Lecture # 6

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29 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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Lecture # 6

Mechanical Properties of Metals


Intended learning Outcomes:


After the end of this lecture the student should
be able to:


Define stress

strain relation.


State Hooke’s law.


Modules of elasticity .


Tensile strength ,percent elongation ,Ductility


Hardness and the different tests methods for
measuring it.

TENSION TESTS:

4


Tensile

stress,
s
:


Shear

stress,
t
:

s

F
t
A
o
original area
before loading
Stress has units:

N/m
2

or lb/in
2

ENGINEERING STRESS

5


Simple

tension: cable

o
s

F
A

Simple

shear
:

o
t

F
s
A
Note:
t

=
M
/
A
c
R

here.

COMMON STATES OF STRESS


ϵ
= Strain.

I
o
= original length

I
i
= instantaneous length

Δ
I= deformation elongation or
change in length

8


Tensile

strain:


Lateral

strain:


Shear

strain:


/2

/2

/2 -


/2

/2

/2

L
/2

L
/2
L
o
w
o

= tan

Strain is always

dimensionless.

ENGINEERING STRAIN

• Typical tensile specimen

9

• Other types of tests:


--
compression:

brittle


materials (e.g., concrete)


--
torsion:
cylindrical tubes,


shafts.

• Typical tensile


test machine

Adapted from Fig. 6.2,


Callister 6e.


Adapted from Fig. 6.3,
Callister 6e.

(Fig. 6.3 is taken from H.W. Hayden,
W.G. Moffatt, and J. Wulff,
The
Structure and Properties of
Materials
, Vol. III,
Mechanical
Behavior
, p. 2, John Wiley and Sons,
New York, 1965.)

STRESS
-
STRAIN TESTING

STRESS

STRAIN BEHAVIOR

For most metals that are stressed in tension and at relatively low levels, stress and
strain are proportional to each other through the relationship:

ELASTIC DEFORMAT ION


Modulus of Elasticity, E
:


(also known as Young's modulus)


Hooke's Law
:

s

=
E

e

Units:

E: [
GPa
] or [psi
]

Elastic
Deformation

Linear Behavior

Behavior of most metals (E)

Non Linear Elastic
Behavior

(Secant and Tangent
Modulus)

Eg
: Gray cast iron
,
concrete,polymers

EXAMPLE:
1

A piece of copper originally
305
mm (
12
in.) long is pulled in tension with a

stress of
276
MPa

(
40
,
000
psi). If the deformation is entirely elastic, what will

be the resultant elongation?

MECHA NICAL BEHAVIOR of META LS

Typical stress

strain behavior for a metal showing

elastic and plastic deformations, the proportional
limitP
, and the yield
strengthy
, as determined using
the
0.002
strain offset method.

14

• Simple tension test:

(at lower temperatures, T < T
melt
/
3
)

PLASTIC (PERMANENT) DEFORMATION

15

• Stress at which
noticeable

plastic deformation has


occurred.

when
e
p

=
0.002

tensile stress,
s
engineering strain,
e
s
y
e
p
= 0.002
YIELD STRENGTH,
s
y

16

Room T values


s
y(ceramics)

>>
s
y(metals)

>>
s
y(polymers)
YIELD STRENGTH: COMPARISON

17

• 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
6
e.

TENSILE STRENGTH, TS

Example
2
:

From the tensile stress

strain behavior for the brass specimen shown in the
following Figure determine the following:

(a) The modulus of elasticity.

(b) The yield strength at a strain offset of
0.002
.

(c) The maximum load that can be sustained by a cylindrical specimen having

an original diameter of
12.8
mm (
0.505
in.).

(d) The change in length of a specimen originally
250
mm (
10
in.) long that is

subjected to a tensile stress of
345
MPa

(
50
,
000
psi).