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
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?
Objective: What essential conditions must be met?
In what manner should implementation excel?
Constraints: What is to be maximized or minimized?
Do not limit options by specifying implementation w/in function
Differentiate between binding and soft constraints
Free variables: Which design variables are free?
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:
Objective:
Length specified Carry load F, w/o failure
Free variables:
F
F
Area, A
L
Minimize mass
Constraints:
Support a tension load
Cross-section area Material
Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005
Objective: m = ALρ Constraint: F / A < σy
Materials Systems Laboratory Materials Selection I – Slide 8
Identifying Desirable Characteristics Example: Materials for a Light, Strong Tie
Objective: m = ALρ Constraint: 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:
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:
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: Protect bulb and lens; focus beam Objective: Photo of headlight Minimize cost removed for copyright Constraints: reasons. 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
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:
Objective:
Minimize electrical Resistance
Constraints:
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: 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:
Length specified Carry load F, without too much deflection
Free variables:
L Area, A
Minimize mass
Constraints:
Support a bending load
Objective:
F
Cross-section area Material
Massachusetts Institute of Technology Cambridge, Massachusetts ©Jeremy Gregory and Randolph Kirchain, 2005
Deflection, δ
Objective: m = ALρ Constraint: F CEI S= ≥ 3 δ L
Materials Systems Laboratory Materials Selection I – Slide 24
The Material Index Example: Materials for a stiff, light beam
Objective: m = ALρ Constraint: S = F ≥ CEI δ L3 Rearrange to eliminate free variable 1/ 2 5/ 2 ⎛ ⎞⎛ ρ ⎞ 4F π L ⎛ ⎞ 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
Energy-limited
M = KIC Choose tough metals, e.g. Ti KIC2 /
M= E Composites and metals compete
Displacement-limited
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:
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
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:
Shape Materials Process
Underlying principles of selection are unchanged
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
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:
Objective:
Minimize mass Maximize slenderness
Performance Equation
m = π r lρ 2
Constraints:
Support compressive loads
Length specified Must not buckle Must not fracture
Free variables:
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
Possibilities: Ceramics, wood, composites Final choice: wood
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:
Objective:
Maximize thermal energy stored per unit cost
Constraints:
Heat storing medium
Heat diffusion time ~12h Wall thickness ≤ 0.5 m Working temp Tmax>100 C
Free variables:
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
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
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