Materials Selection for Mechanical Design I

Materials Selection 

for 

Mechanical Design I 

A Brief Overview of a Systematic Methodology 

Jeremy Gregory 

Research Associate 

Laboratory for Energy and Environment 

Massachusetts Institute of Technology 

Cambridge, Massachusetts Materials Systems Laboratory 

©Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection – Slide 1

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? 



©Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I – Slide 2

Approach Changes as Design Evolves 

Design Detail 

Market need 

Concept 

Embodiment 

Detail 

Production etc. 

# of Candidates 

Selection Methods 



©Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I – Slide 3 

Economic Analysis 

Cost Modeling 

LCA 

Method 

Needed for 

Early Stage

What parameters define material selection? 

Example: SUV Liftgate 

Image removed for copyright reasons. 

Schematic of components in an SUV liftgate (rear door). 




Attractive Options 

May Be Found Outside of Expertise 

Unit Cost 

$300 

$250 

$200 

$150 

$100 

$50 

$0 

Steel 

Aluminum 

SMC 

0 25 50 75 100 125 

Annual Production Volume (1000s) 




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 top ranked candidates 

M.F. Ashby, Materials Selection in Mechanical Design, 3 rd Ed., Elsevier, 2005 




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? 

�� Which are desirable? 




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-section Cross section area 

�� Material 

F F 

Area, A 




L 


� m = ALρ 

�� Constraint: 

� F / A < σ y

Identifying Desirable Characteristics 

Example: Materials for a Light, Strong Tie 


� m = ALρ 


� F / A < σ y 

�� Rearrange to eliminate 

free variable 

≥ ( )( ) ⎜ ⎟ 

m F L 

⎛ ρ ⎞ 

⎜σ⎟ ⎝ y ⎠ 

�� Minimize weight by 

minimizing 

⎛ ρ ⎞ 

⎜ 

⎟ 

σ ⎟ 

⎝ y ⎠ 

F F 

Area, A 

or maximize 




L 

Material Index 

σ y 

⎛ ⎞ 

⎜ ⎟ 

⎝ ρ ⎠

Second Step: Screening 

“Eliminate materials that cannot do the job” 

Need effective way of 

evaluating large range 

of material classes 

and properties 

Alumina 

Si-carbide 

Ceramics 

Si-nitride 

Ziconia 

Soda glass 

Borosilicate 

Glasses 

Silica glass 

Glass ceramic 

Steels 

Cast irons 

Al-alloys 

Metals 

Cu-alloys 

Ti-alloys 

Composites 

Sandwiches 

Hybrids 

Lattices 

Segmented 

PE, PP, PC 

PS, PET, PVC 

PA (Nylon) 

Polymers 

Polyester 

Epoxy 

Isoprene 

Butyl rubber 

Elastomers 

Natural rubber 

Silicones 

EVA 




Comparing Material Properties: 

Material Bar Charts 

Young’s modulus (GPa) 

(Log Scale) 

Steel 

Aluminum 

Copper 

Zinc 

Lead 

PEEK 

PP 

PTFE 

Metals Polymers Ceramics Hybrids 




WC 

Alumina 

Glass 

CFRP 

GFRP 

Fiberboard 

Good for elementary selection (e.g., find materials with large modulus)

Comparing Material Properties: 

Material Property Charts 

Young’s modulus (GPa) 

1000 

100 

10 

1 

0.1 

0.01 

Woods 

Foams 

Composites 

Ceramics 

Polymers 

Elastomers 

0.1 1 10 

Density (Mg/m 3 ) 

Metals 




100

Screening Example: 

Heat Sink for Power Electronics 


�� Heat Sink 


1. Max service temp > 200 C 

2. Electrical insulator �� 

R > 10 20 µohm ohm cm 

3. Thermal conductor �� 

T-conduct. conduct. λ > 100 W/m K 

4. Not heavy �� 

Density < 3 Mg/m 3 

�� Free Variables: 

�� Materials and Processes 




Heat Sink Screening: Bar Chart 

Max service temperature (K) 

Steel 

Copper 

Aluminum 

Zinc 

Lead 

Metals 

PEEK 

PP 

PTFE 

Polymers 

200 C 




WC 

Alumina 

Glass 

Ceramics 

GFRP 

CFRP 

Fiberboard 

Composites

Heat Sink Screening: Property Chart 

Thermal conductivity (W/m K) 

1000 

100 

10 

1 

0.1 

0.01 

Metals 

Composites 

Foams 

1 10 10 10 20 

Electrical resistivity ( µΩ cm) 

Ceramics 

Polymers & 

elastomers 

R > 10 20 µΩ cm 

λ > 100 W/m K 




10 30

Example using Granta Software: 

Automobile Headlight Lens 


�� Protect bulb and lens; focus beam 


�� Minimize cost 


�� Transparent w/ optical quality 

�� Easily molded 

�� Good resistance to fresh and salt water 

�� Good resistance to UV light 

�� Good abrasion resistance (high hardness) 


�� Material choice 

Photo of headlight 

removed for copyright 

reasons. 




Selection Criteria – Limit Stage 

Chart from the CES EduPack 2005, Granta Design Limited, Cambridge, UK. (c) Granta Design. Courtesy of Granta Design Limited. Used with permission. 




Property Chart 

Hardness - Vickers (Pa) 

1e10 

1e9 

1e8 

1e7 

1e6 

100000 

10000 

Concrete 

Soda-lime glass 

Polymethyl methacrylate (Acrylic, PMMA) 

Borosilicate glass 

0.1 1 

Price (USD/kg) 

10 100 

•Cheapest, Cheapest, hardest 

material is soda- 

lime glass – used 

in car headlights 

•For For plastics, 

cheapest is PMMA 

– used in car tail 

lights 





Third Step: Ranking 

“Find Find the materials that do the job best” 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 




Single Property Ranking Example: 

Overhead Transmission Cable 


�� Transmit electricity 


�� Minimize electrical Resistance 

R = ρe 


�� Length L and section A are specified 

�� Must not fail under wind or ice-load ice load �� 

required tensile strength > 80 MPa 


�� Material choice 

Screen on strength, rank on resistivity 




L 

A 

L 

Electrical 

resistivity

Single Property Ranking Example: 

Overhead Transmission Cable 

•Screening Screening on 

strength eliminates 

polymers, some 

ceramics 

•Ranking Ranking on 

resistivity selects 

Al and Cu alloys 

Resistivity (µohm.cm) (µ-ohm cm) 

1e27 

1e24 

1e21 

1e18 

1e15 

1e12 

1e9 

1e6 

1000 

1 

1e-3 

Polystyrene (PS) 

Silica glass 

The selection 

Titanium alloys 

Low alloy steel 

Silicon Carbide 

Magnesium alloys 

Aluminium alloys 

Copper alloys 




Alumina 

PEEK 

Epoxies 

PETE 

Cellulose polymers 

Polyester 

Polyurethane (tpPUR) 

Isoprene (IR) 

Wood 

Cork 

Boron Carbide 

Chart from the CES EduPack 2005, Granta Design Limited, Cambridge, UK. (c) Granta Design. Courtesy of Granta Design Limited. Used with permission.

Advanced Ranking: The Material Index 

The method 

1. Identify function, function, 

constraints, 

constraints, 

objective and free variables 

�� List simple constraints for screening 

2. Write down equation for objective -- the “performance 

performance 

equation” 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. Use this for ranking 




The Performance Equation, P 

P 

⎡⎛Functional ⎞ ⎛Geometric ⎞ ⎛Material ⎞⎤ 

= ⎢⎜ ⎟, ⎜ ⎟, ⎜ ⎟⎥ 

⎣⎝requirements, F⎠ ⎝parameters, G⎠ ⎝properties, M ⎠⎦ 

or 

P= f F, G, M 

( ) 

Use constraints to eliminate free variable 

P from previous example of a light, strong tie: 

≥ ( )( ) ⎜ ⎟ 

m F L 

⎛ ρ ⎞ 

⎜σ⎟ ⎝ y ⎠ 




The Material Index 

Example: Materials for a stiff, light beam 


�� Support a bending load 





�� Carry load F, without too 

much deflection 




Area, A 




F 

L 

Deflection, δ 


� m = ALρ 


F CEI 

�� S = ≥ 

3 

δ L

The Material Index 

Example: Materials for a stiff, light beam 


� m = ALρ 


F CEI 

�� S = ≥ 3 

δ L 

�� Rearrange to eliminate 

free variable 

1/2 5/2 

�� ⎛4Fπ⎞ ⎛ L ⎞⎛ 

ρ ⎞ 

m = ⎜ ⎟ ⎜ 1/2 ⎟⎜ 

1/2 ⎟ 

⎝ δ ⎠ ⎝C ⎠⎝ 

E ⎠ 

�� Minimize weight by 

minimizing 

⎛ ρ ⎞ 

⎜ 1/2 ⎟ 

⎝ E ⎠ 

Area, A 

or maximize 


1/2 ⎛ ⎞ 

E 

⎜ ⎟ 

⎝ ρ ⎠ 




F 

L 

Deflection, δ

Material Index Calculation Process Flow 

FUNCTION 

Tie 

Beam 

Shaft 

Column 

Mechanical, 

Thermal, 

Electrical... 

Each combination of 

CONSTRAINTS 

Stiffness 

specified 

Strength 

specified 

Fatigue limit 

Geometry 

specified 

OBJECTIVE 

Minimum cost 

Minimum 

weight 

Function 

Constraint 

Objective 

Free variable 

Maximum energy 

storage 

Minimum 

eco- impact 

INDEX 

1/2 ⎡ ⎤ 

E 

= ⎢ ⎥ 

⎣ ρ ⎦ 

has a 

characterizing 

material index 




M 

Maximize 

this!

Material Index Examples 

�� An objective defines a performance metric: metric: 

e.g. mass or resistance 

�� The equation for performance metric contains material properties 

�� Sometimes a single property 

Either is a 

�� Sometimes a combination 


Objective: 

Minimize Mass 

Performance Metric: 

Mass 

Material Indices for a Beam 

Loading 

Tension 

Bending 

Torsion 

Stiffness 

Limited 

E/ E/ρρ 

E 1/2 

1/2 /ρρ 

G 1/2 

1/2 /ρρ 

Maximize! 

Strength 

Limited 

σσ f /ρρ 

σσ f 22/3 /3 /ρρ 

σσ f 22/3 /3 /ρρ 




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 

Composites 

Foams 

Woods 

Ceramics 

Metals 

Polymers 

Elastomers 




Material Indices & Property Charts: 

Stiffness 

Example: 

Stiff beam 

�� Maximize: Μ = Ε1/2 /ρ 

�� In log space: 

log E = 

2 (log ρ + log M) 

�� This is a set of lines 

with slope=2 

�� Candidates change 

with objective 

Composites 

Woods 

Foams 

Ceramics 

Metals 

Polymers 

Elastomers 




Material Indices & Property Charts: 

Toughness 

�� Load-limited 

Load limited 

� M = KIC �� Choose tough 

metals, e.g. Ti 

�� Energy-limited 

Energy limited 

� M = K 2 

IC / E 

�� Composites and 

metals compete 

�� Displacement-limited 

Displacement limited 

� M = KIC / E 

�� Polymers, foams 




K IC 

K IC 2 /E 

Foams 

K IC/E 

Composites 

Polymers Woods 

Metals 

Ceramics

Considering Multiple 

Objectives/Constraints 

�� With multiple constraints: 

constraints 

�� Solve each individually 

�� Select candidates based on each 

�� Evaluate performance of each 

�� Select performance based on most limiting 

Select performance based on most limiting 

�� May be different for each candidate 

�� With multiple objectives: 

objectives 

�� Requires utility function to map multiple 

metrics to common performance measures 




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 

Process 

Materials 

Shape 




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-ranked top ranked candidates 




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 




Example Problem: Table Legs 

Figure by MIT OCW. 

�� Want to redesign table with thin unbraced cylindrical 

legs 

�� Want to minimize cross-section cross section and mass without 

buckling 

�� Toughness and cost are factors 




Table Legs: Problem Definition 


�� Support compressive loads 



�� Maximize slenderness 



�� Must not buckle 

�� Must not fracture 




m= π r 

2 

lρ 

2 3 4 




P 

crit 

Performance Equation 

π EI π Er 

= = 

l 

2 

4l 

2

Table Legs: Material Indices 

Use constraints to 

eliminate free variable, r 

1/2 

⎛4P⎞ 2 ⎡ ρ ⎤ 

m l 

⎝ π ⎠ ⎣E⎦ ≥ ⎜ ⎟ () ⎢ 1/2 ⎥ 

Functional 

Requirements 

Minimize mass by 

maximizing M1 M 

Geometric 

Parameters 

1 

= 

1/2 

E 

ρ 

Material 

Properties 

For slenderness, 

calculate r at max load 

1/4 1/4 

1/2 

⎛4P⎞ ⎡1⎤ r l 

⎝π⎠ ⎣E⎦ ≥ ⎜ () 

3 ⎟ ⎢ ⎥ 

Functional 

Requirements 

Geometric 

Parameters 

Maximize slenderness 

by maximizing M2 M 2 = E 

Material 

Properties 




Table Legs: Material Selection 

�� Eliminated 

�� Metals (too heavy) 

�� Polymers 

(not stiff enough) 

�� Possibilities: Ceramics, 

wood, composites 

�� Final choice: wood 

wood 

�� Ceramics too brittle 

�� Composites too 

expensive 

�� Note: higher constraint 

on modulus eliminates 

wood 

Composites 

Woods 

Foams 

Ceramics 

Metals 

Polymers 

Elastomers 




M 1 

M 2

Material Index 1 

Young's Modulus (GPa) 

100 

10 

1 

0.1 

0.01 

1e-3 

Softwood: pine, along grain 

Rigid Polymer Foam (LD) 

Silicon 

CFRP, epoxy matrix (isotropic) 

Hardwood: oak, along grain 

Bam boo 

Boron carbide 

Silicon carbide 

100 1000 

Density (kg/m^3) 

10000 





Material Index 2 

Young's Modulus (Pa) 

1e11 

1e10 

1e9 

1e8 

1e7 

1e6 

Hardwood: oak, along grain 

Bamboo 

Softwood: pine, along grain 

Boron carbide 

CFRP, epoxy matrix (isotropic) 

Silicon carbide 

100 1000 

Density (kg/m^3) 

10000 





Example: Heat-Storing 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. 

Sun 

Air flow to 

extract heat 

from wall 




Heat Storing Wall 

W 

Fan

Heat-Storing Heat Storing Wall: Problem Definition 


�� Heat storing medium 


�� Maximize thermal energy 

stored per unit cost 


�� Heat diffusion time ~12h 

�� Wall thickness ≤ 0.5 m 

�� Working temp Tmax>100 max>100 

C 


�� Wall thickness, w 


Heat content: 

Heat diffusion distance: 

w= 2at 

C = Specific Heat 

Thermal Conductivity 




p 

Q= wρC ∆T 

a = Thermal Diffusivity = 

λ = 

p 

λ 

ρC 

p

Heat-Storing Heat Storing Wall: Material Indices 

Eliminate free variable: 

1/2 

Q= 2t∆Ta 

ρCp 

Insert λ to obtain 

Performance Eqn: 

⎛ λ ⎞ 

Q= 2t∆T⎜ 

1/2 ⎟ 

⎝a⎠ λ 

Maximize: M1 = 1/2 

a 

Thickness restriction: 

2 

w 

a ≤ 

2t 

For w≤ 0.5 m and t = 12 h: 

M = a≤ 

3× 10 




2 

−6 

2 

m/s

Heat-Storing 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

Materials Selection for Mechanical Design I

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