2 - Ashby Method

2.2 - Screening and ranking for optimal selection

Outline

• Basic steps of selection

1. Translation of design requirements into a material specification

2. Screening out of materials that fail constraints

3. Ranking by ability to meet objectives: Material Indices

4. Search for supporting information for promising candidates

Resources:

• M. F. Ashby, “Materials Selection in Mechanical Design” Butterworth Heinemann, 1999

Chapters 1-4

• The Cambridge Material Selector (CES) software -- Granta Design, Cambridge

(www.grantadesign.com)

The design process

Concept

Embodiment

Detail

Production

Use

Disposal

Tools for

life-cycle

analysis

Redesign

Tools for Design(Material needs)

Data for all materials

and processes, low precision

Data for fewer materials

or processes, higher precision

Data for one material

or process, highest precision

Market need

Desig

n p

hase

Life p

hase

Design requirements material specification

From which we obtain …

• Screening criteria: go / no-go criteria (usually many)

• Ranking criteria: an ordering of the materials that “go”

Design requirements“Translation”

Analyse:

What does the component do ?

What essential conditions must be met ?

What is to be maximised or minimised ?

Which design variables are free ?

Function

Objectives

Constraints

Free variables

Example: heat sink for microprocessor

Step 1 -- Screening:“Eliminate materials that can’t do the job”

must

• operate at 200oC

• be electrical insulator

• conduct heat well

Retain materials with:

1. max service temp > 473K

2. must be “good insulator”

3. T-conduct. λ > 100 W/m.K

• minimise cost

Rank materials :

• by price/kg

Step 2 -- Ranking: “Find the material that does the job best”

Objective

Constraints

Screening using a limit stage

Mechanical attributes Minimum Maximum

Density Mg/m3

Young’s modulus GPa

Elastic limit MPa

Thermal attributes

Max. service temp. K

T-expansion W/m.K

T-conductivity 10-6/K

Electrical attributes

Good insulator

Poor insulator

Poor conductor

Good conductor

100

473

bbbb

Using CES to screen materials

� Selection using limits

� Selection using bar-charts

� Selection using property charts

Max

se

rvic

e t

em

pe

ratu

re (

K)

Metals Polymers Ceramics Composites

PEEK

PP

PTFE

WC

Alumina

Glass

CFRP

GFRP

Fibreboard

Steel

Copper

Lead

Zinc

Aluminum

0.1

Metals

Polymers & elastomers

Composites

Foams

1000

1000.1 1 10Price ($/kg)

Th

erm

al

co

nd

uc

tiv

ity (

W/m

.s)

Ceramics

10

1

100

0.01

Ranking: Modelling performance

The steps:

� Identify function, constraints, objective and free variables.

� Write down equation for objective -- the “performance equation”.

� If the “performance equation” contains a free variable other than material identify the constraint that limits it.

� Use this constraint to eliminate the free variable in performance equation.

� Read off the combination of material properties that maximise performance.

Example 1: strong, light tie-rod

Tie-rod

Minimise mass m:

m = A L ρρρρ (1)

Strong tie of length L and minimum mass

L

FF

Area A

• Length L is specified

• Must not fail under load F

• Adequate fracture toughness

Function

Objective

Constraints

Free variables

m = mass

A = areaL = length

ρ = density= yield strength

yσ

Equation for constraint on A:

F/A < σσσσy (2)

PERFORMANCEINDEX

• Material choice• Section area A;

eliminate in (1) using (2):

σ

ρ=

y

FLm Chose materials with smallest

yσρ

Example 2: stiff, light beam

m = massA = area

L = length

ρ = densityb = edge lengthS = stiffness

I = second moment of areaE = Youngs Modulus

Beam (solid square section).

Stiffness of the beam S:

I is the second moment of area:

• Material choice.• Edge length b. Combining the equations gives:

3L

IECS =

12

bI

4

=

ρ

=

2/1

2/15

EC

LS12m

ρ=ρ= LbLAm 2

Chose materials with smallest

ρ2/1E

b

b

L

F

Minimise mass, m, where:

Function

Objective

Constraint

Free variables

( )LE,C,S,fb =

Materials indices

Minimum cost

Minimum

weight

Maximum energy storage

Minimum environ. impact

FUNCTION

OBJECTIVE

CONSTRAINTS

INDEX

Tie

Beam

Shaft

Column

Mechanical,Thermal,

Electrical...

Stiffness

specified

Strengthspecified

Fatigue limit

Geometry

specified

ρ=

2/1EM

Minimise

this!

Each combination of

FunctionObjectiveConstraintFree variable

Has a

characterising material index

Function Stiffness Strength

Tension (tie)

Bending (beam)

Bending (panel)

Demystifying material indices

Cost, Cm

Density, ρ

Modulus, E

Strength, σy

Endurance limit, σe

Thermal conductivity, λ

T- expansion coefficient, α

the “Physicists” view of materials, e.g.

Material properties --

the “Engineers” view of materials

Material indices --

ρ/E yρ/σ

1/2ρ/E

Objective: minimise mass

Many more: see Appendix B of the text

Minimise these!

1/3ρ/E 1/2

yρ/σ

2/3

yρ/σ

Materials indices

Minimum cost

Minimum

weight

Maximum energy storage

Minimum environ. impact

FUNCTION

OBJECTIVE

CONSTRAINTS

INDEX Stiffness

specified

Strengthspecified

Fatigue limit

Geometry

specified

( )[ ]EfM ,ρ=

Minimise

this!

Each combination of

FunctionObjectiveConstraintFree variable

Has a

characterising material index

Function Stiffness Strength

Tension (tie)

Bending (beam)

Bending (panel)

Demystifying material indices

Cost, Cm

Density, ρ

Modulus, E

Strength, σy

Endurance limit, σe

Thermal conductivity, λ

T- expansion coefficient, α

the “Physicists” view of materials, e.g.

Material properties --

the “Engineers” view of materials

Material indices --

ρ/E yρ/σ

1/2ρ/E

2/3

yρ/σ

Objective: minimise mass

Many more: see Appendix B of the text

Minimise these!

1/3ρ/E 1/2

yρ/σ

Optimised selection using charts

Index 1/2E

ρM =

22 M/ρE =

( ) ( ) ( )MLog2Log2ELog −ρ=

Contours of constant

M are lines of slope 2

on an E-ρ chart

CE

=ρ

CE 2/1

=ρ

0.1

10

1

100

Metals

Polymers

Elastomers

Woods

Composites

Foams0.01

1000

1000.1 1 10Density (Mg/m3)

Young’s

modulu

s E

, (G

Pa)

Ceramics

1

2 3

CE 3/1

=ρ

Selection using hard-copy charts

CE 2/1

=ρ

Search

region

Selection using the CES software

D e nsity (M g /m ^3 )1 . 1 0. 10 0 .

Yo

un

g's

Mo

dulu

s (

GP

a)

0 .1

1 .

1 0 .

1 0 0.

1 0 00 .

P o lyU re tha ne

P TFE

P V C foam

S an ds ton e

P oly eth y l en e

C a rbo n S te el

Tun gs ten

A lu m i ni um all oy s )

D i am on d

C F R P

Density (Mg/m3)

Young’s

modulu

s (G

Pa)

Ceramics

Metals

Elastomers

Composites

Polymers

Woods

Foams

Search

region

CE 2/1

=ρ

Modulus – Density chart

� Modulus spans 5 decades

0.01 GPa (foams) to 1000 GPa (diamond)

� Iso-lines E/ρ, E1/2/ρ, E1/3/ρ selection for minimum weight, deflection-limited design

Strength – Density chart

� Spans 5 decades

0.1 MPa (foams) to 104

MPa (diamond)

� Iso-lines σf/ρ, σf2/3/ρ, σf

1/2/ρ

selection for minimum weight, yield-limited design

Fracture Toughness – Density chart

� KIc measures resistance to crack propagation

� Iso-lines KIc4/3 / ρ , KIc

4/5 / ρ

, KIc2/3/ ρ , KIc

1/2/ ρ and KIc

for minimum weight, fracture-limited design

� KIc = 20 MPa m1/2

considered minimum value for conventional

design

Modulus – Strength chart

� Chart is useful in selecting springs

� Iso-lines of “normalized

strength”, defined as σf /E

Modulus – Relative Cost chart

� Relative cost is defined as:

CR = [c/kg of material] /

[c/kg of mild steel rod]

� Iso-lines help to maximize stiffness per unit cost

Strength – Relative Cost chart

� Relative cost is defined as:

CR = [c/kg of material] /

[c/kg of mild steel rod]

� Iso-lines help to maximize strength per unit cost

Basic procedure for materials selection

� Start with all materials

� Narrow choice with primary constraints

Dictated by design/non-negotiable

� Seek subset that maximizes performance

� Combination of properties involved in maximization

� Examine performance indices

Primary constraints

� Designs impose primary constraints

For example, a component must carry a load above 300°C --

this would eliminate all plastics as candidates.

Components which must electrically insulate cannot be

metals, and so forth.

� We can represent this condition by:

P > Pcrit or P < Pcrit

where P is a property (service temperature, for instance) and Pcrit is a critical value of that property, set by the design, which must be exceeded, or (in the case of cost or

corrosion rate) must not be exceeded.

Primary constraints

Performance maximizing criteria

� The next step is to seek, from the subset of materials which satisfy the primary constraints, those which maximize the performance of the component.

� We will use the same example as before -- the design of light, stiff components; the other indices are used in a

similar way.

� Figure shows, as before, the modulus E, plotted against

density ρρρρ, on log scales. The performance index is (tension on light-stiff tie):

E / ρρρρ = C

� Taking logs,

log E = log ρρρρ + log C

is a family of straight parallel lines of slope 1, one line for each value of the constant C.

Performance maximizing criteria

� The index for bending on light-stiff beam is:

E1/2 / ρρρρ = C

gives another family of lines, this time with a slope of 2.

� The index for bending on light-stiff plate is:

E1/3 / ρρρρ = C

gives another family of lines, this time with a slope of 3.

Performance maximizing criteria

Performance maximizing criteria

� All materials which lie on a iso-line of E1/2 / ρρρρ will perform equally well

� Lines to right are worse performers and lines to the left are better.

� The subset of materials with particularly good values of the index is identified by picking a line which isolates a small search region containing a reasonably small number of candidates.

Performance maximizing criteria

The main points

• Design requirements are translated into a prescription for selecting a

material by analysing the function of the component,

the constraints must meet, and

the objective of the design.

• Simple constraints are applied as limits on material attributes,

screening out materials that can’t do the job

• Constraints that limit objectives must be combined with the objective

to identify a material index.

• The objective is best displayed on a material-property chart, allowing optimised selection

• The method allows refined selection while giving a perspective of alternatives in drawn from all classes of materials.