Materials Selection for Mechanical Design I

Transcription

1 Materials Selection for Mechanical Design I A Brief Overview of a Systematic Methodology Jeremy Gregory Research Associate Laboratory for Energy and Environment Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection Slide 1

2 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

3 Approach Changes as Design Evolves Market need Selection Methods Design Detail Concept Embodiment Detail # of Candidates Economic Analysis Cost Modeling LCA Method Needed for Early Stage Production etc. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 3

4 What parameters define material selection? Example: SUV Liftgate Image removed for copyright reasons. Schematic of components in an SUV liftgate (rear door). Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 4

5 Attractive Options May Be Found Outside of Expertise $300 Unit Cost $250 $200 $150 $100 $50 $0 Steel Aluminum SMC Annual Production Volume (1000s) Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 5

6 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, 3 rd Ed., Elsevier, 2005 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 6

7 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? Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 7

8 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 section area Material F Area, A L Objective: m = ALρ Constraint: F / A < σ y F Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 8

9 Identifying Desirable Characteristics Example: Materials for a Light, Strong Tie Objective: m = ALρ Constraint: F Area, A L F F / A < σ y Rearrange to eliminate free variable ( )( ) m F L Minimize weight by minimizing ρ σ y ρ σ y Material Index σ y or maximize ρ Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 9

10 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 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 Soda glass Borosilicate Glasses Silica glass Glass ceramic Isoprene Butyl rubber Elastomers Natural rubber Silicones EVA Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 10

11 Comparing Material Properties: Material Bar Charts Steel WC Young s modulus (GPa) (Log Scale) Copper Aluminum Zinc Lead PEEK PP PTFE Alumina Glass CFRP GFRP Fiberboard Metals Polymers Ceramics Hybrids Good for elementary selection (e.g., find materials with large modulus) Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 11

12 Comparing Material Properties: Material Property Charts 1000 Ceramics Young s modulus (GPa) Woods Foams Composites Polymers Metals 0.01 Elastomers Density (Mg/m 3 ) 100 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 12

13 Screening Example: Heat Sink for Power Electronics Function: Heat Sink Constraints: 1. Max service temp > 200 C 2. Electrical insulator R > µohm cm 3. Thermal conductor T-conduct. λ > 100 W/m K 4. Not heavy Density < 3 Mg/m 3 Free Variables: Materials and Processes Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 13

14 Heat Sink Screening: Bar Chart WC Max service temperature (K) Steel Copper Alumina CFRP Aluminum Zinc PEEK PP PTFE Glass GFRP Fiberboard 200 C Lead Metals Polymers Ceramics Composites Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 14

15 Heat Sink Screening: Property Chart Thermal conductivity (W/m K) Metals Composites Foams Electrical resistivity ( µω cm) Ceramics Polymers & elastomers R > µω cm λ > 100 W/m K Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 15

16 Example using Granta Software: Automobile Headlight Lens Function: Protect bulb and lens; focus beam Objective: Minimize cost Constraints: 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 Photo of headlight removed for copyright reasons. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 16

17 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. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 17

18 Property Chart Hardness - Vickers (Pa) 1e10 1e9 1e8 1e7 1e6 Soda-lime glass Borosilicate glass Concrete Polymethyl methacrylate (Acrylic, PMMA) Cheapest, hardest material is soda- lime glass used in car headlights For plastics, cheapest is PMMA used in car tail lights 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. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 18

19 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 19

20 Single Property Ranking Example: Overhead Transmission Cable Function: Transmit electricity Objective: Minimize electrical Resistance R = ρe Constraints: Length L and section A are specified Must not fail under wind or ice-load required tensile strength > 80 MPa Free variables: Material choice Screen on strength, rank on resistivity L A L Electrical resistivity Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 20

21 Single Property Ranking Example: Overhead Transmission Cable Screening on strength eliminates polymers, some ceramics Ranking on resistivity selects Al and Cu alloys Resistivity (µ-ohm cm) Resistivity (µohm.cm) 1e27 1e24 1e21 1e18 1e15 1e12 1e9 1e e-3 Polystyrene (PS) Silica glass Alumina PEEK The selection Epoxies PETE Cellulose polymers Polyester Polyurethane (tppur) Isoprene (IR) Wood Titanium alloys Low alloy steel Silicon Carbide Cork Boron Carbide 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. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 21

22 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 22

23 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 23

24 The Material Index Example: Materials for a stiff, light beam Function: Support a bending load Objective: Minimize mass Constraints: Length specified Carry load F, without too much deflection Free variables: Cross-section section area Material Area, A F L Deflection, δ Objective: m = ALρ Constraint: F CEI S = 3 δ L Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 24

25 The Material Index Example: Materials for a stiff, light beam Objective: m = ALρ Constraint: 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 Material Index 1/2 E ρ Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 25 or maximize F L Deflection, δ

26 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 M INDEX 1/2 E = ρ has a characterizing material index Maximize this! Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 26

27 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 Sometimes a combination Material Index Objective: Minimize Mass Performance Metric: Mass Material Indices for a Beam Loading Tension Bending Torsion Stiffness Limited E/ρ E 1/2 1/2 /ρ G 1/2 1/2 /ρ Strength Limited σ f /ρ σ 2/3 f /ρ σ 2/3 f /ρ Maximize! Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 27

28 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 28

29 Material Indices & Property Charts: Stiffness Example: Stiff beam Maximize: Μ = Ε 1/2 /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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 29

30 Material Indices & Property Charts: Toughness Load-limited M = K IC Choose tough metals, e.g. Ti Energy-limited M = K IC2 / E Composites and metals compete Displacement-limited limited M = K IC / E Polymers, foams K IC K IC 2 /E Foams K IC /E Composites Polymers Woods Metals Ceramics Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 30

31 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 May be different for each candidate With multiple objectives: Requires utility function to map multiple metrics to common performance measures Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 31

32 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 32

33 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 33

34 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 34

35 Example Problem: Table Legs Figure by MIT OCW. Want to redesign table with thin unbraced cylindrical legs Want to minimize cross-section section and mass without buckling Toughness and cost are factors Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 35

36 Table Legs: Problem Definition Function: Support compressive loads Objective: Minimize mass Maximize slenderness Constraints: Length specified Must not buckle Must not fracture Free variables: Cross-section section area Material m Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 36 P crit Performance Equation 2 = π r lρ π EI = = l π Er l

37 m Table Legs: Material Indices Use constraints to eliminate free variable, r 1/2 4P 2 ρ l π E () 1/2 Functional Requirements Minimize mass by maximizing M 1 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 l π E () 3 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 37 r Functional Requirements Geometric Parameters Maximize slenderness by maximizing M 2 M 2 = E Material Properties

38 Table Legs: Material Selection Eliminated Metals (too heavy) Polymers (not stiff enough) Possibilities: Ceramics, wood, composites Final choice: 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 Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 38

39 Material Index Silicon Boron carbide CFRP, epoxy m atrix (isotropic) Hardwood: oak, along grain Silicon carbide Young's Modulus (GPa) Bam boo Softwood: pine, along grain Rigid Polymer Foam (LD) 1e 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. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 39

40 Material Index 2 Young's Modulus (Pa) 1e11 1e10 1e9 1e8 Boron carbide CFRP, epoxy matrix (isotropic) Hardwood: oak, along grain Bamboo Softwood: pine, along grain Silicon carbide 1e7 1e 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. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 40

41 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 Heat Storing Wall W Air flow to extract heat from wall Fan Figure by MIT OCW. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 41

42 Heat-Storing Wall: Problem Definition Function: Heat storing medium Objective: Maximize thermal energy stored per unit cost Constraints: Heat diffusion time ~12h Wall thickness 0.5 m Working temp T max >100 C Free variables: Wall thickness, w Material Heat content: Heat diffusion distance: w= C = p 2at Specific Heat Q= wρc T a = Thermal Diffusivity = λ = Thermal Conductivity p λ ρc p Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 42

43 Heat-Storing Wall: Material Indices Eliminate free variable: 1/2 Q= 2t Ta ρc p Insert λ to obtain Performance Eqn: λ Q t T a = 2 1/2 Maximize: M λ = a 1 1/2 Thickness restriction: 2 w a 2t For w 0.5 m and t = 12 h: M 2 = a m/s Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 43

44 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. Jeremy Gregory and Randolph Kirchain, 2005 Materials Selection I Slide 44