# Lecture # 6

Πολεοδομικά Έργα

29 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

129 εμφανίσεις

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
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

Callister 6e.

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

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).