Materials Selection for Mechanical Design I

Materials Selection for Mechanical Design I ... Materials Selection in Mechanical Design, ... 2005 Materials Selection I...

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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 ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection – Slide 1

Relationship To Course ‰

A key concept throughout this course is how to select among technology choices ƒ ƒ ƒ

‰

‰

Economic Analysis Cost Modeling Life Cycle Assessment

Focus has been on economic assessment of alternatives How does this fit into larger technology choice problem?

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 2

Approach Changes as Design Evolves Market need

LCA

Detail

Method Needed for Early Stage Cost Modeling

Design Detail

Embodiment

# of Candidates

Concept

Economic Analysis

Selection Methods

Production etc. Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 3

What parameters define material selection? Example: SUV Liftgate

Image removed for copyright reasons. Schematic of components in an SUV liftgate (rear door).

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 4

Attractive Options May Be Found Outside of Expertise $300 Steel Aluminum SMC

Unit Cost

$250 $200 $150 $100 $50 $0 0

25

50

75

100

125

Annual Production Volume (1000s) Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 5

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 M.F. Ashby, Materials Selection in Mechanical Design, 3rd Ed., Elsevier, 2005 Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 6

First Step: Translation “Express design requirements as constraints and objectives”

Using design requirements, analyze four items: ‰ Function: What does the component do? ƒ ‰

Objective: What essential conditions must be met? ƒ

‰

In what manner should implementation excel?

Constraints: What is to be maximized or minimized? ƒ

‰

Do not limit options by specifying implementation w/in function

Differentiate between binding and soft constraints

Free variables: Which design variables are free? ƒ ƒ

Which can be modified? Which are desirable?

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 7

Identifying Desirable Characteristics Example: Materials for a Light, Strong Tie ‰

Function: ƒ

‰

Objective: ƒ

‰

ƒ

Length specified Carry load F, w/o failure

Free variables: ƒ ƒ

F

F

Area, A

L

Minimize mass

Constraints: ƒ

‰

Support a tension load

Cross-section area Material

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

‰

‰

Objective: ƒ m = ALρ Constraint: ƒ F / A < σy

Materials Systems Laboratory Materials Selection I – Slide 8

Identifying Desirable Characteristics Example: Materials for a Light, Strong Tie ‰

‰

‰

Objective: ƒ m = ALρ Constraint: ƒ F / A < σy Rearrange to eliminate free variable

⎛ ρ m ≥ ( F )( L ) ⎜ ⎜σy ⎝

‰

⎞ ⎟⎟ ⎠

Minimize weight by minimizing

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

⎛ ρ ⎜⎜ ⎝σy

F

F L

Area, A

Material Index

⎛σy ⎞ ⎜ ⎟ ⎝ ρ ⎠

⎞ ⎟⎟ or ⎠

e z i xim a m

Materials Systems Laboratory Materials Selection I – Slide 9

Second Step: Screening “Eliminate materials that cannot do the job” Need effective way of evaluating large range of material classes and properties

Steels Cast irons Al-alloys

Metals Cu-alloys Ti-alloys PE, PP, PC PS, PET, PVC PA (Nylon)

Alumina Si-carbide

Ceramics Si-nitride Ziconia

Composites Sandwiches

Hybrids

Polymers Polyester Epoxy

Lattices Segmented Soda glass Borosilicate

Glasses Silica glass Glass ceramic Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Isoprene Butyl rubber

Elastomers Natural rubber Silicones EVA Materials Systems Laboratory Materials Selection I – Slide 10

Comparing Material Properties: Material Bar Charts WC

Young’s modulus (GPa) (Log Scale)

Steel Copper

CFRP Alumina GFRP

Aluminum Zinc Lead

PEEK PP

Glass

Fiberboard

PTFE

Metals

Polymers

Ceramics

Hybrids

Good for elementary selection (e.g., find materials with large modulus) Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 11

Comparing Material Properties: Material Property Charts 1000

Young’s modulus (GPa)

Ceramics 100 Composites Woods

10

Metals 1

Foams

Polymers

0.1 Elastomers

0.01

0.1

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

1

Density

(Mg/m3)

10

100

Materials Systems Laboratory Materials Selection I – Slide 12

Screening Example: Heat Sink for Power Electronics ‰

Function: ƒ

‰ 1. 2.

3.

4.

‰

Heat Sink

Constraints: Max service temp > 200 C Electrical insulator Æ R > 1020 µohm cm Thermal conductor Æ T-conduct. λ > 100 W/m K Not heavy Æ Density < 3 Mg/m3

Free Variables: ƒ

Materials and Processes

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 13

Heat Sink Screening: Bar Chart Max service temperature (K)

WC

Steel Copper

Alumina

CFRP

PEEK PP Aluminum

200 C

GFRP

PTFE Fiberboard

Zinc Lead Metals

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Glass

Polymers

Ceramics

Composites

Materials Systems Laboratory Materials Selection I – Slide 14

Heat Sink Screening: Property Chart Thermal conductivity (W/m K)

1000

R > 1020 µΩ cm

Ceramics

Metals 100

λ > 100 W/m K

10 Polymers & elastomers

Composites 1 0.1 0.01

Foams 1

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

1010

1020

Electrical resistivity ( µΩ cm)

1030

Materials Systems Laboratory Materials Selection I – Slide 15

Example using Granta Software: Automobile Headlight Lens ‰

‰

‰

‰

Function: ƒ Protect bulb and lens; focus beam Objective: Photo of headlight ƒ Minimize cost removed for copyright Constraints: reasons. ƒ Transparent w/ optical quality ƒ Easily molded ƒ Good resistance to fresh and salt water ƒ Good resistance to UV light ƒ Good abrasion resistance (high hardness) Free variables: ƒ Material choice

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 16

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.

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 17

Property Chart Soda-lime glass

1e10

•Cheapest, hardest material is sodalime glass – used in car headlights

Hardness - Vickers (Pa)

1e9

Borosilicate glass 1e8

Concrete 1e7

•For plastics, cheapest is PMMA – used in car tail lights

Polymethyl methacrylate (Acrylic, PMMA)

1e6

100000

10000 0.1

1

10

100

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

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 18

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

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 19

Single Property Ranking Example: Overhead Transmission Cable ‰

Function: ƒ

‰

Objective: ƒ

‰

Minimize electrical Resistance

Constraints: ƒ ƒ

‰

Transmit electricity

L R = ρe A

Length L and section A are specified Must not fail under wind or ice-load Æ required tensile strength > 80 MPa

L

Electrical resistivity

Free variables: ƒ Material choice Screen on strength, rank on resistivity

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 20

Single Property Ranking Example: Overhead Transmission Cable 1e27

Polystyrene (PS) Silica glass

•Ranking on resistivity selects Al and Cu alloys

Epoxies

Alumina PEEK

PETE Cellulose polymers

1e21

Resistivity (µ-ohm cm) Resistivity (µohm.cm)

•Screening on strength eliminates polymers, some ceramics

1e24

Polyester Polyurethane (tpPUR)

1e18

Isoprene (IR) Wood

1e15

Silicon Carbide 1e12

Cork

1e9

Boron Carbide 1e6

The selection 1000

Titanium alloys Low alloy steel

1

1e-3

Magnesium alloys Aluminium alloys Copper alloys

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

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 21

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. Use this for ranking

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 22

The Performance Equation, P ⎡⎛ Functional ⎞ ⎛ Geometric ⎞ ⎛ Material ⎞⎤ P = ⎢⎜ ⎟,⎜ ⎟,⎜ ⎟⎥ ⎣⎝ 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:

⎛ ρ m ≥ ( F )( L ) ⎜ ⎜σy ⎝ Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

⎞ ⎟⎟ ⎠ Materials Systems Laboratory Materials Selection I – Slide 23

The Material Index Example: Materials for a stiff, light beam ‰

Function: ƒ

‰

‰

ƒ

Length specified Carry load F, without too much deflection

Free variables: ƒ ƒ

L Area, A

Minimize mass

Constraints: ƒ

‰

Support a bending load

Objective: ƒ

F

Cross-section area Material

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

‰

‰

Deflection, δ

Objective: ƒ m = ALρ Constraint: F CEI ƒ S= ≥ 3 δ L

Materials Systems Laboratory Materials Selection I – Slide 24

The Material Index Example: Materials for a stiff, light beam ‰

‰

‰

‰

Objective: ƒ m = ALρ Constraint: ƒ S = F ≥ CEI δ L3 Rearrange to eliminate free variable 1/ 2 5/ 2 ⎛ ⎞⎛ ρ ⎞ 4F π L ƒ ⎛ ⎞ m=⎜ ⎟ ⎜ 1/ 2 ⎟ ⎜ 1/ 2 ⎟ δ ⎝ ⎠ ⎝ C ⎠⎝ E ⎠

F L Area, A

Minimize weight by ⎛ ρ ⎞ ⎜ 1/ 2 ⎟ minimizing ⎝ E ⎠ or

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Deflection, δ

Material Index

⎛ E1/ 2 ⎞ ⎜ ⎟ ⎝ ρ ⎠ ze i im x ma Materials Systems Laboratory Materials Selection I – Slide 25

Material Index Calculation Process Flow Each combination of

FUNCTION Tie

CONSTRAINTS Beam

Shaft Column

Mechanical, Thermal, Electrical... Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Stiffness specified

Function Constraint Objective Free variable

Maximize this! OBJECTIVE Minimum cost

Strength specified

Minimum weight

Fatigue limit Geometry specified

has a characterizing material index

INDEX ⎡ E1/ 2 ⎤ M =⎢ ⎥ ρ ⎣ ⎦

Maximum energy storage Minimum eco- impact Materials Systems Laboratory Materials Selection I – Slide 26

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 Either is a Material Index Sometimes a combination

Material Indices for a Beam Objective: Minimize Mass Performance Metric: Mass

Tension

Stiffness Limited E/ρ

Strength Limited σf/ρ

Bending

E1/2/ρ

σf2/3/ρ

Torsion

G1/2/ρ

σf2/3/ρ

Loading

Maximize! Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 27

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 Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Ceramics Composites Metals Woods Polymers Elastomers Foams

Materials Systems Laboratory Materials Selection I – Slide 28

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 Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Ceramics Composites

Woods

Foams

Metals

Polymers

Elastomers

Materials Systems Laboratory Materials Selection I – Slide 29

Material Indices & Property Charts: Toughness ‰

Load-limited ƒ ƒ

‰

Energy-limited ƒ ƒ

‰

M = KIC Choose tough metals, e.g. Ti KIC2 /

M= E Composites and metals compete

Displacement-limited ƒ ƒ

KIC/E

KIC

Composites

2/E

KIC

Polymers

Metals

Woods Ceramics

Foams

M = KIC / E Polymers, foams

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 30

Considering Multiple Objectives/Constraints ‰

With multiple constraints: ƒ ƒ ƒ ƒ

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: ƒ

Requires utility function to map multiple metrics to common performance measures

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 31

Method for Early Technology Screening ‰

Design performance is determined by the combination of: ƒ ƒ ƒ

‰

Shape Materials Process

Underlying principles of selection are unchanged ƒ

Materials

Process Shape

BUT, do not underestimate impact of shape or the limitation of process

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 32

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 candidates Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 33

Summary ‰

Material affects design based on ƒ ƒ ƒ ƒ

‰ ‰ ‰ ‰

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

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 34

Example Problem: Table Legs

Figure by MIT OCW.

‰

‰

‰

Want to redesign table with thin unbraced cylindrical legs Want to minimize cross-section and mass without buckling Toughness and cost are factors

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 35

Table Legs: Problem Definition ‰

Function: ƒ

‰

Objective: ƒ ƒ

‰

Minimize mass Maximize slenderness

Performance Equation

m = π r lρ 2

Constraints: ƒ ƒ ƒ

‰

Support compressive loads

Length specified Must not buckle Must not fracture

Free variables: ƒ ƒ

Pcrit =

π EI 2

l

2

=

π Er 3

4l

4

2

Cross-section area Material

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 36

Table Legs: Material Indices Use constraints to eliminate free variable, r 1/ 2

⎛ 4P ⎞ m≥⎜ ⎟ ⎝ π ⎠ Functional Requirements

(l )

2

⎡ ρ ⎤ ⎢⎣ E1/ 2 ⎦⎥

Geometric Material Parameters Properties

Minimize mass by maximizing M1

M1 =

E1/ 2

ρ

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

For slenderness, calculate r at max load 1/ 4

⎛ 4P ⎞ r ≥⎜ 3 ⎟ ⎝π ⎠ Functional Requirements

(l )

1/ 2

1/ 4

⎡1⎤ ⎢E⎥ ⎣ ⎦

Geometric Material Parameters Properties

Maximize slenderness by maximizing M2

M2 = E Materials Systems Laboratory Materials Selection I – Slide 37

Table Legs: Material Selection ‰

Eliminated ƒ ƒ

‰

‰

Possibilities: Ceramics, wood, composites Final choice: wood ƒ ƒ

‰

Metals (too heavy) Polymers (not stiff enough)

Ceramics too brittle Composites too expensive

Note: higher constraint on modulus eliminates wood

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

M1

Ceramics Composites Woods

M2 Metals

Polymers

Foams

Elastomers

Materials Systems Laboratory Materials Selection I – Slide 38

Material Index 1 Silicon

Boron carbide

Silicon carbide

CFRP, epoxy m atrix (isotropic)

100

Young's Modulus (GPa)

Hardw ood: oak, along grain Bam boo 10

Softw ood: pine, along grain 1

Rigid Polym er Foam (LD)

0.1

0.01

1e-3

100

1000

10000

Density (kg/m^3) Chart from the CES EduPack 2005, Granta Design Limited, Cambridge, UK. (c) Granta Design. Courtesy of Granta Design Limited. Used with permission.

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 39

Material Index 2 Boron carbide

Silicon carbide

CFRP, epoxy m atrix (isotropic) 1e11

Hardw ood: oak, along grain Bam boo

Young's Modulus (Pa)

1e10

Softw ood: pine, along grain

1e9

1e8

1e7

1e6

100

1000

10000

Density (kg/m^3) Chart from the CES EduPack 2005, Granta Design Limited, Cambridge, UK. (c) Granta Design. Courtesy of Granta Design Limited. Used with permission.

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 40

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

Sun

Air flow to extract heat from wall

Heat Storing Wall

‰

W Fan

Figure by MIT OCW.

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 41

Heat-Storing Wall: Problem Definition ‰

Function: ƒ

‰

Objective: ƒ

‰

Maximize thermal energy stored per unit cost

Constraints: ƒ ƒ ƒ

‰

Heat storing medium

Heat diffusion time ~12h Wall thickness ≤ 0.5 m Working temp Tmax>100 C

Free variables: ƒ ƒ

Heat content: Q = wρ C p ∆T Heat diffusion distance: w = 2at C p = Specific Heat

λ a = Thermal Diffusivity = ρC p λ = Thermal Conductivity

Wall thickness, w Material

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 42

Heat-Storing Wall: Material Indices Eliminate free variable:

Thickness restriction:

Q = 2t ∆Ta1/ 2 ρ C p

w2 a≤ 2t For w ≤ 0.5 m and t = 12 h:

Insert λ to obtain Performance Eqn: ⎛ λ ⎞ Q = 2t ∆T ⎜ 1/ 2 ⎟ ⎝a ⎠ Maximize: M 1 = Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

M 2 = a ≤ 3 × 10−6 m2 /s

λ a1/ 2 Materials Systems Laboratory Materials Selection I – Slide 43

Heat-Storing Wall: Material Selection ‰

Eliminated ƒ ƒ

‰

‰

Foams: Too porous Metals: Diffusivity too high

Possibilities: Concrete, stone, brick, glass, titanium(!) Final Choices ƒ ƒ

Concrete is cheapest Stone is best performer at reasonable price

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

Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005

Materials Systems Laboratory Materials Selection I – Slide 44