Progettazione di Materiali e Processi Modulo 1 – Lezione 3 Progettazione e selezione di materiali e processi A.A. 2015 – 2016 Vanni Lughi vlughi@units.it

In the previous lecture…

Materials Data Example of material property table See CES

Materials Data Example of comparison table See CES

Materials Data Example of single property graph See CES

Materials Data Example of two-property graph See CES

The selection process All materials Screening: apply property limits Innovative choices Ranking: apply material performance indices Subset of materials Shortlisting: apply supporting information Prime candidates Final selection: apply local conditions Final material choice

Function – Objectives - Constraints What does the component do? e.g.: support load, seal, transmit heat, bycicle fork, etc. Objective What do we want to maximize (minimize)? e.g.: minimize cost, maximize energy storage, minimize weight, etc. Constraints What conditions must be met? (non-negotiable or negotiable) e.g. geometry, resist a certain load, resist a certain environment, etc. Implicit functions (e.g. tie, beam, shaft, column) Constraints often translate to property limits (temperature, conductivity, cost, …) Some constraints are more complex (e.g. stiffness, strength, etc.) as they are coupled with geometry -> need of a specific objective Material indices help unravel such complexity

Functional requirements Material indices Performance = f (F, G, M) Functional requirements Material properties Geometry If separable: Performance = f1(F) f2(G) f3(M) Material index

Min. environmental impact Material indices Material index: E/ Material index: E0.5/ Function Objective Constraint Tie Beam Shaft Column ….. Minimum cost Max energy storage Minimum weight Min. environmental impact …… Stiffness Strength Fatigue resistance Geometry ….. Material index: /

In this lecture: Examples of materials indexes for ties and beams Example of ranking Selection stategy Examples of screening Tables of solved problems of elasticity etc. Table of momentum of intertia

Minimum weight design Tensile ties Main spar - beam Compression strut Undercarriage- compression The marked components of this plane perform different functions. The ties carry tension, the struts carry compression (they act as columns) and the beams carry bending moments. They are chose to be as light as possible: thus the objective is to minimize mass. The mass of a tensile tie of prescribed strength depends two material properties – yield strength and density – in the combination; it is the material index for this component. The mass of a strut that must carry a compressive load without buckling elastically is proportional to the material group so this becomes the material index. The mass of a beam, loaded in bending, that must not yield plastically is proportional to the combination so that it the index. Thus the index depends on the mode of loading (tension, compression, bending) and on the requirement for stiffness or strength. The marked components of this plane perform different functions. The ties carry tension, the struts carry compression (they act as columns) and the spars carry bending moments – they are beams. They are chose to be as light as possible: thus the objective is to minimize mass. The mass of a tensile tie of prescribed strength depends two material properties – yield strength and density – in the combination ; it is the material index for this component. The mass of a strut that must carry a compressive load without buckling elastically is proportional to the material group so this becomes the material index. The mass of a beam, loaded in bending, with restriction on elastic deflection is also proportional to so the index here is the same as that for the strut. Thus the index depends on the mode of loading (tension, compression, bending) and on the requirement for stiffness or strength. E = Young’s modulus = Density = Yield strength

Minimum cost design Structural Structural panels beam Tensile ties The marked components of this building, like those of the plane, perform different functions. The ties carry tension, the struts carry compression (they act as columns) and the beams carry bending moments. They are chose to be as cheap as possible: thus the objective is to minimize cost. The cost of a tensile tie of prescribed strength depends three material properties – yield strength, material cost per kg, and density – in the combination shown here; it is the material index for this component. The cost of a strut that must carry a compressive load without buckling elastically is proportional to the material group involving yield strength, material cost per kg, and density shown. This becomes the material index. Similarly, the cost of a beam, loaded in bending, that must not yield plastically is proportional to the combination shown here. It is the index. Thus the index depends on the mode of loading (tension, compression, bending) and on the requirement for stiffness or strength. Compression strut (column) Cm = Material cost / kg = Density = Yield strength

Criteria of excellence: material indices Material index = combination of material properties that limit performance Sometimes a single property Sometimes a combination Either is a material index Stiffness Strength Constraints Objective minimise mass Explore these! The material properties listed in handbooks – density, modulus and so on – are those that are measured to characterize the fundamental properties of materials – the physicists’ view of materials, one might say. The performance of an engineering component depends on the values of these, butit usually depends not on one property but on a combination of two or more – it is these that we call material indices. They, too, are material properties; they are the ones that characterize engineering performance – the engineers’ view of materials, so to speak. The ones highlighted in the red box of this frame all depend on density ρ and modulus E. They provide criteria of merit that allow the merit of a new hybrid to be assessed and compared with existing materials. Remember this one too! 14

Criteria of excellence: material indices Material index = combination of material properties that limit performance Sometimes a single property Sometimes a combination Either is a material index Stiffness Strength Constraints Objective minimise cost Material cost/kg The material properties listed in handbooks – density, modulus and so on – are those that are measured to characterize the fundamental properties of materials – the physicists’ view of materials, one might say. The performance of an engineering component depends on the values of these, butit usually depends not on one property but on a combination of two or more – it is these that we call material indices. They, too, are material properties; they are the ones that characterize engineering performance – the engineers’ view of materials, so to speak. The ones highlighted in the red box of this frame all depend on density ρ and modulus E. They provide criteria of merit that allow the merit of a new hybrid to be assessed and compared with existing materials. 15

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Ranking, using charts Light stiff beam: Ceramics Composites E = ρ2 M2 0.1 10 1 100 Metals Polymers Elastomers Woods Composites Foams 0.01 1000 100,000 10,000 Density ρ (kg/m3) Young’s modulus E, (GPa) Ceramics Increasing M 2 Index Rearrange: E = ρ2 M2 Log E = 2 log  + 2 log M Take logs: We take the index M = E1/2/ρ as an example (E is modulus and ρ is density ). Rearranging and taking logs gives Log(E) = 2Log(ρ) + 2 Log(M) The schematic shows the chart used in Unit 2; its axes are Log(E) and Log(ρ). The equation describes a family of lines of slope 2, each corresponding to a value of M. Materials above the line have higher values of M than those below it; the ones above are the best choice. By moving the line upwards the number of materials above it decreases, narrowing the list of those that maximize performance. The other indices involving E and ρ can be shown on the same chart. The index M = E/ρ appears as a line of slope 1; that for M = E1/3/ ρ as a line of slope 3. They are used in the same way. Function Index Slope Tie 1 Beam 2 Panel 3

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 Enter slope 1 Cancel OK The chart management tool bar provides tools for Exploring the chart by zooming into selected areas of it Selection – applying a box or line selection, and removing it again Customizing the chart – adding text labels, adding envelopes round the families of materials, making materials that have failed other selection stages appear in grey or disappear altogether.

Optimized selection using charts 2 3 1 Search area This frame show index-based selection on a real property chart. The selection can be done using a hard copy chart, as illustrated here. The EduPack software gives greater flexibility, allowing the selection line to be moved and additional constraints to be applied. It lists, in the Results window, the materials that meet all the constraints and makes records for them immediately accessible. The list can be ranked by the value of any property used as a constraint or by the value of the index. Here it is interesting to point out an interesting fact brought out by the method. Many components of aircraft are stiffness-limited – the wing spar is an example – and the objective here is to minimize mass. Materials texts often assert that, for aerospace, material with high specific modulus E/ρ are the best choice when stiffness is important. But aluminum and steel have the same value of specific stiffness, and steel is much cheaper that aluminum – so why are wing spars not made of steel? The answer is that they are loaded in bending, and then the correct criterion of choice is not E/ρ but E1/2/ρ . By that criterion aluminum is much better than steel, as the chart shows. Results 22 pass Material 1 2230 Material 2 2100 Material 3 1950 etc... Ranked by Index

Plotting indices as bar charts Browse Search Select Tools Bar chart of index 1. Selection data Edu Level 2: Materials List of properties Density Modulus Yield strength etc + - * / ^ ( ) ( Modulus ^ 0.5 ) / Density X-axis Y-axis 2. Selection Stages Graph Limit Tree Advanced List of properties Density Modulus Yield strength etc Indices can be plotted as bar-charts. Functions of properties, such as Young’s modulus / Density, E/ρ ,are plotted by selecting the axis (x or y) for the function and using the Advanced option in the Graph stage dialog box to create it, as shown here. On closing the dialog boxes, the function of properties is plotted on the chosen axis. Results 22 pass Material 1 2230 Material 2 2100 Material 3 1950 etc... Ranked by Index

Plotting indices as functions Index This is a CES plot of the index E1/2/ρ. The materials captured in the red box have the highest values: magnesium alloys, aluminum alloys, CFRP and certain woods – the materials of aerospace, past and present. Results 22 pass Material 1 2230 Material 2 2100 Material 3 1950 etc... Ranked by Index

Function – Objectives - Constraints What does the component do? e.g.: support load, seal, transmit heat, bycicle fork, etc. Objective What do we want to maximize (minimize)? e.g.: minimize cost, maximize energy storage, minimize weight, etc. Constraints What conditions must be met? (non-negotiable or negotiable) e.g. geometry, resist a certain load, resist a certain environment, etc. Implicit functions (e.g. tie, beam, shaft, column) Constraints often translate to property limits (temperature, conductivity, cost, …) Some constraints are more complex (e.g. stiffness, strength, etc.) as they are coupled with geometry -> need of a specific objective Material indices help unravel such complexity

CES Selection Toolbox Browse Select Search Tools 1. Selection data Choice… Select from 2. Selection Stages Graph Limit Tree Level 2: Materials Custom Define your own subset Edu Level 1 Materials Processes ….. Edu Level 2 Materials with Durability props Materials with Eco properties Plotting and selection tools The CES Selection Toolbox is accessed as shown here. Clicking on the Select button in the toolbar activates a dialog box asking you to choose what Level (1, 2 or 3) and which Universe (Materials or Processes) you want to plot. This brings up the three selection tool: Graph, allowing graphical selection Limit, allowing selection by setting limits for material properties Tree, allowing material selection to meet processing constraints. The use of each tool is illustrated in the next three overheads, starting with a Limit stage.

Screening with a LIMIT STAGE Young’s modulus GPa Yield strength MPa Hardness Vickers Fracture toughness MPa.m1/2 Mechanical properties Min. Max. General properties Thermal properties Min. Max. Max service temp C T-conductivity W/m.K T-expansion 10-6/C Specific heat J/kg.K Electrical properties Eco properties Limit 200 1 10 1600 100 50 70 16 Ceramics Metals Foams Polymers Glasses 0.1 1 10 100 Insulator Thermal conductivity (W/m.K) Conductor The frame illustrates screening using a Limit stage. A Limit stage applies numeric and discrete constraints. Required lower or upper limits for material properties are entered into the Limit stage property boxes. If a constraint is entered in the Minimum box, only materials with values greater than the constraint are retained. If it is entered in the Maximum box, only materials with smaller values are retained. The Results window at the lower left then lists the selection. The list can be ranked by the value of any one of the selected properties. It is helpful, in setting the upper or lower limits for a property to know the range that the property spans for each material family. Clicking on the icon to the left of the Min. box generates a bar chart showing the property ranges. Results X out of 100 pass Material 1 2230 113 Material 2 2100 300 Material 3 1950 5.6 etc... Ranking Prop 1 Prop 2

Screening with a GRAPH STAGE Line/gradient selection tool Line selection Enter slope 1 Cancel OK Box selection tool Property Bar chart Property 2 Property 1 Bubble chart Graph 1 The use of the Graph facility to create bar charts and bubble charts was described in Unit 2. The tool bar that appears above a chart contains selection tools. Two are illustrated here. A box selection isolates a chosen part of a chart. Any material bar or bubble lying in, or overlapping the box is selected; all others are rejected. The selected materials appear in the Results window, where they can be ranked by the value of the property. A line selection divides a bubble chart into two regions. The user is free to choose the slope of the line, and to select the side on which materials are to be chosen. This allows selection of materials with given values of combinations of material properties such as E/ρ, where E is Young’s modulus and ρ is density. This is explained more fully in Unit 5. As before, the selected materials appear in the Results window where they can be ranked by either property or by the combination. Graph stages can be combined with Limit stages (and with Tree stages, coming next) in any combination and any order. The Results window lists the materials that meet all the constraints, regardless of the way they are applied. Results X out of 100 pass Material 1 2230 113 Material 2 2100 300 Material 3 1950 5.6 etc... Ranking Prop 1 Prop 2

Screening with a TREE STAGE Materials Universe Ceramics and glasses Hybrids: composites Metals and alloys Polymers and elastomers Material Universe + Trees Selected records Tree Joining Shaping Surface treatment Process Universe + - Die casting Shaping – Die casting Results X out of 100 pass Material 1 Material 2 Material 3 etc... Materials that can be die-cast A Tree stage allows the search to be limited to either: a subset of materials, or materials that can be processed in chosen ways. Opening a Tree stage gives access to the tree-like hierarchical classification of materials (exactly as in the Browse window), or to the of processes. If any part of either tree is selected, only materials that belong to that subset of materials, or that can be processed in the chosen way, are retained. A Tree stage can be combined with Limit stages and Graph stages in any combination and any order. The Results window lists the materials that meet all the constraints, regardless of the way they are applied.

Organizing information: the CES Edu database Suppliers data-table References Materials data-table DATA FOR Metals & alloys Polymers Ceramics & glasses Hybrids Processes data-table DATA FOR Joining Shaping Surface treatment Links Select on links This overhead shows the structure of the CES EduPack database. It contains 4 linked data-tables: Materials: metal, polymers, ceramics and hybrids Processes for shaping, joining and finishing materials References to more information about any given record in the data-tables Supplier information for materials or processes. Each record in the Materials data-table contains data for material properties, and is linked to similar records for the processes that can shape, join and finish it. Each record in the Process data-table is similarly linked to the materials it can treat and to reference and supplier information. This allows selection of materials by specifying required properties, or by specifying how it can be processed.  

Materials for riot shields Protective visor for law enforcers Design requirement Translation Constraints Transparent - of optical quality Tough – high fracture toughness Able to be molded Young’s modulus GPa Yield strength MPa Fracture toughness MPa.m1/2 Mech. properties Min. Max. Optical properties. Opaque Translucent Transparent Optical quality Transparency Limit stage Plus graph stage Best choice: Polycarbonate ? Here is an example of how limit and graph stages can be combined during screening.