Mechanical Properties of Metals (1)

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29 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Bruce Mayer, PE

Registered Electrical & Mechanical Engineer

BMayer@ChabotCollege.edu

Engineering 45

Mechanical
Properties of
Metals (1)

BMayer@ChabotCollege.edu • ENGR
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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Learning Goals.1


Mech Props


STRESS and STRAIN:


What they are and why they are they used
instead of LOAD and DEFORMATION


ELASTIC Behavior


How Much Deformation occurs when
Loads are SMALL?


Which Materials Deform Least


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Bruce Mayer, PE

Engineering
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Learning Goals.2


Mech Props


PLASTIC Behavior


Determine the point at which dislocations
cause permanent deformation


Which materials are most resistant to
permanent deformation


TOUGHNESS and Ductility


What they are


How to Measure them

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Materials Testing


In The USA the American Society for
Testing and Materials (ASTM) Sets
Many, Many Materials
-
Test Standards


Founded in 1898, ASTM International is a not
-
for
-
profit

organization that provides a global forum for the

development and publication of voluntary consensus

standards for materials, products, systems, and services.

Over 30,000 individuals from 100 nations are the

members of ASTM International, who are producers,

users, consumers, and representatives of government

and academia. In over 130 varied industry areas, ASTM

standards serve as the basis for manufacturing, procurement, and regulatory
activities.
Formerly

known as the American Society for Testing and Materials,
ASTM International

provides standards that are accepted and used in research
and development, product testing, quality systems, and commercial transactions
around the globe.

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

ELASTIC Deformation


Apply/Remove a SMALL Force Load to a Specimen

1. Initial

3. Unload

return to

initial

2. SMALL load

bonds

stretch

F

d


F


Force Load

(lb or N)


d



Deformation in
Response to the
Load (in or m)

F

d

Linear
-


elastic

Non
-
Linear
-

elastic

ELASTIC means
REVERSIBLE

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Bruce Mayer, PE

Engineering
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PLASTIC Deformation


Apply/Remove a LARGE Force Load to a Specimen

PLASTIC means
PERMANENT

1. Initial

3. Unload

Planes

Still

Sheared

& planes

2. LARGE load

bonds

stretch

shear

F

d
elastic+plastic

d
灬慳p楣

F

d

linear

elastic

linear

elastic

d
plastic

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7

Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Engineering Stress,

=

Normalize Applied
-
Force to Supporting Area


TENSILE Stress,
σ

A

rea, A

F

t

F

t



=

F

t

A

o

original area

before loading


SHEAR Stress,


A

rea, A

F

t

F

t

F

s

F

F

F

s


Engineering Stress Units →
N/m
2

(Pa) or lb/in
2

(psi)

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Bruce Mayer, PE

Engineering
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5

• Simple tension: cable

o

=
F
A
• Simple shear: drive shaft

o

=
F
s
A
Note:


= M/
A
o
R

here.

Ski lift

(photo courtesy P.M. Anderson)

Common States Of Stress

A

o


= cross sectional

Area (when unloaded)

F

F

M

M

A

o

2R

F

s

A

c

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Bruce Mayer, PE

Engineering
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Canyon Bridge, Los Alamos, NM
6

• Simple COMPRESSION:

Note: These are

COMPRESSIVE

structural members

(
σ

< 0; i.e., a NEGATIVE

number)

(photo courtesy P.M. Anderson)

Common Stress States cont.1

A

o

(photo courtesy P.M. Anderson)

Balanced Rock, Arches

National Park

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Bruce Mayer, PE

Engineering
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Common Stress States cont.2


BIAXIAL Tension


z
> 0


> 0
Pressurized tank

(photo courtesy

P.M. Anderson)

Tank Surface


HYDROSTATIC Compression

Fish under water

(photo courtesy

P.M. Anderson)




< 0

h

Surface

Element

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Engineering Strain,

=

LATERAL Strain

d
/2
d
/2
d
L
/2
d
L
/2
L
o
w
o


SHEAR Strain



Engineering STRAIN Units
→ NONE (Dimensionless)


To Save Writing Exponents


µ
-
in/in


µm/m


TENSILE Strain

90
º

90
º
-




x



g

=

x
/
y

= tan

y



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Bruce Mayer, PE

Engineering
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Tensile Testing


Cyl Specimen


Std Specimen


Tension Tester

3/4
-
10 Thd


Other Tests


Compression Test for

Brittle Materials


e.g.; Concrete → GREAT in
Compression, Fractures in
Tension/Shear


Torsion (twist) Test


Drive Shafts, Torsion Bars
for Vehicle Suspension

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Linear Elastic Deformation


Consider a Tension Test With SMALL
loads; Plotting

σ

vs.
ε

Find


The Data Plots as a

Line Through the

Origin


Thus
σ


=
ε


The Constant of Proportionality is the Slope, E


E is the “Modulus of Elasticity”, or

“Young’s Modulus”


Linear Elastic Materials are said to follow

Hooke’s (spring) Law

F

F

simple

tension

test



Linear
-


elastic

1

E






=
E

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Linear Elastic Deformation


During a Pull
-
Test the Material
CONTRACTS Laterally,
ε
L
,

as it
Extends Longitudinally,
ε
. Plotting


This Data Also Plots

as a Line


Thus
ε
L


=
ε


The Constant of

Proportionality is the Slope,





is “Poisson’s Ratio” as Defined by


F

F

simple

tension

test




L


=


L



1




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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Shear Modulus


Data From



vs.
g

Shear

Stress Test


Where


G


Modulus of

Rigidity (Shear Modulus)

g

G

=

Leads to Hooke’s
Law in Pure Shear

THIN Walled Cylinder

http://www.efunda.com/materials/common_matl/Common_Matl.cfm?MatlPhase=Solid&MatlProp=M
echanical#Mechanical



1

G

g

g


=




R
a
L
a

arctan
arctan
=
=

g
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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Bulk Modulus


Data From

P

vs.

V

Tests


Leads to Hooke’s
Law in Pure
HydroStatic
Compression

Pressure
Test:

Init. vol =V
o
.

Vol chg. =

V

P

P

P

P

P



V

1

-
K

V

o

O
V
V
K
P


=

Where


K


Modulus of

Compression

(Bulk Modulus)

in GPa or Mpsi

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Elastic (Hooke’s) Relations


Uniaxial Tension


Isotropic Material
“Modulus Relations”

E
ε

=


Also Poisson’s Ratio





=
1
2
E
G
g

G

=

Pure Shear




L


=
O
V
V
K
P


=

All
-
Over
Compression




2
1
3

=
E
K

Steel Properties


E = 190
-
210 GPa


G = 75
-
80 GPa


K = 150
-
160 GPa




= 0.27
-
0.3

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Elastic Properties of Metals

Metal
Young's Modulus
E (Mpsi)
Shear modulus,
G (Mpsi)
Bulk Modulus,
K (Mpsi)
Poisson's
ratio,

Aluminum
10.2
3.8
10.9
0.3
Brass, 30 Zn
14.6
5.4
16.2
0.4
Chromium
40.5
16.7
23.2
0.2
Copper
18.8
7.0
20.0
0.3
Iron (soft)
30.7
11.8
24.6
0.3
Iron (cast)
22.1
8.7
15.9
0.3
Lead
2.3
0.8
6.6
0.4
Magnesium
6.5
2.5
5.2
0.3
Molybdenum
47.1
18.2
37.9
0.3
Nickel (soft)
28.9
11.0
25.7
0.3
Nickel (hard)
31.8
12.2
27.2
0.3
Nickel-silver, 55CU-18Ni-27Zn
19.2
5.0
19.1
0.3
Niobium
15.2
5.4
24.7
0.4
Silver
12.0
4.4
15.0
0.4
Steel, mild
30.7
11.9
24.5
0.3
Steel, 0.75 C
30.5
11.8
24.5
0.3
Steel, 0.75 C, hardened
29.2
11.3
23.9
0.3
Steel, tool
30.7
11.9
24.0
0.3
Steel, tool, hardened
29.5
11.4
24.0
0.3
Steel, stainless, 2Ni-18Cr
31.2
12.2
24.1
0.3
Tantalum
26.9
10.0
28.5
0.3
Tin
7.2
2.7
8.4
0.4
Titanium
17.4
6.6
15.7
0.4
Tungsten
59.6
23.3
45.1
0.3
Vanadium
18.5
6.8
22.9
0.4
Zinc
15.2
6.1
10.1
0.2
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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Metals

Alloys

Graphite

Ceramics

Semicond

Polymers

Composites

/fibers

E
(GPa)

Based on data in Table B2,

Callister 7e
.

Composite data based on

reinforced epoxy with 60 vol%

of aligned

carbon (CFRE),

aramid (AFRE), or

glass (GFRE)

fibers.

Young’s Moduli: Comparison

10
9

Pa

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)*

E
ceramics

>

E
metals

>>

E
polymers

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Temperature Effects


Affect of Temperature on an Aluminum Alloy


In General for Increasing T


E↓


d
L
↑ at Fracture



↓ at Fracture

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Bruce Mayer, PE

Engineering
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45: Materials of Engineering

Some Linear Elastic Relations


UniAxial Tension


Simple Torsion, Solid
Cylinder

M=moment


=angle of twist

2r

o

L

o


Material, geometric, and loading
parameters contribute to deflection


Larger elastic moduli minimize
elastic deflection

F

A

o

d

/2

d

L

/2

L
o

w

o

d

=

FL

o

E

A

o

d

L

=





Fw

o

E

A

o



=

2

ML

o

p

r

o

4

G

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Bruce Mayer, PE

Engineering
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WhiteBoard Work

6.66 kN

6.66 kN

Cu

380 mm

d


Consider this Situation:


Given for Cu


E = 110 GPa (16 Mpsi)



y

= 240 MPa (35 ksi)


Find PreLoad/PreStrain
Diameter,
d
, for a
PostLoad/PostStrain

Axial Extension
δ

= 0.5 mm