Progettazione di Materiali e Processi Università degli Studi di Trieste Modulo 1 – Lezione 8 Corso di Laurea in Ingegneria Chimica e dei Materiali A.A. 2017-2018

Visita a Buttrio, 11-12-2017 ore 15.00 (partenza ore 13.00).  

Designing new materials

Outline Holes in material property space History of hole-filling Fundamental limits Hybrid materials as a way forward Resources “Materials Selection in Mechanical Design”, 4th edition by M.F. Ashby, Butterworth Heinemann, Oxford, 2011, Chapters 11 and 12. The outline of the Unit. 6

Material-property space: E and  HOLE HOLE Materials have many properties. Think of them as the axes of a multi-dimensional material-property space. The property charts are sections through this space. Here is the familiar E-ρ section. Any such section has areas that are filled with materials and areas that are empty: holes. Two are shown here.

Material-property space: E and  Contours of the index Interesting HOLE Is anything to be gained by developing materials (or material-combinations) that lie in these holes? The material indices show where this is profitable. A grid of lines of one index – E/ρ – is plotted on this chart. If the filled areas can be expanded in the direction of the arrow (i.e. to greater values of E/ρ ) it will enable lighter, stiffer structures to be made. The arrow lies normal to the index lines. It defines a vector for material development. 8

Material-property space: a and l Contours of the index HOLE Here is a second example. It shows the α – λ section through material property space. The index λ/α is shown as a grid of diagonal lines. Developing materials to fill the hole at the lower right enables structures that are more resistant to thermal distortion than any we have at present. (Details of the derivation and use of this index can be found in “Materials Selection in Mechanical Design”, 4th edition, Chapter 6, Section 6.16.)

The evolution of structural materials Franklin Roosevelt 1933 - 1945 21st Century Queen Victoria 1837 - 1901 Henry VIII Julius Caesar The first king: Menes Early history 3000 BC It is worth looking back to see the way in which the filled parts of material property space have expanded over time. We take the σy – ρ section as an example. The (animated) chart is plotted for six successive points in historical time, ending with the present day. The materials of pre-history, shown at (a), cover only a tiny fraction of this strength-density space. By the time of the peak of the Roman empire, around 50 BC (b), the area occupied by metals has expanded considerably, giving Rome critical advantages in weaponry and defence. The progress thereafter was slow: 1500 years later (c) not much has changed, although, significantly, cast iron now appears. Even 500 years after that (d) expansion of the occupied area of the chart is small; aluminium only just creeps in. Then things accelerate. By 1945 the metals envelope has expanded considerably and a new envelope – that of synthetic polymers – now occupies a significant position. Between then and the present day the expansion has been dramatic. Much of the space is now filled and the filled area starts to approach fundamental limits (not shown here) beyond which it is not possible to go. 50,000 BC Glass, pottery, natural mats and gold. 10

Boundaries of material property space Foams and lattices True solids Osmium density Theoretical strength of diamond E/20 Strength - Density Boundary of space Hole How much further can this filling go? There are some fundamental limits, sketched here. Limits on density are set by the mass of and size of atoms. Osmium (density 22,500 kg/m3 ) is the element with the highest density that is stable and solid at room temperature. Lithium (density 535 kg/m3 ) is the element with the lowest. An “solid” with a density lower than lithium is porous: a foam or a lattice. The limit on strength is set by the breaking load and packing density of atomic bonds – this, too, can be quantified. Thus some parts of material property space are accessible, others are not. The figure shows that there remain some unfilled regions of this section that, in principle, could be filled.

Filling holes: hybridization All copper ? Hole 30% Cu 10% Cu 5% Cu Here is an example of a section with an enormous hole. How could materials be created to fill it? The traditional routes of materials science are not much help: alloy development cannot lower Young’s modulus of metallic conductors much below 10 GPa; and making new polymer compositions or blends cannot increase the thermal conductivity above about 1 W/m.K. The answer is to make hybrids: mixtures of two materials in a configuration and relatve fraction that gives both low modulus and high conductivity. All rubber

Hybrids or “multi-materials” “A hybrid material is a combination of two or more materials in a pre-determined configuration and scale, optimally serving a specific engineering purpose” Kromm et al, 2002 Design variables: Choice of materials Volume fractions Configuration Connectivity Scale The hybrid synthesizer Explore configurations, with free material choice Explore structured-structures A shell: insert models for other configurations Here is a more formal definition of a hybrid material, listing the new design variables. Hybrids are combinations of two or more materials assembled in such a way as to have attributes not offered by either one alone. Particulate and fibrous composites are examples of one type of hybrid, but there are many others: sandwich structures, lattice structures, segmented structures and more. Their properties depend the choice of the components, their configuration, their relative volume fraction and their scale. The new variables expand design space, allowing the creation of new “materials” with specific property profiles. More detail can be found in Lecture Unit 20 and the white paper on the “Hybrid Synthesizer Tool”. The white paper is available in the Help menu of CES EduPack or from Granta’s Teaching Resource Website. http://teaching.grantadesign.com.

Designing hybrid materials Three parallel approaches Materials – relate properties to microstructure: controlled nature, scale through alloy design and processing. Mechanics – accept properties as “given”, optimise the geometry Traditional approaches to optimizing components for structural applications, there have followed two paths. The approach of materials science: material development to improve the intrinsic properties. The approach of mechanics: to assume a set of intrinsic properties and optimize the geometry . To these we add a third: that of adapting the techniques of textile technology to exploit the exceptional properties of thin fibers. Textile technology – exploit unique strength and blending properties of fibers

Combining textile technology, mechanics and material (a) Simple weave Woven carbon fiber CFRP product These are examples of combining textile technology with mechanics and material. Carbon fiber weave formed to a stiff composite shell Examples of 3-D weaving now being adapted to advanced composite design A Kagome lattice with a structure derived from a textile weave. (c) The kagome weave (b) 3-dimensional weaving

Architected Cellular Materials This final frame summarizes the main points.

Architected Cellular Materials This final frame summarizes the main points.

Material-property space: E and  Contours of the index HOLE Modulus – density space has a hole at the upper left. The vector shows the desirable direction of material development for high E/ρ.

Foams and micro-lattices Polymer foams 2mm Bending-dominated micro-lattices Foams and lattices, when on a small scale, can be thought of as “materials”, just as we think of wood as a material. Their mechanical properties – stiffness, strength, toughness etc – depend critically on the connectivity of the lattice. 500m Stretch-dominated micro-lattices

Architected Cellular Materials for Enhancing E/ Foams vs Trusses  Bending-dominated vs Stretch-dominated structures This final frame summarizes the main points.

Architected Cellular Materials for Enhancing E/ Best performing materials J. B. Berger, H. N. G. Wadley & R. M. McMeeking, Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness, Nature 543, 533–537 (2017) This final frame summarizes the main points.

Bending and stretch dominated structures Pin-jointed frame with b bars and j joints Lock joints in a mechanism prevents rotation, deformation by bending Number of joints = j bars = b Force F Statically determinate 0 degrees of freedom 0 states of self-stress Lock joints in a structure - stretching still dominates A mechanism -- 1 degree of freedom 0 states of self-stress This frame explains the difference between bend and stretch-dominated structures. Maxwell’s equations at the lower left express the condition for stretch dominated behaviour. Stretch dominant structures are much stiffer and stronger that those that are bending dominated. Condition for stretch dominance M = b - 2j + 3 = 0 2-dimensions M = b - 3j + 6 = 0 3-dimensions

Micro-trusses HOLE HOLE Plus: multifunctionality Alu micro-trusses Alu foams Almost all foams are bending dominated. Their value of E/ρ are not exceptional. The E/ρ values for stretch-dominated lattices, by contrast, lie in the hole – they are exceptional. The frame illustrates the areas occupied by aluminum foams and lattices. Plus: multifunctionality

Functionality Enabled by Architecture This final frame summarizes the main points.

Material-property space: a and l Contours of the index HOLE This is where the low expansion hybrid made from aluminum triangles in a nickel frame lies in α – λ space.

Configuration: controlling expansion Almost all solids expand when heated. This frame shows how a hybrid design can be tuned to give zero overall thermal expansion by combining mechanics with material properties.

Segmented structures Segments Load – deflection response Assemble, compressive boundary conditions Monolithic Segmented Segmentation is another way of exploiting configuration and geometry. A brittle solid, segmented and assembled as shown, exhibits “tough” behavior when loaded as shown. It is also damage-tolerant: if one segment is damaged or removed, the assemble retains stiffness and strength.

Advanced Cellular Design This final frame summarizes the main points.

Optimizing Structural Topology Since structural topology has such a major impact on the product properties, it is important to identify approaches for optimizing such topology. Here is a general scheme: from the designer specification, we have an optimization engine of some sort (computational, analytical, euristic?), which generates the optimal solution; this, in turn, can be repeated periodically to generate the material. In the following there is an illustration of a computational (FEM-based) approach to topology optimization. Annu. Rev. Mater. Res. 2016. 46:211–33

Finite Element Modeling for Topology Optimization Annu. Rev. Mater. Res. 2016. 46:211–33

Example of Topology Optimization Maximum Stiffness vs Minimum Density Annu. Rev. Mater. Res. 2016. 46:211–33

Additive Manufacturing (AM) A convenient way to fabricate components with complex structural topologies Now the question is: “we have obtained, via topology optimization, the optimal structure geometry; how can we realize it?”. One emerging way is additive manufacturing

Additive Manufacturing (AM) A convenient way to fabricate components with complex structural topologies

Complex, Light Topologies Using AM + Thin film deposition techniques The next step is to make such topologies as light as possible, for example as in these structures which are based on empty elements

So what? Multi-dimensional material-property space Only part-filled by monolithic materials True of mechanical, thermal, electrical, magnetic and optical properties Material development strategies Classical (classical alloy development, polymer chemistry….) “Nano” (sub-micron) scale (exploiting scale-dependence of properties) Hybridization (exploiting materials, configuration and connectivity) The strategy: Map out the filled areas Explore the ultimate boundaries Explore ways of filling the empty space. Hybrids, exploiting potential of novel configurations, have potential for this

The Hybrids Synthesizer: a tool for design and dissemination

Outline Holes in material-property space Hybrids materials – expanding the filled space Example1 – cellular materials Example 2 – sandwich structures New developments – Multi-layers Resources Text: “Materials Selection in Mechanical Design”, 4rd edition by M.F. Ashby, Butterworth Heinemann, Oxford, 2011, Chapters 11 - 12. White paper “The hybrid synthesizer” , available from CES EduPack Help file Software: CES EduPack Hybrids synthesizer tool (Grantadesign.com) “Hybrid synthesizer – Model writer’s guide” for CES Selector users (Grantadesign.com) This unit introduces the hybrid materials and the CES EduPack tool (the Hybrid synthesizer) that lets you create records for their properties. These properties can be compared directly with those of all the other materials in the CES EduPack databases, allowing selection that includes hybrids.

Modulus and Density HOLE HOLE Contours of Vector for material development HOLE Material property space, of which this Modulus / Density chart is a section, is only partly filled with materials. There are holes where no materials lie. If materials could be devised to fill them it would enable innovative engineering design. 38

Strength - Density HOLE Contours of HOLE Vector for material development HOLE Here is a second section though material property space – the Strength / Density section. It too has holes. If materials could be devised that lay in the hole in the upper left, it would allow lighter, stronger structures to be built. 39

Hybrid materials Design variables: The hybrid synthesizer Choice of materials Volume fractions Configuration Connectivity Scale The hybrid synthesizer Explore configurations, with free material choice Explore structured-structures A shell: insert models for other configurations Hybrids are combinations of two or more materials assembled in such a way as to have attributes not offered by either one alone. Particulate and fibrous composites are examples of one type of hybrid, but there are many others: sandwich structures, lattice structures, segmented structures and more. Their properties depend the choice of the components, their configuration, their relative volume fraction and their scale. The new variables expand design space, allowing the creation of new “materials” with specific property profiles.

Configurations and equivalent properties Material properties of a monolithic material with the same mechanical, thermal and electrical response. Foams and Lattice structures Sandwich structures How are we to compare a hybrid like a sandwich with monolithic materials like – say – polycarbonate or titanium? To do this we must think of the sandwich not only as a hybrid with faces on one material bonded to a core of another, but as a “material” in its own right, with its own set of equivalent properties; it is these that allow the comparison. Composite structures

What the synthesizer does CES retrieves models for Physical properties Equivalent density, ρ Mechanical properties Equivalent Young’s modulus E, shear modulus G, bulk modulus K, flexural modulus Eflex Yield strength σy, compressive strength σc, tensile strength σts, flexural strength σflex Fracture toughness Kic Thermal properties Thermal conductivity λ, expansion coefficient α and specific heat Cp On pressing “Create” the synthesizer retrieves models for the properties of the chosen configuration and constructs records with the properties shown here for the set selected by the control parameters. Electrical properties Resistivity ρe, dielectric constant εr and dielectric loss tangent D

Foam and lattice models Configurations Triangulated cell faces Lattice cell Mechanical response As an example, the models for Foams and for Lattice structures include elastic deformation, plastic collapse, cell-edge buckling and cell-edge fracture, plus further models for thermal and electrical properties. Plus thermal and electrical properties

Typical record General properties Mechanical properties Al 6061 Foam (0.1) General properties Density 110 kg/m^3 Relative density 0.037 Mechanical properties Young's modulus 1.3 - 1.4 GPa Flexural modulus 1.3 - 1.4 GPa Shear modulus 0.5 - 0.51 GPa Bulk modulus 1.3 - 1.4 GPa Poisson's ratio 0.33 Yield strength (elastic limit) 4.7 - 5.1 MPa Tensile strength 6.3 - 7 MPa Compressive strength 4.7 - 5.1 MPa Flexural strength 6.3 - 7 MPa Fracture toughness 0.88 - 1.2 MPa.m^0.5 Thermal properties Thermal conductivity 2.1 - 2.2 W/m.°C Specific heat capacity 920 - 940 J/kg.°C Thermal expansion coefficient 15 µstrain/°C Electrical properties Electrical resistivity 230 µohm.cm Notes Source Materials: Bulk material = Al-20%SiC(p), powder product This is what a record for a lattice structure, created by the synthesizer, looks like. Here the material chosen by the user for the cell edges and walls was a metal matrix composite, Aluminum – 20% particulate silicon carbide, chosen because it is a material from which real metal foams have been made.

The Hybrid-material synthesizer Add record Eco Audit Synthesizer Cellular structures Foams Triangulated lattices Choice of configuration Select: Configuration Materials Control parameters Click “Create” Sandwich structures Symmetric sandwiches The Hybrid synthesizer is opened from the Tools button in the main tool-bar of CES EduPack. Doing so allows the choice of configuration: Cellular structures (with option of Foams or Lattice structures) Sandwich structures Composites (with options of uni-directional, quasi-isotropic or particulate) To use the synthesizer you select a configuration, choose materials from a pull down of the CES materials tree, enter the control parameters, and click “Create”. Composites Unidirectional Quasi-isotropic Particulate

Exploring metal foams - inputs Source material Bulk material Aluminum 20% SiC (p) Browse Model variables Number of densities Relative density range - % 2 35 15 Model Previous Create Cancel This is a cartoon of the user interface of the synthesizer when the configuration Foam is selected. The Browse button opens the materials tree of whichever database (Levels1, 2 or 3) that is chosen when CES EduPack is first opened. The material for the foam is selected from it. The control parameters, which the user now chooses, determine the number of relative densities (here 15) and the range they should cover. On clicking “Create” the synthesizer creates 15 records covering the chosen range of relative density.

Aluminum SiC composite foams Here an example, plotted on axes of Modulus and Density, of the properties of a set of Foams and of Lattice structures made from aluminum 20% particulate silicon carbide. The foams (yellow dots) can be compared with the properties of real aluminum-SiC foams (larger red ellipses) to get an idea of the precision with which the synthesizer predicts the properties. The criterion of excellence for a light stiff beam is plotted as broken lines. The lattices extend to higher values of the criterion.

The Hybrid-material synthesizer Add record Eco Audit Synthesizer Cellular structures Foams Triangulated lattices Choice of configuration Select: Configuration Materials Control parameters Click “Create” Sandwich structures Symmetric sandwiches The Hybrid synthesizer is opened from the Tools button in the main tool-bar of CES EduPack. Doing so allows the choice of configuration: Cellular structures (with option of Foams or Lattice structures) Sandwich structures Composites (with options of uni-directional, quasi-isotropic or particulate) To use the synthesizer you select a configuration, choose materials from a pull down of the CES materials tree, enter the control parameters, and click “Create”. Composites Unidirectional Quasi-isotropic Particulate

Aluminum SiC composite foams 2 Criterion of excellence E1/2/ρ Here an example, plotted on axes of Modulus and Density, of the properties of a set of Foams and of Lattice structures made from aluminum 20% particulate silicon carbide. The foams (yellow dots) can be compared with the properties of real aluminum-SiC foams (larger red ellipses) to get an idea of the precision with which the synthesizer predicts the properties. The criterion of excellence for a light stiff beam is plotted as broken lines. The lattices extend to higher values of the criterion.

Lattices expand material property space 2 Criterion of excellence E1/2/ρ 2800 materials Here a further 2000 material have been added to the picture (using CES Edupack Level 3) to indicated the filled and empty parts of the space. The lattices extend into a previously empty region.

Sandwich panel models Configuration Collapse response Elastic response Here is a second example, this time for Sandwich structures. The models include simple bending, core shear, face yield, face buckling and core failure, plus further models for thermal and electrical properties. Plus thermal and electrical properties

Sandwich panels - inputs Source material Face sheet Aluminum 6061 T4 Browse Core PVC cross-linked rigid foam (0.09) Browse Model variables Face-sheet thickness mm Number of values Core thickness - mm Number of values 0.1 - 3 5 10 - 50 3 Model parameters This is a cartoon of the user interface of the synthesizer when the configuration Sandwich panel is selected. The Browse button opens the materials tree of whichever database (Levels1, 2 or 3) that is chosen when CES EduPack is first opened. A material for the face sheet and a material for the core are selected from it. The control parameters, which the user now chooses, determine the number of face sheet thicknesses and core thicknesses and the ranges they should cover. On clicking “Create” the synthesizer creates records covering the chosen ranges. Support and load conditions Span m 3 Model Previous Create Cancel 52

Stiff sandwich panels 3 Enhanced performance Slope 3 Here an example, plotted on axes of Flexural modulus and Density, of the properties of a set of sandwich panels with aluminum 6061 faces and PVC foam cores with a foam density of 0.1 kg/m3. The yellow dots show the flexural stiffness of the panels.

Sandwiches expand material property space Slope 3 3 2800 materials Here a further 2000 material have been added to the picture (using CES EduPack Level 3) to indicated the filled and empty parts of the space. The sandwiches extend into a previously empty region. .

Strong sandwich panels Slope 2 Enhanced performance 2 Plotting flexural strength instead of stiffness again shows the superior performance of the same sandwich panels.

Lattice cored sandwich panels Slope 3 The synthesizer can be used in innovative ways. Here records were first created for a set of lattice structures (green dots). Then the synthesizer was opened a second time and a set of sandwich panels created using one of the lattices a the material of the core of the panel. The result is a set of panels with properties that lie even further into the previously empty space.

Structures expand material property space 2800 materials Once again the rest of the Level 3 database has been added to show the filled part of the space. The innovative panels have properties that lie even further into the previously unfilled part of material property space.

So what? The synthesizer allows Display of potential properties of novel material combinations Testing and deploying of models for “architectured” materials Direct comparison with the standard materials of engineering Exploration of structured-structures This is a first generation tool – models very simple Welcome ideas for refining it. This final frame summarizes the main points.

There are 200+ resources available Including: Author There are 200+ resources available Including: 77 PowerPoint lecture units Exercises with worked solutions Recorded webinars Posters White Papers Solution Manuals Interactive Case Studies Mike Ashby University of Cambridge, Granta Design Ltd. www.grantadesign.com www.eng.cam.ac.uk Reproduction These resources are copyright Mike Ashby. You can reproduce these resources in order to use them with students, provided you have purchased access to Granta’s Teaching Resources. Please make sure that Mike Ashby and Granta Design are credited on any reproductions. You cannot use these resources for any commercial purposes. Accuracy We try hard to make sure these resources are of a high quality. If you have any suggestions for improvements, please contact us by email at teachingresources@grantadesign.com Granta is always interested in hearing about good teaching resources in the materials area. If you use something successfully with your students that you think we should link to from our web site, please get in touch. teachingresources@grantadesign.com We continue to coordinate annual Materials Education Symposia. You can read about that here: http://www.grantadesign.com/symposium/index.htm © M. F. Ashby, 2012 Granta’s Teaching Resources website aims to support teaching of materials-related courses in Engineering, Science and Design. The resources come in various formats and are aimed at different levels of student. This resource is part of a set created by Mike Ashby to help introduce materials and materials selection to students. The website also contains other resources contributed by faculty at the 800+ universities and colleges worldwide using Granta’s CES EduPack. The teaching resource website contains both resources that require the use of CES EduPack and those that don’t. www.grantadesign.com/education/resources 59