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
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