ISSUES TO ADDRESS...

frizzflowerUrban and Civil

Nov 29, 2013 (3 years and 10 months ago)

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Chapter 23
-

1

ISSUES TO ADDRESS...

• Price and availability of materials
.


How do we select materials based on optimal


performance?

• Applications:


--

shafts under torsion


--

bars under tension


--

plates under bending


--

materials for a magnetic coil.

CHAPTER 22: MATERIALS SELECTION AND
DESIGN CONSIDERATIONS

Chapter 23
-

MATERI
A
LS ENGINEERING

TETRAHEDRON

A characteristic trait possessed by a
certain material. Properties of
interest relate to a given application

The way in which
the
product
functions


To put a given
material through
steps of a prescribed

procedure to obtain
the final product


The interrelation between the parts
and the whole


Chapter 23
-

3

• Current Prices on the web:
e.g.,

http://www.metalprices.com


--

Short term trends: fluctuations due to supply/demand.


--

Long term trend: prices will increase as rich deposits


are depleted.

• Materials require energy to process them:

--

Energy to produce


materials (GJ/ton)

Al

PET

Cu

steel

glass

paper

237
(17)

103
(13)


97
(20)


20


13


9

--

Cost of energy used in


processing materials ($/MB
TU or GJ
)

elect resistance

propane

oil

natural gas

25

17

13

11

Energy using recycled

material indicated in green.

PRICE AND AVAILABILITY

Energy prices from
http://www.npga.org/i4a/pages/index.
cfm?pageid=914

(B
TU: British thermal unit=1.06 kJ
)

Chapter 23
-

4

RELATIVE COST,
c
, OF MATERIALS

• Reference material:


--

Rolled A36 plain


carbon steel.

• Relative cost, ,


fluctuates
less


over time than


actual cost.

Based on data in Appendix

C,
Callister, 7e
.

AFRE, GFRE, & CFRE

= Aramid,

Glass, & Carbon fiber reinforced
epoxy composites.

c
material

ref
)
kg
/
($
kg
/
$

c
Graphite/

Ceramics/

Semicond

Metals/

Alloys

Composites/

fibers

Polymers

Relative Cost (
c
)

pl. carbon

Au

Si wafer

PET

Epoxy

Nylon 6,6

0.05

0.1

5

100000

10000

2

0000

5

0000

5

000

2

000

1

000

5

00

2

00

1

00

5

0

2

0

1

0

2

1

0.5

Steel

high alloy

Al alloys

Cu


alloys

Mg


alloys

Ti


alloys

Ag


alloys

Pt

Tungsten

Al oxide

Concrete

Diamond

Glass
-
soda

Si carbide

Si nitride

PC

LDPE,HDPE

PP

PS

PVC

Aramid fibers

Carbon fibers

E
-
glass fibers

AFRE prepreg

C

FRE prepreg

G

FRE prepreg

Wood

Chapter 23
-

PERFORMANCE INDEX


The design of a
mechanical component is specified by three
things:

1.
F
:

the specified Functional Requirements


the functional requirements (the need to carry loads, transmit
heat, store elastic

energy

or thermal energy, etc)

2.
G
:
the specified Geometrical Parameters,
the geometry, and

3.
M
:

the Material Properties



the properties of the material of which it is made, including its
cost.

p
:
the performance of

the
element
that is to be optimised

(

its
mass, volume, cost or life for example
)

5

Chapter 23
-

6

• Bar must not lengthen by more than
d


under force
F
; must have initial length
L
.

• Maximize the
Performance Index
:

--

Stiffness relation:

--

Mass of bar:

L
E
c
F
d

2
(
s
=
E
e
)

2
Lc
M


• Eliminate the "free" design parameter,
c
:

E
FL
M

d

2


E
P
specified by application

minimize for small
M

(stiff, light tension members)

STIFF

&
LIGHT

TENSION MEMBERS

F
,
d


L

c

c

Chapter 23
-

7

• Bar must carry a force
F

without failing;


must have initial length
L
.

• Maximize the
Performance Index
:

--

Strength relation:

--

Mass of bar:

• Eliminate the "free" design parameter,
c
:

specified by application

minimize for small M

(strong, light tension members)

STRONG

&
LIGHT

TENSION MEMBERS

F
,
d


L

c

c

2
c
F
N
f

s
2
Lc
M


f
FLN
M
s



s

f
P
Chapter 23
-

8

• Bar must carry a moment,
M
t

;


must have a length
L
.

• Maximize the
Performance Index
:

--

Strength relation:

--

Mass of bar:

• Eliminate the "free" design parameter,
R
:

specified by application

minimize for small M

(strong, light torsion members)

STRONG & LIGHT
TORSION

MEMBERS

L
R
M
2


3
2
R
M
N
t
f



3
/
2
3
/
2
)
2
(
f
t
L
NM
M







3
/
2

f
P
L

2
R

M

t





Chapter 23
-

9

DATA: STRONG & LIGHT
TENSION/TORSION MEMBERS

Adapted from Fig. 22.2,
Callister 7e
. (Fig. 22.2 adapted
from M.F. Ashby,
Materials
Selection in Mechanical
Design
, Butterworth
-
Heinemann Ltd., 1992.)

0.1



1



10



30

1



10



10

2



10

3



10

4



Density,


(Mg/m
3
)

Strength,
s
f

(MPa)

Increasing
P


for strong


tension


members

0.1



Metal



alloys

Steels



Ceramics



PMCs

Polymers

|| grain



grain



Cermets

Increasing
P


for strong


torsion members

Chapter 23
-

10

0.1



1



10



3

0



0.1



1



10



10

2



10

3



10

4



Cermets



Steels





Strength,
s
f

(MPa)



Increasing P


for strong


bending members







Metal



alloys



Ceramics



PMCs



Polymers





• Maximize the
Performance Index
:


P

s
1
/
2

Adapted from Fig. 6.22,
Callister 6e
. (Fig. 6.22 adapted
from M.F. Ashby,
Materials
Selection in Mechanical
Design
, Butterworth
-
Heinemann Ltd., 1992.)

DATA: STRONG & LIGHT

BENDING MEMBERS

Density,


(Mg/m
3
)

grain

|| grain

Chapter 23
-

11

• Other factors:


--
require
s
f

> 300 MPa.


--
Rule out ceramics and glasses:
K
Ic

too small.

• Maximize the
Performance Index
:

• Numerical Data:

• Lightest: Carbon fiber reinforced epoxy


(CFRE) member.

material

CFRE (
v
f

= 0.65)

GFRE (
v
f

= 0.65)

Al alloy (2024
-
T6)

Ti alloy (Ti
-
6Al
-
4V)

4340 steel (oil


quench & temper)



(Mg/m
3
)

1.5

2.0

2.8

4.4

7.8

P

[(MPa)
2/3
m
3
/Mg]

73

52

16

15

11

Data from Table 22.1,
Callister 7e
.


f

(MPa)

1140

1060


300


525


780

DETAILED STUDY I: STRONG, LIGHT
TORSION MEMBERS




3
/
2

f
P
Chapter 23
-

12

• Lowest cost: 4340 steel (oil quench & temper)

• Need to consider machining, joining costs also.

DETAILED STUDY I
I
: STRONG, LOW
COST TORSION MEMBERS

• Minimize Cost:

Cost Index ~
M

~ /
P

(since M ~ 1/P)

where

M

= mass of material

c
c
c
=
relative cost

=

cost/mass of low
-
carbon steel

cost/mass of material

• Numerical Data:

material

CFRE (
v
f

= 0.65)

GFRE (
v
f

= 0.65)

Al alloy (2024
-
T6)

Ti alloy (Ti
-
6Al
-
4V)

4340 steel (oil


quench & temper)


80

40

15

110

5

P [(MPa)
2/3
m
3
/Mg]

73

52

16

15

11

(

/P)x100

112

76

93

748

46

Data from Table 22.2,
Callister 7e
.

c
c
Chapter 23
-

13

• Material costs fluctuate but rise over the long


term as:


--

rich deposits are depleted,


--

energy costs increase.

• Recycled materials reduce energy use significantly.

• Materials are selected based on:


--

performance

or
cost indices
.

• Examples:


--

design of minimum mass, maximum strength of:


• shafts under torsion,


• bars under tension,


• plates under bending,


SUMMARY

Chapter 23
-

14

Ch22
-
Case Study:

Failure of an Automobile Rear Axle,

Callister, web page W101.


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