Materials Selection for Mechanical Design I

(1)

Materials Selection

for

Mechanical Design I

A Brief Overview of a Systematic Methodology

Jeremy Gregory

Research Associate

Laboratory for Energy and Environment

(2)

Relationship To Course

A key concept throughout this course is

how to select among technology choices

Economic Analysis

Cost Modeling

Life Cycle Assessment

Focus has been on economic assessment

of alternatives

How does this fit into larger technology

choice problem?

(3)

Concept

Embodiment

Detail

Market need

Production etc.

# of Candidates

Design Detail

Cost Modeling

Economic Analysis

LCA

Selection Methods

Method

Needed for

Early Stage

Approach Changes as Design Evolves

(4)

What parameters define material selection?

Example: SUV Liftgate

Image removed for copyright reasons.

(5)

$0

$50

$100

$150

$200

$250

$300

0

25

50

75

100

125

Annual Production Volume (1000s)

Uni

t Co

st

Steel

Aluminum

SMC

Attractive Options

May Be Found Outside of Expertise

(6)

Need Method for Early Material Selection:

Ashby Methodology*

Four basic steps

1.

Translation:

express design requirements

as constraints & objectives

2.

Screening:

eliminate materials that cannot

do the job

3.

Ranking:

find the materials that do the job

best

4.

Supporting information:

explore pedigrees

of top

-

ranked candidates

(7)

First Step: Translation

“Express design requirements as constraints and objectives”

Using design requirements, analyze four items:

Function:

What does the component do?

Do not limit options by specifying implementation w/in

function

Objective:

What essential conditions must be met?

In what manner should implementation excel?

Constraints:

What is to be maximized or minimized?

Differentiate between binding and soft constraints

Free variables:

Which design variables are free?

Which can be modified?

(8)

F

Area, A

L

Identifying Desirable Characteristics

Example: Materials for a Light, Strong Tie

Function:

Support a tension load

Objective:

Minimize mass

Constraints:

Length specified

Carry load F, w/o failure

Free variables:

Cross-

Cross

-section area

section area

Material

Objective:

m = AL

ρ

Constraint:

F / A <

σ

y

(9)

F

Area, A

L

Identifying Desirable Characteristics

Example: Materials for a Light, Strong Tie

Objective:

m = AL

ρ

Constraint:

F / A <

σ

y

Rearrange to eliminate

free variable

Minimize weight by

minimizing

( )( )

y

m

F L

ρ

σ

⎛

⎞

≥

⎜

⎟

⎝

⎠

y

ρ

σ

⎛

⎞

⎜

⎟

⎜

⎟

⎝

⎠

Material Index

y

σ

ρ

⎛

⎞

⎜

⎟

⎝

⎠

or m

axi

miz

e

(10)

Second Step: Screening

“Eliminate materials that cannot do the job”

Need effective way of

evaluating large range

of material classes

and properties

Composites Sandwiches

Hybrids

Lattices Segmented PE, PP, PC PS, PET, PVC PA (Nylon)

Polymers

Polyester Epoxy Soda glass Borosilicate

Glasses

Silica glass Glass ceramic Isoprene Butyl rubber

Elastomers

Natural rubber Silicones Alumina Si-carbide

Ceramics

Si-nitride Ziconia Steels Cast irons Al-alloys

Metals

Cu-alloys Ti-alloys

(11)

Comparing Material Properties:

Material Bar Charts

Metals Polymers Ceramics Hybrids

PEEK

PP

PTFE

WC

Alumina

Glass

CFRP

GFRP

Fiberboard

Y

o

u

n

g

’s

m

o

d

u

lu

s

(G

P

a)

(L

o

g

S

ca

le

)

Steel

Copper

Lead

Zinc

Aluminum

(12)

Comparing Material Properties:

Material Property Charts

0.1

10

1

100

Metals

Polymers

Elastomers

Ceramics

Woods

Composites

Foams

0.01

1000

100

0.1

1

10

Density (Mg/m

3

)

(13)

Screening Example:

Heat Sink for Power Electronics

Function:

Heat Sink

Constraints:

1.

Max service temp > 200 C

2.

Electrical insulator

Æ

R > 10

20

µ

ohm

cm

3.

Thermal conductor

Æ

T

-

conduct.

λ

> 100 W/m K

4.

Not heavy

Æ

Density < 3 Mg/m

3

Free Variables:

(14)

Heat Sink Screening: Bar Chart

200 C

M

ax

s

er

vi

ce

t

e

m

p

er

at

u

re

(

K

)

PEEK

PP

PTFE

WC

Alumina

Glass

CFRP

GFRP

Fiberboard

Steel

Copper

Lead

Zinc

Aluminum

Composites

Ceramics

Polymers

Metals

(15)

Heat Sink Screening: Property Chart

λ

> 100 W/m K

R > 10

20

µΩ

cm

1000

0.1

Metals

Polymers &

elastomers

Composites

Foams

10

30

1

10

20

Electrical resistivity (

µΩ

cm)

Thermal conductivity (W/m K)

Ceramics

10

1

100

0.01

(16)

Example using

Granta

Software:

Automobile Headlight Lens

Function:

Protect bulb and lens; focus beam

Objective:

Minimize cost

Constraints:

Transparent w/ optical quality

Easily molded

Good resistance to fresh and salt water

Good resistance to UV light

Good abrasion resistance (high hardness)

Free variables:

Material

choice

Photo of headlight

removed for copyright

reasons.

(17)

Selection Criteria

–

Limit Stage

(18)

Property Chart

•

Cheapest, hardest

material is soda

-

-lime glass

lime glass

–

used

in car headlights

•

For plastics,

cheapest is PMMA

–

used in car tail

lights

Price (USD/kg)

0.1 1 10 100

H

a

rdnes

s

V

ick

er

s (

P

a)

10000 100000 1e6 1e7 1e8 1e9 1e10 Concrete Soda-lime glass Borosilicate glass

(19)

Third Step: Ranking

“

Find the materials that do the job best

”

What if multiple materials are selected after

screening?

Which one is best?

What if there are multiple material parameters

for evaluation?

Use Material Index

(20)

Single Property Ranking Example:

Overhead Transmission Cable

Function:

Transmit electricity

Objective:

Minimize electrical Resistance

Constraints:

Length L and section A are specified

Must not fail under wind or ice

-

load

Æ

required

tensile strength > 80

MPa

Free variables:

Material

choice

L

e

L

R

A

ρ

=

Electrical

resistivity

(21)

The selection Re si st iv ity ( µ o h m .c m ) 1e-3 1 1000 1e6 1e9 1e12 1e15 1e18 1e21 1e24 1e27 Copper alloys Aluminium alloys Magnesium alloys Titanium alloys Low alloy steel Polystyrene (PS) Silica glass Cork Silicon Carbide Boron Carbide Alumina PEEK Epoxies PETE Cellulose polymers Polyester Polyurethane (tpPUR) Isoprene (IR) Wood

Single Property Ranking Example:

Overhead Transmission Cable

R

esis

tiv

ity

(

µ

-ohm cm)

•

Screening on

strength eliminates

polymers, some

ceramics

•

Ranking on

resistivity selects

Al and Cu alloys

(22)

Advanced Ranking: The Material Index

The method

1.

Identify

function

,

constraints

,

objective

and

free variables

List simple constraints for screening

2.

Write down equation for

objective

--

the

“

performance

equation

”

If objective involves a

free variable

(other than the material):

Identify the

constraint

that limits it

Use this to

eliminate the free variable

in performance

equation

3.

Read off the combination of material properties that

maximizes performance

--

the

material index

4.

(23)

The Performance Equation,

P

(

)

Functional

Geometric

Material

,

requirements, parameters, properties,

or

, ,

P

F

G

M

P

f F G M

⎡

⎛

⎞ ⎛

⎞

⎤

= ⎢

⎜

⎟ ⎜

⎟

⎥

⎝

⎠ ⎝

⎠

⎣

⎦

=

( )( )

y

m

F L

ρ

σ

⎛

⎞

≥

⎜

⎟

⎝

⎠

Use constraints to eliminate free variable

P

(24)

F

Area, A

L

The Material Index

Example: Materials for a stiff, light beam

Function:

Support a bending load

Objective:

Minimize mass

Constraints:

Length specified

Carry load F, without too

much deflection

Free variables:

Cross-

Cross

-section area

section area

Material

Objective:

m = AL

ρ

Constraint:

Deflection,

δ

3

F

CEI

S

L

δ

=

≥

(25)

The Material Index

Example: Materials for a stiff, light beam

Objective:

m = AL

ρ

Constraint:

Rearrange to eliminate

free variable

Minimize weight by

minimizing

1/ 2

5/ 2

1/ 2

4

F

L

m

C

E

π

ρ

δ

⎛

⎞

⎛

⎞

⎛

⎞

=

⎜

⎟

⎜

⎟

⎜

⎟

⎝

⎠

⎝

⎠

⎝

⎠

1/ 2

E

ρ

⎛

⎞

⎜

⎟

⎝

⎠

Material Index

1/ 2

E

ρ

⎛

⎞

⎜

⎟

⎝

⎠

or

ma

xim

ize

3

F

CEI

S

L

δ

=

≥

F

Area, A

L

Deflection,

δ

(26)

Material Index Calculation Process Flow

FUNCTION

Tie

Beam

Shaft

Column

Mechanical,

Thermal,

Electrical...

Each combination of

Function

Constraint

Objective

Free variable

has a

characterizing

material index

CONSTRAINTS

Stiffness

specified

Strength

specified

Fatigue limit

Geometry

specified

Minimum cost

Minimum

weight

Maximum energy

storage

Minimum

eco- impact

OBJECTIVE

I

NDEX

1/ 2

E

M

ρ

⎡

⎤

= ⎢

⎥

⎣

⎦

Maximize

this!

(27)

Material Index Examples

An objective defines a

performance metric

: e.g. mass or resistance

The equation for performance metric contains

material properties

Sometimes a single property

Sometimes a combination

Either is a

Material Index

σ

f

2

/3

/

ρ

G

1/2

/

ρ

Torsion

σ

f

2

/3

/

ρ

E

1/2

/

ρ

Bending

σ

f

/

ρ

E/

ρ

Tension

Strength

Limited

Stiffness

Limited

Loading

Material Indices for a Beam

Objective:

Minimize Mass

Performance Metric:

Mass

Maximize!

(28)

Optimized Selection Using

Material Indices & Property Charts: Strength

Example:

Tension Load,

strength limited

Maximize:

M

=

σ

/

ρ

In log space:

log

σ

= log

ρ

+ log

M

This is a set of lines

with slope=1

Materials above line

are candidates

Foams

Elastomers

Polymers

Woods

Composites

Metals

Ceramics

(29)

Material Indices & Property Charts:

Stiffness

Example:

Stiff beam

Maximize:

Μ

=

Ε

1/2

/ρ

In log space:

log

E

=

2 (log

ρ

+ log

M

)

This is a set of lines

with slope=2

Candidates change

with objective

Foams

Elastomers

Polymers

Woods

Composites

Metals

Ceramics

(30)

Material Indices & Property Charts:

Toughness

Load

-

limited

M = K

IC

Choose tough

metals, e.g. Ti

Energy

-

limited

M = K

IC

2

/

E

Composites and

metals compete

Displacement

-

limited

M = K

IC

/

E

Polymers, foams

K

IC

K

IC

2

/

E

K

IC

/

E

Foams

Polymers

Woods

Composites

Metals

Ceramics

(31)

Considering Multiple

Objectives/Constraints

With multiple

constraints

:

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

¾

May be different for each candidate

With multiple

objectives

:

Requires utility function to map multiple

metrics to common performance measures

(32)

Method for Early Technology Screening

Design performance is

determined by the

combination of:

Shape

Materials

Process

Underlying principles of

selection are unchanged

BUT, do not underestimate

impact of shape or the

limitation of process

Materials

Process

(33)

Ashby Method for Early Material Selection:

Four basic steps

1.

Translation:

express design requirements

as constraints & objectives

2.

Screening:

eliminate materials that cannot

do the job

3.

Ranking:

find the materials that do the job

best

4.

Supporting information:

explore pedigrees

of top

(34)

Summary

Material affects design based on

Geometric specifics

Loading requirements

Design constraints

Performance objective

Effects can be assessed analytically

Keep candidate set large as long as is feasible

Materials charts give quick overview; software can

be used to more accurately find options

Remember, strategic considerations can alter best

choice

(35)

Example Problem: Table Legs

Want to redesign table with thin unbraced cylindrical

legs

Want to minimize cross

-

section and mass without

buckling

Toughness and cost are factors

(36)

Function:

Support compressive loads

Objective:

Minimize mass

Maximize slenderness

Constraints:

Length specified

Must not buckle

Must not fracture

Free variables:

Cross-

Cross

-section area

section area

Table Legs: Problem Definition

2

m

=

π ρ

r l

2

3

4

2

4

2

crit

EI

Er

P

l

π

=

Performance Equation

(37)

Table Legs: Material Indices

Use constraints to

eliminate free variable,

r

( )

1/ 2

2

1/ 2

4

P

m

l

E

ρ

π

⎛

⎞

⎡

⎤

≥ ⎜

⎟

⎢

⎥

⎝

⎠

⎣

⎦

Minimize mass by

maximizing

M

1

1/ 2

1

E

M

ρ

=

Functional

Requirements

Geometric

Parameters

Material

Properties

For slenderness,

calculate

r

at max load

( )

1/ 4

1/ 2

3

4

P

1

r

l

E

π

⎛

⎞

⎡ ⎤

≥ ⎜

⎝

⎟

⎠

⎢ ⎥

⎣ ⎦

Maximize slenderness

by maximizing

M

2

M

=

E

Functional

Requirements

Geometric

Parameters

Material

Properties

(38)

Table Legs: Material Selection

Eliminated

Metals (too heavy)

Polymers

(not stiff enough)

Possibilities: Ceramics,

wood, composites

Final choice:

wood

Ceramics too brittle

Composites too

expensive

Note: higher constraint

on modulus eliminates

wood

Elastomers

Polymers

Woods

Composites

Metals

Ceramics

Foams

M

₂

M

₁

(39)

Material Index 1

Density (kg/m^3)

100 1000 10000

Yo

u

n

g

's

M

o

d

u

lu

s (

G

Pa

)

1e-3 0.01 0.1 1 10 100

Softw ood: pine, along grain Bamboo

Hardw ood: oak, along grain CFRP, epoxy matrix (isotropic)

Silicon Boron carbide _{Silicon carbide}

Rigid Polymer Foam (LD)

(40)

Material Index 2

Density (kg/m^3) 100 1000 10000 Y o ung's M odul u s ( P a) 1e6 1e7 1e8 1e9 1e10 1e11 Bamboo

Softw ood: pine, along grain

Hardw ood: oak, along grain CFRP, epoxy matrix (isotropic)

(41)

Example: Heat

-

Storing Wall

Outer surface

heated by day

Air blown over

inner surface to

extract heat at

night

Inner wall must

heat up ~12h after

outer wall

Figure by MIT OCW.

Air flow to

extract heat

from wall

Fan

Sun

H

ea

t S

to

ri

ng

W

al

l

W

(42)

Heat

-

Storing Wall: Problem Definition

Function:

Heat storing medium

Objective:

Maximize thermal energy

stored per unit cost

Constraints:

Heat diffusion time ~12h

Wall thickness

≤

0.5 m

Working temp

T

_max_max

>100 C

Free variables:

Wall thickness,

w

Material

2

Heat content:

Heat diffusion distance:

Specific Heat

Thermal Diffusivity

Thermal Conductivity

p

Q w C T

w

at

C

a

C

ρ

λ

ρ

λ

=

∆

=

(43)

Heat

-

Storing Wall: Material Indices

1/ 2

1

1/ 2

2

Eliminate free variable:

Insert to obtain

Performance Eqn:

Maximize:

p

Q

t Ta

C

Q

t T

a

M

a

ρ

λ

=

∆

⎛

⎞

=

∆ ⎜

⎟

⎝

⎠

=

2

6

2

0.5

12

3 10

2

Thickness restriction:

For

m and

h:

m /s

w

a

t

w

t

M

a

−

≤

=

= ≤ ×

(44)

Heat

-

Storing Wall: Material Selection

Eliminated

Foams: Too

porous

Metals: Diffusivity

too high

Possibilities:

Concrete, stone,

brick, glass,

titanium(!)

Final Choices

Concrete is

cheapest

Stone is best

performer at

reasonable price

Granta Design