + plastic

F
F
Plastic means permanent! linear linear
elastic elastic
d
dplastic
Chapter 6 - 14
Chapter 6 - 15
Chapter 6 - 16
Chapter 6 - 17
 metals: n ~ 0.33
ceramics: n ~ 0.25
polymers: n ~ 0.40

Chapter 6 - 18
Chapter 6 - 19
Chapter 6 - 20
 Young’s Moduli: Comparison
Graphite
Metals Composites
Ceramics Polymers
Alloys /fibers
Semicond
1200
10 00 Diamond
800
600
Si carbide
400 Tungsten Al oxide Carbon fibers only
Molybdenum Si nitride
E(GPa) 200
Steel, Ni
Tantalum <111>
C FRE(|| fibers)*
Platinum Si crystal
Cu alloys <100> Aramid fibers only
10 0 Zinc, Ti
80 Silver, Gold
Glass -soda A FRE(|| fibers)* Composite data based on
Aluminum Glass fibers only
60
40
Magnesium,
Tin G FRE(|| fibers)* reinforced epoxy with 60 vol%
Concrete of aligned
109 Pa 20 GFRE*
CFRE *
carbon (CFRE),
aramid (AFRE), or
G raphite G FRE( fibers)*
10 glass (GFRE)
8 C FRE( fibers) *
6 AFRE( fibers) *
fibers.
Polyester
4 PET
PS
PC Epoxy only
2
PP
1 HDP E
0.8
0.6 Wood( grain)
PTF E
0.4

0.2 LDPE Chapter 6 - 21

 Useful Linear Elastic Relationships
• Simple tension:

d = FL o d = - n Fw o
L
EA o EA o
F
d/2
Ao
Lo
wo

dL /2
• Material, geometric, and loading parameters all
contribute to deflection.
• Larger elastic moduli minimize elastic deflection.
Chapter 6 - 22
Stress-Strain Behavior: Plastic Deformation

Chapter 6 - 23
 Plastic (Permanent) Deformation
(at lower temperatures, i.e. T < Tmelt/3)

• Example: Simple tension test:

Elastic+Plastic
engineering stress, s at larger stress

Elastic
initially
permanent (plastic)
after load is removed

ep engineering strain, e

plastic strain

Chapter 6 - 24
Dislocations movement will cause plastic deformations.

Similar to the movement of a caterpillar.

Chapter 6 - 25
Ice-cream, dislocations and plastic deformations.

Chapter 6 - 26
Formation and observation of slip.

Under microscope.
Chapter 6 - 27
Real observation of dislocations movement.

Chapter 6 - 28
Stress at which noticeable
plastic deformation has
occurred.

Chapter 6 - 29
Chapter 6 - 30
 Yield Strength : Comparison
Graphite/
Metals/ Composites/
Ceramics/ Polymers
Alloys fibers
Semicond
20 00
Steel (4140) qt

10 00
Yield strength, sy (MPa)

Ti (5Al-2.5Sn) a

in ceramic matrix and epoxy matrix composites, since

700 W (pure)

since in tension, fracture usually occurs before yield.

in tension, fracture usually occurs before yield.

600 Cu (71500) cw
500 Mo (pure)
400 Steel (4140) a
Steel (1020) cd
300
Room T values
Hard to measure ,

Hard to measure,
Al (6061) ag
200 Steel (1020) hr ¨
Ti (pure) a
Ta (pure)
Cu (71500) hr a = annealed
hr = hot rolled
100 ag = aged
dry
70 PC
cd = cold drawn
60 Al (6061) a Nylon 6,6 cw = cold worked
50 PET
qt = quenched & tempered
40 PVC humid
PP
30 HDPE

20

LDPE
Tin (pure) Chapter 6 - 31
10
Chapter 6 - 32
 Tensile Strength : Comparison
Graphite/
Metals/ Composites/
Ceramics/ Polymers
Alloys fibers
Semicond
5000 C fibers
Aramid fib
3000 E-glass fib
Tensile strength, TS (MPa)

2000 Steel (4140) qt

A FRE(|| fiber)
1000 W (pure) Diamond GFRE(|| fiber)
Ti (5Al-2.5Sn)aa CFRE(|| fiber) Room Temp. values
Steel (4140)cw
Cu (71500) Si nitride
Cu (71500) hr Al oxide
Steel (1020)
300 ag
Al (6061) a a = annealed
Ti (pure) hr = hot rolled
200 Ta (pure)
ag = aged
Al (6061) a
100 Si crystal wood(|| fiber) cd = cold drawn
<100> Nylon 6,6
Glass-soda PC PET cw = cold worked
40 PVC GFRE( fiber) qt = quenched & tempered
Concrete PP
30 CFRE( fiber)
A FRE( fiber) AFRE, GFRE, & CFRE =
HDPE aramid, glass, & carbon
20 Graphite
LDPE fiber-reinforced epoxy
composites, with 60 vol%
10 fibers.

wood ( fiber)

1 Chapter 6 -
 Quiz:

Please determine the following:

1) The modulus of elasticity
2) The yield strength at a strain offset of 0.2%
3) The maximum load that can be sustained by a cylindrical specimen having an
original diameter of 12.8mm.
4) The change in length of a specimen originally 250mm long that is subjected to a
tensile stress of 345MPa.
Chapter 6 - 34
Chapter 6 - 35
Chapter 6 - 36
 Toughness
• Energy to break a unit volume of material / the ability to
absorb energy up to fracture
• Approximate by the area under the stress-strain curve.

Engineering small toughness (ceramics)

tensile large toughness (metals)
stress, s
very small toughness
(unreinforced polymers)

Engineering tensile strain, e

Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
Chapter 6 - 37
 Resilience, Ur
• Ability of a material to store energy when deformed elastically.
– Energy stored best in elastic region

ey
Ur =  sde
0
If we assume a linear stress-
strain curve this simplifies to

1
Ur @ sy e y
2
Example of application: Spring

Chapter 6 - 38
Useful relationship:

sT = s1  e 
eT = ln1  e 

Chapter 6 - 39
 Strain Hardening
• An increase in sy due to plastic deformation.
s
large hardening
sy
1
sy small hardening
0

e
• Curve fit to the stress-strain response:
hardening exponent:
sT = K eT  
n n = 0.15 (some steels)
to n = 0.5 (some coppers)
“true” stress (F/A) “true” strain: ln(L/Lo)
Chapter 6 - 40
Chapter 6 - 41
 Hardness
• Hardness is a measure of the material’s resistance to localized plastic
deformation. (e.g. dent or scratch)
• Large hardness means:
--resistance to plastic deformation or cracking in
compression.
--better wear properties.
apply known force measure size
e.g., of indent after
10 mm sphere removing load

Smaller indents
D d mean larger
hardness.

most brasses easy to machine cutting nitrided

plastics Al alloys steels file hard tools steels diamond

increasing hardness
Chapter 6 - 42
Hardness measurement

Chapter 6 - 43
 Hardness: Measurement
Table 6.5

Chapter 6 - 44
Relationship between Hardness and Tensile Strength

Chapter 6 - 45
 Variability in Material Properties
• Elastic modulus is material property
• Critical properties depend largely on sample flaws
(defects, etc.). Large sample to sample variability.
• Statistics
n
 xn
– Mean x=
n
1
n 2
 
2
 xi - x 
– Standard Deviation s=
 n -1 
 
where n is the number of data points
Chapter 6 - 46
Chapter 6 - 47
 Design or Safety Factors
• Design uncertainties mean we do not push the limit.
• Factor of safety, N Often N is
sy between
sworking = 1.2 and 4
N
• 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.
d
sy
sworking = 1045 plain
carbon steel:
N sy = 310 MPa Lo
220 ,000 N 5 TS = 565 MPa

 d2 / 4
F = 220,000N
d = 0.067 m = 6.7 cm
Chapter 6 - 48
 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.

Chapter 6 - 49