# CHAPTER 7: MECHANICAL PROPERTIES

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Nov 29, 2013 (4 years and 5 months ago)

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1

Chapter 7:

MECHANICAL
PROPERTIES

Chapter Outline

Terminology for Mechanical Properties

The Tensile Test: Stress
-
Strain Diagram

Properties Obtained from a Tensile Test

True Stress and True Strain

The Bend Test for Brittle Materials

Hardness of Materials

3

Stress

and
strain
: What are they and why are they

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?

Toughness

and
ductility
: What are they and how
do we measure them?

Ceramic Materials:
What special provisions/tests

4

Stress
-
Strain Test

specimen

machine

5

Tensile Test

6

Important Mechanical Properties

from a Tensile
Test

Young's
Modulus
:
This
is the slope of the linear
portion of the stress
-
strain curve, it is usually
specific to each material; a constant, known value.

Yield Strength
:
This
is the value of stress at the
yield point,
calculated
by plotting young's modulus
at a specified percent of offset (usually offset =
0.2%).

Ultimate Tensile Strength
:
This
is the highest
value of stress on the stress
-
strain curve.

Percent Elongation
:
This
is the change in gauge
length divided by the original gauge length.

Terminology

-

The force applied to a material during
testing.

Strain gage or Extensometer

-

A device used for
measuring change in length (strain).

Engineering stress

-

divided by the original cross
-
sectional area of the
material.

Engineering strain

-

The amount that a material
deforms per unit length in a tensile test.

8

F

bonds
stretch
initial
1. Initial

Elastic means
reversible.

Elastic Deformation

9

1. Initial

Plastic means
permanent.

F

linear
elastic
linear
elastic

plastic
Plastic Deformation
(Metals)

10

Typical stress
-
strain
behavior for a metal
showing elastic and
plastic deformations,
the
proportional limit P
and the
yield strength
σ
y
,
as determined
using the
0.002 strain
offset

method
(where there
is noticeable plastic deformation).

to plastic transition.

11

Plastic Deformation (permanent)

From an atomic perspective,
plastic
deformation

corresponds to the
breaking of
bonds

with original atom neighbors and
then
reforming bonds

with new neighbors.

After removal of the stress, the large
number of atoms that have relocated, do

Yield strength
is a measure of
resistance
to plastic deformation
.

12

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

Localized deformation of a ductile material during a
tensile test produces a necked region.

The image shows necked region in a fractured sample

14

Permanent Deformation

Permanent deformation for metals is
accomplished by means of a process called
slip
, which involves the
motion of
dislocations
.

Most structures are designed to ensure that
only
elastic deformation

results when stress
is applied.

A structure that has plastically deformed, or
experienced a permanent change in shape,
may not be capable of functioning
as
intended.

15

tensile stress,

engineering strain,

y

p
= 0.002
Yield Strength,

y

Stress
-
Strain Diagram

Strain ( ) (
D
䰯䱯L

4

1

2

3

5

Elastic

Region

Plastic

Region

Strain

Hardening

Fracture

ultimate

tensile
strength

Elastic region

slope =Young’s (elastic) modulus

yield strength

Plastic region

ultimate tensile strength

strain hardening

fracture

necking

yield

strength

UTS

y

ε
E
σ

ε
σ
E

1
2
y
ε

ε
σ
E

Stress
-
Strain Diagram
(cont)

Elastic Region

(Point 1

2)

-

after the material is unloaded( like a rubber band).

-

The stress is linearly proportional to the strain in

this region.

ε
E
σ

: Stress(psi)

E

:
Elastic modulus

(
Young’s Modulus
) (psi)

: Strain (in/in)

σ
ε
-

Point 2 :
Yield Strength

: a point where permanent

deformation occurs. ( If it is passed, the material will

ε
σ
E

or

Strain Hardening

-

If the material is loaded again from Point 4, the

curve will follow back to Point 3 with the same

Elastic Modulus (slope).

-

The material now has a higher yield strength of

Point 4.

-

Raising the yield strength by permanently straining

the material is called
Strain Hardening.

Stress
-
Strain Diagram
(cont)

Tensile Strength

(Point 3)

-

The largest value of stress on the diagram is called

Tensile Strength
(TS) or

Ultimate Tensile Strength

(UTS)

-

It is the maximum stress which the material can

support without breaking.

Fracture

(Point 5)

-

If the material is stretched beyond Point 3, the stress

decreases as necking and non
-
uniform deformation

occur.

-

Fracture will finally occur at Point 5.

Stress
-
Strain Diagram
(cont)

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

The stress
-
strain curve for an aluminum alloy.

21

Stress
-
strain
behavior
found for
some steels
with
yield
point
phenomenon.

22

T

E

N

S

I

L

E

P

R

O

P

E

R

T

I

E

S

23

Room T values

a = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

qt = quenched & tempered

Yield Strength
: Comparison

24

After yielding, the stress necessary to
continue plastic deformation in metals
increases to a
maximum point (M)
and
then decreases to the eventual

fracture
point (F).

All
deformation

up to the maximum
stress is
uniform

throughout the tensile
sample.

However, at
max stress
, a small
constriction or neck begins to form.

Subsequent deformation will be
confined to this neck area.

Fracture strength
corresponds to the
stress at fracture.

Region between M and F:

Metals: occurs when noticeable
necking

starts.

• Ceramics: occurs when
crack propagation

starts.

• Polymers: occurs when
polymer backbones

are aligned and about to break.

Tensile Strength, TS

25

In an
undeformed

thermoplastic polymer
tensile sample,

(a)
the polymer chains
are randomly
oriented.

(b)
When a stress is
applied, a neck
develops as chains
become aligned
locally. The neck
continues to grow
until the chains in the
entire gage length
have aligned.

(c)
The strength of the
polymer is increased

26

Room T values

Based on data in Table B4,
Callister

6e
.

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
.

Tensile Strength
: Comparison

27

Tensile

stress,

:

Shear

stress,
t
:

F
t
A
o
original area
Stress has units: N/m
2

or lb/in
2

Engineering Stress

28

VMSE

http://www.wiley.com/college/callister/0470125373/
vmse
/strstr.htm

http://www.wiley.com/college/callister/0470125373/vmse/
index
.htm

Example 1

Tensile Testing of Aluminum Alloy

Convert the change in length data in the table to engineering
stress and strain and plot a stress
-
strain curve.

Example 1 SOLUTION

31

Another ductility measure:

100
%
x
A
A
A
AR
o
f
o

• Ductility may be expressed as either
percent elongation
(%
plastic strain at fracture) or
percent reduction in area
.

%AR > %EL is possible if internal voids form in neck.

100
%
x
l
l
l
EL
o
o
f

Ductility, %EL

Ductility is a measure of the
plastic deformation that has
been sustained at fracture:

A material that
suffers very
little plastic
deformation is
brittle
.

32

Toughness

Lower toughness: ceramics

Higher toughness: metals

Toughness is
the ability to
absorb
energy up to
fracture
(energy
per unit volume of
material).

A “
tough

material has
strength

and
ductility
.

Approximated
by the area
under the
stress
-
strain

curve.

• 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,

E
ngineering
tensile
stress,

smaller toughness (ceramics)
larg
er toughness
(metals, PMCs)
Toughness

34

Linear Elastic Properties

Modulus of Elasticity, E
:

(Young's modulus)

Hooke's Law
:

=
E

Poisson's ratio
:

metals:
n

~ 0.33

ceramics:
n

~0.25

polymers:
n

~0.40

Units:

E: [GPa] or [psi]

n
:
dimensionless

n  
x
/

y

35

Engineering Strain

Strain is dimensionless.

36

Axial (z) elongation (positive strain) and lateral (x and y)
contractions (negative strains) in response to an imposed
tensile stress.

True Stress and True Strain

True stress

The load divided by the actual cross
-
sectional
area of the specimen at that load.

True strain

The strain calculated using actual and not
original dimensions, given by
ε
t

ln(
l
/
l
0
).

The relation between the
true
stress
-
true strain diagram and
engineering

stress
-
engineering strain diagram.

The curves are identical to the yield
point.

38

Stress
-
Strain Results for Steel Sample

Example 2:
Young’s Modulus
-

Aluminum Alloy

From the data in Example 1, calculate the modulus of
elasticity of the aluminum alloy.

Use the modulus to determine the length after
deformation of a bar of initial length of 50 in.

Assume that a level of stress of 30,000 psi is applied.

Example 2: Young’s Modulus
-

Aluminum Alloy
-

continued

41

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
2
0
4
0
6
0
8
0
10
0
2
00
6
00
8
00
10
00
1200
4
00
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTF
E
HDP
E
LDPE
PP
Polyester
PS
PET
C
FRE( fibers)
*
G
FRE( fibers)*
G
FRE(|| fibers)*
A
FRE(|| fibers)*
C
FRE(|| fibers)*
Metals

Alloys

Graphite

Ceramics

Semicond

Polymers

Composites

/fibers

E(GPa)

10
9

Pa
Composite data based on

reinforced epoxy with 60 vol%

of aligned carbon (CFRE),

aramid (AFRE), or glass (GFRE)

fibers.

Young’s Moduli: Comparison

Example 3: True Stress and True Strain
Calculation

Compare engineering stress and strain with true stress and
strain for the aluminum alloy in Example 1 at (a) the
in. and at fracture is 0.398 in.

Example 3 SOLUTION

Strain Hardening

An increase in

y

due to
plastic deformation.

44

Strain Hardening (n, K
or C

values)

47

Mechanical Behavior
-

Ceramics

The stress
-
strain behavior of brittle
ceramics is not usually obtained by a
tensile test.

1.
It is difficult to prepare and test
specimens with specific geometry.

2.
It is difficult to grip brittle materials without
fracturing them.

3.
Ceramics fail after roughly 0.1% strain;
specimen have to be perfectly aligned.

The Bend Test for Brittle Materials

Bend test

-

Application of a force to the center of a bar
that is supported on each end to determine the
resistance of the material to a static or slowly applied

Flexural strength or modulus of rupture

-
The stress
required to fracture a specimen in a bend test.

Flexural modulus

-

The modulus of elasticity calculated
from the results of a bend test, giving the slope of the
stress
-
deflection curve.

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

The stress
-
strain behavior of brittle materials compared with
that of more ductile materials

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

(a) The bend test often used for measuring the strength
of brittle materials, and (b) the deflection
δ obtained by
bending

51

Schematic for a 3
-
point bending test.

Able to measure the
stress
-
strain behavior
and flexural strength
of brittle ceramics.

Flexural strength
(modulus of rupture or
bend strength) is the
stress at fracture.

Flexural Strength

See Table 7.2 for more values.

23

Room T behavior is usually elastic, with brittle failure.

3
-
Point Bend Testing

often used.

--
tensile tests are difficult for brittle materials.

Determine elastic modulus according to:

E

F

L
3
4
bd
3

F

L
3
12

R
4
rect.
cross
section
circ.

cross
section
MEASURING ELASTIC MODULUS

24

3
-
point bend test to measure room T strength.

F
L/2
L/2
cross section
R
b
d
rect.
circ.
location of max tension

Flexural strength:

rect.

fs

m
fail

1
.
5
F
max
L
bd
2

F
max
L

R
3

Typ. values:

Material

fs
(MPa) E(GPa)
Si nitride

Si carbide

Al oxide

glass (soda)

700
-
1000

550
-
860

275
-
550

69

300

430

390

69

Data from Table 12.5,
Callister 6e.

MEASURING STRENGTH

54

--
brittle response (aligned chain, cross linked & networked case)

--
plastic response (semi
-
crystalline case)

Stress
-
Strain Behavior: Elastomers

3 different responses:

A

brittle failure

B

plastic failure

C
-

highly elastic (
elastomer
)

Hardness of Materials

Hardness test

-

Measures the resistance of a material to
penetration by a sharp object.

Macrohardness

-

Overall bulk hardness of materials

Microhardness
Hardness of materials typically measured
using loads less than 2 N using such test as Knoop
(HK).

Nano
-
hardness

-

Hardness of materials measured at 1

10 nm length scale using extremely small (~100 µN)
forces.

56

Hardness

Hardness is a measure of a material’s resistance
to localized plastic deformation (a small dent or
scratch).

Quantitative hardness techniques have been
developed where a small indenter is forced into
the surface of a material.

The depth or size of the indentation is measured,
and corresponds to a hardness number.

The softer the material, the larger and deeper the
indentation (and lower hardness number).

57

• Resistance to permanently indenting the surface.

• Large hardness means:

--
resistance to plastic deformation or cracking in

compression.

--
better wear properties.

Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Properties and Applications of Pla
sti
cs, p. 202, John Wiley and Sons, 1957.)

Hardness

58

Hardness Testers

59

60

Conversion of
Hardness
Scales

Also see: ASTM E140
-

07

Volume 03.01

Standard Hardness Conversion
Tables for Metals Relationship
Among Brinell Hardness, Vickers
Hardness, Rockwell Hardness,
Superficial Hardness, Knoop
Hardness, and Scleroscope
Hardness

61

Correlation
between
Hardness and
Tensile
Strength

Both hardness and tensile
strength are indicators of
a metal’s resistance to
plastic deformation.

For cast iron, steel and
brass, the two are roughly
proportional.

Tensile strength (psi) =
500*BHR

63

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
.

Toughness
: The energy needed to break a unit

volume of material.

Ductility
: The plastic strain at failure.

Summary