2.2 - Screening and ranking for optimal selection. Outline

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1 2 - Ashby Method Screening and ranking for optimal selection Outline Basic steps of selection 1. Translation of design requirements into a material specification 2. Screening out of materials that fail constraints 3. Ranking by ability to meet objectives: Material Indices 4. Search for supporting information for promising candidates Resources: M. F. Ashby, Materials Selection in Mechanical Design Butterworth Heinemann, 1999 Chapters 1-4 The Cambridge Material Selector (CES) software -- Granta Design, Cambridge (

2 The design process Design phase Market need Concept Embodiment Detail Tools for Design (Material needs) Data for all materials and processes, low precision Data for fewer materials or processes, higher precision Data for one material or process, highest precision Life phase Production Use Disposal Redesign Tools for life-cycle analysis Design requirements material specification Translation Design requirements Analyse: Function What does the component do? Constraints Objectives Free variables What essential conditions must be met? What is to be maximised or minimised? Which design variables are free? From which we obtain Screening criteria: go / no-go criteria (usually many) Ranking criteria: an ordering of the materials that go

3 Example: heat sink for microprocessor Step 1 -- Screening: Eliminate materials that can t do the job Constraints must operate at 200 o C be electrical insulator conduct heat well Retain materials with: 1. max service temp > 473K 2. must be good insulator 3. T-conduct. λ > 100 W/m.K Step 2 -- Ranking: Find the material that does the job best Objective minimise cost Rank materials : by price/kg Screening using a limit stage Mechanical attributes Minimum Maximum Density Mg/m 3 Young s modulus Elastic limit GPa MPa Thermal attributes Max. service temp. T-expansion 473 K W/m.K T-conductivity /K Electrical attributes Good insulator Poor insulator b Poor conductor Good conductor

Using CES to screen materials Selection using limits WC Steel Copper Alumina CFRP Selection using bar-charts Selection using property charts Thermal conductivity (W/m.

4 Using CES to screen materials Selection using limits WC Steel Copper Alumina CFRP Selection using bar-charts Selection using property charts Thermal conductivity (W/m.s) Max service temperature (K) Aluminum Zinc PEEK PP PTFE Glass GFRP Fibreboard Lead Metals Polymers Ceramics Composites Metals Composites Polymers & elastomers Foams Price ($/kg) 10 Ceramics 100 Ranking: Modelling performance The steps: Identify function, constraints, objective and free variables. Write down equation for objective -- the performance equation. If the performance equation contains a free variable other than material identify the constraint that limits it. Use this constraint to eliminate the free variable in performance equation. Read off the combination of material properties that maximise performance.

5 Example 1: strong, light tie-rod Function Objective Constraints Free variables Tie-rod Minimise mass m: m = A L (1) F Area A Length L is specified Must not fail under load F Adequate fracture toughness Equation for constraint on A: F/A < σ y (2) Material choice Section area A; eliminate in (1) using (2): m = FL σ y Strong tie of length L and minimum mass L m = mass A = area L = length = density σ y = yield strength PERFORMANCE INDEX Chose materials with smallest σ y F Example 2: stiff, light beam Function Beam (solid square section). b F Objective Constraint Free variables 12 S L m = C Minimise mass, m, where: 2 m = AL = b L Stiffness of the beam S: CEI S = 3 L I is the second moment of area: 4 b I= 12 Material choice. Edge length b. Combining the equations gives: 1/ 2 5 1/ E 2 b = f( S,C,E,L ) b m = mass A = area L = length = density b = edge length S = stiffness I = second moment of area E = Youngs Modulus Chose materials with smallest L 1/ E 2

6 Materials indices FUNCTION Tie Beam Each combination of OBJECTIVE Minimum cost Function Objective Constraint Free variable CONSTRAINTS Has a characterising material index Shaft Column Mechanical, Thermal, Electrical... Minimum weight Maximum energy storage Minimum environ. impact Stiffness specified Strength specified Fatigue limit Geometry specified INDEX M = 1/ 2 E Minimise this! Demystifying material indices Material properties -- the Physicists view of materials, e.g. Cost, Density, Modulus, Strength, Endurance limit, Thermal conductivity, C m E σ y σ e T- expansion coefficient, α λ the Engineers view of materials Function Stiffness Strength Tension (tie) Bending (beam) Bending (panel) Material indices -- Objective: minimise mass /E 1/2 /E 1/3 /E /σy 2/3 /σ y 1/2 /σ y Minimise these! Many more: see Appendix B of the text

7 Materials indices FUNCTION Each combination of Function Objective Constraint Free variable Has a characterising material index OBJECTIVE Minimum cost Minimum weight Maximum energy storage Minimum environ. impact CONSTRAINTS Stiffness specified Strength specified Fatigue limit Geometry specified INDEX [ f ( E) ] M =, Minimise this! Demystifying material indices Material properties -- the Physicists view of materials, e.g. Cost, Density, Modulus, Strength, Endurance limit, Thermal conductivity, C m E σ y σ e T- expansion coefficient, α λ the Engineers view of materials Function Stiffness Strength Tension (tie) Bending (beam) Bending (panel) Material indices -- Objective: minimise mass /E 1/2 /E 1/3 /E /σy 2/3 /σ y 1/2 /σ y Minimise these! Many more: see Appendix B of the text

8 Log Index M = 1/2 E E = 2 / M 2 ( E) = 2Log( ) 2Log( M) Contours of constant M are lines of slope 2 on an E- chart Optimised selection using charts Young s modulus E, (GPa) Composites Woods C E 1 / 3 = Ceramics C E 1 / 2 = Polymers Foams Elastomers Density (Mg/m 3 ) Metals E = C 100 Selection using hard-copy charts Search region C E 1 / 2 =

9 Selection using the CES software Search region Ceramics D i am on d Tun gs ten Young s modulus (GPa) Young's Modulus (GPa ) Composites Woods C F R P P oly eth yl en e A lu m i ni um all oy s) S an ds ton e P TFE Polymers Carbon Steel Metals C E 1 / 2 = 0.1 PVC foam Foams P o lyu re tha ne Elastomers Density (Mg/m 3 ) D e nsity (M g /m ^3 ) Modulus Density chart Modulus spans 5 decades 0.01 GPa (foams) to 1000 GPa (diamond) Iso-lines E/, E 1/2 /, E 1/3 / selection for minimum weight, deflection-limited design

10 Strength Density chart Spans 5 decades 0.1 MPa (foams) to 104 MPa (diamond) Iso-lines σf/, σf2/3/, σf1/2/ selection for minimum weight, yield-limited design Fracture Toughness Density chart KIc measures resistance to crack propagation Iso-lines KIc4/3 /, KIc4/5 /, KIc2/3/, KIc1/2/ and KIc for minimum weight, fracture-limited design KIc = 20 MPa m1/2 considered minimum value for conventional design

11 Modulus Strength chart Chart is useful in selecting springs Iso-lines of normalized strength, defined as σf /E Modulus Relative Cost chart Relative cost is defined as: CR = [c/kg of material] / [c/kg of mild steel rod] Iso-lines help to maximize stiffness per unit cost

12 Strength Relative Cost chart Relative cost is defined as: C R = [c/kg of material] / [c/kg of mild steel rod] Iso-lines help to maximize strength per unit cost Basic procedure for materials selection Start with all materials Narrow choice with primary constraints Dictated by design/non-negotiable Seek subset that maximizes performance Combination of properties involved in maximization Examine performance indices

13 Primary constraints Designs impose primary constraints For example, a component must carry a load above 300 C -- this would eliminate all plastics as candidates. Components which must electrically insulate cannot be metals, and so forth. We can represent this condition by: P > P crit or P < P crit where P is a property (service temperature, for instance) and P crit is a critical value of that property, set by the design, which must be exceeded, or (in the case of cost or corrosion rate) must not be exceeded. Primary constraints

14 Performance maximizing criteria The next step is to seek, from the subset of materials which satisfy the primary constraints, those which maximize the performance of the component. We will use the same example as before -- the design of light, stiff components; the other indices are used in a similar way. Figure shows, as before, the modulus E, plotted against density, on log scales. The performance index is (tension on light-stiff tie): Taking logs, E / = C log E = log + log C is a family of straight parallel lines of slope 1, one line for each value of the constant C. Performance maximizing criteria The index for bending on light-stiff beam is: E 1/2 / = C gives another family of lines, this time with a slope of 2. The index for bending on light-stiff plate is: E 1/3 / = C gives another family of lines, this time with a slope of 3.

15 Performance maximizing criteria Performance maximizing criteria All materials which lie on a iso-line of E 1/2 / will perform equally well Lines to right are worse performers and lines to the left are better. The subset of materials with particularly good values of the index is identified by picking a line which isolates a small search region containing a reasonably small number of candidates.

16 Performance maximizing criteria The main points Design requirements are translated into a prescription for selecting a material by analysing the function of the component, the constraints must meet, and the objective of the design. Simple constraints are applied as limits on material attributes, screening out materials that can t do the job Constraints that limit objectives must be combined with the objective to identify a material index. The objective is best displayed on a material-property chart, allowing optimised selection The method allows refined selection while giving a perspective of alternatives in drawn from all classes of materials.

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon. Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie