1. © MFA and DC 2007 New approaches to Materials Education - a course authored by Mike Ashby and David Cebon, Cambridge, UK, 2007 Unit 4. Ranking: refining the choice

2. © MFA and DC 2007 Unit 3 This Unit Outline Step 2Screening: eliminate materials that cannot do the job Step 3Ranking: find the materials that do the job best Step 4Documentation: explore pedigrees of top-ranked candidates Step 1Translation: express design requirements as constraints and objectives Selection has 4 basic steps Exercises More info: “Materials: engineering, science, processing and design”, Chapter 3, 4 and 6 “Materials Selection in Mechanical Design”, Chapters 5 and 6

3. © MFA and DC 2007 Analysis of design requirements Express design requirements as constraints and objectives Must be  Stiff enough  Strong enough  Tough enough  Able to be welded A label Bike frame Design requirements Constraints What essential conditions must be met ? Objectives What is the criterion of excellence ? Function What does the component do ? Free variable What can be varied ? Choice of material Minimize  Cost  Weight  Volume  Eco-impact

4. © MFA and DC 2007 The CD case, with an objective Free variable Choice of material Function CD enclosure Translation Constraints 1. Can be injection molded 2. Optically clear 3. Toughness K 1c > that of PS 4. Can be recycled  Injection-moldable  Contain and protect CD better than the PS case.  As transparent as PS  Eco-friendly  As cheap as possible Design requirements OBJECTIVE Minimise material cost

5. © MFA and DC 2007 Screening and ranking: the CD case Volume of material in case, V, fixed Density , cost per unit mass C m Material cost/case C = V C m  OBJECTIVE Minimise material cost C Rank on this index Select Level 2: Materials Fracture toughness Polystyrene Keep these! 2 Ranking 2 1 3 Cost metric C m  Polycarbonate Cellulose acetate PMMA Polystyrene Surviving materials Tree stage: injection mold 1 Optical properties Transparency Eco properties Recycle Optical quality Transparent Translucent Opaque 3

6. © MFA and DC 2007 Advanced ranking: modelling performance 3. Read off the combination of material properties that maximises performance -- the material index If the performance equation involves a free variable (other than the material): Identify the constraint that limits it. Use this to eliminate the free variable in performance equation. 1. Identify function, constraints, objective and free variables (list simple constraints for screening). 2. Write down equation for objective -- the “performance equation”. 4. Use this for ranking The method:

7. © MFA and DC 2007 Example 1: strong, light tie-rod Minimize mass m: m = A L  (2) Objective Length L is specified Must not fail under load F Constraints Material choice Section area A. Free variables Equation for constraint on A: F/A <  y (1) Strong tie of length L and minimum mass L F F Area A Tie-rod Function m = mass A = area L = length  = density = yield strength (or maximize ) Chose materials with smallest Eliminate A in (2) using (1): Performance metric m

8. © MFA and DC 2007 Example 2: stiff, light beam Beam Function Minimize mass m: m = A L  (2) Objective Length L is specified Must have bending stiffness > S* Constraints m = mass A = area L = length  = density E = Young’s modulus I = second moment of area (I = b 4 /12 = A 2 /12) C = constant (here, 48) Material choice Section area A. Free variables Equation for constraint on A: (1) Stiff beam of length L and minimum mass L Square section, area A = b 2 b Chose materials with smallest Eliminate A in (2) using (1): Performance metric m

9. © MFA and DC 2007 Material “indices” FUNCTION Tie Beam Shaft Column Mechanical, Thermal, Electrical... Each combination of Function Constraint Objective Free variable has a characterising material index CONSTRAINTS Stiffness specified Strength specified Fatigue limit Geometry specified Minimum cost Minimum weight Minimum volume Minimum eco- impact OBJECTIVE I NDEX Minimise this!

10. © MFA and DC 2007 Demystifying material indices A material index is just the combination of material properties that appears in the equation for performance (eg minimizing mass or cost). Sometimes a single property Sometimes a combination Either is a material index Example: Objective -- minimise mass Performance metric = mass Tension (tie) Bending (beam) Bending (panel) Function Stiffness Strength Constraints (Or maximize reciprocals) Minimize these!

11. © MFA and DC 2007 0.1 10 1 100 Metals Polymers Elastomers Woods Composites Foams 0.01 1000 100 0.1 1 10 Density (Mg/m 3 ) Young’s modulus E, (GPa) Ceramics Optimized selection using charts 2 Contours of constant M are lines of slope 2 on an E-  chart Index Light stiff beam: Rearrange: Take logs: Log E = 2 log  - 2 log M Decreasing M Slope 2

12. © MFA and DC 2007 The chart-management tool bar Box selection tool Cancel selection Add text Zoom Add envelopes Un-zoom Black and white chart Hide failed materials Grey failed materials Line selection tool

13. © MFA and DC 2007 Optimized selection using charts

14. © MFA and DC 2007 Needed for optimized selection The main points The four steps of selection 1. Translation, giving constraints and objectives 2. Screening, using constraints 3. Ranking, using objectives, giving indices 4. Documentation for prime candidates CES allows screening using limit stages, graph stages and tree stages ranking, using graph stages search for supporting information, using web portal.

15. © MFA and DC 2007 Demo

16. © MFA and DC 2007 Exercise: selecting light, strong materials (1) 4.1 The material index for selecting light strong materials is M = where is the yield strength and the density. Make a Graph stage with these two properties as axes Impose a selection line (slope 1) to find materials with the highest values of M. Add a Limit stage to impose the additional constraint: Elongation > 10% Results: Age-hardening wrought Al-alloys Nickel-based superalloys Titanium alloys Wrought magnesium alloys

17. © MFA and DC 2007 Exercise: selecting light, strong materials (2) 4.2 Repeat the selection of 4.1, but use the Advanced facility to make a bar-chart with the index M = on the Y-axis. Impose a Box selection to find materials with the highest values of M. Add a Limit stage to impose the additional constraint: Elongation > 10% Index  y /  High

18. © MFA and DC 2007 Exercise: selecting materials for springs (1) 4.3 A material is required for a spring that may be exposed to shock loading, and must operate in fresh and salt water. Constraints:  Fracture toughness > 15 MPa.m 1/2  Very good durability in fresh and salt water Objective:  Maximise stored elastic energy Strain Stress Elastic energy The best materials for springs are those with the greatest value of the index Make a graph with  Young’s modulus E on the X-axis  Yield strength on the Y-axis  Put on a line of slope 0.5 (corresponding to power 2)  Select materials above the line  Add the other constraints using a limit stage

19. © MFA and DC 2007 Exercise: selecting materials for springs (2) 4.4 Repeat the selection of 4.3, but use the Advanced facility to make a bar-chart with the index on the Y-axis.. Index  y 2 /E High Plot the bar chart  Use a box selection to select the materials with high values of the index  Add the other constraints using a limit stage Results: CFRP, epoxy matrix (isotropic) Nickel-based superalloys Titanium alloys

20. © MFA and DC 2007 End of Unit 4