Advanced Materials and Structuresand their Fabrication Processes

Book manuscript, Narvik University College, HiN

Dag Lukkassen and Annette Meidell

August 23, 2007

Contents

I Materials and Structures 81 Ceramics and glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.1 Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2 Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Industrial Importance of Ceramics and Glasses . . . . . . . . . . . 131.4 Industrially Important Glasses . . . . . . . . . . . . . . . . . . . . 141.5 Technical Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5.1 High-performance ceramics . . . . . . . . . . . . . . . . . . 152 Metals and metal alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.1 High-peformance Metals . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.1 High-Performance Aluminum . . . . . . . . . . . . . . . . 192.1.2 High-Performance Steel . . . . . . . . . . . . . . . . . . . . 202.1.3 Space-age metals . . . . . . . . . . . . . . . . . . . . . . . 20

3 Polymers and Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1 The structure of polymers . . . . . . . . . . . . . . . . . . . . . . 233.2 Crystallinity in polymers . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 The glass transition temperature and melting temperature 263.3 Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.4 Properties of plastics . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4.1 Thermosettings . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4.2 Types of Thermosettings . . . . . . . . . . . . . . . . . . . 303.4.3 Thermoplastics . . . . . . . . . . . . . . . . . . . . . . . . 323.4.4 Types of Thermoplastics . . . . . . . . . . . . . . . . . . . 34

3.5 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.6 Additives in Plastics . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6.1 Oriented Plastics . . . . . . . . . . . . . . . . . . . . . . . 413.7 Elastomers & Rubbers . . . . . . . . . . . . . . . . . . . . . . . . 41

3.7.1 Rubber and Artificial Elastomers . . . . . . . . . . . . . . 433.8 Biopolymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.8.1 What makes a polymer a biopolymer? . . . . . . . . . . . 473.8.2 Applications of biopolymers . . . . . . . . . . . . . . . . . 483.8.3 Properties of biopolymers . . . . . . . . . . . . . . . . . . 483.8.4 Additional information on raw materials in biopolymers . . 503.8.5 Plastic taste better with sugar . . . . . . . . . . . . . . . . 51

4 Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.1 The history of composites . . . . . . . . . . . . . . . . . . . . . . 564.2 Natural composites . . . . . . . . . . . . . . . . . . . . . . . . . . 564.3 Man-made Composites . . . . . . . . . . . . . . . . . . . . . . . . 58

4.3.1 Fiber-Reinforced Composites . . . . . . . . . . . . . . . . . 604.3.2 Classification of composites . . . . . . . . . . . . . . . . . 60

4.4 Ceramic matrix composites CMC . . . . . . . . . . . . . . . . . . 614.5 Metal Matrix Composites MMC . . . . . . . . . . . . . . . . . . . 644.6 Polymer Matrix Composites PMC . . . . . . . . . . . . . . . . . . 654.7 Fiber reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.7.1 Choosing fibers . . . . . . . . . . . . . . . . . . . . . . . . 674.7.2 Glass fibers . . . . . . . . . . . . . . . . . . . . . . . . . . 694.7.3 Carbon fibers . . . . . . . . . . . . . . . . . . . . . . . . . 704.7.4 Boron fiber . . . . . . . . . . . . . . . . . . . . . . . . . . 714.7.5 Ceramic fibers . . . . . . . . . . . . . . . . . . . . . . . . . 714.7.6 Polymer Fibers . . . . . . . . . . . . . . . . . . . . . . . . 724.7.7 Carbon nanotube (CNT) fibers . . . . . . . . . . . . . . . 744.7.8 Fiber hybrids . . . . . . . . . . . . . . . . . . . . . . . . . 754.7.9 Spider silk . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.8 Aerogel composites . . . . . . . . . . . . . . . . . . . . . . . . . . 764.9 Textile composites . . . . . . . . . . . . . . . . . . . . . . . . . . 784.10 Bio-inspired materials . . . . . . . . . . . . . . . . . . . . . . . . 784.11 Self-healing composites . . . . . . . . . . . . . . . . . . . . . . . . 79

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4.12 Left-handed metamaterials . . . . . . . . . . . . . . . . . . . . . . 815 Smart (intelligent) Materials and Structures . . . . . . . . . . . . . . . 875.1 Color Changing Materials . . . . . . . . . . . . . . . . . . . . . . 88

5.1.1 Photochromic materials . . . . . . . . . . . . . . . . . . . 885.1.2 Thermochromic materials . . . . . . . . . . . . . . . . . . 88

5.2 Light Emitting Materials . . . . . . . . . . . . . . . . . . . . . . . 885.2.1 Electroluminescent materials . . . . . . . . . . . . . . . . . 895.2.2 Fluorescent materials . . . . . . . . . . . . . . . . . . . . . 895.2.3 Phosphorescent materials . . . . . . . . . . . . . . . . . . . 90

5.3 Moving Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.3.1 Conducting polymers . . . . . . . . . . . . . . . . . . . . . 915.3.2 Dielectric elastomers . . . . . . . . . . . . . . . . . . . . . 925.3.3 Piezoelectric materials . . . . . . . . . . . . . . . . . . . . 925.3.4 Polymer gels . . . . . . . . . . . . . . . . . . . . . . . . . . 935.3.5 Shape memory materials (SMM) . . . . . . . . . . . . . . 945.3.6 Nanostructured Shape Memory Materials . . . . . . . . . . 955.3.7 Magnetic Shape Memory (MSM) Materials . . . . . . . . . 96

5.4 Temperature Changing Materials . . . . . . . . . . . . . . . . . . 975.4.1 Thermoelectric materials . . . . . . . . . . . . . . . . . . . 97

6 Functional Gradient Materials . . . . . . . . . . . . . . . . . . . . . . . 987 Solar Cell Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.1 Light-absorbing materials . . . . . . . . . . . . . . . . . . . . . . 1017.2 Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.3 Thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.4 Silicon solar cell device manufacture . . . . . . . . . . . . . . . . . 104

8 Nano - materials - and technology . . . . . . . . . . . . . . . . . . . . . 1068.1 Carbon Nanotubes (CNT) . . . . . . . . . . . . . . . . . . . . . . 107

8.1.1 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1088.2 Nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1098.3 Flexible ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . 1108.4 New type of High-performance Ceramic . . . . . . . . . . . . . . . 1118.5 Back to square one? . . . . . . . . . . . . . . . . . . . . . . . . . 112

9 Cellular Solids, Structures & Foams . . . . . . . . . . . . . . . . . . . . 1169.1 Metal Foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

9.1.1 Aluminium foam: . . . . . . . . . . . . . . . . . . . . . . . 1189.2 Polymeric foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.3 Refractory foams / Ceramic foam . . . . . . . . . . . . . . . . . . 122

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9.3.1 Carbon foam . . . . . . . . . . . . . . . . . . . . . . . . . 1239.4 Hierarchical structures (multiscale structures) . . . . . . . . . . . 1239.5 Biomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

II Sandwich Constructions 12710 Why use sandwich constructions? . . . . . . . . . . . . . . . . . . . . . 12810.1 Face materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13010.2 Core materials and structures . . . . . . . . . . . . . . . . . . . . 131

10.2.1 Foam Cores . . . . . . . . . . . . . . . . . . . . . . . . . . 13210.2.2 Honeycomb Cores . . . . . . . . . . . . . . . . . . . . . . . 13210.2.3 Corrugated Cores . . . . . . . . . . . . . . . . . . . . . . . 13510.2.4 Wood Cores . . . . . . . . . . . . . . . . . . . . . . . . . . 136

10.3 Adhesives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13711 Design of sandwich constructions . . . . . . . . . . . . . . . . . . . . . 14011.1 Design of sandwich beams . . . . . . . . . . . . . . . . . . . . . . 14011.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14111.3 The Flexural Rigidity and Shear Rigidity . . . . . . . . . . . . . . 14311.4 Tensile and Compressive Stresses . . . . . . . . . . . . . . . . . . 144

11.4.1 Due to bending (transversal loading) . . . . . . . . . . . . 14411.4.2 Due to in-plane loading (axial) . . . . . . . . . . . . . . . 147

11.5 Shear stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14811.5.1 Summary of approximations . . . . . . . . . . . . . . . . . 153

11.6 Sandwich design: stiffness, strength and weight . . . . . . . . . . 15511.7 Example of beam calculations . . . . . . . . . . . . . . . . . . . . 15711.8 Strength and stiffness design example . . . . . . . . . . . . . . . . 160

12 Failure modes of sandwich panel . . . . . . . . . . . . . . . . . . . . . . 16312.1 Failure loads and stresses . . . . . . . . . . . . . . . . . . . . . . . 16412.2 Failure-mode maps . . . . . . . . . . . . . . . . . . . . . . . . . . 167

12.2.1 Transition equation between face yielding and face wrinkling 16712.2.2 Transition equation between face yield and core shear . . . 16912.2.3 Transition equation between face wrinkling and core shear 169

13 Design Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17413.1 The stiffness of sandwich structures and its optimization . . . . . 174

13.1.1 Example of minimum weight design for given stiffness . . . 177

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III Cellular Solids 18014 Some definitions of cellular solids . . . . . . . . . . . . . . . . . . . . . 18014.1 Mechanics of honeycombs . . . . . . . . . . . . . . . . . . . . . . 18314.2 In-plane deformation properties, uniaxial loading of hexagonal hon-

eycombs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18314.2.1 Linear-elastic deformation . . . . . . . . . . . . . . . . . . 184

14.3 Out-of-plane deformation properties . . . . . . . . . . . . . . . . . 18714.3.1 Linear-elastic deformation . . . . . . . . . . . . . . . . . . 188

IV Mechanics and Effective Properties of CompositeStructures and Honeycombs 19115 On effective Properties of Composite Structures . . . . . . . . . . . . . 19116 The thermal problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19117 Isotropic elastic materials . . . . . . . . . . . . . . . . . . . . . . . . . . 19318 Orthotropic composites . . . . . . . . . . . . . . . . . . . . . . . . . . . 19419 Square symmetric unidirectional two-phase structure . . . . . . . . . . 19619.1 Calculation of stiffness and compliance matrix . . . . . . . . . . . 198

20 Numerical methods for periodic structures . . . . . . . . . . . . . . . . 20020.1 Coordinate transformation . . . . . . . . . . . . . . . . . . . . . . 202

21 A computational example . . . . . . . . . . . . . . . . . . . . . . . . . 206

V Fabrication processes 21022 Fabrication of plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . 21022.1 Processing of Rubber and elastomers . . . . . . . . . . . . . . . . 218

23 Fabrication of Fiber-Reinforced Composites (FRC) . . . . . . . . . . . 22123.1 Manufacturing processes of Reinforcements . . . . . . . . . . . . 22123.2 Prepregs, Preforms and Compounds . . . . . . . . . . . . . . . . . 22323.3 Fabrication processes of FRC . . . . . . . . . . . . . . . . . . . . 22423.4 Fabrication of Functionally Gradient Materials . . . . . . . . . . . 22923.5 Fabrication of sandwich constructions . . . . . . . . . . . . . . . . 229

24 Layer Manufacturing Technology (LMT) . . . . . . . . . . . . . . . . . 23324.1 Ballistic particle manufacturing (inkjet) BMP . . . . . . . . . . . 23524.2 Fused deposition modelling - FDM . . . . . . . . . . . . . . . . . 23524.3 LOM - Laminated object manufacturing . . . . . . . . . . . . . . 23624.4 Selective laser sintering - SLS . . . . . . . . . . . . . . . . . . . . 236

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24.5 Laser Engineered Net Shaping (LENS) . . . . . . . . . . . . . . . 23724.6 Stereo lithography - SLA . . . . . . . . . . . . . . . . . . . . . . . 23824.7 Solid ground curing - SGC . . . . . . . . . . . . . . . . . . . . . . 23924.8 Three dimensional printing (3DP) . . . . . . . . . . . . . . . . . . 24024.9 PowderProcessing/PowderMetallurgy . . . . . . . . . . . . . . . . 24124.10Vapor Deposition CVD/PVD . . . . . . . . . . . . . . . . . . . . 24324.11Selection of a layered manufacturing process . . . . . . . . . . . . 243

25 Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 24725.1 Designing for Manufacturability (DFM) ) . . . . . . . . . . . . . . 24725.2 Product design guidelines . . . . . . . . . . . . . . . . . . . . . . 24825.3 Evaluation of design alternatives . . . . . . . . . . . . . . . . . . . 24925.4 The meaning of colors . . . . . . . . . . . . . . . . . . . . . . . . 250

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Preface

This manuscript is written in order to use it as lecture notes in the course ”Ad-vanced materials” given at Narvik University College for master students in thefield of Engineering Design. In the course the students will be familiar with differ-ent kind of advanced materials and structures such as for instance smart materials,functional gradient materials, polymers and plastics, nano-materials, elastomersand rubbers, biopolymers, cellular solids and structures, and different types ofcomposite materials, which can be found in Part 1 of this report. In Part 2, thefabrication-processes of different advanced materials, structures and forms is de-scribed. The different types of sandwich constructions included the design of suchstructures are subjects that are discussed in Part 3, while in Part 4 we will havea closer look at mechanics and effective properties of composite structures andhoneycombs.This report may also be used as literature for students studying mechanical

engineering, material science, production engineering. We assume that the readerhas a bachelor degree in Engineering.

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Figure 0.1: Classes of materials.

Part I

Materials and StructuresIn this part we will mainly consider the concepts of materials and structures. Thedifference between a material and a structure is not clearly defined. Many drawthe lines between what you understand as a homogeneous material when you seeit with your bare eyes, and the inhomogeneous material structure that you clearlysee is made up of a fixed geometry or mixing of materials. For instance an alloy isby this definition a material even though it consists of two or more components,but a honeycomb core built up of two different components is a structure.Materials are often classified into the six broad classes that are shown in figure

0.1; metals, ceramics, glasses, elastomers, polymers and composites. But, whenwe also include material structures, the number is bigger, and the classificationof the term ”materials and structures”, even though it is not a conventional wayof making a classification, may look like the one purposed in figure 0.2. We willin this book briefly mention main properties of each group in figure 0.2, but theadvanced term in the title of the book refers to a thoroughly study of composites,polymers, smart materials, sandwich constructions, nano-technology, functionalmaterials, cellular structures.

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Figure 0.2: Classes of materials and structures.

High Performance Materials (HPM)

High-performance materials (or Advanced Engineering Materials) are materi-als that provide specific performance advantages in comparison with the counter-part conventional materials. Often it is difficult to place materials strictly into thegroup of high-performance group or other groups, but we often divide materialsinto the following main groups:• Standard materials, which are used in products that is exposed to non-

critical environments and low-stress applications• Standard Engineering Materials, which are used in products that must

have general bearing and wear properties• High-performance materials or advanced engineering materials, which

are used in products that must have superior properties (extreme service environ-ments, superior chemical resistance, wear resistance, and loading properties)

There are several types of materials currently called high-performance mate-rials, for instance high-performance concrete, high-performance composites, high-performance plastics, high-performance aluminum, high-performance ceramics,and high-performance steel. What they all have in common is that they haveoutstanding properties compared to the materials we used earlier. In short time

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maybe the materials we know as HPM today may not be so high-performancetomorrow, since the materials-science is rapidly changing and growing.While research laboratories are still exploring ways to exploit these materi-

als, some of them are ready for use. Because there is little data available on thelong-term results of many high-performance materials and because there is fre-quently a relatively high initial cost, states are reluctant to take on such a ventureindependently.

Questions:What is the conventional way of making a classification of materials?What is the new way of making a classification of materials?What is so special about high performance materials?

References:High-performance materials:http://www.hiper-group.com/hcproducts.htmhttp://www.greatachievements.org/?id=3809

free internet books:http://books.nap.edu/

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1. Ceramics and glasses

A ceramic is often broadly defined as any inorganic nonmetallic material. By thisdefinition, ceramic materials would also include glasses; however, many materialsscientists add the stipulation that ”ceramics” must also be crystalline. Recallthat crystalline materials have their molecules arranged in repeating patterns, seeFigure 1.1. Therefore we often divide the ceramics and glasses into two separate

Figure 1.1: Crystalline structure.

subgroups of materials.

1.1. Ceramics

Examples of ceramic materials can be anything from NaCl (table salt) to clay(a complex silicate).The term ceramic comes from the Greek word keramikos,which means burnt stuff, indicating that desirable properties of these materialsare normally achieved through a high-temperature heat treatment process calledfiring. Ceramics are refractory (fireproof) materials, and has therefore a meltingtemperature > 1580

◦C.

Due to the covalent character of the chemical bond refractory ceramics exhibitvery high (about 3000◦C) melting point, low mobility of atoms, low plasticityand high hardness at temperatures up to 2000◦C. Therefore, refractory materi-als can substitute metals, alloys and intermetallics in a lot of high temperatureengineering, chemical and electronic applications.Ceramics are in general hard, brittle, high-melting-point materials with low

electrical and thermal conductivity, low thermal expansion, good chemical andthermal stability, good creep resistance, high elastic modulus, high compressivestrength, low density, high stiffness, high hardness, high wear resistance, and high

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corrosion resistance. Many ceramics are good electrical and thermal insulators.Some ceramics have special properties: some ceramics are magnetic materials;some are piezoelectric materials; and a few special ceramics are superconductorsat very low temperatures. Ceramics are widely used in the electrical industrymostly due to their high electrical resistance. Ceramics and glasses have onemajor drawback: they are brittle. Their extremely low fracture toughness is thedrawback of ceramics in comparison with metals. It means that ceramics have avery low tolerance of crack-like flaws.Ceramic fibers such as graphite and aluminum oxide with their extremely high

stiffness have led to the production of fiber-reinforced composites. These materialsare only a few of an ever-growing list of industrially important ceramics. Recently,new groups of ceramics have emerged with the possibility to use them as load-bearing materials.

1.2. Glasses

Glass is an inorganic nonmetallic material that does not have a crystalline struc-ture. Such materials are said to be amorphous. Recall that amorphous materialshave their molecules arranged randomly and in long chains which twist and curve

Figure 1.2: Amorph structure.

around one-another, making large regions of highly structured morphology un-likely, see Figure 1.2. Examples of glasses range from the soda-lime silicate glassin soda bottles to the extremely high purity silica glass in optical fibers.The major raw material of glass is sand (or "quartz sand") that contains

almost 100 % crystalline silica in the form of quartz. Most glass formulationscontain about 70—72 % by weight of silicon dioxide (SiO2). Soda-lime glass whichis the most common form of glass contains nearly 30 % sodium and calcium oxides

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Figure 1.3: A transmission cable containing hundreds of glass optical fibers.

or carbonates. Pyrex is borosilicate glass containing about 10 % boric oxide. Leadcrystal is a form of lead glass that contains a minimum of 24 % lead oxide.Large natural single crystals of quartz are pure silicon dioxide, and upon crush-

ing are used for high quality specialty glasses. Synthetic amorphous silica, analmost 100 % pure form of quartz, is the raw material for the most expensivespecialty glasses.

1.3. Industrial Importance of Ceramics and Glasses

Silicon [Si] (do not confuse it with Silicone which are mixed inorganic-organicpolymers) has many industrial uses, for instance is it the principal componentof most semiconductor devices (whose electrical conductivity is in between thatof a conductor and that of an insulator), most importantly integrated circuits ormicrochips. Silicon has been THE material which has made computers possible.In the form of silica and silicates, silicon forms useful glasses, cements, and

ceramics. It is also a component of silicones, a class-name for various syntheticplastic substances made of silicon, oxygen, carbon and hydrogen, often confusedwith silicon itself.Glasses have historically been used for low technology applications such as

soda bottles and window panes. However, glasses, like ceramics, have recentlyfound new application in high technology fields (particularly the semiconductormicroelectronics industry where silica is widely used as an insulator in transistorsand the fiber optic cable industry where high purity silica glass has made advancedtelecommunications possible, see Figure 1.3).As with ceramics, the list of industrially important glasses also continues to

grow. As a result of their unique properties, ceramics and glasses are materialswhich will be used extensively in areas such as aerospace, automobiles, microelec-tronics, and telecommunications.

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1.4. Industrially Important Glasses

Silicon [Si] (do not confuse with Silicone which are mixed inorganic-organic poly-mers) has many industrial uses, for instance is it the principal component ofmost semiconductor devices (whose electrical conductivity is in between that ofa conductor and that of an insulator), most importantly integrated circuits ormicrochips.In the form of silica and silicates, silicon forms useful glasses, cements, and

ceramics. It is also a component of silicones, a class-name for various syntheticplastic substances made of silicon, oxygen, carbon and hydrogen, often confusedwith silicon itself.

• Silica glass (SiO2) is used for optical fibers when it is very pure.

• Soda-lime glass (SiO2-Na2O-CaO) is the standard glass used for bottles andwindows due to its low cost and easy manufacturing.

• Borosilicate glass (SiO2-B2O3) is good in applications where thermal shockresistance is necessary (e.g. laboratory glassware) because of its low coeffi-cient of thermal expansion

• Lead glass (SiO2-PbO) commonly known as ”crystal”, this glass has a highindex of refraction causing it to sparkle (much like a diamond)

1.5. Technical Ceramics

Technical Ceramics covers ceramic materials and products for technical applica-tion. Terms such as:· functional ceramics (Components which fulfill an electrical, magnetic, dielectri-cal, optical etc. function)· structural ceramics, engineering ceramics, or industrial ceramics (Componentswhich are subjected mainly to mechanical loads.)· electro-ceramics· cutting ceramics· bio-ceramics· high-performance ceramics (see below)describe the products groups of Technical Ceramics, but due to overlapping

there is not a clear classification.

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Figure 1.4: Products made of ceramic material.

1.5.1. High-performance ceramics

High-performance ceramics are ceramics with incredibly light weight, high hard-ness, non-corrodable, high melting points, high price and advanced applications,see Figure 1.4.Components made from high-performance ceramics are often determining the

functionality of machinery by possessing excellent corrosion resistance, very highthermal stability and wear resistance, as well as high biocompatibility. Density,porosity, electrical and optical characteristics can be varied within a wide range.Highly specialized and flexible production techniques enable us to match our prod-ucts to the specific customer demands.In ENV 12212 (classification system for European comity for standardiza-

tion, CEN) high-performance ceramics are defined as ”highly developed, high-performance applicable ceramic material, which is mainly non-metallic and inor-ganic, and has certain functional properties.” The term is seen as a differentiationto traditional clay based ceramic that includes china-ware, sanitary ceramic tilesand bricks and covers all technical ceramics. The materials for electrical engineer-ing are standardized according to the international standard IEC 627 (Interna-tional Electrotechnical Commission, IEC).

The terms used above are often still used in classify technical ceramics. How-ever a precise classification is only possible if the materials are listed under theirfollowing chemical composition:

• silicate ceramics

— technical porcelain (quartz, feldspar and kaolin. )

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— steatite (major component: soapstone, additives: clay and flux)

— cordierite (these magnesium silicates occur during the sintering of soap-stone with added clay, kaolin, corundium and mullite.)

— mullite-ceramic (Al2O3 and SiO2,where mullite: (3 Al2O3 2 SiO2) andcorundium (Al2O3) )

• oxide ceramics

— aluminium oxide (AL2O3)

— magnesium oxide (MgO)

— zirconium oxide (ZrO2)

— aluminium titanate (AT)

— piezo ceramic (PZT), (the most important piezoelectrical ceramic ma-terials are based on the oxide mixed crystals system lead zirconate andlead titanate)

• nonoxide ceramics:

— carbide: Silicon carbide (SIC), Sintered silicon carbide (SSIC), Reac-tion bonded silicom infiltrated silicon carbide (SSIC), Recrystallizedsilicon carbide (RSIC), and Nitride bonded silicom carbide (NSIC)

— nitride: Silicon nitride (Si3N4), Silicon aluminium oxynitride (SIALON),and Aluminium nitride (ALN).

Questions:•What is the special properties of ceramics and glasses?•What are they used for?•What are the industrally important glasses?•What kind of different ceramics are there?•What is a high-performance ceramic?•What is the drawback of ceramics compared to metals?References:http://www.keramverband.de/keramik/englisch/fachinfo/werkstoffe/definitionen.htm

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http://www.globaltechnoscan.com/31stOct-6thNov02/high_performance_ceramics.htm

http://www.globaltechnoscan.com/http://www.sciam.com/explore_directory.cfmhttp://www.mse.cornell.edu/courses/engri111/ceramic.htmhttp://www.mse.cornell.edu/courses/engri111/impglass.htmhttp://biotsavart.tripod.com/327.htmhttp://www.engr.sjsu.edu/WofMatE/

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Figure 2.1: A suspension bridge.

2. Metals and metal alloys

Metals are elements that generally have good electrical and thermal conductivity.Many metals have high strength, high stiffness, and have good ductility. Somemetals, such as iron, cobalt and nickel are magnetic. Many metals and alloys havehigh densities and are used in applications which require a high mass-to-volumeratio.At extremely low temperatures, some metals and intermetallic compounds be-

come superconductors (a superconductor can conduct electricity without electricalresistance at temperatures above absolute zero. The change from normal electricalconductivity to superconductivity occurs suddenly at a critical temperature Tc).

Pure metals are elements which comes from a particular area of the periodictable. Examples of pure metals include copper in electrical wires and aluminumin cooking foil and beverage cans.Metal Alloys contain more than one metallic element. Their properties can be

changed by changing the elements present in the alloy. Examples of metal alloysinclude stainless steel which is an alloy of iron, nickel, and chromium; and goldjewelry which usually contains an alloy of gold and nickel.Some metal alloys, such as those based on aluminum, have low densities and

are used in aerospace applications for fuel economy. Other examples: Many metalalloys also have high fracture toughness, which means they can withstand im-pact and are durable. Many beverage cans are made of aluminum metal. Manystructures, such as this suspension bridge, are made of steel alloys, see Figure2.1. Aircraft skins are made of lightweight aluminum alloys with high fracturetoughness.

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2.1. High-peformance Metals

When metal components must perform under critical conditions, manufacturersneed high-performance metals. Titanium-base alloys, and specialty steels for theaerospace industry are metals of exceptional wear resistance, corrosion resistance,heat resistance, toughness, and strength. Nickel- and cobalt-based materials areknown as superalloys. Turbine blades are for instance made of superalloys inorder to withstand the temperatures well above 2,000◦ F (1093.3

◦C). The most

advanced of these turbine blades are grown from molten metal as single crys-tals in ceramic molds, in order to obtain maximum possible resistance to high-temperature deformation.

2.1.1. High-Performance Aluminum

Aluminum bridge decks have a number of advantages over concrete and steel decks.Aluminum is about 80 percent lighter than concrete. This substantial weightsavings allows many bridges to be strengthened without extensive reengineeringof substructures.Aluminum requires fewer welds than steel, eliminating many potential failure

points. Compared to steel, aluminum is less expensive, both in the short term andthe long term. An aluminum deck is also more resistant to corrosion and otherenvironmental degradation.Aluminium alloys are often used in Defense and Aerospace, which is one of

the most demanding industries, see Figure 2.2. These industries use high strength5xxx series (Al-Mg) which are non-heat treatable base alloys for some applications,but also make use of some of the more specialized heat treatable aluminum alloyswith superior mechanical properties.Aluminum armor plating is used for its impact strength and strength-to-weight

ratio, and here alloy 5083, 7039 (Al-Zn) and and 2519 (AL-Cu ) are used as basematerials. Missiles are constructed of alloys 2019 and 2219. Perhaps the mostexotic aluminum alloys, with exceptional strength over a wide range of operatingtemperatures, are used in the aerospace industry. Some of these alloys are 2219,2014, 2090, 2024, and 7075. These base materials are typically used in specializedhigh performance applications and have their own welding characteristics andassociated problems that require special considerations when joining.

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Figure 2.2: Aerospace industry.

2.1.2. High-Performance Steel

A new grade of high performance steel, HPS-485W or HPS-70W, uses a newchemical composition that provides improved welding and toughness properties.The increase in strength and performance will allow targeted use of HPS that willextend the useful life of steel bridge structures; and even greater savings with thereduction of the total steel weight.Structural components in new cars are for example made from high-performance

steel that is 3 times stronger than ordinary steel (900 MPa instead of 300 whichis ususal). This makes the new cars very crash resistant such that the passengersare much more protected if there should be a collision.

2.1.3. Space-age metals

In jet aircrafts, rockets, missiles and nuclear reactors, the metals columbium (Nb,41), titanium (Ti, 22), hafnium (Hf, 72), zirconium (Zr, 40) and tantalum (Ta,73) are used. Columbium (niobium) can withstand high temperatures and can beused for the skin and structural members of aerospace equipment and missiles. Itis a lightweight metal and a superconductor of electricity (which means that itcould be possible to use it in storing and transferring large amounts of energy inthe future). Titanium is as strong as steel and 45% lighter, and is often used forjet engine components (rotors, fins, and compressor parts) and other aerospace

20

parts. Hafnium and zirconium are always found together are they make it possibleto control nuclear reactors in a precise way. The superior corrosion resistance ofzirconium makes it (and its alloys) very useful in the chemical industry and forsurgical implants. Pure zirconium has for a long time been used as the lightsource in photo flash tubes, since it is a reactive metal that burns in air with abrilliant white light. Tantalum (often occurs as the mineral columbitetantalite) isvery malleable and ductile. Its melting point is at 2996

◦C, and is often used as a

replacement for platinium in chemical, and dental equipment and instruments. Itis also used to make electrolytic capacitors and are used in vacuum furnaces.A superconducting material transmits electricity with virtually no energy loss.

Superconductivity, which occurs in many metals and alloys, is very new and istherefore not yet in widespread use. Superconductivity is a phenomenon occurringin certain materials at extremely low temperatures, characterized by exactly zeroelectrical resistance and the exclusion of the interior magnetic field (the Meiss-ner effect). Superconductivity occurs in a wide variety of materials, includingsimple elements like tin and aluminium, various metallic alloys and some heavily-doped semiconductors. Superconductivity does not occur in noble metals (metalsthat are resistant to corrosion or oxidation, for instance gold, silver, tantalum,platinum, palladium and rhodium; unlike most base metals), nor in most ferro-magnetic metals.

Questions:•Why are metals and metal alloys used?•What is so special about high performance metals?• In the space-age, what features in a material or material structure would beimportant in the future?•What kind of metals are used in space equipment, and why are they used?References:http://www.mse.cornell.edu/courses/engri111/metal.htmhttp://www.allvac.com/http://www.greatachievements.org/http://www.hiper-group.com/hcproducts.htmhttp://www.spacedaily.com/news/materials-02zh.htmlhttp://www.alcotec.com/ataafi.htmhttp://www.weldreality.com/aluminumalloys.htmHigh Performance Steel Designers’ Guide:http://www.fhwa.dot.gov/bridge/guidetoc.htm

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http://www.mmc.co.jp/alloy/english/products/taisyoku/gijyutsu3.htmlR. Gregg Bruce, Mileta M. Tomovic, John E. Neely and Richard R. Kibble, Mod-ern materials and manufacturing processes, ISBN: 0-13-186859-4, Second edition,Prentice Hall, 1998.

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Figure 3.1: Polymerization by addition of equal monomers.

3. Polymers and Plastics

Polymer etymology: The word polymer comes from Greek: poly means ‘many’and mer comes from merous which roughly means ‘parts’. Polymers are organicmaterials characterized by long chain-like molecules built up from many units(monomers), see Figure 3.1, generally repeated hundreds or thousands of times.All atoms in a chain are bonded by covalent bond to each other, while Van derWaals bonding keeps the chains together. Starch, cellulose, and proteins arenatural polymers. Nylon and polyethylene are synthetic polymers.From organic chemistry, polymer is defined as: ”a large molecule formed by

the union of at least five identical monomers; it may be natural, such as celluloseor DNA, or synthetic, such as nylon or polyethylene; polymers usually containmany more than five monomers, and some may contain hundreds or thousands ofmonomers in each chain.”

3.1. The structure of polymers

Polymerization is the word for the process of forming large molecules from smallmolecules. When there are no possibility to add any more atoms, the moleculesare said to be saturated. When molecules do not have the maximum numberof atoms, because atoms in the molecule are held together with double or triplecovalent (shared) bonds, they are called unsaturated. The unsaturated moleculesare important in the polymerization process, which means that small moleculesare linked together to form large molecules, as you can see in Figure 3.1, wherethe process has taken place through addition mechanism. Here, a large molecule

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Figure 3.2: Methane and ethane.

(polymer) is formed by a repeated unit (mer). Activators or catalysts (benzoylperoxide) are often required to drive the reaction. A polymer can also be madefrom a condensation process which means that reactive molecules combine withone another to produce a polymer plus small, by-product molecules, such as water.Often, heat, pressure or a catalyst are required to drive the reaction. In mostcommercial available plastics the number of mers in the polymer (which is knownas the degree of polymerization) range from 75 to 750. When two different types ofmers are combined into the same addition chain, we call them copolymers. And,in terpolymers three different monomers are included.The molecular structure of polymers are often based on paraffin-type hydro-

carbons where carbon and hydrogen are linked in the relationship

CnH2n+2,

as we see in Figure 3.2. Hydrogen can be replaced by chlorine, flouring and alsobenzene. Carbon can be replaced by oxygen, silicon, sulfur or nitrogen. Thesepossibilities are the reason why a wide range of organic compounds can be created.By the description of polymers we see that wood (cellulose-type materials, see

Figure 3.3) are included in the group of polymer. It has been accepted for manyyears that cellulose is a long chain polymer, made up of repeating units of glucose,a simple sugar. As a carbohydrate, the chemistry of cellulose is primarily thechemistry of alcohols; and it forms many of the common derivatives of alcohols,such as esters, ethers, etc. These derivatives form the basis for much of theindustrial technology of cellulose in use today. Cellulose derivatives are usedcommercially in two ways, as transient intermediates or as permanent products.

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Figure 3.3: The structure of cellulose.

3.2. Crystallinity in polymers

We need to distinguish between crystalline (see Figure 1.1) and amorphous ma-terials (see Figure 1.2) and then show how these forms coexist in polymers. Thereasons for the differing behaviors lie mainly in the structure of the solids.The morphology of most polymers is semi-crystalline. That is, they form mix-

tures of small crystals and amorphous material, see Figure 3.4 and melt over arange of temperature instead of at a single melting point. The crystalline mate-rial shows a high degree of order formed by folding and stacking of the polymerchains. The amorphous or glass-like structure shows no long range order, and the

Figure 3.4: A polymer with the combination of amorphous and crystalline areas, from:http://plc.cwru.edu/tutorial/enhanced/files/polymers/orient/orient.htm

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chains are tangled. There are some polymers that are completely amorphous, butmost are a combination with the tangled and disordered regions surrounding thecrystalline areas. Most thermoplastics have crystalline regions alternating withamorphous regions, while

3.2.1. The glass transition temperature and melting temperature

The glass transition temperature Tg (also called the glass temperature), describesthe temperature at which amorphous polymers undergo a second order phase tran-sition from a rubbery, viscous amorphous solid to a brittle, glassy amorphous solid.Tg is a property of amorphous polymers which do not have a sharp melting point,and is defined as the temperature at which the specific volume vs temperature plothas a change in slope, see Figure 3.5. When we cool an amorphous material fromthe liquid state, there is no abrupt change in volume such as occurs in the caseof cooling of a crystalline material through its freezing point, Tf (=Tm). Instead,at the glass transition temperature, Tg, there is a change in slope of the curve ofspecific volume vs. temperature, moving from a low value in the glassy state to ahigher value in the rubbery state over a range of temperatures. This comparisonbetween a crystalline material (1) and an amorphous material (2) is illustrated inFigure 3.5. Note that the intersections of the two straight line segments of curve(2) defines the quantity Tg. When a polymer is cooled below Tg, the moleculeshave little relative mobility, and the material becomes hard and brittle, like glass.Some polymers are used above their glass transition temperatures, and some areused below. Tg is usually referred to wholly or partially amorphous phases inglasses and polymers. As the temperature of a polymer drops below Tg, it be-haves in an increasingly brittle manner. As the temperature rises above the Tg,the polymer becomes more rubber-like. In general, values of Tg well below roomtemperature define the domain of elastomers and values above room temperaturedefine rigid, structural polymers.

The glass transition is not the same thing as melting. Among synthetic poly-mers, (crystalline) melting temperature Tmcrystalline melting is only discussedwith regards to thermoplastics, as thermosetting polymers will decompose at hightemperatures rather than melt. Tm (also called flow temperature for amorphousmaterials) happens when the polymer chains fall out of their crystal structures,and become a disordered liquid.Even crystalline polymers will have a some amorphous portion. This portion

usually makes up 40-70% of the polymer sample. This is why the same sample of a

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Figure 3.5: Comparison between a crystalline material (1) and an amorphous material(2). From: http://plc.cwru.edu/tutorial/enhanced/files/polymers/therm/therm.htm

polymer can have both a glass transition temperature and a melting temperature.But you should know that the amorphous portion undergoes the glass transitiononly, and the crystalline portion undergoes melting only.

According to Wikipedia, the disaster of the space Shuttle Challenger wascaused by rubber O-rings that were below their Tg, on an unusually cold Floridamorning, and thus could not flex enough to form proper seals between sectionsof the two solid-fuel rocket boosters (SRB), see Wikipedia. SRB’s are used toprovide the main thrust (reaction force) in spacecrafts launches from the eartheup to about 45 kilometres.

Polymer science is a broad field that includes many types of materials whichincorporate long chain structure of many repeat units as discussed above. Thetwo major polymer classes are:

• Elastomers

• Plastics

Another important property of polymers, also strongly dependent on theirtemperatures, is their response to the application of a force, as indicated by two

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Figure 3.6: Plastics.

main types of behavior: elastic and plastic. Elastic materials will return to theiroriginal shape once the force is removed. Plastic materials will not regain theirshape. In plastic materials, flow is occurring, much like a highly viscous liquid.Most materials demonstrate a combination of elastic and plastic behavior, showingplastic behavior after the elastic limit has been exceeded.

3.3. Plastics

Plastics, see Figure 3.6, are a large group of polymers that has properties betweenelastomers and fibers, and has plastic behavior. As such, plastics have a widerange of properties such as flexibility and hardness and can be synthesized tohave almost any combination of desired properties.Plastics are polymers which, under appropriate conditions of temperature and

pressure, can be molded or shaped (such as blowing to form a film). In contrastto elastomers, plastics have a greater stiffness and lack reversible elasticity. Allplastics are polymers but not all polymers are plastics.Cellulose is an example of a polymeric material which must be substantially

modified before processing with the usual methods used for plastics. Every dayplastics such as polyethylene and poly(vinyl chloride) have replaced traditionalmaterials like paper and copper for a wide variety of applications.

3.4. Properties of plastics

New types of plastics are developed all the time, and therefore it is helpful to havea brief knowledge of the following general basic properties of plastics.

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• Light weight: Most plastics have a specific gravity (SG) between 1.1 and1.6. Magnesium has a SG about 1.75. Specific gravity is the heaviness ofa substance compared to that of water, and it is expressed without units. Inthe metric system specific gravity is the same as in the English system. Ifsomething is 7.85 times as heavy as an equal volume of water (such as ironis) its specific gravity is 7.85. Its density is 7.85 grams per cubic centimeter,or 7.85 kilograms per liter, or 7.85 metric tons per cubic meter.

• Corrosion resistance: Many plastics perform well in hostile, corrosiveenvironments.

• Electrical resistance: Plastics are often used as insulating materials.

• Low thermal conductivity: Plastics are relatively good thermal insula-tors.

• Variety of optical properties: You can get a plastic in almost any coloryou would like, and the color can go throughout (not only at the surface).You can also get transparent or opaque plastics.

• Formability: Plastics are easy to form (often in only one single operation).Extrusion, casting and molding are widely used.

• Surface finish: You can get the surface you want, from rough to excellentsurface finish.

• Comparatively low cost: Both material and processing/manufacturingprocesses are cheap. Tool costs are also low.

• Low energy content: Plastics melt at low temperature compared withmetals, and are therefore produced with little energy.

The mechanical strength of plastics are not especially high, compared to met-als, but the low density makes them comparable to metals due to their strength-to-weight ratio (or specific strength). A material has high specific strength if theratio of its strength to its weight is high.Plastics are usually divided into two main groups: thermosettings or thermo-

plastics. The terms refer to the materials response to elevated temperature. It isimportant to know whether the plastic is a thermosetting or a thermoplastic sinceit determines how the plastic will perform in service.

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3.4.1. Thermosettings

In some plastics, polymerization produces cross linkage between long molecularweight chain molecules. These plastics are known as thermosetting plastics be-cause they are permanently hardened by heat. The setting process is irreversible,so that these materials do not become soft under high temperatures. Additionalheating do not lead to softening, but the material maintain their mechanical prop-erties up to the temperature at which they char, or burn.Thermosetting plastics usually have a highly cross-linked or three dimensional

framework structure in which all atoms are connected by strong, covalent bonds.They are generally produced by the process of condensation polymerization whereelevated temperature promotes the irreversible reaction, hence the term thermoset-ting.The thermosettings are stronger and more rigid than the thermoplastics, but

have a lower ductility and poorer impact properties. These plastics also resistwear and attack by chemicals and they are very durable, even when exposed toextreme environments.Typical thermosetting-type plastics are the aminos, most polyesters, alkyds,

epoxies, phenolics and urethanes.

3.4.2. Types of Thermosettings

PUR - Polyurethane/polyurethene (or PU)PUR is found in a variety of forms ranging from stiff to soft types. Stiff PUR is

used for casings and modelling material (artificial wood). Softer rubber-like PURis used for handtools. Expanded PUR is used for mattresses and car inner panelswhere it both forms the foam and the leather-like skin. Expandable insulationfoam and moisture hardening glue are also made from PUR. Large parts are oftenmade from PUR due to low tooling cost. In general it has excellent outdoorperformance and resistance to most acids and solvents.Genoa stacking chair. PUR can be made from a wide variety of raw materials

to give hard, clear resins for surface coating: soft flexible resins for oil resistant andabrasion resistant rubbers; rigid or flexible foams for thermal insulation, cushionand fabric stiffeners. In building surface coating and thermal insulation are theirmain applications.Products: Mil-Tek high pressure cleaner, Panton chair, Shoe soles, and it is

used as modelling material (produced by Westnofa) in the Product Design courseat HiN .

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EP - EpoxyEpoxy is a strong and very resistant thermoset plastic. It is used as an adhesive

agent, as filling material, for moulding dies, and as a protective coating on steeland concrete. Many composite materials are reinforced epoxy.Epoxy is resistant to almost all acids and solvents, but not to strong bases or

solvents with chlorine content.By adding a hardening agent curing takes place. The type of hardener has a

major influence on properties and applications of epoxies.Products: Surfing board, Composite bicycle, Badminton racket, Wheel chair,

Knee support, Soda stream pressure, container, Skull, model, Car space frame,Wheel chair ramp, Swing wheel.

UP - Unsaturated PolyesterUP is widely used as filler material with glass fibre in sailing boats, hard tops

for cars, furniture, etc. In general UP is not resistant to solvents and bases.Apart from sulphuric acid it resists acids. To improve appearance and resistancea surface layer (gel coat or paint) is often added. UP does not require expensiveequipment or tooling to work with UP, and it is therefore often used for prototypesand low-volume production.Products: Sailing boat, Chair, Hard top for car, Printed circuit board, Pedes-

trian bridge.

UF - Urea formaldehydeUrea thermoset molding compounds offer a wide range of applications for

every-day living and industry. Urea formaldehyde (UF) thermosets are economi-cally priced, they are strong, glossy, and durable. They are not affected by fats,oils esters, ether, petrol, alcohol or acetone, nor by detergents or weak acids, andthey exhibit good resistance to weak alkalis.Their high mechanical strength, heat and fire resistance, and good electrical

arc and tracking resistance make them an ideal plastic for numerous industrial andhousehold applications, from doorknobs and toilet seats to electrical componentsand cosmetics enclosures. You name it — if it can be plastic, it can be strongerand brighter as a (Perstorp) urea thermoset.

MF - Melamine formaldehydeMelamine thermoset plastics are similar to urea molding compounds, but

melamine has even better resistance to heat, chemicals, moisture, electricity andscratching.

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Melamine formaldehyde (MF) thermosets are ideal for dinnerware, kitchenutensils, bathroom accessories, and electrical components. The molded com-pounds are bright, inviting, and highly resistant to scratches and staining. (Per-storp’s) melamine thermosets are approved for contact with foodstuffs, and theydo not affect the food’s flavor - even at high temperatures. They are very, verydurable.Like urea molding compounds, melamine thermosets consist of plastic that has

high surface hardness and gloss, brilliant and precise colors, and light fastness.

UF or MF thermosets can be manufactured in a precise and vibrant array ofcolors. Two-tone compression molding using doublepunch tools will enable youto express your creative designs. For example, your cups or sinks can have whiteinside and tasteful color outside. The choice of color and shape is limited only byyour imagination.

Alkyd resinsThis group of polyesters are usually compression moulded from powders. Orig-

inally produced for inclusions in paints, they are resistant to heat and electricityand will withstand attack by acids and solvents. Alkyd plastics find applicationsin enamels for cars, refrigerators and washing machines and are also used forelectric motor insulation and some television parts.

SiliconesSilicon is an element whose atoms have similar linking properties to those of

carbon, but it is stable at much higher temperatures. To utilize the properties ofsilicon, certain plastics, called silicones have been developed based on the element.Although they are much more expensive, they contain excellent properties. Thesesuper materials are available as oil, plastics and rubbers. To quote an exampleillustrating their value: silicone rubber will retain its elasticity over a temperaturerange of -80◦C to 250◦C. The stability of silicones under widely varying serviceconditions make them valuable materials for applications such as laminates in theaerospace industry, gaskets and seals for engineering purposes and cable insulationfor aircraft electrical systems.

3.4.3. Thermoplastics

Thermoplastics, alternatively thermosoftenings, as the name implies, are hard atlow temperatures but soften when they are heated. The softening and hardeningcan be repeated without any change in the chemical structure. Although they are

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Figure 3.7: The easiest way to identify the type of thermoplastic you’re working withis to look for the Plastic ID symbol the backside of the part.

less commonly used than thermosetting plastics they do have some advantages,such as greater fracture toughness, long shelf life of the raw material, capacity forrecycling and a cleaner, safer workplace because organic solvents are not neededfor the hardening process.Thermoplastics have weak bonds between the neighboring molecules and they

are weakened by elevated temperature which means they soften at high temper-ature and are stronger and harder when cooled. They do not have any definitemelting temperature, they have a range of temperatures where they soften. Whencooled below the glass transition temperature, Tg, the linear polymer retains itsamorphous structure, but becomes hard, brittle, and glasslike.Thermoplastics are not cross-linked and can be softened and hardened over and

over again. The majority of polymers are thermoplastic. Today there are primar-ily six commodity polymers in use, namely polyethylene terephthalate (PETE),polyethylene (PE), polyvinyl chloride (PVC), polypropylene (PP), polystyrene(PS) and polycarbonate (PC). These make up nearly 98% of all polymers andplastics encountered in daily life, see ref.[33].The Society of the Plastics Industry, Inc. (SPI) introduced its resin identifica-

tion coding system in 1988 at the urging of recyclers around the country. The SPIcode was developed to meet recyclers needs while providing manufacturers a con-sistent, uniform system that could apply nationwide, see figure 3.7. Look at thebottom of a recyclable plastic bottle - chances are you will see a PE or PS whichmeans polyethylene or polystyrene. These materials are examples of what happens

33

to polymers when they solidify: the chains are entangled and packed together tomake light, tough, flexible materials. If you heat up PE or PS to moderate tem-peratures, if the chains have not been chemically stuck together (‘cross-linked’)they will melt, and turn into goopy liquids, which are called polymer melts. Somepolymers melts even at room temperature, like polydimethylsiloxane (PDMS), orpoly(ethylene-propylene) (PEP).

3.4.4. Types of Thermoplastics

PET - Polyethylene terephthalate (or PETE)PET has good barrier properties against oxygen and carbon dioxide. There-

fore, it is utilized in bottles for mineral water. Other applications include foodtrays for oven use, roasting bags, audio/video tapes as well as mechanical compo-nents.PET exists both as an amorphous (transparent) and as a semi-crystalline

(opaque and white) thermoplastic material. Generally, it has good resistanceto mineral oils, solvents and acids but not to bases.The semi-crystalline PET has good strength, ductility, stiffness and hardness.

The amorphous PET has better ductility but less stiffness and hardness.Danish Name PET - thermoplastic polyesterProducts: Bottle for mineral water, Trays for oven use, Oven foils, Audio and

video tapes, Thermo scarf (fleece)

PE - PolyethylenePE is a semi-crystalline thermoplastic material and one of the most commonly

used plastics. It is generally ductile, flexible and has low strength. PE is oneof the most commonly used thermoplastic material due to the good propertiescombined with a low price.There are two basic families: LDPE (low density), and HDPE (high density):

• LDPE - low density polyethylene: LDPE is the low density version ofPE. This has less hardness, stiffness and strength compared to HDPE, butbetter ductility. It is opaque and only thin foils can be transparent. LDPEis used for packaging like foils, trays and plastic bags both for food andnon-food purposes. Used as protective coating on paper, textiles and otherplastics, for instance in milk cartons. Products: Wrapping foil for packaging,Plastic bag (soft type that does not crackle), Garbage bag, Tubes, Ice cubeplastic bag.

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• HDPE - high density polyethylene: HDPE is the high density versionof PE plastic. It is harder, stronger and a little heavier than LDPE, but lessductile. Dishwasher safe. HDPE is lighter than water, and can be moulded,machined, and joined together using welding (difficult to glue). The appear-ance is wax-like, lusterless and opaque. The use of UV-stabilizators (carbonblack) improves its weather resistance but turns it black. Some types can beused in contact with food. Products: Milestone, Bottle for motor oil, Bot-tle for organic solvents, Street bollard, Hedge cutter, Gasoline tank, Milkbottles, Plastic bag (stiff type that crackles), Children’s toys, Lid for honeypot, Beer crate, Dolphin bicycle trailer.

PVC - Polyvinyl chloride (vinyl)PVC is one of the oldest and most commonly used thermoplastic material, it

is a heavy, stiff, ductile and medium strong amorphous (transparent) material.By adding softeners, a range of softer materials can be achieved, ranging froma flexible to an almost rubber-like elastic soft material. Softeners also help toincrease the manufacturability. PVC has brilliant resistance to acids and bases,but is affected by some solvents. Soft PVC is exceptionally resistant to mostchemicals. The poor weather resistance can be improved using additives. PVChas good barrier properties to atmospheric gasses. PVC has a Tg of 83◦C, makingit good, for example, for cold water pipes, but unsuitable for hot water. PVC willalso always be a brittle solid at room temperature.Products: Boat fender, garden hose, electrical wire insulation, vinyl flooring,

roof gutter, vinyl record, children’s doll, wrapping film, medical transparent tube,Pneumatic chair.

PP - PolypropylenePP is an inexpensive, ductile, low strength material with reasonable outdoor

performance. The material surface is soft wax-like and scratches easily. It has ahigh stiffness, good strength even in relatively high temperatures, abrasion resis-tant, good elastic properties and a hard glossy surface. In low temperatures PPgets brittle (< 0◦C). Stiffness and strength are often improved using reinforcementof glass, chalk or talc. The color is opaque and white, but it can be dyed in manycolors. In many ways, PP is similar to HDPE, but it is stiffer and melts at 165-170◦C. PP can be manufactured by all the methods used for thermoplastics. PPhas high crystallinity (70-80 %), and is one of the lightest thermoplastics on themarked. The chemical properties are good. PP is resistant to inorganic chemicals

35

and water. It is resistant to most strong mineral acids and basics. PP is notresistant to nitrous gasses, halogens and strong oxidizing acids.Products: Childrens toy bin, transport box, fuel tank, suitcase, garbage bin,

rope, shaver (rechargeable), air intake, tubes, packing material, auto parts etc.The material is often used for hinges as it can be flexed millions of times beforebreaking.

PS - PolystyrenePolystyrene is an inexpensive amorphous thermoplastics that has good me-

chanical proprieties. It is vitreous, brittle and has low strength. However it isalso hard and stiff. Foamed PS is used for packaging and insulation purposes.PS is not weather resistant, and therefore not suitable for outdoor uses. PS istransparent (it transmits about 90% of the sunlight) and has unlimited dyeingpossibilities. Assembly can be done with gluing.Products: CD and MC covers, disposable drinking glass, glass for bicycle

lamp, salad bowl, razor (ordinary), razor (biodegradable), disposable articles,signs, machine parts and picture frames etc.

PC - PolycarbonatePolycarbonate is an amorphous plastic with very high impact strength, good

ductility and high stiffness. It is very difficult to break and the material is thereforeconsidered fracture-proof (e.g. bullet-proof glass).Light transmission is 85-90% but depends on the thickness. It has good out-

doors resistance in the UV-stabilized form, but it tends to turn yellow by longexposition to sunlight. PC is transparent and can be dyed in many colors. PChas a relatively good chemical resistance.Products: PC is commonly used for shielding of work places and machines,

sight glass, tubes etc. due to its transparency and high impact resistance, CDcompact disc, bullet-proof glass, water container.

ABS -Acrylonitrile-butadiene- styreneAcrylnitrile contributes with thermal and chemical resistance, and the rub-

berlike butadiene gives ductility and impact strength. Styrene gives the glossysurface and makes the material easily machinable and less expensive.Generally, ABS has good impact strength also at low temperatures. It has sat-

isfactory stiffness and dimensional stability, glossy surface and is easy to machine.If UV-stabilizators are added, ABS is suitable for outdoor applications.Products: LEGO building bricks, Computer mouse, Vacuum jug, KimBox

suitcase, Ceramic advanced wet shave razor, Hedge cutter handle, Handle for

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high pressure cleaner, Shaver, rechargeable, Ensemble chair (ABS blended withPA), auto body parts, suitcases, toys etc. Extruded profiles, tubes and bolts canbe made from ABS when the requirements are high impact resistance and a nicesurface.

PA - Polyamide (nylon)PA is a group of amorphous (transparent) and semi-crystalline (opal-white)

plastics. Arguments for using PA include strength (fishing line, axe handle),wear resistance (bearings), barrier properties (food packaging) and machinability.Polamide is recognised for good abrasion resistance, low friction coefficient, goodresistance to heat and good impact resistance. PA absorbs water which makes itsofter. UV-stabilizators are required for outdoor applications.Products: Nylons (stockings), fishing line, bicycle trailer (rainproof cover),

bearing, axe, hedge cutter, handle for, high pressure cleaner, bottle for tomatoketchup (barrier layer), ensemble chair (PA blended with ABS), bottle-opener.Kevlar (aramid fibre) is a family of nylons.

Acrylic - PMMA (plexiglas)PMMA (polymethyl-methacrylate) is an amorphous thermoplastic material

with very good optical properties (as transparent as glass and it allows 92% ofthe sunlight to pass!).PMMA is hard, stiff and medium strong, easy to scratch, notch sensitive,

but easy to polish and has a very good weather resistance. Exceptional outdoorperformance, such as weather and sunlight resistance, without reduction neither ofoptical nor mechanical properties. PMMA is resistant to water, basics, inorganicsalts diluted in water, most diluted acids. It is not resistant to strong acids, basicsand polar solvents.Products: Tail light glass, exhibition case, folding chair, kitchen scale, decora-

tion articles, transparent tubes, signs, windows, level glass etc..

POM - (polyoxymethylene) AcetalAcetal is a crystalline plastic often used for technical applications due to its

strength, ductility and good machinability. It has good creep properties whichmakes it suitable for click connections (e.g. bicycle lamp holder). It exhibits goodstiffness, strength and hardness up to 120◦C, and the elasticity is comparablewith that of many metals. Acetal is wear resistant and has a very low frictioncoefficient. The color is opaque white. To protect it from UV-light carbon blackcan be added, changing its color into black.

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Products: Vacuum jug (top), Holder for bicycle lamp, Fitting for Vico Duochair, Gearwheel.

PTFE - Fluoropolymer (Teflon)Fluoropolymers can be used to make a variety of articles having a combination

of mechanical, electrical, chemical, temperature and friction-resisting propertiesunmatched by articles made of any other material. Commercial use of these andother valuable properties combined in one material has established TEFLON R°resins as outstanding engineering materials for use in many industrial and mil-itary applications. TEFLON R° resins may also be compounded with fillers orreinforcing agents to modify their performance in use.TEFLON R° PTFE resins have a continuous service temperature of 260◦C

(500◦F). Much higher temperatures can be satisfactorily sustained for shorterexposures.Teflon is used in: Food processing, Electrical parts, Coaxial cable connectors,

Terminal insulators, Transformers, Relays, Medical industry, Washers, Gaskets,Flanges, Valve components, Pump Components, Baffles, Seals, Bearings, Rings,Bushings , High heat applications. Teflon is available as: Sheets, Rods, Tubes,Heavy wall tubing, Film, Rectangular bar, Pressure sensitive, tape.

TPUR - Thermoplastic urethane (or TPU)TPU is a urethane based TPE (thermoplastic elastomer). It is made of long

chained molecules of diols and diisocyanates. Urethane is the unit which is re-peated in polyurethane. TPU has a very good abrasion resistance. It is a toughmaterial with a good elasticity over a wide temperature range. TPU is filling thegap between rubber material and the more traditional thermoplastics.The electrical conductance is very low. TPU is a hygroscopic material, and

the conductance is dependent on the content of moisture. TPU is resistant tooil, fat, gasoline, and ozone. It is not resistant to hot water, steam, strong acidsand basics. Polyether based TPU is resistant to microbes. TPU is available in avariety of qualities.Products: Bumpers, hoses, tubes, sleeves, cushions, coating, insulators, apron

rollers etc.

PEEK - PolyetheretherketonePEEK is a high temperature resistant engineered thermoplastic with excel-

lent chemical and fatigue resistance plus thermal stability. They exhibit superiormechanical and electrical properties. With a maximum continuous working tem-perature of 249◦C (480◦F), they have excellent retention of mechanical properties

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up to 299◦C (570◦F) in a steam or high-pressure water environment. Superiorchemical resistance has allowed them to work effectively as a metal replacementin harsh environments. They are inert to all common solvents and resist a widerange of organic and inorganic liquids. When ∆extensive machining is required,a secondary annealing process should be considered.PEEK is an excellent material for a wide spectrum of applications where ther-

mal,chemical, and combustion properties are critical to performance. The addi-tion of glass fiber and carbon fiber reinforcements enhances the mechanical andthermal properties of the basic PEEK material.Products: automobile engine parts, medical equipment, aerospace products.

Today there are primarily six commodity polymers in use, namely polyethylene,polypropylene, polyvinyl chloride, polyethylene terephthalate, polystyrene andpolycarbonate. These make up nearly 98% of all polymers and plastics encoun-tered in daily life.

3.5. Classification

• Standard plastics used in non-critical and low-stress applications are mate-rials like PS, ABS, PVC, PP, HDPE, and LDPE.

• Engineering plastics that are used in general structural, bearing and wearpurpose are plastics like PPO (Polyphenylene oxide, modified), Acrylic, PC(Polycarbonate), PET-P (Polyethylene Terephtalate), POM (Poly-oxymethylene=Acetal), PA (Polyamide = Nylon), and UHMW-PE (Ultra high mole wt.Polyethylene).

• Advanced engineering plastics that have superior properties and can beused in extreme environments are plastics like PSU (Polysulfone), PPSU(Polyphenylsulfone), PEI (Polyetherimide), PTFE (Polytetraflouroethylene= Teflon), PPS (Polyphenylene sulfide), PEEK (Polyetheretherketone), PI(Polyimid), PAI (Polyamide-imide), and PBI (Polybenzimidazole).

3.6. Additives in Plastics

Very often, some additional materials are mixed into plastics, to obtain:

• improved properties

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• reduced cost

• improved moldability

• wanted color

These additional materials are classified as fillers, plasticizers, lubricants, color-ing agents, stabilizers, antioxidants, flame retardants, foaming or blowing agents,antifogging agents, antistatic agents, clarifying agents and optical brighteners.New ones are added to the list continuously, so we briefly mention a few of them.

FillersImprove mechanical properties, reduce shrinkage, reduce weight or provide

bulk. Fillers comprise a large percentage of the total volume of the plastic. Ex-ample of fillers can be: wood flour, cloth fibers, glass fibers, clay.

PlasticizersIncrease flexibility, improve flow during molding, reduce shrinkage, reduce

weight.

LubricantsComparison of both internal lubricants and external lubricants which can be

blended with various materials to reduce friction, and wear, improve mar resis-tance, and extend the useful life of products which are subject to friction. Theyalso improve moldability and extraction from molds.

Coloring AgentsColoring Agents are put in the plastic to Impart color.

StabilizersStabilizers retard degradation due to heat or light.

AntioxidantsAntioxidants retard degradation due to oxidation.

Flame retardantsFlame retardants reduce flammability.

Foaming AgentsFoaming Agents, also known as Blowing or Nucleating Agents, can eliminate

sink marks, reduce density, shorten cycle time and reduce total production costs.In extrusion and injection molding, foaming agents can save material weight andlower total cost. They also improve extrusion rates by increasing the volume that

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can be processed per extruder in a given period of time, and endothermic foamingagents absorb heat and improve injection molding cycle time.

Antifogging agentsAntifogging agents reduce the formation of condensed droplets on the surface

of polyolefin films, such as for food-packaging or agricultural films, resulting inbetter film transparency and consequently providing better food preservation.

Antistatic agentsThese new permanent antistatic agents, form a conductive network throughout

the polymer matrix which dissipates the electrical charge as it builds up. Theyare already effective for processing and even work at low environmental humidity.

Clarifying agents/Optical brightenersClarifying agents/optical brighteners are designed to give brilliance and whiten-

ing to a variety of applications. Synthetic fibers for example, have an inherentyellowish tint. Add optical brighteners and the fibers appear cleaner and whiter.IRGACLEAR R° is a range of products that not only improves the clarity andtransparency of polypropylene, but also enhances the mechanical properties.

3.6.1. Oriented Plastics

The strength of the intermolecular bond increases with reduced separation dis-tance, and that is why a processing that makes the molecules align parallel makethe long-chain thermoplastic higher strength in a given direction. This is calledan orientation process, and can be obtained by stretching, rolling, or extrusion, asshown in the Figure 3.8. When a polymer (amorphous or crystalline) is subjectedto stress (tensile), the molecular chains become aligned or oriented parallel to thedirection of applied stress. The polymer is then in an oriented state. Orientingmay increase the tensile strength by more than 200%, but 25% is more typical.

3.7. Elastomers & Rubbers

Elastomers, or rubbery materials, have a loose cross-linked structure. Natural andsynthetic rubbers are both common examples of elastomers. Elastomers possessmemory, that is, they return to their original shape after a stress is applied.Elastomers are amorphous polymers and consist of long polymer chains above

their glass transition temperature. The structure of elastomers is tightly twistedor curled.

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Figure 3.8: Presentation of the alignment of the plastic molecules in the orientingprocess.

Figure 3.9: Elastomers.

Elastomers are reversibly stretchable for small deformations. When stretched,the polymer chains become elongated and ordered along the deformation direction.When no longer stretched, the chains randomize again. The cross-links guide theelastomer back to its original shape. They are very flexible and elastic, whichmeans that they can undergo large elastic deformations without ruptures andrecover substantially in shape and size after the load has been removed. Manyelastomers can be stretched to several times their original length. Also, the cyclecan be repeated numerous times with identical results, as with the stretching ofa rubber band.Elastomers are generally resistant to oil and fuel, impermeable to liquids and

gases, but tend to deteriorate by oxidation.

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Like plastics, elastomers are either thermoplastic material (they can be remelted)or thermoset material (that cannot be remelted). Rubber is an older name forelastomers.Elastomeric polymers do not follow Hooks’s law (as most engineering material

do). The behavior of the elastomers is a bit more complex due to the molecularshape and the fact that small degree of viscous deformation in produced whenload is applied.

3.7.1. Rubber and Artificial Elastomers

The oldest commercial elastomer is natural rubber, which is made from a processessap of a tropical tree. Natural rubber (NR) is a biopolymer which is known aspolyisoprene. The rubber tree (Hevea brasiliensis) is the most common source ofnatural rubber used today. Polyisoprene can also be synthesized by polymerizationfrom its monomer isoprene (CH2=C(CH3)CH=CH2), (IR). This is a rare exampleof a natural polymer that we can make almost as well as nature does. Rubber hasbeen used for centuries by the South American Indians. They most probably werethe people who discovered that if latex (a milky fluid that circulates in the innerportions of the bark of many tropical and subtropical trees and shrubs) is dried,it can be pressed into useful objects such as bottles, shoes and balls. Figure 3.10shows the common use of rubber.However, it was not until the 1830s (when John Haskins and Edward Chaffee

organized the first rubber-goods factory in the United States) that the commer-cial rubber industry really began to flourish. But rubber had many weaknesses;it softened with heat and hardened with cold; it was tacky, odorous, and per-ishable. In 1834 the German chemist Friedrich Ludersdorf and the Americanchemist Nathaniel Hayward discovered that if they added sulfur to gum, thenrubber lessened or eliminated the stickiness of finished rubber goods. CharlesGoodyear discovered in 1839, that cooking natural rubber with sulfur removedthe gum’s unfavorable properties and could be strengthened by cross-linking itwith approximately 30% sulfer and heating it to a suitable temperature. Thisprocess is called vulcanization, and led to many and varied applications of nat-ural rubber, since the rubber then has got increased strength and elasticity andgreater resistance to changes in temperature. It is also impermeable to gases, andresistant to abrasion, chemical action, heat, and electricity, in addition to havehigh frictional resistance on dry surfaces and low frictional resistance on water-wetsurfaces. The vulcanization process remains fundamentally the same as it was in

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Figure 3.10: Common use of rubber.

1839.

Vulcanized rubber has numerous practical applications, such as

• excellent abrasion resistance which makes it valuable for the treads of vehicletires, conveyor belts (soft rubber), pump housings and piping used in thehandling of abrasive sludges (hard rubber).

• flexibility characteristics which makes it suitable for use in hoses, tires, androllers for a wide variety of devices ranging from domestic clothes wringersto printing presses.

• its elasticity makes it suitable for various kinds of shock absorbers and forspecialized machinery mountings designed to reduce vibration. Since it itsrelatively impermeable to gases its used as air hoses, balloons, balls, andcushions.

• resistance to water and to the action of most fluid chemicals has led to itsuse in rainwear, diving gear, and chemical and medicinal tubing, and as alining for storage tanks, processing equipment, and railroad tank cars.

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• high electrical resistance, soft rubber goods are used as insulation and forprotective gloves, shoes, and blankets. Hence, hard rubber is used for articlessuch as telephone housings, parts for radio sets, meters, and other electricalinstruments.

• coefficient of friction (resistance to movement) of vulcanized rubber, whichis high on dry surfaces and low on wet surfaces, leads to the use of rubberboth for power-transmission belting and for water-lubricated bearings indeep-well pumps.

• uncertainty of price and supply of natural rubber led to the developmentof artificial elastomers. Some artificial elastomers are inferior to naturalrubber, others have superior characteristics.

Rubber that has not undergone the vulcanization process has few practicaluses because of its poor heat resistance and high plasticity. It is used for cements,adhesive, insulating, friction tapes and for crepe rubber used in insulating blanketsand footwear.

Some other elastomers include:

Polybutadiene (BR): Polybutadiene was one of the first types of syntheticelastomer, or rubber, to be invented. It is very similar to natural rubber, poly-isoprene, and is good for uses which require exposure to low temperatures. Tirestreads are often made of polybutadiene copolymers. Belts, shoe soles, hoses, gas-kets and other automobile parts are made from polyubutadiene, because it standsup to cold temperatures better than other elastomers.

Polyisobutylene (PIB): Polyisobutylene is a synthetic rubber, or elastomer.It is the only rubber that is gas impermeable, (can hold air for long periods oftime). For instance, balloons will go flat after a few days because they are madeof polyisoprene, which is not gas impermeable. Since polyisobutylene will holdair, it is used to make things like the inner liner of tires, and the inner liners ofbasketballs.Polyisobutylene, sometimes called butyl rubber, is a vinyl polymer, and is very

similar to polyethylene and polypropylene in structure, except that every othercarbon is substituted with two methyl groups.

Poly(styrene-butadiene-styrene) (SBS) : Poly(styrene-butadiene-styrene),is a hard rubber, and is therefore used in soles of shoes, tire treads, and other places

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Figure 3.11: Poly(styrene-butadiene-styrene), or SBS.

where durability is important. It is a type of copolymer called a block copolymer.Its backbone chain is made up of three segments, where the first is a long chainof polystyrene, the middle a long chain of polybutadiene, and the last segment isanother long section of polystyrene, see Figure 3.11.Polystyrene is a tough hard plastic, which gives SBS its durability, while

polybutadiene is a rubbery material, and gives SBS its rubber-like properties.The material the ability to retain its shape after being stretched; SBS is a type ofunusual material called a thermoplastic elastomer.

Polyurethanes (AU or EU): (See also 3.4.2) Polyurethanes are the mostwell known polymers that are used to make foams. But, polyurethanes are morethan foam. Polyurethanes are the single most versatile family of polymers there is.Polyurethanes can be elastomers, and they can be paints. They can be fibers, andthey can be adhesives. You can find them everywhere. A well-known polyurethaneis spandex (DuPont sells it under the trade name Lycra). Lycra is a fiber thatacts like an elastomer, and allows us to make fabric that stretches for exerciseclothing and the like.

Polychloroprene (CR) : Polychloroprene is usually sold under the tradename Neoprene, and it is especially resistant to oil, and was the first syntheticelastomer that became a hit commercially. It was Arnold Collins, while work-ing under the same fellow who invented nylon, Wallace Carothers that inventedpolychloroprene.

Silicones (Q): (See also 3.4.2) Silicones can be used for a lot of things. Sili-cones are inorganic polymers, that is, there are no carbon atoms in the backbonechain. The backbone is a chain of alternating silicon and oxygen atoms. Eachsilicone has two groups attached to it, and these can be any organic groups. Sili-

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Figure 3.12: Biopolymers.

cones can stand high temperatures without decomposing, but they have very lowglass transition temperatures.

3.8. Biopolymers

Biopolymers are an alternative to petroleum-based polymers (traditional plastics)produced by living organisms. The field of biopolymers, is still in its early stage,but is growing in popularity every day. The term biopolymers is often used for allpolymers that are made from natural renewable resources and/or are completelybiodegradable. Biopolymers can be produced by biological systems like micro-organisms, plants and animals, or chemically synthesized from biological startingmaterials (e.g. sugars, starch, natural fats or oils, etc.). Most of the biopolymersare biodegradable, some of them are even water soluble, most of the biopolymersare compostable or will biodegrade in landfill, time can vary from a couple of daysto even years, but they will eventually degrade.Biopolymers can be used in all kinds of applications, and with all kinds of pro-

duction techniques, like injection moulding, thermoforming and blow moulding!Some biopolymers can directly replace synthetic plastics in traditional applica-tions, while others possess unique properties that may open new applications.

3.8.1. What makes a polymer a biopolymer?

Biopolymers are defined as biologically degradable polymers. Biopolymers arepolymers that are generated from renewable natural sources, are often biodegrad-

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able, and not toxic to produce. According to the American Society for Testing andMaterials (ASTM), biopolymers are degradable polymers in which degradationresults from the action of naturally occurring micro-organisms such as bacteria,fungi and algae.

3.8.2. Applications of biopolymers

Biopolymers can be used for a lot of applications, from packaging to disposables,from diapers to cottonsticks, from carparts to bottles, etc. In theory conventionalplastics may be substituted by biopolymers in many applications. In practice sub-stitution is not always feasible, wanted or the most lucrative way to use biopoly-mers. Besides technical development which is needed for some applications, theapplications have to be economically feasible within a reasonable term. The eco-nomic feasibility depends on the investments needed for material and productdevelopment and the added value of the biopolymer in the application.

3.8.3. Properties of biopolymers

Properties of biopolymers depend on the raw material they are based on, onadditives used and on the (chemical) modifications during production.

Different types of biopolymersStarch, proteins and peptides, and DNA and RNA are all examples of biopoly-

mers, in which the monomer units, respectively, are sugars, amino acids, and nu-cleic acids. Biopolymers found in and used by living cells can be divided into thefollowing four classes:

• Lipids (fats, oils, phospholipids waxes, and steroids)

• Carbohydrates (Starch, Cellulose, and Sugars as polysaccharides)

• Proteins (Protein is a polymer with the monomer made up of amino-acidresidues, and is contained in skin, bones, muscles, blood and hair )

• Nucleic acids (complex polymeric molecules which store and translate ge-netic information )

The most common way to divide biopolymers in different types is on thebasis of the raw material used for production. However, some biopolymers can

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be produced from different raw materials. Some examples of different types ofbiopolymers are:

Starch-based polymers (SBP) are often a blend of starch and other plas-tics (e.g PE), which allows for enhanced environmental properties. Starch is apolymeric carbohydrate (a polysaccharide), in which the monomers are glucoseunits joined to one anotherStarch is abundantly present in many crops. The starch is stored in granules

within the plant. This facilitates the isolation from the plant. Starch may bemodified in order to become a thermoplastic. This makes the starch polymersuitable for current processes in the plastics industry like: injection mouldingand extrusion. Thermoplastic starch has an affinity with moisture. The materialtherefore is not suitable for wet food packaging applications. Direct contact withwater only is possible for a short time. By acetylation a certain resistance towater may be achieved. By adding PCL the flexibility of the bioplastic increases.Starch polymer has good oxygen barrier properties. Starch polymers are the mostproduced and used biopolymers at the moment. Starch (in particular cornstarch)is used in cooking for thickening foods such as sauce. In industry, it is used in themanufacturing of adhesives, paper, textiles and as a mold in the manufacture ofsweets such as wine gums and jelly beans. It is a white powder, and dependingon the source, may be tasteless and odourless.

Cellulose polymers (cellulose esters, cellulose ethers, cellophane)Cellophane is one of the oldest packaging materials. Cellulose pulp from trees

or cotton may be used to produce cellophane. It is a relatively expensive packagingmaterial which can be used for a wide range of products such as cd’s, candy andcigarettes. The higher price is a reason why a large market share was lost topolypropylene. At the moment new applications in which the specific propertiesmay be used, are sought for. The material is transparent and has good foldingproperties. The foil has a high gas barrier and if a coating is applied may resistwater vapor as well.

Protein polymersThere is no information about protein polymers available yet, but see for in-

stance http://www.ppti.com/Technology/technology.htm.

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3.8.4. Additional information on raw materials in biopolymers

Lactic acid is produced by the microbial fermentation of sugars such as glu-cose or hexose. Feedstocks can include potato skins and corn. The lactic acidmonomers can be used to create low or high molecular weight polylactide poly-mers (PLA). PLA commodity polymers are being developed for use as pulpingadditives in paper manufacturing and as biodegradable packing materials, clothes,cups, packaging and many other everyday products.

Polylactic acid (PLA) is derived from lactic acid for which carbohydratesin sugar beets, potatoes, wheat, maize and milk are the source. Polylactic acidis a substance familiar to the human body, as we ourselves produce it by everymuscle contraction. It can be broken down by the body.PLA can be processed through for example injection moulding, foil blowing

and deep drawing. PLA may be applied as a coating. PLA is water resistant butcannot withstand high temperatures (>55◦C). In comparison to starch biopolymerthe degradation process is very slow. However, within a composting facility it canbe broken down in 3 to 4 weeks.

Polyhydroxyalkanoates (PHAs) (polyhydroxybutyrate (PHB), polyhydrox-ybutyrate/valerate (PHB/HV))PHA’s are generally derived through fermentation of glucose, sucrose of fatty

acids by micro-organisms.PHB can be processed through for example injection moulding and deep draw-

ing. It is an excellent material for the coating of paper coffee cups. The mostimportant features of PHB are the resistance to high temperatures up to 120◦Cand the resistance to water.

Chitin, a polysaccharide found in the exoskeletons of insects and shellfish,possesses many desirable characteristics. Chitin’s most important derivative, chi-tosan, is nearly a ”model” biopolymer with it’s useful physical and chemical prop-erties, high strength, biodegradability, and nontoxicity. In fact, chitosan bringsnew meaning to the word ”biodegradable” as the human body easily breaks itdown into simple carbohydrates, carbon dioxide, and water. This accounts forthe research that is trying to use chitosan in drug delivery systems.

Other natural Biopolymers:

ProteinProteins are biopolymers consisting of one or more strings of amino acid

residues joined head-to-tail via peptide bonds. Protein also makes up much of

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the structure of animals: collagen and keratin are components of skin, hair, andcartilage; and muscles are composed largely of proteins.

PeptidesPeptides are the family of molecules formed from the linking, in a defined

order, of various amino acids. Peptides differ from proteins, which are also longchains of amino acids, by virtue of their size. Traditionally, those peptide chainsthat are short enough to make synthetically from the constituent amino acids arecalled peptides rather than proteins. The dividing line is at approximately 50amino acids in length, since naturally-occurring proteins tend, at their smallest,to be hundreds of residues long.

DNADeoxyribonucleic acid (DNA) is the molecule in living things that contains

the coding information for creating proteins. It is also the molecule of heredity—whenever an organism reproduces, each offspring gets a copy of its parents’ DNA.

RNARibonucleic acid, a nucleic acid structurally distinguished from DNA by the

presence of an additional hydroxyl group attached to each pentose ring, and func-tionally distinguished by its multiple roles in the intracellular transmission ofgenetic information from the site of transcription (from DNA) to the site of trans-lation (into protein).

3.8.5. Plastic taste better with sugar

Chemists in India are lacing plastics with sugar to make them palatable to soilbacteria. The plastics, which normally survive for decades in landfills, start tobiodegrade within days.The tweaked plastics are polythene, polystyrene and polypropylene. These

make up around a fifth of urban waste by volume. Bottles, bags and sacks aremade of polyethylene, food packaging is made of polypropylene, and drinkingcups, fast-food cartons and the hard casing of electronic equipment are fashionedfrom polystyrene.Digambar Gokhale and colleagues at the National Chemical Laboratory in

Pune mix the styrene subunits of polystyrene with small amounts of anothersubstance that provides a chemical hook for sucrose or glucose pieces. They thenadd sugars to the styrene chains like pendants on a necklace.

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Figure 3.13: One fifth of urban rubbish is plastics like polystyrene. c° GettyImages

By weight, less than 3% of the final polymer is sugar, so the material is moreor less the same. But bacteria such as Pseudomonas and Bacillus break open thechains when they chomp on these sugary snacks, kicking off decay.It remains to be seen whether the polymer biodegrades into entirely non-toxic

substances. Fully broken down, the end products are carbon dioxide and water.But along the way, all sorts of other compounds are produced, such as organicacids and aldehydes.Indeed, it is not yet clear how far, or how quickly, the plastic will break down

in the real world. And adding the sugar would require significant manufacturingchanges, which could be costly.Other additives that make polythene, polystyrene and polypropylene biodegrad-

able have been toxic and can leach out of garbage. Another approach is to initiatethe breakdown process using heat, ultraviolet light or exposure to oxygen, butthis is cumbersome and expensive.Published in: Nature News Service, 2.december 2002; see alsohttp://www.nature.com/nsu/021125/021125-12.html.

References:

Polymers:http://www-materials.eng.cam.ac.uk/mpsite/http://www.plasticsusa.com/http://www.polymer-age.co.uk/directry/plastic.htmhttp://www.mse.cornell.edu/courses/engri111/http://www.amco.ws/home.asp

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http://naturalrubber.cjb.net/http://www3.jaring.my/inro/http://www.phy.uni-bayreuth.de/theo/tp3/members/elast.htmhttp://www.psrc.usm.edu/macrog/crystal.htmhttp://www.uvi.edu/Physics/SCI3xxWeb/Structure/Polymerization.htmlhttp://www.zeusinc.com/http://islnotes.cps.msu.edu/trp/toc.htmlhttp://abalone.cwru.edu/tutorial/enhanced/files/textbook.htmhttp://www.thermosets.com/thermosets.htmlhttp://www.aipma.org/t&ti/thermos.htmhttp://www.polymer-age.co.uk/techlink.htmhttp://en.wikipedia.org/wiki/Glass_transition_temperaturehttp://en.wikipedia.org/wiki/Polymer#Polymer_science

Elastomers:http://www.psrc.usm.edu/macrog/elas.htm

Biopolymers:http://www.biopolymer.net/http://www.biopolymer.com/http://www.biotec.dehttp://www-classes.usc.edu/engr/ms/125/MDA125/biopolymers/http://online.itp.ucsb.edu/online/infobio01/lancet2/http://www.cheresources.com/biopoly2zz.shtmlhttp://www.proterra.nl/norms.htmlhttp://www.dblab.helsinki.fi/~rtuma/biopolymers.htmhttp://www.wikipedia.org/wiki/Biopolymerhttp://www.brooklyn.cuny.edu/bc/ahp/SDPS/PSLectNotes/SD.PS.LectP2.htmlhttp://www.bipp.nl/about_3.htmlhttp://www.forskning.no/Artikler/2002/desember/1038997297.18http://www.nature.com/nsu/021125/021125-12.htmlhttp://www.ppti.com/Technology/technology.htm

Galgali, P., Varma, A. J., Puntambekar, U. S. & Gokhale, D. V. Towards biodegradablepolyolefins: strategy of anchoring minute quantities of monosaccharides and dis-accharides onto functionalized polystyrene, and their effect on facilitating polymerbiodegradation. Chemical Communications, 2002, 2884 - 2885, (2002).

Questions• Explain the expression thermosetting and thermoplastic.

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• What is the glass transition temperature?• What is the difference between an amorphous and crystalline plastic?• What happens to a thermoplastic when it is cooled down below melting tem-perature?• How do thermosetting polymers respond to subsequent heating?• What is the difference between a saturated and an unsaturated molecule?• Describe the two different processes of forming polymers: addition and conden-sation.• What are some attractive engineering properties of plastics, and in what areado they fall?• What are some reasons that additive agents are incorporated into plastics?• What kind of additive agents are there, and what are their objective?• What is the primary engineering benefit of an oriented plastic?• What is the unique mechanical property of elastomeric materials?• What is vulcanization?• What is rubber?• What is a SPI code, and what is it good for?• What groups of SPI codes are there?• What is a biopolymer?• What kind of different biopolymers exist?• What products can be made from biopolymers?

Polymers can be described as being thermosetting or thermoplastica. Why are the thermosetting polymers so different from thermoplastic polymers?b. What decides if a polymer will be thermosetting or thermoplastic?c. What are three important, common thermosetting polymers?d. What are three important, common thermoplastic polymers?

Polymers can be described as being amorphous or crystalline polymersa. Compare the physical and chemical properties of amorphous and crystallinepolymers.b. What are three important amorphous polymers?c. What are three important crystalline polymers?d. How does light penetration qualities depend on the degree of crystallization?

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4. Composites

Composite materials are materials that combine two or more materials (a selectedfiller or reinforcing elements and compatible matrix binder) that have quite differ-ent properties that when combined offer properties which are more desirable thanthe properties of the individual materials . The different materials work togetherto give the composite unique properties, but within the composite you can easilysee the different materials, they do not dissolve or blend into each other.The key characteristic of composites is the

• Specific strength (the strength to weight ratio σ/ρ)

• Specific stiffness or specific modulus (the stiffness-to-weight ratio E/ρ)

• Tailored material ( since composites are composed of 2 or more ”phases”,they can be formulated to meet the needs of a specific application withconsiderable ease)

Composites are not a single material but a family of materials whose stiffness,strength, density, and thermal and electrical properties can be tailored. Thematrix, the reinforcement material, the volume and shape of the reinforcement,the location of the reinforcement, and the fabrication method etc. can all bevaried to achieve required properties.

Composite applicationsSpecific composite applications are detailed in each market category:• Transportation• Electrical/Electronics• Building Construction• Infrastructure• Aerospace/Defense• Consumer/Recreation• Medical Products• Sport equipment

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4.1. The history of composites

The theory behind the construction of composite materials comes from the needto create a strong stiff and light material.Materials such as glass, carbon and Kevlar have extremely high tensile and

compressive strength, but in solid form, many random surface flaws present in suchmaterials, cause them to crack and fail at a much lower stress that it theoreticallyshould.To overcome this problem, the material is produced in a fibre form, although

the flaws will occur at the same frequency, the flaws will be reduced to a smallnumber of fibres at any one point, and the remaining ones will carry the load withthe materials theoretical strength. To prevent flaws occurring from abrasion onthe surface of the material, or from existing flaws transferring to other fibres, it isnecessary to isolate the fibres. This is why a resin matrix system is used.Another well-known composite is concrete. Here, aggregate (small stones or

gravel) is bound together by cement. Concrete has good strength under compres-sion, and it can be made stronger under tension by adding metal rods, wires, meshor cables to the composite (so creating reinforced concrete).Most composites are made up of just two materials. One material (the matrix

or binder) surrounds and binds together a cluster of fibres or fragments of a muchstronger material (the reinforcement). There are both natural and man-madecomposites.

4.2. Natural composites

Composites exist in nature.A piece of wood is a composite, see Figure 4.1, with long fibres of cellulose

(a very complex form of starch) held together by a much weaker substance calledlignin. Cellulose is also found in cotton and linen, but it is the binding power ofthe lignin that makes a piece of timber much stronger than a bundle of cottonfibres. Other examples of natural composites are:

Spider silkSpider silk is a biopolymer fibre and a natural composite material, see Figure

4.2.Its composition is a mix of an amorphous polymer (which makes the fibre

elastic), and the two simplest proteins (which give it toughness), in other words,it is simply a protein. The result is a good combination of strength and toughness.

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Figure 4.1: The cell-structure of a natural composite, a tree.

It is five times as strong as steel, twice as strong as Kevlar at same weight,twice as elastic as polyamide fibres (it can be stretched by 31% without breaking),more elastic than aramid fibre, finer than a human hair, and lighter than cotton.Promises are: bulletproof vests, parachute cords, bridge suspension cables,

wear-resistant shoes and clothing, seat belts, rustfree bumpers for automobiles,artificial tendons and ligaments, etc.Spider silk is produced either by spider or (in the future) by bacteria or plants,

therefore in an environment-friendly way. It is an environment-friendly biopolymerand is easy to recycle. Spider silk does not decompose like other proteins by fungi,or bacteria because they contain substances that makes it durable.The thread of the garden spider (Araneus) would have to be 80 km long before

it would snap under its own weight. When synthesis of spider silk in bacteria orplants becomes efficient, spider silk will have a commercial relevance.

Human hair, bone and muscles are also natural composites. These kind ofstructures are also called hierarchical structures since they have structures inmany levels, see also chapter 9.4.

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Figure 4.2: Spidersilk.

4.3. Man-made Composites

Humans have been using composite materials for thousands of years. Take mudbricks for example. A cake of dried mud is easy to break by bending, which putsa tension force on one edge, but makes a good strong wall, where all the forcesare compressive. A piece of straw, on the other hand, has a lot of strength whenyou try to stretch it but almost none when you crumple it up. But if you embedpieces of straw in a block of mud and let it dry hard, the resulting mud brickresists both squeezing and tearing and makes an excellent building material. Putmore technically, it has both good compressive strength and good tensile strength.In the case of mud bricks, the two roles are taken by the mud and the straw; inconcrete, by the cement and the aggregate; in a piece of wood, by the celluloseand the lignin. In fiberglass, the reinforcement is provided by fine threads or fibresof glass, often woven into a sort of cloth, and the matrix is a plastic.Composite materials are composed of a matrix material reinforced with any of

a variety of fibers made from ceramics, metals, or polymers. The reinforcing fibersare the primary load carriers of the material, with the matrix component trans-ferring the load from fiber to fiber. Reinforcement of the matrix material may beachieved in a variety of ways. Fibers may be either continuous or discontinuous,see Figure 4.3. Reinforcement may also be in the form of particles. The matrixmaterial is usually one of the many available engineering plastics/polymers. Selec-tion of the optimal reinforcement form and material is dependent on the propertyrequirements of the finished part.

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Figure 4.3: Composite materials with different types of reinforcements.

The threads of glass in fiberglass are very strong under tension but they arealso brittle and will snap if bent sharply. The matrix not only holds the fibrestogether, it also protects them from damage by sharing any stress among them.The matrix is soft enough to be shaped with tools, and can be softened by suitablesolvents to allow repairs to be made. Any deformation of a sheet of fiberglassnecessarily stretches some of the glass fibres, and they are able to resist this, soeven a thin sheet is very strong. It is also quite light, which is an advantage inmany applications.Over recent decades many new composites have been developed, some with

very valuable properties. By carefully choosing the reinforcement, the matrix,and the manufacturing process that brings them together, engineers can tailorthe properties to meet specific requirements. They can, for example, make thecomposite sheet very strong in one direction by aligning the fibres that way, butweaker in another direction where strength is not so important. They can alsoselect properties such as resistance to heat, chemicals, and weathering by choosingan appropriate matrix material.

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4.3.1. Fiber-Reinforced Composites

Fiber Reinforced Plastics (FRP) is a general term for composite materials or partsthat consist of a resin matrix that contains reinforcing fibers such as glass or fiberand have greater strength or stiffness than the resin. FRP is most often used todenote glass fiber-reinforced plastics.Reinforcing fibers can be made of metals, ceramics, glasses, or polymers that

have been turned into graphite and known as carbon fibers.Fibers increase the modulus of the matrix material. The strong covalent bonds

along the fiber’s length gives them a very high modulus in this direction becauseto break or extend the fiber the bonds must also be broken or moved. Fibers aredifficult to process into composites, making fiber-reinforced composites relativelyexpensive.Fiber-reinforced composites are used in some of the most advanced, and there-

fore most expensive, sports equipment, such as a time-trial racing bicycle framewhich consists of carbon fibers in a thermoset polymer matrix. Body parts ofrace cars and some automobiles are composites made of glass fibers (fiberglass) orcarbon fibers in a thermoset matrix.On the basis of stiffness and strength alone, fibre reinforced composite ma-

terials do not have a clear advantage particularly when it is noted that theirelongation to fracture is much more lower than metals with comparable strength.The advantage of composite materials appear when the modulus per unit weight(specific modulus) and strength per unit weight (specific strength) are considered.The higher specific weight and high specific strength of the composite materialsmeans that the components weight can be reduced.Although glass fibres are by far the most common reinforcement, many ad-

vanced composites now use fine fibres of pure carbon. Carbon fibres are muchstronger than glass fibres, but are also more expensive to produce. Carbon fibrecomposites are light as well as strong. They are used in aircraft structures and insporting goods (such as golf clubs), and increasingly are used instead of metals torepair or replace damaged bones. Even stronger (and more costly) than carbonfibres are threads of boron.

4.3.2. Classification of composites

Many terms have been used to define FRP composites. Modifiers have been usedto identify a specific fiber such as Glass Fiber Reinforced Polymer (GFRP), Car-bon Fiber Reinforced Polymer (CFRP), and Aramid Fiber Reinforced Polymer

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(AFRP). Another familiar term used is Fiber Reinforced Plastics. In addition,other acronyms were developed over the years and its use depended on geograph-ical location or market use. For example, Fiber Reinforced Composites (FRC),Glass Reinforced Plastics (GRP), and Polymer Matrix Composites (PMC) canbe found in many references. Although different, each of before mentioned termsmean the same thing; FRP composites.There are many ways of classifying composite materials. For instance, we can

classify the microcomposite materials based on the size, shape and distribution ofthe different phases in the composite for instance like this:

• Continuous fibres in matrix: aligned, random• Short fibres in matrix: aligned, random• Particulates (spheres, plates, ellipsoids, irregular, hollow or solid) in matrix• Dispersion strengthened, as for the point above, but the particle size <

10−8m• Lamellar structures (used in laminates)• Skeletal or interpenetrating networks• Multicomponent, fibres, particles etc.

Clearly, the distinction between the different groups is not always a sharp one.

Nanocomposites are composites on nanoscale (10−9 meter). They have con-stituents that are mixed on a nanometer-length scale.

Mostly, we classify composites according to their matrix phase. The role of thematrix is to act as a medium to keep the fibers properly oriented and to protectthem from the environment. There are ceramic matrix composites (CMC’s), metalmatrix composites (MMC’s), and polymer matrix composites (PMC’s). Materialswithin these categories are often called ”advanced” if they combine the propertiesof high strength and high stiffness, low weight, corrosion resistance, and in somecases special electrical properties. This combination of properties makes advancedcomposites very attractive for aircraft and aerospace structural parts.

4.4. Ceramic matrix composites CMC

Monolithic ceramics have the disadvantage of being brittle, see Figure 4.4 from:www.ms.ornl.gov/programs/ energyeff/cfcc/iof/chap24-6.pdf.A reinforcing phase can improve the toughness of these materials, while still

taking advantage of the matrix’s other properties such as wear resistance, hard-ness, corrosion resistance, and temperature resistance. A wide range of ceramic

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Figure 4.4: Failure modes for monolithic ceramic and CFCCs.

matrix composites (CMCs) have thus been developed that combine a matrix mate-rial with a reinforcing phase of different composition (such as alumina and siliconcarbide) or the same composition (alumina/alumina or silicon carbide/silicon car-bide).

Figure 4.5 compares the approximate service temperature ranges of some im-portant polymers, metals and ceramics.The CMC market is divided into two classes; the oxide and non-oxide mate-

rials. Some of the more common oxide matrices include alumina, silica, mullite,barium aluminosilicate, lithium aluninosilicate and calcium aluminosilicate. Ox-ide matrices are often more mature and environmentally stable, but non-oxideceramics have more superior structural properties and hardness are rapidly enter-ing the marketplace. Examples of non-oxide ceramics are silicone carbide (SiC),silicone nitride (Si3N4), boron carbide (B4C) and aluminium nitride (AlN).The oxide CMCs often consist of oxide fibers (for instance alumina Al2O3),

while the non-oxide CMCs consist of non-oxide fibers (for instance SiC) (see alsoChapter 4.7 for more information concerning fibers). Non-oxide CMCs are moreadvanced than oxide CMCs since they have higher thermal conductivity, lower

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Figure 4.5: Service temperature ranges of some important polymers, metals and ce-ramics.

thermal expansion and are more stable at high temperatures than oxide CMCs.The non-oxide CMCs are used in thermally loaded components (combustor liners,vanes, blades and heat exchangers). The oxide CMCs have good oxidation resis-tance, alkali corrosion resistance, low dielectric constants and potentially low cost,and are therefore used for hot gas filters, exhaust components of aircraft engines,and in long-life, lower temperature components.

The reinforcements of CMCs can include carbides, borides and oxides. Specificexamples of reinforcements include carbon, silicon carbide, titanium diboride,silicon nitride and alumina. Some of the more common ceramic discontinuousreinforcement include whiskers, platelets, and particulates having compositions ofSi3N4, SiC, AlN, titanium dibori, boron carbide, and boron nitride.

Ceramics and CMCs can also result in fuel efficiency in heat engines because ofhigher operating temperatures, and reduction or elimination of cooling systems.The temperature requirement in such applications is not as high as in aerospacematerials applications. Other applications of CMCs include wear parts, such asseals, nozzles, pads, liners, grinding wheels, brakes, etc. For instance, carbon fiberreinforced carbon composites are being used in aircraft brakes.

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4.5. Metal Matrix Composites MMC

Metal Matrix Composites (MMC’s) are increasingly found in the automotive in-dustry. They consist of a metal such as aluminium as the matrix, and a reinforce-ment that could be continuos fibres such as silicon carbide, graphite or alumina,wires such as tungsten, beryllium, titanium and molybdenium, and discontinuousmaterials. Metals containing ceramic particles, whiskers or (short or long) fibersare also gaining importance. MMC are said to be materials for the demands ofthe future.When the demands for high thermal conductivity, reduced weight, heat dissi-

pation, and high strength are factors for design, MMCs represent the Next Genera-tion of solutions for today’s electronic requirements. Metal-matrix composites areeither in use or prototyping for the Space Shuttle, commercial airliners, electronicsubstrates, bicycles, automobiles, golf clubs, and a variety of other applications.While the vast majority are aluminum matrix composites, a growing number ofapplications require the matrix properties of superalloys, titanium, copper, mag-nesium, or iron.Regardless of the variations, however, aluminum composites offer the advan-

tage of low cost over most other MMCs. In addition, they offer excellent thermalconductivity, high shear strength, excellent abrasion resistance, high-temperatureoperation, nonflammability, minimal attack by fuels and solvents, and the abilityto be formed and treated on conventional equipment. Aluminum MMCs are ap-plied in brake rotors, pistons, and other automotive components, as well as golfclubs, bicycles, machinery components, electronic substrates, extruded angles andchannels, and a wide variety of other structural and electronic applications.

Compared to monolithic metals, MMCs have:• Higher strength-to-density ratios• Higher stiffness-to-density ratios• Better fatigue resistance• Better elevated temperature properties: -Higher strength

-Lower creep rate• Lower coefficients of thermal expansion• Better wear resistance

The advantages of MMCs over polymer matrix composites (PMCs) are:

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• Higher temperature capability• Fire resistance• Higher transverse stiffness and strength• No moisture absorption• Higher electrical and thermal conductivities• Better radiation resistance• No outgassing• Fabricability of whisker and particulate-reinforced MMCs with conventional metalworking equipment

Some of the disadvantages of MMCs compared to monolithic metals and poly-mer matrix composites are:

• Higher cost of some material systems• Relatively immature technology• Complex fabrication methods for fiber-reinforced systems (except for casting)• Limited service experience

4.6. Polymer Matrix Composites PMC

Polymer Matrix Composites (PMC’s) are the most common composites, and arealso known as FRP - Fibre Reinforced Polymers (or Plastics). These materials usea polymer-based resin as the matrix, and a variety of fibres such as glass, carbonand aramid as the reinforcement. Matrix materials are either thermosetting orthermoplastic polymers. Reinforcing fibers are either continuous or chopped. Ingeneral, polymer composites processing includes contracting of polymer and fibers,shaping, controlled heating and/or reactions, and cooling. The technology ofpolymer composites has been driven to a large extent by aerospace and militaryapplications.

Advantages of Polymer CompositesPolymer composites make the largest and most diverse use of composites due

to ease of fabrication, low cost and good properties. Also, they have:• High specific strength properties (20-40% weight savings)• Ability to fabricate directional mechanical properties• Outstanding corrosion resistance• Excellent Fatigue and fracture resistance• Lower tooling cost alternatives• Lower thermal expansion properties

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Figure 4.6:

• Simplification of manufacturing by parts integration• Potential for rapid process cycles• Ability to meet stringent dimensional stability requirementsGlass-fiber reinforced composites (GFRC) are strong, corrosion resistant and

lightweight, but not very stiff and cannot be used at high temperatures. Applica-tions include auto and boat bodies, aircraft components.Carbon-fiber reinforced composites (CFRC) use carbon fibers, which have the

highest specific module (module divided by weight). CFRC are strong, inert,allow high temperature use. Applications include fishing rods, golf clubs, aircraftcomponents.

4.7. Fiber reinforcement

Fibers (see [14]) are pliable hair-like substances, built up by long chains of basicmolecules. Fibres are very small in diameter in relation to their length. Longcontinuous strands of fibers are called filaments. The only natural filament fibreis silk from butterflies or spiders. Fibre’s properties depend strongly on boththe external and internal fibre structure as well as the chemical composition.Properties therefore vary significantly. Crystalline areas give tensile strength,stiffness and stability, while amorphous areas are weaker but more movable.The fibers can be individual strands as thin as a human hair or they can be

multiple fibers braided in the form of a yarn (or tow).

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4.7.1. Choosing fibers

The fibers in advanced composites are usually non-metallic in nature, consistingof such materials as glass, carbon, silicon carbide, alumina, boron or Kevlar.Other fibers such as spectra and quartz are also available, but these are usuallyreserved for specialized application. The table below shows some advantages anddisadvantages of some fibertypes, while Figure 4.7 shows some properties of somefibers.

Fiber Advantages DisadvantagesE-, S-Glass - High strength - Low stiffness

- Low cost - Short fatigue life- High temp sensitivity

Aramid (Kevlar) - High tensile strength - Low comp. strength- Low density - High moisture absorp.

Boron - High stiffness - High cost- High comp. strength

Carbon (AS4, T300) - High strength - Moderate cost- High stiffness

Graphite (pitch) - Very high stiffness - Low strength- High cost

Ceramic (silicon - High stiffness - Low strengthcarbide, alumina) - High use temp - High cost

Figure 4.8 shows a plot of specific strength vs. specific stiffness of some fibers.

High-strength fibers utilized in high-performance composites include carbon,glass, aramid, ultrahigh molecular-weight polyethylene (PE), boron, quartz, ce-ramic and hybrid combinations. Continuous bundles (tow or roving) are the basicfiber forms for high-performance composite applications. These forms may be useddirectly in processes such as filament winding or pultrusion or may be convertedinto tape, fabric and other forms.In high-performance composites, the structural properties of the finished part

are derived primarily from the fiber. A fiber-to-matrix ratio of 60:40 or higheris common for both thermoset- and thermoplastic-matrix composites. Desirableproperties are not achieved, however, without effective adhesion between fiber andmatrix, which requires sufficient saturation with resin (wetout) at the fiber-matrix

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Figure 4.7: Properties of some fibers.

Figure 4.8: Specific strength vs. specific stiffness of some fibers.

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interface. Attention to fiber surface preparation, such as use of a surface finishor coupling agent and selection of a compatible fiber and matrix combination,ensures good adhesion.We will have a closer look at some types of fibers.

4.7.2. Glass fibers

Glass fibers (GF) are the most widely used reinforcement for plastic and rubberproducts, and are also the finest (smallest diameter) of all fibers, typically 1 to 4microns in diameter. Glass fibers, see Figure 4.9, are made of silicon oxide withaddition of small amounts of other oxides. Glass fibers are characteristic for theirhigh strength, good temperature and corrosion resistance, and low price. Over90% in the composite industry is glass fibers. Properties of glass fibers are bound

Figure 4.9: Glass fiber.

to the chemical composition of the mixture, but they are also influenced by thespinning way. Usually, they are divided into:

Use Type of glassMultipurpose fibers glass EAcid resistant fibers glass A, C, CRAlkali resistant fibers glass R, SHigh strength fibers glass R, SFibers with good dielectric properties glass D

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The two types of glass fibers that are most common are the E-glass and S-glass. The first type is the most used, and takes its name from its good electricalproperties (no electrical interference in thunderstorms, and no sparks). The secondtype is very strong (S-glass), stiff, and temperature resistant. They are used asreinforcing materials in many sectors, e.g. automotive and naval industries, sportequipment. S-glass are used for instance in aircraft flooring, helicopter blades etc.Some properties for E- and S- glass are listed in the following table:

E-glass S-glass- softens at ≈850◦C - softens at ≈1000◦C- most inexpensive fiber ≈ 30% stronger than E-glass- most commonly used fiber today ≈ 15% stiffer than E-glass- insulators and capacitors ≈ 3 times as expensive as E-glass

- high quality glass fiber- high technical purposes

The most widely used composite material is fiberglass in polyester resin, whichis commonly referred to as just fiberglass. Fiberglass is light weight, corrosionresistant, economical, easily processed, has good mechanical properties, and hasover 50 years of history. It is the dominant material in industries such as boatbuilding and corrosion equipment, and it plays a major role in industries such asautomotive, medical, recreational, and industrial equipment.

Quartz fibers Quartz fibers (SiO2) are very high silica version of glass withmuch higher mechanical properties and excellent resistance to high temperaturesand can be used continuously to 1048.9

◦C and for short-temperature applications,

even to 1248,9◦C. They are more expensive than E-glass and S-glass, provide

significantly better electromagnetic properties than glass, making them a goodchoice for parts such as aircraft radomes.

4.7.3. Carbon fibers

Carbon fibers (CF) appeared on the market in 1960 and are produced of organicfibers (rayon, acrylics etc.) or from remaining of petroleum or tar distillation.

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Figure 4.10: Carbon fibre.

Carbon fibers, see Figure 4.10, are the stiffest and strongest reinforcing fibres forpolymer composites, the most used after glass fibres. Made of pure carbon inform of graphite, they have low density and a negative coefficient of longitudi-nal thermal expansion. Carbon fibres are very expensive and can give galvaniccorrosion in contact with metals. They are generally used together with epoxy,where high strength and stiffness are required, i.e. race cars, automotive and spaceapplications, sport equipment.

4.7.4. Boron fiber

Boron (BF) is a metal known for its exceptional resistance and form. BF is fivetimes as strong and twice as stiff as steel. Boron provides strength, stiffness,light weight and excellent compressive properties, as well as buckling resistance.Use of boron composites ranges from sporting goods, such as fishing rods, golfclub shafts, skis and bicycle frames, to aerospace applications such as aircraftempennage skins, space shuttle truss members and prefabricated aircraft repairpatches. It has a melting point at 2180

◦C.

4.7.5. Ceramic fibers

Ceramic fibers (CEF) are mostly used as refractory fibers in uses over 1000◦C andare characterized by a polycrystalline structure rather than amorphous. Someof the more common ceramic continuous reinforcements include silica, mullite,

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alumina, carbon, zirconia, and silicon carbide in addition. The more sophisticatedkinds of fibers, have a basis of borate, carbide, silicon nitrure and borate nitrure.They are very expensive fibers because only a small quantity is produced, andthey are used in particular fields such as aerospace.Ceramic fibers offer high to very high temperature resistance but poor im-

pact resistance and relatively poor room-temperature properties. They are oftendivided into the following two groups:* Non-oxide fibers can be such as Siliconcarbide (SiC), boron nitride (BN),

silicon nitride (SiN), aluminium nitride (AlN) and multiphase fibers consisting ofsilicon, carbon, boron, nitride, titanium, (Si-C-B-N-Ti).*Oxide fibers can be such as aluminium oxide (Al2O3), alumina zirconia mix-

tures (Al2O3+Zr2O2), yttria-alumina-garnet (YAG), and mullite (3Al2O3-2SiO2).Ceramic fibers of pure Al2O3 in a single crystalline microstructure are called sap-phire fibers.

4.7.6. Polymer Fibers

Aramid fiber (Kevlar)Aramids are a family of nylons, including Nomex R° and Kevlar R° ( Polyamide

-PA). Aramid fibers, see Figure 4.11 are known for their large hardness and resis-tance to penetration. Thanks to their toughness aramid fibres are used where high

Figure 4.11: Aramid fibre.

impenetrability is required, e.g. bulletproof vests, bike tires, airplanes wings, andsport equipment. These fibres are not as spread as glass or carbon fibres, mostlybecause of their cost, high water absorption, and their difficult post-processing.

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(References: DuPont (Kevlar R°) Fibers of KEVLAR R° consist of long molec-ular chains produced from poly-paraphenylene terephthalamide). PPTA is theacronym for para-phenylen-terephthalamid.Polymers are not only used for the matrix, they also make a good reinforcement

material in composites. For example, Kevlar is a polymer fibre that is immenselystrong and adds toughness to a composite. It is used as the reinforcement incomposite products that require lightweight and reliable construction (e.g., struc-tural body parts of an aircraft). Composite materials were not the original usefor Kevlar; it was developed to replace steel in radial tires and is now used inbulletproof vests and helmets. Kevlar, and aramid-fiber composite can be usedas textile fibers. Applications include bullet-proof vests, tires, brake and clutchlinings. Servicetemperature of Aramid fibre is up to 250

◦C, and its melting tem-

perature is 426.7◦C.

UHMW-PE - Ultra-high molecular weight polyethyleneUHMW, see Figure 4.12, is a polymer material composed of long chains with

Figure 4.12: UHMW.

a very high molecular weight. It even replaced Kevlar R° for making bullet-proofvests! UHMW-PE combines the traditional abrasion and cut resistance of metalalloys with the impact and corrosion resistance of synthetic materials. Tough asa metal, self-lubricating and slippery. UHMW-PE fibres have the tendency toelongate under load (creep). They are extremely low density, and they can float.Melting-point between 120

◦and 150

◦C. Applications are being developed partic-

ularly in the areas of ballistic protection and ropes. The material is inflammable.These fibres have a tensile strength 20 times greater than that of steel, and

40% stronger than aramid. Their free breaking length is around 330 km (steelbreaks at 25, glass at 135, carbon at 195 and aramid at 235).

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Figure 4.13: Liquid crystal polymer.

Products: Bullet-proof vest, Cut-resistant gloves, Psychiatric clothing.

LCP - Liquid crystal polymerLCP, see Figure 4.13 is a thermoplastic fibre with exceptional strength and

rigidity (five times that of steel), and about 15 times the fatigue resistance ofaramid. Very good impact resistance. It doesn’t absorb moisture, has very lowstretch, it doesn’t creep like UHMW-PE fibre, and has excellent abrasion, wear,and chemical resistance. Its high melting-point (320

◦C) allows the retention of

these properties over broad ranges of temperatures. It is suitable for industrial,electronic, and aerospace applications, as well as for ropes, and sport equipment.Products: Fishing line, High performance rope, Tennis racket.

4.7.7. Carbon nanotube (CNT) fibers

Strong and versatile carbon nanotubes are finding new applications in improvingconventional polymer-based fibers and films. For example, composite fibers madefrom single-walled carbon nanotubes (SWNTs) and polyacrylonitrile, a carbonfiber precursor, are stronger, stiffer and shrink less than standard fibers.Nanotube-reinforced composites could ultimately provide the foundation for a

new class of strong and lightweight fibers with properties such as electrical andthermal conductivity unavailable in current textile fibers

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Figure 4.14: Spidersilk.

4.7.8. Fiber hybrids

Fiber hybrids capitalize on the best properties of various fiber types, while re-ducing raw material costs. Hybrid composites combining carbon/aramid andcarbon/glass fibers have been used successfully in ribbed aircraft engine thrustreversers, telescope mirrors, drive shafts for ground transportation and infrastruc-ture column-wrapping systems. For example, in hybrid-fiber flywheels for electricvehicles, the composite components withstand energy forces as high as 2.5 millionft-lb.

4.7.9. Spider silk

Spider silk is a biopolymer fiber and a natural composite, see Figure 4.14 andchapter 4.2. It is 5 times as strong as steel and 2 times as strong as Kevlar.Man-made spider silk has now become a reality. "Spider-goats," ( goats that

are created having one spider gene added to the 70,000 genes that make a goat agoat) for example, produce an extra protein in their milk that can be spun intoman-made spider silk. Spider silk is stronger, by weight, than anything else onearth. The hope was to spin silk from milk - and use the ultra-light material forthings like bulletproof vests. It turns out that it takes a lot of goat milk to makejust a small bit of silk, so for now the idea of making bulletproof vests out ofspider silk has been put aside. Other uses of the material, medical sutures, forexample are in progress instead.

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Figure 4.15: Crayons on Aerogel over a flame.

4.8. Aerogel composites

Aerogel is 99.8% air, and provides 39 times more insulating than the best fiberglassinsulation, and is 1,000 times less dense than glass, see Figure 4.15 http://stardust.jpl.nasa.gov/tech/aerogel.html where the picturecan be found. A cube of 1x1x1 meter of aero-gel will only weight three kg. It can also be exposed to temperatures up to 1400◦Cbefore it will soften.Aerogel is not like conventional foams, but is a special porous material with

extreme microporosity on a micron scale. It is composed of individual featuresonly a few nanometers in size. These are linked in a highly porous dendritic-likestructure.This exotic substance has many unusual properties, such as low thermal con-

ductivity, refractive index and sound speed - in addition to its exceptional abilityto capture fast moving dust. Aerogel is made by high temperature and pressure-critical-point drying of a gel composed of colloidal silica structural units filled withsolvents.Silica aerogel is just another form of glass. If aerogel is handled roughly, it will

break just like glass. However, if care is taken, the material can be handled andshaped effectively.Silica aerogels are inorganic solids, very brittle and usually very low density

materials. A collapse of the solid network in the material occurs gradually, spread-ing the force of impact out over a longer time, and is why they can be very usefulas energy absorbing materials.Aerogels can be added different materials/particles in order to obtain special

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effect of the materials. For instance can we add metal salts, or other compoundsto a sol before gelation. Then we may obtain a deep blue aerogel by adding nickel;while a pale green color appears by adding copper; a black gel contains carbonand iron; and orange aerogel is added iron oxide. It is also possible to obtain amagnetic aerogel by using chemical vapor infiltration to get iron oxide introducedin the material. The aerogel can also be made photoluminescent, which meansthat it glows-in-the-dark by using a pigment that absorbs light and emits thatenergy over a period of time -even after the light source has been removed. Thepigment is rechargeable.

Flexible aerogelsIn the mid to late 1990’s, Aspen Systems perfected proprietary changes in

the formulation, processing and drying of aerogels, reducing drying time to a fewhours. Besides a cost effective drying time, the aerogels were also isolated in theform of thin, flexible blankets. The blankets were much more robust than themonoliths and beads, and could also be easily installed like any other flexible bat-ting. These breakthroughs led to the formation of Aspen Aerogels, Inc. in 2001,and the commercialization of aerogel technology for broad use, see for instancethe Figure 4.16Aspen Aerogels has created a variety of organic and inorganic/organic hy-

brid aerogel formulations including those made from polydimethylsiloxane/silica,cellulose polyurethane, polyimide, polymethylmethacrylate/silica, and polybuta-diene rubber. These materials show enhanced physical and mechanical propertiesrelative to pure silica aerogel.As shown in the table below, aerogels offer significantly more insulating value

per unit of material than other insulations:

Material Thermal Conductivity (k) [ WmK ]Aerogel 0.012Polyurethane foam 0.021Polystyrene foam 0.038Microporous silica 0.019-0.038fiberglass 0.040Mineral wool 0.038Perlite 0.040-0.060Calcium Silicate 0.047

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Figure 4.16: Areas that Aspens flexible aerogels can be used in. The picture is from:http://www.aerogel.com/markets.htm

4.9. Textile composites

There is a new ”class” of composites, called textile composites. The materialcomes from a new technique which instead of the reinforcing fibres being put inplace individually, which is slow and costly, they can be knitted or woven togetherto make a sort of cloth. This can even be three-dimensional rather than flat, seeFigure 4.17. The spaces between and around the textile fibers may be filled withthe matrix material (such as a resin) to make the final product.This process can quite easily be done by machines rather than by hand, making

it faster and cheaper. Connecting all the fibres together also means that thecomposite is less likely to be damaged when struck.

4.10. Bio-inspired materials

Researchers are making rapid progress in the design and synthesis of non-naturaloligomers and polymers that emulate the properties of natural proteins (also calledbio-inspired materials). For instance is NASA trying to tailor new materials thatcan mimic the extraordinary structural and self-repairing properties of biological

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Figure 4.17: Three dimensional braiding of composite structures.

substances such as bone or sea shells, also called bio-inspired materials. Suchbiologically inspired materials can adapt to changing conditions and thereforethey can help to make airplanes and spacecraft lighter, stronger and more reliable.New advanced materials can also be able to change their shapes (i.e. airplanewings which today is done with hydraulics). The hope is to find materials thatchange shape on command because then we could improve for instance airplanestremendously.Also the so-called ’self-healing’ materials could be very important to space

exploration, thus even small sand grain particle of a meteor could puncture thehull of existing space vehicles.

4.11. Self-healing composites

Inspired by biological systems in which damage triggers an autonomic healing re-sponse, researchers at the University of Illinois have developed a synthetic materialthat can heal itself when cracked or broken.The material — consisting of a microencapsulated healing agent and a special

catalyst embedded in a structural composite matrix — could increase the reliabilityand service life of thermosetting polymers used in a wide variety of applicationsranging from microelectronics to aerospace.”Once cracks have formed within typical polymeric materials, the integrity of

the structure is significantly compromised,” said Scott White, a UI professor ofaeronautical and astronautical engineering and lead author of a paper published inthe Feb. 15 (2001) issue of the journal Nature that described the new self-healingmaterial.

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Figure 4.18: Self healing composite from http://www.cerncourier.com.

”Often these cracks occur deep within the structure where detection is diffi-cult and repair is virtually impossible.” In the new material, however, the repairprocess begins as soon as a crack forms.”When the material cracks, the microcapsules rupture and release the healing

agent into the damaged region through capillary action,” White said. ”As thehealing agent contacts the embedded catalyst, polymerization is initiated whichthen bonds the crack face closed.”In recent fracture tests, the self-healed composites recovered as much as 75

percent of their original strength. And because microcracks are the precursors tostructural failure, the ability to heal them will enable structures that last longerand require less maintenance.The concept of the autonomic healing system.”Filling the microcracks will also mitigate the harmful effects of environ-

mentally assisted degradation such as moisture swelling and corrosion cracking,”White said. ”This technology could increase the lifetime of structural components,perhaps by as much as two or three times.”The ability to self-repair and restore structural integrity also could extend the

lifetimes of polymer composite circuit boards, where microcracks can lead to bothmechanical and electrical failure.

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Figure 4.19: (a) In a right-handed material, where both permittivity and permeabilityare positive, the index of refraction is positive and the law of optics follow our intuition.(b) This is not the case in a left-handed material with negative permittivity and perme-ability. In that case the index of refraction is negative and a convergent lens becomesdivergent. Figure from: http://www.ifh.ee.ethz.ch/~martin/res10.en.html

4.12. Left-handed metamaterials

Metamaterials are engineered composites exhibiting properties that are not ob-served in the constituent materials and not observed in nature.The response of a material to electromagnetic fields is entirely characterized by

its permittivity and its permeability. The former gives the response to an appliedelectric field, while the latter describes the response to a magnetic field. Theydetermine how electromagnetic waves (including microwaves and visible light)interact with the material. These two parameters are not constant, but dependon the illumination frequency (for example a semiconductor can be opaque inthe visible range, but transparent in the infrared). Quite surprising effects canalso arise for specific values of these two parameters. For example, when thepermittivity takes particular negative values plasmon resonances can be excitedin the material, see Figure 4.19.

Composite Material with ”reversed” physical propertiesMinneapolis, MN-Physicists at the University of California, San Diego (UCSD)

have produced a new class of composite materials with unusual physical propertiesthat scientists theorized might be possible, but have never before been able toproduce in nature.”Composite materials like this are built on a totally new concept,” said the

two co-leaders of the UCSD team, Sheldon Schultz and David R. Smith, who

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announced their discovery at a news conference. ”While they obey the laws ofphysics, they are predicted to behave totally different from normal materials andshould find interesting applications.”The unusual property of this new class of materials is essentially its ability

to reverse many of the physical properties that govern the behavior of ordinarymaterials. One such property is the Doppler effect, which makes a train whistlesound higher in pitch as it approaches and lower in pitch as it recedes. Accordingto Maxwell’s equations, which describe the relationship between magnetic andelectric fields, microwave radiation or light would show the opposite effect in thisnew class of materials, shifting to lower frequencies as a source approaches and tohigher frequencies as it recedes.Similarly, Maxwell’s equations further suggest that lenses that would normally

disperse electromagnetic radiation would instead focus it within this compositematerial. This is because Snell’s law, which describes the angle of refractioncaused by the change in velocity of light and other waves through lenses, waterand other types of ordinary material, is expected to be exactly opposite withinthis composite.”If these effects turn out to be possible at optical frequencies, this material

would have the crazy property that a flashlight shining on a slab can focus thelight at a point on the other side,” said Schultz. ”There’s no way you can do thatwith just a sheet of ordinary material.”Underlying the reversal of the Doppler effect, Snell’s law, and Cerenkov ra-

diation (radiation by charged particles moving through a medium) is that thisnew material exhibits a reversal of one of the ”right-hand rules” of physics whichdescribe a relationship between the electric and magnetic fields and the directionof their wave velocity.The new materials are known by the UCSD team colloquially as ”left-handed

materials,” after a term coined by Veselago, because they reverse this relationship.What that means is physically counterintuitive-pulses of electromagnetic radiationmoving through the material in one direction are composed of constituent wavesmoving in the opposite direction.The UCSD physicists emphasized that while they believe their new class of

composites will be shown to reverse Snell’s law, the specific composite they pro-duced will not do so at visible-light frequencies. Instead, it is now limited totransmitting microwave radiation at frequencies of 4 to 7 Gigahertz-a range some-where between the operation of household microwave ovens (3.3 Gigahertz) andmilitary radars (10 Gigahertz).

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The composite constructed by the UCSD team-which also consisted of WillieJ. Padilla, David C. Vier, and Syrus C. Nemat-Nasser-was produced from a seriesof thin copper rings and ordinary copper wire strung parallel to the rings. It isan example of a new class of materials scientists call ”metamaterials.” ”Eventhough it is composed of only copper wires and copper rings, the arrangement hasan effective magnetic response to microwaves that has never been demonstratedbefore,” said Schultz.What’s unusual about the new class of materials produced by the UCSD team

is that it simultaneously has a negative electric permittivity and a negative mag-netic permeability, a combination of properties never before seen in a natural orman-made material.”And the interesting thing is that it’s produced with no magnetic material,”

said Schultz. ”It’s all done with copper.””The bottom line,” said Smith, ”is that this material- this metamaterial, at

frequencies where both the permittivity and permeability are negative, behavesaccording to a left-handed rule, rather than a right-handed rule.”

Questions• What is the theory behind composite materials?• What is a composite material?• How do we classify composite materials according to their matrix phase?• What is the greatest advantage of composite materials?• What is the greatest disadvantage of composite materials?• Why is specific modulus and specific strength important?• What does Fiber Reinforced Plastics (FRP) mean?• What kind of reinforcement can composites have? Illustrated them.• What kind of fibers are there, and what are their advantages/disadvantages?•What is so special about spider silk, can you find out the prospect for commer-cialisation of spider silk?• What is the primary function of the reinforcement and the matrix in the com-posite material?• How do we find the modulus of the entire composite?• How do we classify composites?•What is so special about high performance materials?• What is the strength of the composite primarily depending on?• What is CMC, MMC, and PMC? What are the differences? Where are theapplications?

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•What is the advantages of MMCs compared to monolithic metals?•What is the advantages of MMCs compared to PMC’s?•What is the disadvantages of MMCs compared to PMC’s and monolithic metals?• How does a self-healing composite work?•What is a left-handed material?•What is a metamaterial?

References:Natural composites:http://www.imb-jena.de/~sponner/Current.html

Fibershttp://www.azonano.com/news.asp?newsID=82

MMC:http://www.tms.org/pubs/journals/JOM/0104/Rawal-0104.htmlhttp://www.electrovac.com/metall/indexe.htmhttp://www.machinedesign.com/bde/materials/compsites/rvmat2d.htmlhttp://www.pcc-aft.com/tech/mmc/mmc.html

Ceramics:http://www-materials.eng.cam.ac.uk/mpsite/properties/non-IE/max_service_temp.htmlhttp://www.albint.com/web/techweav/techw.nsf/http://www.engr.utk.edu/~cmc/http://www.onera.fr/dmsc-en/matcer/http://www.mmat.ubc.ca/other/courses/mmat382/cnc63.htmhttp://books.nap.edu/books/0309059968/html/7.html#pagetophttp://www.ms.ornl.gov/programs/energyeff/cfcc/iof/chap24-6.pdf

PMChttp://www.npl.co.uk/npl/cmmt/cog/cmmthm098.htmlhttp://www.egr.msu.edu/cmsc/nsf/polymeric.htmlhttp://www.raypubs.comhttp://www.raypubs.com/hpcsb/sbover2.html#partdesign

High-performance composites:http://www.etcusa.com/hpc/

Material database on internet:http://www.matweb.com/index.asp?ckck=1

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Composites:http://composite.about.com/mbody.htmhttp://composite.about.com/cs/aboutcomposites/http://www.mil17.org/http://www.netcomposites.com/http://www.science.org.au/nova/059/059key.htmhttp://www.efunda.com/materials/polymers/properties/polymer_cat.cfm?MajorID=PA

http://www.sdplastics.com/http://www.howstuffworks.com/ question87.htmhttp://www.users.globalnet.co.uk/~weeks/Composite%20Materials.htmhttp://callisto.my.mtu.edu/my472/http://home.earthlink.net/~ttc/about.htmlhttp://www.mech.utah.edu/~rusmeeha/labNotes/composites.htmlhttp://ice.chem.wisc.edu/materials/composite.htmlhttp://www.psrc.usm.edu/macrog/index.htmhttp://callisto.my.mtu.edu/MY472/http://www.matweb.com/searchcompenglish.htmhttp://plastics.about.com/library/weekly/aa980323.htmhttp://www.advancedcomposites.com/technology.htmhttp://www.nap.edu/books/0309059968/html/index.htmlhttp://www.technica.net/NF/NF2/efibreinorganiche.htmhttp://www.fibreglast.com/

Aerogel materials:http://www.ntnu.no/gemini/2002-05/16-19.htmhttp://www.tu.no/snadder/article.jhtml?articleID=14148http://stardust.jpl.nasa.gov/tech/aerogel.htmlhttp://www.taasi.com/what.htmhttp://www.aspensystems.com/http://www.aerogel.com/technology.htm

Textile composites:http://www.mtm.kuleuven.ac.be/Research/C2/poly/Modelling.htmhttp://www.muratec.net/braider/http://www.engr.ukans.edu/~rhale/textiles/index.htmhttp://www.ntcresearch.org/pdf-rpts/AnRp00/I00-A06.pdfhttp://www.innovationave.com/storage/PDF/advmaterials/ghosh.pdf

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http://fiberarchitects.com/http://www.mtm.kuleuven.ac.be/Research/C2/poly/wisetex.htmlhttp://www.stru.polimi.it/Compositi/Compositi_dx.htmJohn Summerscales, Microstructural characterisation of fibre-reinforced compos-ites, ISBN 1 85573 240 8, 320 pages, 1998.

General:http://claymore.engineer.gvsu.edu/~jackh/eod/

Race-car:http://www.mse.cornell.edu/courses/engri111/racecar.htm

FRP manufact:http://www.owenscorning.com/owens/composites/about/introduction.asp

Sspace-age materials:http://www.spacedaily.com/news/materials-02zh.html

High-performance composites:http://www.etcusa.com/hpc/http://www.raypubs.com/hpcsb/sboverview.htmlhttp://www.atlcomposites.com/products_composite_duflex_intro.htmhttp://www.quadrantepp-europe.com/idqua001.asphttp://www.bayplastics.co.uk/http://www.tstar.com/pdf/quadrant-DF.pdf

High-performance materials:http://www.hiper-group.com/hcproducts.htm

Self-healing material:http://www.news.uiuc.edu/scitips/01/0214selfheal.htmlhttp://www.globaltechnoscan.com/21stFeb-27thFeb01/biological.htm

Left-handed composite materials/metamaterials:http://ucsdnews.ucsd.edu/newsrel/science/mccomposite.htmhttp://www-physics.ucsd.edu/lhmedia/http://www.ing.dk/konf/root/redproduktion/sub/graenseland/html/0106.htmlhttp://physics.ucsd.edu/~drs/left_home.htmhttp://www.ifh.ee.ethz.ch/~martin/res10.en.htmlhttp://physics.ucsd.edu/lhmedia/

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5. Smart (intelligent) Materials and Structures

Smart materials are not smarter than you. Smart materials respond to environ-mental stimuli with particular changes in some variables. For that reason theyare often also called responsive materials or functional materials. Depending onchanges in some external conditions, ”smart” materials change either their prop-erties (mechanical, electrical, appearance), their structure or composition, or theirfunctions. They are materials able to transform other forms of energy to mechan-ical energy and, sometimes, vice versa. These are unique type of materials andhave similarities in microstructures and deformation mechanisms. Fundamentalunderstanding on the behavior of these materials is still on the way, meanwhile,various novel applications of these materials are found of successful.The technological field of smart materials (see [16]) has evolved over the past

decades with increasing pace during the 1990s.

At a more sophisticated level, such smart materials become intelligent whenthey have the ability to respond intelligently and autonomously to dynamically-changing environmental conditions.Potential applications are widespread and have excited interest in industrial,

military, commercial, medical, automotive and aerospace fields. Embedded fibre-optic sensing systems are employed in many engineering disciplines to monitorcritical characteristics. Several smart skins programmes have been initiated forboth civil and military aircraft. Large space structures are also candidates for theincorporation of smart structural systems because of the variable service condi-tions in which they operate. Typical applications include, sensors and actuators,vibration suppression and damping device, micro-electro-mechanical-system, bio-medical engineering, space, robot, etc., to name a few. These materials will greatlyhelp us to further improve the way of living of our human being (see i.e.[19]).

Furthermore, one should note that the terms Smart materials, Intelligent Ma-terials, Active Materials, Adaptive Materials, (and to some extent) actuators andsensors, are almost always, used interchangeably. We will consider the following4 main groups of smart materials in more detail

• — Color Changing Materials— Light Emitting Materials— Moving Materials— Temperature Changing Materials

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5.1. Color Changing Materials

Color changing materials are materials that change color due to different externalstimuli.

5.1.1. Photochromic materials

Photochromic materials change reversibly color with changes in light intensity,see Figure 5.1. Usually, they are colorless in a dark place, and when sunlight orultraviolet radiation is applied molecular structure of the material changes and itexhibits color. When the relevant light source is removed the color disappears.Changes from one color to another color are possible mixing photochromic

colors with base colors. They are used in paints, inks, and mixed to mould or

Figure 5.1: Photochromic material.

casting materials for different applications.

5.1.2. Thermochromic materials

Thermochromic materials change reversibly color with changes in temperature,see Figure 5.2. They usually are semi-conductor compounds. The change in colorhappens at a determined temperature, which can be varied doping the material.They are used to make paints, inks or are mixed to moulding or casting ma-

terials for different applications.

5.2. Light Emitting Materials

Light emitting materials are materials that change the light in some sense, due tosome external stimuli.

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Figure 5.2: Thermochromic material.

5.2.1. Electroluminescent materials

Electroluminescent materials produce a brilliant light of different colors whenstimulated electronically, see Figure 5.3.

Figure 5.3: Electroluminescent material.

Electroluminescent materials are a combination of phosphorous and fluorocar-bons that produce a brilliant light of different colors when stimulated electronically(e.g. by AC current). While emitting light no heat is produced.They can be used for making lightstripes for decorating buildings, or for in-

dustrial and public vehicles safety precautions.

5.2.2. Fluorescent materials

Fluorescent materials produce visible or invisible light as a result of incident lightof a shorter wavelength (i.e. X-rays, UV-rays, etc.). The effect ceases as soon as

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the source of excitement is removed, see Figure 5.4.

Figure 5.4: Fluorescent material.

Fluorescent pigments in daylight have a white or light color, whereas underexcitation by UV radiation they irradiate an intensive fluorescent color.They can be used for paints, inks or mixed to moulding or casting materials

for different applications.

5.2.3. Phosphorescent materials

Phosphorescent materials (or afterglow materials) produce visible or invisible lightas a result of incident light of a shorter wavelength (i.e. X-rays, UV-rays, etc.),detectable only after the source of the excitement has been removed, see Figure5.5.

Figure 5.5: Phosphorescent material.

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Afterglow effect pigments are polycrystalline inorganic zinc sulphide (greenafterglow) or alkaline earth sulphides (red or blue afterglow), and can be used inpaints, inks or mixed to moulding or casting materials for different applications.

5.3. Moving Materials

Moving materials are materials that in some sense move when exposed to somespecial external source.

5.3.1. Conducting polymers

Conducting polymers are conjugated polymers, through which electrons can movefrom one end of the polymer to the other. The most common are polyaniline

Figure 5.6: Conducting polymer.

(PAni) and polypyrrole (PPY). Polipyrrole has been used for the developmentof micro muscles. Polyaniline films sandwiched around a ion-conducting film areconsidered as material for artificial muscles for robots. A current flow reduces oneside and oxidizes the other. Ions are transferred. One side expands and the othercontracts, resulting in a bending of the sandwich, see Figure 5.6. Electrical andchemical energies are in this way transformed into mechanical energy.Conducting polymers are still at a research level. Presently, the expected

lifetime of the muscle is of 100.000 actuations. In the Year 2000 Alan Heeger gotthe Nobel Price in chemistry for the invention of a conducting polymer.

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5.3.2. Dielectric elastomers

Dielectric elastomers (also called electrostrictive polymers) exhibit a mechanicalstrain when subjected to an electric field as shown in Figure 5.7. The most com-

Figure 5.7: Dielectric elastomers.

mon are PMMA-based electrostrictive polymers. Thanks to their electrostrictivestrain, they can be sandwiched between two electrodes to emulate the operation ofmuscles. In an electric field, the elastomer expands in the plane of the electrodes,amplifying the normal compression due to the electrostatic charges on the elec-trodes. The result is a muscle with large strain capability, and a large actuationpressure.

5.3.3. Piezoelectric materials

Piezoelectric materials produce an electric field when exposed to a change in di-mension caused by an imposed mechanical force (piezoelectric or generator effect),see Figure 5.8. Conversely, an applied electric field will produce a mechanicalstress (electrostrictive or motor effect). They transform energy from mechanicalto electrical and vice-versa and are used for sensing purposes (e.g. microphone,transducer), and for actuating applications. Similar to piezoelectric materials areelectrostrictive and magnetostrictive materials used in high precision actuation.They are ferromagnetic materials which experience an elastic strain when sub-jected to an electric or magnetic field respectively.Products: Smart skis, Mothra plain, Acoustic transducer, Multilayer cofired

actuator, Magnetostrictive linear motor, Smart skin.

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Figure 5.8: Piezoelectric material.

5.3.4. Polymer gels

Polymer gels consist of a cross-linked polymer network inflated with a solventsuch as water, see Figure 5.9. They have the ability to reversibly swell or shrink

Figure 5.9: Polymer gels.

(up to 1000 times in volume) due to small changes in their environment (pH,temperature, electric field). Micro sized gel fibres contract in milliseconds, whilethick polymers layers require minutes to react (up to 2 hours or even days). Theyhave high strength and can deliver sizeable stress (approximately equal to that ofhuman muscles).The most common are polyvinylalcohol (PVA), polyacrylicacid (PAA) and

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polyacrylonitrile (PAN). There are many potential applications for these mate-rials (e.g. artificial muscles, robot actuators, adsorbers of toxic chemicals), butpresently, few of them have a commercial diffusion. Response time is still notfast enough for artificial muscles. Lifetime of a gel actuator is very short. Theirstructure gradually degrades and they become unusable. Commercial reality isstill far away.

5.3.5. Shape memory materials (SMM)

Shape memory alloys (SMA) are metals that, after being strained, at a certaintemperature revert back to their original shape, see Figure 5.10. A change in theircrystal structure above their transformation temperature causes them to return totheir original shape. SMAs enable large forces (generated when encountering anyresistance during their transformation) and large movements actuation, as theycan recover large strains.

Figure 5.10: Shape memory alloys (SMA).

Shape-memory materials are also superelastic, namely they are able to sustaina large deformation at a constant temperature, and when the deforming forceis released they return to their original undeformed shape. Typically, they canundergoe elastic strain up to 10%.The shape memory effect is a unique property of certain alloys. Even though

the alloy is deformed in the low temperature phase, it recovers its original shape onbeing heated to a critical higher temperature. The material is one that undergoesa change of crystal structure at a certain temperature called the transformationtemperature. Above this temperature the material has one crystal structure (cubic

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in the case of Cu-Al-Ni) and below this temperature it has another (orthorhombicfor Cu-Al-Ni). The low temperature structure of these types of materials allowsthe material to be easily and apparently permanently deformed. However onheating the material returns to its high temperature structure which has onlyone possible shape. Thus the material has ”remembered” its shape (see also[20]). Generally, these materials can be plastically deformed at some relativelylow temperature, and upon exposure to some higher temperature will return totheir shape prior to the deformation. Materials that exhibit shape memory onlyupon heating are referred to as having a one-way shape memory. Some materialsalso undergo a change in shape upon recooling. These materials have a two-wayshape memory.Products: SMA stent for veins, Superelastic glasses, Coffeepot thermostat,

Electrical connector.Also shape-memory ceramics and polymers (SMP) exist. Shape-memory poly-

mer for instance, converts from a temporary shape (top) to its parent shape (bot-tom) in 45 seconds at 65oC.

Commercial SME AlloysThe only two alloy systems that have achieved any level of commercial ex-

ploitation are the NiTi alloys and the copper-base alloys. Properties of the twosystems are quite different. The NiTi alloys have greater shape memory strain (upto 8% versus 4 to 5% for the copper-base alloys), tend to be much more thermallystable, have excellent corrosion resistance compared to the copper-base alloys’medium corrosion resistance and susceptibility to stress-corrosion cracking, andhave much higher ductility. On the other hand, the copper-base alloys are muchless expensive, can be melted and extruded in air with ease, and have a widerrange of potential transformation temperatures. The two alloy systems thus haveadvantages and disadvantages that must be considered in a particular application.

5.3.6. Nanostructured Shape Memory Materials

Nanoscale materials have enjoyed recent interest because of the changes that oc-cur in material behavior as surface effects and grain boundary behavior play alarger role in the overall mechanical behavior of the material. Shape memoryalloys continue to be explored for more dramatic superelastic behavior and sev-eral of these alloys have already proven to have wide ranging applications in theaerospace, biomedical, and microelectronics industries. A nanostructured shapememory alloy is on the leading edge of materials development and will allow fur-

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Figure 5.11: Magnetically controlled shape memory materials (MSM) replace machines.

ther advances in the application of shape memory alloys to microscopic structuresand miniaturized devices.Foils of nickel-titanium alloy with nanoscale structure have been successfully

fabricated. Preliminary characterization testing has been conducted which con-firms that the primary phase present in the material is NiTi which is the phasedisplaying shape memory behavior.

5.3.7. Magnetic Shape Memory (MSM) Materials

Magnetic Shape Memory effect is a new invention in actuator materials field, al-lowing even 50 times greater strains than in previous magnetically controlled ma-terials (magnetostrictive materials). In MSM materials the magnetic field movesmicroscopical parts of the material (so called twins) that creates a net shapechange of the material. The mechanism enables also more complicated shapechanges than conventional linear strain, such as bending and shear. Strains canbe even 5 % (depending on the material). Typically, present MSM materials pro-duce 2 % strain at 0 to 2 MPa stress in actuator use. AdaptaMat is developing acommercial grade MSM alloy. MSM material samples can be produce for researchuse.MSM materials field of application seems to be very wide, ranging from auto-

motive applications to home electronics. They can simplify complicated mechan-ical structures. Consider a sewing machine, as in Figure 5.11: traditional sewingmachine has a rotating electric motor and a large number of parts in a rathercomplicated mechanical transmission system, although the desired motion of theneedle is up and down. A sewing machine based on MSM technology could consist

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of an electromagnet (coil) and a needle made of MSM-material.

5.4. Temperature Changing Materials

Temperature changing materials are materials that change temperature in someway, when exposed to some sort of external source.

5.4.1. Thermoelectric materials

Thermoelectric materials are special types of semiconductors that, when coupled,function as a ”heat pump”, see Figure 5.12. By applying a low voltage DC power

Figure 5.12: Thermoelectric materials.

source, heat is moved in the direction of the current (+ to -). Usually, they areused for thermoelectric modules where a single couple or many couples (to obtainlarger cooling capacity) are combined. One face of the module cools down whilethe other heats up, and the effect is reversible. Thermoelectric cooling allows forsmall size and light devices, high reliability and precise temperature control, andquiet operation. Disadvantages include high prices and high operating costs, dueto low energy efficiency.

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Figure 6.1: Aluminium foam / functional gradient material in car.

6. Functional Gradient Materials

Functional (FGM) gradient materials are materials that have a gradual variationof material properties from one end to another, as shown in Figure 6.1.The concept of Functionally Gradient Materials (FGM) was first put for-

ward for reducing thermal stress. A kind of special materials which can be usedlong-term in high temperature and large difference of temperature is needed asaerospace industry is developing at high speed. The thermal stress in materials isso large that neither pure metals, pure ceramics nor cladding materials can meetthis strict condition.Man-made functionally graded materials (FGMs) copy natural biomaterials,

such as bamboo, teeth and shell etc., with a gradient in chemical composition ormicrostructure from one side to the other side in the material. Materials with agradual change in chemical composition or microstructure are expected to haveadvanced or new properties. The concept of functionally graded materials wasproposed in 1984 by material scientists in the Sendai area in Japan. Since thenstudies to develop high-performance heat-resistant materials using functionallygraded technology have continued. In recent years, another attempt to apply theFGM concept to the functional materials has been initiated.The typical design of the FGMs is that the varying composition of the FGMs

from high ceramic content on one side of bulk material to high metal content onthe other side. This may lead to good wear resistance, good corrosion resistance,good heat resistance on the high ceramic content side and good fracture resistance,

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Figure 6.2: Functional (FGM) gradient materials.

good thermal conductivity on the high metal content side.The joining of ceramics to metals is of great engineering significance for vari-

ous advanced technologies, including high-temperature structural applications in,e.g., turbine airfoils and combustors. A crucial matter in the ceramic-metal jointsystem is to develop an efficient means to suppress the damage to be induced bythermal stresses (cracking, interfacial decohesion, etc.), see Figure 6.2.

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Figure 6.3: Functional (FGM) gradient materials.

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Figure 7.1: The picture shows a solar cell which is made from a monocrystalline siliconwafer.

7. Solar Cell Materials

A solar cell or photovoltaic cell is a device that converts light energy into electricalenergy. Sometimes the term solar cell is reserved for devices intended specificallyto capture energy from sunlight, while the term photovoltaic cell is used when thelight source is unspecified.Fundamentally, the device needs to fulfill only two functions: photogeneration

of charge carriers (electrons and holes) in a light-absorbing material, and separa-tion of the charge carriers to a conductive contact that will transmit the electricity(simply put, carrying electrons off through a metal contact into a wire or othercircuit). This conversion is called the photovoltaic effect, and the field of researchrelated to solar cells is known as photovoltaics.Solar cells have many applications. They have long been used in situations

where electrical power from the grid is unavailable, such as in remote area powersystems, Earth-orbiting satellites and space probes, consumer systems, e.g. hand-held calculators or wrist watches, remote radiotelephones and water pumpingapplications. More recently, they are starting to be used in assemblies of so-lar modules (photovoltaic arrays) connected to the electricity grid through aninverter, often in combination with a net metering arrangement (ref. wikipedia).

7.1. Light-absorbing materials

All solar cells require a light absorbing material contained within the cell struc-ture to absorb photons and generate electrons via the photovoltaic effect. Thematerials used in solar cells tend to have the property of preferentially absorbingthe wavelengths of solar light that reach the earth surface; however, some solarcells are optimized for light absorption beyond Earth’s atmosphere as well. Lightabsorbing materials can often be used in multiple physical configurations to take

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advantage of different light absorption and charge separation mechanisms. Manycurrently available solar cells are configured as bulk materials that are subse-quently cut into wafers and treated in a "top-down" method of synthesis (siliconbeing the most prevalent bulk material). Other materials are configured as thin-films (inorganic layers, organic dyes, and organic polymers) that are depositedon supporting substrates, while a third group are configured as nanocrystals andused as quantum dots (electron-confined nanoparticles) embedded in a supportingmatrix in a "bottom-up" approach. Silicon remains the only material that is well-researched in both bulk and thin-film configurations. The following is a currentlist of light absorbing materials, listed by configuration and substance-name:

7.2. Silicon

By far, the most prevalent bulk material for solar cells is crystalline silicon (ab-breviated as a group as c-Si), also known as "solar grade silicon". Bulk siliconis separated into multiple categories according to crystallinity and crystal size inthe resulting ingot, ribbon, or wafer.

• monocrystalline silicon (c-Si): often made using the Czochralski process.Single-crystal wafer cells tend to be expensive, and because they are cutfrom cylindrical ingots, do not completely cover a square solar cell modulewithout a substantial waste of refined silicon. Hence most c-Si panels haveuncovered gaps at the corners of four cells.

• Poly- or multicrystalline silicon (poly-Si or mc-Si): made from cast squareingots – large blocks of molten silicon carefully cooled and solidified. Thesecells are less expensive to produce than single crystal cells but are less effi-cient.

• Ribbon silicon: formed by drawing flat thin films from molten silicon andhaving a multicrystalline structure. These cells have lower efficiencies thanpoly-Si, but save on production costs due to a great reduction in siliconwaste, as this approach does not require sawing from ingots.

• New Structures: These new compounds are special arrangements of siliconthat can dramatically improve efficiency such as ormosil.

[edit]

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7.3. Thin films

The various thin-film technologies currently being developed reduce the amount(or mass) of light absorbing material required in creating a solar cell. This canlead to reduced processing costs from that of bulk materials (in the case of siliconthin films) but also tends to reduce energy conversion efficiency, although manymulti-layer thin films have efficiencies above those of bulk silicon wafers.

• CdTe: Cadmium telluride is an efficient light-absorbing material for thin-film solar cells. CdTe is easier to deposit and more suitable for large-scaleproduction. Despite much discussion of the toxicity of CdTe-based solarcells, this is the only technology (apart from amorphous silicon) that can bedelivered on a large scale.

• CIGS: are multi-layered thin-film composites. The abbreviation stands forcopper indium gallium diselenide. The best efficiency of a thin-film solarcell as of December 2005 was 19.5% with CIGS absorber layer. Higherefficiencies (around 30%) can be obtained by using optics to concentrate theincident light.

• CIS: CIS is an abbreviation for general chalcopyrite films of copper indiumselenide (CuInSe2), CIGS mentioned above is a variation of CIS. While thesefilms can achieve 13.5% efficiency, their manufacturing costs at present arehigh when compared with a silicon solar cell but continuing work is leadingto more cost-effective production processes

• Gallium arsenide (GaAs) multijunction:High-efficiency cells have been devel-oped for special applications such as satellites and space exploration. Thesemultijunction cells consist of multiple thin films produced using molecularbeam epitaxy. A triple-junction cell, for example, may consist of the semi-conductors: GaAs, Ge, and GaInP2. GaAs multijunction devices are themost efficient solar cells to date, reaching a record high of 40.7% efficiencyunder solar concentration and laboratory conditions. In production, GaAstriple-junction cells reach efficiencies above 28.3%. They are also some ofthe most expensive cells per unit area (up to US$40/cm2).

• Dye-sensitized solar cells are a relatively new class of low-cost solar cells.They are based on a semiconductor formed between a photo-sensitized an-ode and an electrolyte, a photoelectrochemical system. Typically a ruthe-nium metalorganic dye (Ru-centered) used as a monolayer of light-absorbing

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material. The dye-sensitized solar cell depends on a mesoporous layer ofnanoparticulate titanium dioxide to greatly amplify the surface area (200-300 m2/gram TiO2, as compared to approximately 10 m2/gram of flat singlecrystal).

• Organic solar cells and Polymer solar cells are built from thin films (typically100 nm) of organic semiconductors such as polymers and small-moleculecompounds like polyphenylene vinylene, copper phthalocyanine (a blue orgreen organic pigment) and carbon fullerenes. Energy conversion efficienciesachieved to date using conductive polymers are low at 6% efficiency for thebest cells to date.

• Silicon: Silicon thin-films are mainly deposited by Chemical vapor deposi-tion (typically plasma enhanced (PE-CVD)) from silane gas and hydrogengas. Depending on the deposition’s parameters, this can yield: Amorphoussilicon (a-Si or a-Si:H), protocrystalline silicon or nanocrystalline silicon (nc-Si or nc-Si:H).

• Nanocrystalline solar cells: These structures make use of some of the samethin-film light absorbing materials but are overlain as an extremely thinabsorber on a supporting matrix of conductive polymer or mesoporous metaloxide having a very high surface area to increase internal reflections (andhence increase the probability of light absorption).

• CPV: Concentrating photovoltaic systems use a large area of lenses or mir-rors to focus sunlight on a small area of photovoltaic cells. If these systemsuse single or dual-axis tracking to improve performance, they may be re-ferred to as Heliostat Concentrator Photovoltaics (HCPV).

7.4. Silicon solar cell device manufacture

Because solar cells are semiconductor devices, they share many of the same process-ing and manufacturing techniques as other semiconductor devices such as com-puter and memory chips. However, the stringent requirements for cleanliness andquality control of semiconductor fabrication are a little more relaxed for solarcells. Most large-scale commercial solar cell factories today make screen printedpoly-crystalline silicon solar cells. Single crystalline wafers which are used in thesemiconductor industry can be made into excellent high efficiency solar cells, butthey are generally considered to be too expensive for large-scale mass production.

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Poly-crystalline silicon wafers are made by wire-sawing block-cast silicon ingotsinto very thin (180 to 350 micrometer) slices or wafers. The wafers are usuallylightly p-type doped. To make a solar cell from the wafer, a surface diffusionof n-type dopants is performed on the front side of the wafer. This forms a p-njunction a few hundred nanometers below the surface.Antireflection coatings, which increase the amount of light coupled into the so-

lar cell, are typically applied next. Over the past decade, silicon nitride has gradu-ally replaced titanium dioxide as the antireflection coating of choice because of itsexcellent surface passivation qualities (i.e., it prevents carrier recombination at thesurface of the solar cell). It is typically applied in a layer several hundred nanome-ters thick using plasma-enhanced chemical vapor deposition (PECVD) (which isprocess that REC Scancell AS in Narvik uses). Some solar cells have texturedfront surfaces that, like antireflection coatings, serve to increase the amount oflight coupled into the cell. Such surfaces can usually only be formed on single-crystal silicon, though in recent years methods of forming them on multicrystallinesilicon have been developed.The wafer is then metallized, whereby a full area metal contact is made on the

back surface, and a grid-like metal contact made up of fine "fingers" and larger"busbars" is screen-printed onto the front surface using a silver paste. The rearcontact is also formed by screen-printing a metal paste, typically aluminium. Usu-ally this contact covers the entire rear side of the cell, though in some cell designsit is printed in a grid pattern. The metal electrodes will then require some kindof heat treatment or "sintering" to make Ohmic contact with the silicon. Afterthe metal contacts are made, the solar cells are interconnected in series (and/orparallel) by flat wires or metal ribbons, and assembled into modules or "solarpanels". Solar panels have a sheet of tempered glass on the front, and a polymerencapsulation on the back. Tempered glass cannot be used with amorphous siliconcells because of the high temperatures during the deposition process.References: http://en.wikipedia.org/wiki/Solar_cell#Light-absorbing_materials.

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Figure 8.1: A ”nano-tube”, 1nm in diameter and may be 1000nm long. Carbon-atomsin a ”periodic tube”.

8. Nano - materials - and technology

Nanoelectronics, Nanotechnology, Nanoconductor, Nanocomputer, Nanobots, from[13] are all technology based on nanoparticles which is a new functional mater-ial with length from 1 to 100nm, where 1 nanometer is 1·10−9 meter. In recentyears, it has attracted worldwide attention in research and development of nanomaterials. The immediately available applications for these materials range fromtransparent skin-care products to microelectronic components and high-stress en-gine parts.In this near to atomic size range, the particles and dynamic properties of

surface atoms can be exploited to modify and enhance the performance of basicraw materials (e.g. iron, aluminum and titanium). These materials have uniqueelectrical, optical, chemical, structural and magnetic properties with potentialapplications including information storage, color imaging, bioprocessing, magneticrefrigeration, and ferrofluids.This type of new composite materials can be molecularly engineered. The

capabilities allow products to achieve levels of strength and durability. It canalso be use to produce designer materials with electronic, mechanical, chemical,magnetic, and optical behavior, beyond the capability of traditional materials.New generations of products and processes become possible.Nanoparticles are also widely applied in such fields as astronavigation, national

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defense, magnetic recording devices, computerization, environmental protections,surface modification and medical/biological engineering etc.Manufactured products are made from atoms (see [17]). The properties of

those products depend on how those atoms are arranged. If we rearrange theatoms in coal we can make diamond. If we rearrange the atoms in sand (and adda few other trace elements) we can make computer chips. If we rearrange theatoms in dirt, water and air we can make potatoes.It’s like trying to make things out of LEGO blocks with boxing gloves on

your hands. Yes, you can push the LEGO blocks into great heaps and pile themup, but you can’t really snap them together the way you’d like. In the future,nanotechnology will let us take off the boxing gloves. We’ll be able to snap togetherthe fundamental building blocks of nature easily, inexpensively and in almost anyarrangement that we desire. This will be essential if we for instance want tocontinue the revolution in computer hardware.The greatest problem of nanocrystalline materials have been to move the tech-

nology out of the laboratory and put into commercial applications by developingmeans to produce quality materials in commercial volume at affordable cost. How-ever, these difficulties have been overcome. Todays manufacturing methods havebeen very crude at the molecular level. Casting, grinding, milling and even litho-graphy move atoms in great thundering statistical herds.

8.1. Carbon Nanotubes (CNT)

Figure 8.1 gives a picture of a carbon nanotube (CNT), see ref. Aftenposten(graphics: J. P. MÆHLEN ). One gram of these tubes costs about 5000 NOK,and is produced by Carbon Nanotechnology Inc. (CNI) which founder is RichardSmalley who got the Nobelprize for the invention of the technology of the nano-tubes in 1996.It’s worth pointing out that the word nanotechnology has become very popular

and is used to describe many types of research where the characteristic dimensionsare less than about 1,000 nanometers. For example, continued improvements inlithography have resulted in line widths that are less than one micron: this workis often called nanotechnology. Sub-micron lithography is clearly very valuablebut it is equally clear that lithography will not let us build semiconductor devicesin which individual dopant atoms are located at specific lattice sites. Many of theexponentially improving trends in computer hardware capability have remainedsteady for the last 50 years. There is fairly widespread confidence that these

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trends are likely to continue for at least another ten years, but then lithographystarts to reach its fundamental limits.Whatever we call it, nano-technology should let us:

• — Get essentially every atom in the right place.

— Make almost any structure consistent with the laws of physics andchemistry that we can specify in atomic detail.

— Have low manufacturing costs (not greatly exceeding the cost of therequired raw materials and energy).

There are two more concepts commonly associated with nanotechnology:

• — Positional assembly.

— Self replication.

Clearly, we would be happy with any method that simultaneously achievedthe first three objectives. However, this seems difficult without using some formof positional assembly (to get the right molecular parts in the right places) andsome form of self replication (to keep the costs down).The need for positional assembly implies an interest in molecular robotics,

e.g., robotic devices that are molecular both in their size and precision. Thesemolecular scale positional devices are likely to resemble very small versions oftheir everyday macroscopic counterparts. Positional assembly is frequently usedin normal macroscopic manufacturing today, and provides tremendous advantages.The requirement for low cost creates an interest in self replicating manufac-

turing systems. These systems are able both to make copies of themselves andto manufacture useful products. If we can design and build one such system themanufacturing costs for more such systems and the products they make (assumingthey can make copies of themselves in some reasonably inexpensive environment)will be very low.

8.1.1. Strength

Carbon nanotubes are one of the strongest and stiffest materials known, in termsof tensile strength and elastic modulus respectively. Multi-walled carbon nanotubewas tested in 2000, and was found to have a tensile strength of 63 GPa. (high-carbon steel has a tensile strength ≈ 1.2 GPa). CNTs have very high elastic-moduli, on the order of 1 TPa. Since CNTs have a low density for a solid (1.3-1.4

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Figure 8.2: Picture from http://www.forskning.no.

g/cm3), its specific strength of up to 48462 kN·m/kg is the best of knownmaterials,( the specific strength of high-carbon steel is 154 kN·m/kg).The tubes will undergo plastic deformation under excessive tensile strain,

which starts at strains of approximately 5%. CNTs are not so strong under com-pression. Due to their hollow structure and high aspect ratio, they tend to undergobuckling when placed under compressive, torsional or bending stress.

8.2. Nanocomposites

Materials with features on the scale of nanometers often have properties dramat-ically different from their bulk-scale counterparts. For example, nanocrystallinecopper is five times harder than ordinary copper with its micrometer-sized crys-talline structure. The development of such materials is currently a research areaof great interest.Nature makes fabulous nanocomposites, and scientists are trying to emulate

such processes. The abalone shell, for example, has alternating layers of calciumcarbonate and a rubbery biopolymer; it is twice as hard and a thousand timestougher than its components.The study of nanocomposite materials requires a multidisciplinary approach,

involving novel chemical techniques and an understanding of physics, mathemat-ics, material science and surface science. It is a field of broad scientific interestwith impressive technological promise.

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Figure 8.3: (Left) This transmission electron micrograph of the cubic structure ofthe new hybrid material shows pores of about 10 nanometers across. (Right) Thisdiagram shows molecular architecture of the flexible ceramic phase called a ”plumber’snightmare.” Wiesner Research Group

8.3. Flexible ceramics

Using nanoscale chemistry, researchers at Cornell developed in 2002 a new class ofhybrid materials that they describe as flexible ceramics, , see Figure 8.3 . The newmaterials appear to have wide applications, from microelectronics to separatingmacromolecules, such as proteins.The Cornell researcher reasoned that the simplest way to mimic nature’s path-

ways was to use organic (or carbon-based) polymers — more particularly materialsknown as diblock copolymers — that have the ability to self-assemble chemicallyinto nanostructures with different symmetries. If the polymer could somehow bemelded with an inorganic material — a ceramic, specifically a silica-type material —the resulting hybrid would have a combination of properties: flexibility and struc-ture control from the polymer and functionality from the ceramic. This, Wiesner’sgroup has now achieved.”The resulting material has properties that are not just the simple sum of

polymers plus ceramic, but maybe something quite new,” said Wiesner. Thusfar the Cornell researchers have made only small pieces of the flexible ceramic,weighing a few grams, in petri dishes, but that is enough to test the material’sproperties. It is transparent and bendable but with considerable strength, and

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Figure 8.4: Flexible ceramics, from http://www.polytec.com/default.asp.

unlike pure ceramic will not shatter. In one form the hybrid material is an ionconductor (an ion is an electrically charged atom), with great promise as highlyefficient battery electrolytes. There also is the possibility that the new materialcould be used in fuel cells, he said.PublishedMarch 21, 2002, http://www.news.cornell.edu/Chronicle/02/3.21.02/

Wiesner-ceramics.htmlFor example, Cotronics´ Flexible Ceramics, see Figure 8.4 are easy to use to

1650◦C, highly efficient insulation products. They are available as:Fiber blankets, Ceramic Papers, Moldable Sheets, Ceramic Boards, Cloths and

Sleevings, Tapes, Ropes and Fabrics. They have advantages as:high purity, outstanding thermal insulation, low heat storage, lightweigh, high

resilienc, high mechanical and thermal shock resistance and are resistant to oxi-dizing.

8.4. New type of High-performance Ceramic

When a racing driver brakes, the discs and linings become red-hot. These partsare commonly made of carbon-fiber-reinforced carbon and are black at moderatetemperatures. Car manufacturers and their suppliers would dearly like to extendthe use of these special brake pads and other hard-wearing parts developed forracing vehicles to perfectly normal family cars - if only the cost was not prohibitive.This may now be possible using a new fiber-composite material that could almostbe referred to as a renewable ceramic. Its carbon matrix is made of carbonizedflax, hemp or wood fibers, which are then permeated with liquid silicon to form ahigh-strength, wear- and temperature-resistant silicon carbide.

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A great deal of know-how is needed even to produce the sheets of carbon fiber,reveals Dr. Stefan Siegel, team leader at the Fraunhofer Institute for CeramicTechnologies and Sintered Materials IKTS. Our starting material are boards ofresin-coated plant fibers, which are produced for us by our colleagues at the Fraun-hofer Institute for Wood Research WKI. These sheets then undergo a processcalled carbonization, in which the natural-fiber composite is heated in a nitrogenflooded furnace to temperatures of over 1000◦C. This process has to be carefullycontrolled to ensure that the shrinkage of the material - i.e. its reduction in vol-ume - proceeds homogeneously and without distortion. All that is left in the endis carbon; practically all other compounds present in the original material havedecomposed and evaporated. The black sheets resulting from the carbonizationof the raw natural fiber can be used, for example, as structural elements or asan insulating lining for furnaces. Alternatively, this intermediate product can beshaped into components using standard industrial machining techniques such assawing, drilling or milling.But let us return to the ceramics. At temperatures above 1410◦C, silicon

liquefies, and is soaked up like a sponge by the sheets of carbon (at present up toone square meter in size) or the pre-shaped components. The silicon undergoes afast-acting reaction with the carbon, forming a fiber-composite ceramic material.This stage of the process, unlike carbonization, does not alter the shape or sizeof the parts. The post-processing of hard ceramic materials like silicon carbideis relatively difficult. The new wood ceramic, by contrast, can be shaped beforeit is hardened, thus presenting manufacturers who use machine tools to produceparts subject to high mechanical and thermal stress with a simple-to-use, low-costalternative. (published nov. 2002).

8.5. Back to square one?

Published in : http://www.forskning.no/Artikler/2002/oktober/1034170456.0 10.October 2002

An up-and-coming young physicist at Bell Labs in Murray Hill, New Jersey,has been dismissed after being found guilty of 16 counts of scientific misconductby a review panel charged with investigating his research.Formerly a rising star in the field of nanotechnology, Schön was renowned for

creating field-effect transistors, the backbone of modern electronics, out of tinymolecules. His work won him numerous awards from magazines and scientificorganizations, and colleagues were beginning to tip him for a Nobel Prize.

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But not everything was as it seemed. Many scientists were unable to reproduceSchön’s results. In April, a small group of physicists noticed that graphs in threeunrelated papers appeared identical down to what should have been random noise.Bell Labs rapidly launched an independent investigation, which soon expanded toinclude two dozen papers.What they found, according to Malcolm Beasley, a professor of electrical engi-

neering at Stanford University, who chaired the panel, was that Schön substitutedwhole figures from other papers, removed data points that disagreed with predic-tions, and even used mathematical functions in place of real data points.

References:

Nano SMM:http://mrsec.wisc.edu/Seed_shape_memory/seed_shape_memory_alloys.htmhttp://en.wikipedia.org/wiki/Carbon_nanotube

Aerogel:http://eande.lbl.gov/ECS/aerogels/aerogels.htmhttp://www.ntnu.no/gemini/2002-05/16-19.htm

FGM:http://kenwww.pi.titech.ac.jp/Current_Subjects#Topic-3http://www.grc.nasa.gov/http://WWW/RT2000/5000/5920arnold3.htmlhttp://www.lucifer.com/~sean/Nano.htmlhttp://www.zyvex.com/nano/http://web.mit.edu/tdp/www/composite.html

CVD:http://chiuserv.ac.nctu.edu.tw/~htchiu/cvd/home.htmlhttp://www.ultramet.com/4.htm

nano:http://www.aftenposten.no/nyheter/iriks/article.jhtml?articleID=199118http://www.aftenposten.no/nyheter/iriks/article.jhtml?articleID=198172http://www.aftenposten.no/nyheter/iriks/article.jhtml?articleID=198173http://www.dr.dk/videnom/12nano/nano2.htmhttp://www.dr.dk/orbitalen/artikler/aktnat/nanoroer.shtmhttp://www.tekblad.no/show_article.asp?id=4112http://www.pa.msu.edu/cmp/csc/nanotube.html

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http://www.sciencesite.dtu.dk/nano/http://www.sciam.com/nanotech/http://www.forskning.no/Artikler/2003/juni/1055493430.67http://www.forskning.no/Artikler/2003/september/1063028534.1

Nanocomposites:http://www.mse.cornell.edu/materials_science_discovering/nanocomposites.htmlhttp://www.nanocor.com/nclays/nanocomposites.htmhttp://www.pnl.gov/nano/conferences/smart.htmlhttp://www.ntnu.no/gemini/2002-05/16-19.htm

Flexible cramics:http://www.news.cornell.edu/Chronicle/02/3.21.02/ Wiesner-ceramics.html

Solar Cell materials:http://en.wikipedia.org/wiki/Solar_cell#Light-absorbing_materials

Misconduct in nanotechnology:http://www.smalltimes.com/document_display.cfm?document_id=4079http://www.nature.com/nsu/020923/020923-9.htmlhttp://www.nanoelectronicsplanet.com/briefs/http://nanotechweb.org/articles/news/1/9

Questions• What is the difference between a material and a structure?• What is a smart material?• What kind of smart materials are there, and how do they act?• What is a FGM?• What is the advantage of a functional gradient material compared with tradi-tional ”solid” materials?• What kind of products do you think could be made from a functional gradientmaterial?•What kind of products is FGM used in today? Who make them? What kind ofmaterials are they made of?•What kind of Solar cell materials are there?• What is nano-technology?• What future is there in nano-technology?• What is a nanotube? What is the principle of fabrication of the nanotubes?•What kind of commercial nano-tube-based products are available in the market,and what can they be used as?

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•What is a flexible ceramic?

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Figure 9.1: Cellular structure.

9. Cellular Solids, Structures & Foams

When modern man builds large load-bearing structures, he uses dense solids; steel,concrete, glass. When nature does the same, she generally uses cellular materials;wood, bone, coral. There must be good reasons for it ref: (Prof. M. F. Ashby,University of Cambridge)Cellular solids are defined as ”...an assembly of cells with solid edges of faces,

packed together so that they fill space...”, see [5], p. 1, and see Figure 9.1. Suchmaterials can be found in nature, for instance cork and wood. Man-made cellularstructures will in the future replace conventional materials because of the possi-bility to construct structures with tailored properties. Cellular structures can ei-ther consist of two-dimensional structures, like honeycombs, or three-dimensionalstructures, like foam-structures.Honeycombs are usually thought of as cells in a hexagonal form, but they

can also be in a triangular, square or rhombic form. We can find honeycombs inthe nature, like the bee-honeycomb and as the cross-section of the bambootree.Honeycombs are often used as a core material in sandwich-constructions. The verygood stiffness-to-weight ratio and strength-to-weight ratio and the good shockabsorption ability in addition to the possibility for man-made tailored propertiesof the structures are some of the answers to why the honeycomb-structures havebecome so interesting as material structures.Foams can now also be made of almost any material, like polymers, met-

als, ceramics, glasses, and composites. The properties of a foam are related to

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its structure and the material of which the cell walls are made. Cellular solidsare often used for thermal insulation, packaging, filtering, structural applicationsor for their buoyancy property among many other applications. Recently, therehas been an increased interest in the use of cellular solids that perform morethan just one function. These multi-functional materials would possess uniquecombinations of thermophysical and mechanical properties. For example, a loadbearing cellular solid could also provide for additional things such as impact/blastabsorption, thermal management, conductance of electricity and/or shielding ofelectromagnetic waves, electrical power storage, filtering or impeding of fluid flow,retardation of chemical reactions and fire or in-growth of biological tissue. Thelargest obstacle in creating these materials thus far has been the inability formany manufacturers (using foaming or other methods) to gain control over thedistribution of material/pores at the cell level. In addition, the limited choice ofbase material types has slowed the introduction of cellular solids as materials ofchoice for multifunctional applications.The foam industry grows because cellular materials offer unique advantages

over traditional materials and non-cellular polymers.

9.1. Metal Foams

Metal foams are a new type of materials, that is unknown to most engineers. Theyare not perfectly characterized, but generally we say that they have low densitiesand new type of physical, mechanical, thermal, electrical and energy absorption.In recent years there has been an increased interest in metal foams in the field

of material science. The stress absorbing potential is one of the most interestingproperties for the application of aluminium foam (e.g. car manufacturing). Mate-rial scientists need to investigate the structure of metal foams in order to optimizetheir deformation behavior.Most available metal foams are based on aluminium or nickel, but there also

exist methods for foaming magnesium, lead, zinc, copper, bronze, titanium, steeland even gold. The methods are still imperfectly controlled. Metallic foams(metfoams) offer significant performance gains in light, stiff structures since theyhave an excellent stiffness-to-weight ratio. They can also be used as core materialsin sandwich constructions since they have low density with good shear and fracturestrength. The damping capacity of metal foams is larger than that of solid metalsby up to a factor of 10.The most promising applications for metal foams appear to be as cores for

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Figure 9.2: Example of aluminium foam.

light-stiff sandwich panels; as stiffeners to inhibit buckling in light shell structures;as energy absorbing units, both inside and outside of motor vehicles and trains; asefficient heat exchanges to cool high powered electronics (by blowing air throughthe open cells of the aluminium foam, , attached to the heat source) and as lightcores for shell casting. Several industrial designers have seen potential in exploitingthe reflectivity and light-filtering of open cell foams, and the interesting texturesof those with closed cells.

9.1.1. Aluminium foam:

Also aluminium foam, see Figure 9.2, is beginning to be a large group of foamcores. It can be difficult to distinguish between aluminium foam as core materialor as a functional gradient material, which is used in for instance car production.The properties (mechanical, thermal et.) of foam materials is studied in the

field of cellular solids.Blocks of foam can be used as energy absorbers in various transportation-

related applications, such as automobiles, trucks and trains and highway crashbarriers. Cymat is capable of producing aluminum foam panels up to four feetwide and 50 feet long with thickness ranging from 1 inch to 4 inches. The densitiesavailable are from 2.5% dense aluminum (0.0675 g/cc) to 20% dense aluminum(0.54 g/cc).

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9.2. Polymeric foam

Polymeric foams have important economic impact on nearly every aspect of lifetoday. High-density cellular plastics are used in furniture, transportation, andbuilding products. Low-density foams are used as shock mitigation, insulation,and rigid packaging.Foams can be manufactured from a variety of synthetic polymers includ-

ing polyvinyl chloride (PVC), polystyrene (PS), polyurethane (PU), polymethylmethacrylamide (acrylic), polyetherimide (PEI) and styreneacrylonitrile (SAN).

Polyvinyl chloride PVC - Often used in the manufacture of racing boats,as the linear construction foams are flexible, and can be heat moulded aroundcurves.Closed-cell polyvinyl chloride (PVC) foams are one of the most commonly

used core materials for the construction of high performance sandwich structures.Although strictly they are a chemical hybrid of PVC and polyurethane, they tendto be referred to simply as ’PVC foams’.PVC foams offer a balanced combination of static and dynamic properties and

good resistance to water absorption. They also have a large operating tempera-ture range of typically -240◦C to +80◦C , and are resistant to many chemicals.Although PVC foams are generally flammable, there are fire-retardant grades thatcan be used in many fire-critical applications, such as train components. Whenused as a core for sandwich construction with fiber reinforced polymer (FRP)skins, its reasonable resistance to styrene means that it can be used safely withpolyester resins and it is therefore popular in many industries. It is normallysupplied in sheet form, either plain, or grid-scored to allow easy forming to shape.There are two main types of PVC foam: crosslinked and uncrosslinked with

the uncrosslinked foams sometimes being referred to as ’linear’. The uncrosslinkedfoams are tougher and more flexible, and are easier to heat-form around curves.However, they have some lower mechanical properties than an equivalent densityof cross-linked PVC, and a lower resistance to elevated temperatures and styrene.Their cross-linked counterparts are harder but more brittle and will produce astiffer panel, less susceptible to softening or creeping in hot climates. Typicalcross-linked PVC products include the Herex C-series of foams, Divinycell H andHT grades and Polimex Klegecell and Termanto products.A new generation of toughened PVC foams is now also becoming available

which trade some of the basic mechanical properties of the cross-linked PVCfoams for some of the improved toughness of the linear foams. Typical products

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include Divincell HD grade.Owing to the nature of the PVC/polyurethane chemistry in cross-linked PVC

foams, these materials need to be thoroughly sealed with a resin coating beforethey can be safely used with low-temperature curing prepregs. Although specialheat stabilisation treatments are available for these foams, these treatments areprimarily designed to improve the dimensional stability of the foam, and reducethe amount of gassing that is given off during elevated temperature processing.Applications of PVC foam are in maringe, aerospace, transportation, military

and defence, and industry.

Polystyrene (PS)- Very light - around 40kg/m3, inexpensive and easily shaped.Although polystyrene foams are used extensively in sail and surf board man-

ufacture, where their light weight (40kg/m3), low cost and easy to sand charac-teristics are of prime importance, they are rarely employed in high performancecomponent construction because of their low mechanical properties. They cannotbe used in conjunction with polyester resin systems because they will be dissolvedby the styrene present in the resin (ester-based matrices cannot be used as adhe-sives). PS or EPS (extruded PS) is primary used as thermal insulation materialsbut also in some load carrying structures. Extruded polystyrene insulation offersa service temperature range of (-183◦C to +74◦C).

Polyurethane (PU) (PUR earlier)- Is very rigid and has and good mechanicalproperties, but tends to deteriorate with age and become delaminated.Polyurethane foams exhibit only moderate mechanical properties and have a

tendency for the foam surface at the resin/core interface to deteriorate with age,leading to skin delamination. Their structural applications are therefore normallylimited to the production of formers to create frames or stringers for stiffeningcomponents. However, polyurethane foams can be used in lightly loaded sandwichpanels, with these panels being widely used for thermal insulation. The foam alsohas reasonable elevated service temperature properties (150◦C), and good acousticabsorption. The foam can readily be cut and machined to required shapes orprofiles.

Polymethyl methacrylamide (PMI)For a given density, polymethyl methacrylamide (acrylic) foams such as Roha-

cell offer some of the highest overall strengths and stiffnesses of foam cores. Theirhigh dimensional stability also makes them unique in that they can readily beused with conventional elevated temperature curing prepregs. However, they areexpensive, which means that their use tends to be limited to aerospace composite

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parts such as helicopter rotor blades, and aircraft flaps. Acrylics has the high-est specific strength and stiffness for a given density. High stability makes themideal for use with prepregs, but they do not fit curves well. Maximum servicetemperature of PMI is 180◦C.

Styrene acrylonitrile (SAN) co-polymer FoamsSAN foams behave in a similar way to toughened cross-linked PVC foams.

They have most of the static properties of cross-linked PVC cores, yet have muchhigher elongations and toughness. They are therefore able to absorb impact levelsthat would fracture both conventional and even the toughened PVC foams. How-ever, unlike the toughened PVC’s, which use plasticisers to toughen the polymer,the toughness properties of SAN are inherent in the polymer itself, and so do notchange appreciably with age.SAN foams are replacing linear PVC foams in many applications since they

have much of the linear PVC’s toughness and elongation, yet have a higher tem-perature performance and better static properties. However, they are still thermo-formable, which helps in the manufacture of curved parts. Heat-stabilised gradesof SAN foams can also be more simply used with low-temperature curing prepregs,since they do not have the interfering chemistry inherent in the PVC’s. Maximumservice temperature of PMI is 125◦C.

Polyethylene (PET)- A crystalline polyethylene terephthalate (PET) foamby applying high-expansion foam extrusion and thermoforming to PET resin.The PET foam combines light weight and outstanding shock resistance with goodthermal insulation. Because it withstands temperatures up to 220◦C, PET foamis an excellent material for oven-proof food containers. And because of its superiorshock absorption and moldability, it makes an ideal packing material for multipleproducts.

Other thermoplasticsAs new techniques develop for the blowing of foams from thermoplastics, the

range of expanded materials of this type continues to increase. Typical is PEIfoam, an expanded polyetherimide/polyether sulphone, which combines outstand-ing fire performance with high service temperature. PEI is expensive, but can beused in temperatures from -194◦C - +180◦C, and can be used in structural, ther-mal and fire protection applications, for instance in aircrafts and train interiors,as it can meet some of the most stringent fire resistant specifications.

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9.3. Refractory foams / Ceramic foam

Refractory materials are ceramics that have been designed to provide acceptablemechanical or chemical properties while at high temperatures.Refractory foams are a new class of open cell, low density materials which

Ultramet has developed to produce lightweight refractory structures for a varietyof aerospace and industrial applications including thermal insulation, lightweight,precision mirrors, impact absorption, catalyst support, and metal and gas filtra-tion. By pyrolyzing a polymer foam, a reticulated vitreous carbon (RVC) foamis created which has substantial mechanical and thermal properties. By furtherCVI (chemical vapor infiltration) processing, ceramic (e.g. silicon carbide [SiC])and/or metal or mixed material foams can be fabricated.These cellular materials can be simultaneously optimized for stiffness, strength,

thermal conductivity, active surface area, and gas permeability. They are ther-mally stable, low in weight and density, chemically pure, resistant to thermalstress and shock, and are relatively inexpensive.

June 2001: A team of scientists from Technion, Israel, has succeeded in manu-facturing the worlds lightest ceramic foam material, implementing a unique mech-anism its members have developed. The new material is a ceramic foam thatcontains 94% to 96% air by volume, but can resist temperatures above 1700◦C.The material is made of aluminum oxide, a common high-temperature ceramic,

but gets its extraordinary insulating powers from the many tiny air bubbles withinthe material. The foam is generated from special crystals that contain the metalcomponents and all the foaming ingredients. Upon heating, the crystals form asolution. Within this solution a reaction takes place, forming polymer chains.After the chains grow sufficiently, the solution suddenly separates into a puresolvent and the polymer. At this point, the solvent begins to boil, forming trillionsof tiny bubbles that blow the polymer into a foam, stabilized by the polymerchains. Subsequent heating to high temperatures leaves behind the ceramic, metaloxide foam.The material will be used for a wide variety of advanced applications such

as acoustic insulation, thermal insulation, adsorption of environmental pollutantsor as a platform for bio-technology applications. The estimated market for thisproduct is worth billions of dollars.

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Figure 9.3: Human bone is a hierarchical structure.

9.3.1. Carbon foam

Touchstone makes thee carbon foam product, CFoam by transforming high-sulfurbituminous coal into a strong but lightweight, fire-resistant, and thermally insu-lating material. A slice of Carbon foam that is exposed to a 3000◦ flame, can beheld by a hand in the other end due to its conductivity which makes that the endremains cool enough to touch. The carbon foam material can be used as for in-stance lightweight thermal protection in aircraft and spacecraft, as a fire blockingmaterial in military vehicles, as a porous electrode for lightweight energy storage,and to provide insulation and fire protection in home construction.

9.4. Hierarchical structures (multiscale structures)

Some cellular structures are made up in a different matter than the previous ones.The hierarchical structures (also called multiscaled structures) are structures thatconsist of structures in many size scales or levels. They are also called multiscaledstructures. Many such structures can be found in nature, and humans have begunto imitate the nature and build man-made hierarchical structures. Weight-savingsand tailored properties are some of the benefit of such structures.Human bone (bones in general) is for instance a natural hierarchical structure,

see Figure 9.3.

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Figure 9.4: The Eiffel tower is also a hierarchical structure.

Eiffel-tower, on the other hand, is an example of an artifical/man-made hier-archical structure, see Figure 9.4, is a hierarchical structure.Most common materials or structures have a Poissons ratio 0.5 > ν > 0

(approximately 0.5 for rubbers and for soft biological tissues, 0.45 for lead, 0.33for aluminum, 0.27 for common steels, 0.1 to 0.4 for cellular solids such as typicalpolymer foams, and nearly zero for cork). In an isotropic material (a materialwhich does not have a preferred orientation) the allowable range of Poisson’s ratiois from -1.0 to +0.5. Hierarchical structures and foams have also been made withnegative Poissons ratio (ν < 0), and Poisson’s ratio > 1, which give excitingrespond to loads. The applications for such structures/materials are not widelyknown, but will certainly increase in future when the fabrication of such structureswill be easier. Rod Lakes (at: http://silver.neep.wisc.edu/~lakes/sci87.html) ismaybe the person who has done most in this field.

9.5. Biomaterials

A biomaterial is any material, natural or man-made, that comprises whole or partof a living structure or biomedical device which performs, augments, or replacesa natural function.

References:

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Cellular structures:http://ansatte.hin.no/dl//homo.htmlhttp://web.mit.edu/dmse/csg/Research.htmhttp://silver.neep.wisc.edu/~lakes/

Metal foam:http://www.metalfoam.net/http://www.porvair.com/fuelcell/metalfoam.htmhttp://www.porvair.com/fuelcell/http://www.ultramet.com/foamtech.htmhttp://www.cymat.com/http://www.npl.co.uk/npl/cmmt/metal_foams/index.htmlhttp://www.grantadesign.com/solutions/metalfoams.htm

Polymer foam:http://www.vitec.org.uk/http://www.foamandform.com/seminars/foam/

Ceramic foams:http://www.emgroup.nlhttp://www.solgel.com/articles/june01/news06_101.htm

Refractory foams:http://www.ultramet.com/http://voyager.cet.edu/iss/techcheck/techcheck3/wvproduct.html

General:http://www.npl.co.uk/npl/cmmt/metal_foams/applications.html

Hierarchical structureshttp://silver.neep.wisc.edu/~lakes/Hierarch.html

Negative Poissons ratio materialshttp://silver.neep.wisc.edu/~lakes/sci87.html

Biomaterials:http://www.engr.sjsu.edu/WofMatE/Biomaterials.htm

Questions• What is the definition of ”cellular solids”?• What types of foams are there, and what products are they used in?

125

• What is the advantages of foam materials compared to conventional solid ma-terials?• What are the applications of foam materials?• What is a refractory material/structure?• What is hierarchical structures?• Find two examples of man-made hierarchical structures and two examples ofnatural hierarchical structures.• Does foam with negative Poissons ratio exist? How does such a material act?• Does foam with Poissons ratio >1 exist?

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Part II

Sandwich ConstructionsComposite materials used today are often in the form of a sandwich construction,see Figure 9.5.A sandwich panel is built up by two thin skins, also called the

Face sheet

Adhesive

Honeycomb core(metal, composite or paper)

Face sheet

Figure 9.5: A sandwich construction.

facings, separated by a lightweight core. The core helps to increase the moment ofinertia such that the structure becomes efficient for resisting bending and bucklingloads. This is why sandwich panels are being used in applications where weight-saving is critical, for instance in aircraft and in portable structures.Sandwich designs are also used by nature itself for instance in a human skull

and in plants. While nature often uses the same material in the facings as inthe core and only vary the density, man-made sandwich panels usually consist ofdifferent materials, or even structures, in the facings and in the core.A sandwichconstruction is built up by different face- and core materials and forms, see Figure9.6 and [36, p.18].

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Figure 9.6: Sandwich materials and forms.

10. Why use sandwich constructions?

The mechanical behavior of a sandwich panel depends on the properties of theface and the core materials and on its geometry.The Figure 10.1 shows how the sandwich design works, the so-called sandwich-

effect.In Figure 10.2 we see the sandwich-effect in and aluminium-sandwich compared

to solid aluminium plates of different thickness.

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Figure 10.1: The sandwich effect.

Figure 10.2: Aluminium foam used as core material compared with aluminium plate.

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10.1. Face materials

The face material in a sandwich panel can be made of almost any material thatcan be formed into thin sheets. The properties we seek for in a face material are:• high stiffness, which gives high flexural rigidity• high tensile and compressive strength• impact resistance• surface finish• environmental resistance (chemical, UV, heat etc.)• wear resistanceThe most usual type of material used as facings are listed in the Table with a

summary of face materials.

MaterialMetals: Mild steel

Stainless steelAluminium AlloyTitanium Alloy

Wood: PinePlywood

Unidirectional fibre composites Carbon/Epoxy(vf = 0.6− 0.7) Glass/Epoxy

Kevlar/EpoxyBi-directional fibre composites Kevlar/Polyester(vf = 0.3− 0.4) Glass weave/Polyester

Glass WR /PolyesterRandom fibres Glass CSM(vf = 0.15− 0.25) SMC

, (10.1)

where WR=(woven roving), CSM= chopped strand mat, SMC = sheet mould-ing compound and vf is the volume fraction of fibers.

The most used group of face-materials is the fibre composites since they havea similar or even higher strength properties than metals, and are much easier tofabricate. Also, the possibility to tailor the face materials because the anisotropicbehavior of the fibres offer a very interesting addition. In this way fibres can beplaced in the direction where the loadcarrying is most important.

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Figure 10.3: Core exposed to shear.

10.2. Core materials and structures

The essential property of any core material is that it increases the thickness of thelaminate, without causing a great weight increase (engineering theory shows thatthe flexural stiffness of any panel is proportional to the cube of its thickness). Thepurpose of a core in a composite laminate is therefore to increase the laminate’sstiffness by effectively ’thickening’ it with a low-density core material. This canprovide a dramatic increase in stiffness for very little additional weight.Figure 10.3 shows a cored laminate under a bending load. Here, the sandwich

laminate can be likened to an I-beam, in which the laminate skins act as theI-beam flange, and the core materials act as the beam’s shear web. In this modeof loading it can be seen that the upper skin is put into compression, the lowerskin into tension and the core into shear. It therefore follows that one of the mostimportant properties of a core is its shear strength and stiffness.In addition, particularly when using lightweight, thin laminate skins, the core

must be capable of taking a compressive loading without premature failure. Thishelps to prevent the thin skins from wrinkling, and failing in a buckling mode.

The properties of primary interest for the core:• Low density (add little weight to the total weight of the sandwich)• Shear modulus (prevents wrinkling)• Shear strength (prevents wrinkling)• Stiffness perpendicular to the faces (prevents decrease in core thickness and

therefore a rapid decrease in the flexural rigidity)• Thermal insulation• Acoustic insulationThere are four main groups of core material used,

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Figure 10.4: Honeycomb core.

• Foams• Honeycombs• Corrugated• Wood

10.2.1. Foam Cores

Foams are one of the most common forms of core material. They can be manu-factured from a variety of synthetic polymers including polyvinyl chloride (PVC),polystyrene (PS), polyurethane (PU), polymethyl methacrylamide (acrylic), poly-etherimide (PEI) and styreneacrylonitrile (SAN). They can be supplied in densi-ties ranging from less than 30kg/m3 to more than 300kg/m3, although the mostused densities for composite structures range from 40 to 200 kg/m3. They arealso available in a variety of thicknesses, typically from 5mm to 50mm.

10.2.2. Honeycomb Cores

Honeycomb cores are available in a variety of materials for sandwich structures,which ranges from paper and card for low strength and stiffness, low load appli-cations (such as domestic internal doors) to high strength and stiffness, extremelylightweight components for aircraft structures. Honeycombs can be processed intoboth flat and curved composite structures, and can be made to conform to curveswithout excessive mechanical force or heating.Figure 10.4 shows the usual honeycomb shape. The cells can be triangular,

square or hexagonal cells which also can be filled with a rigid foam in order to

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provide a greater bond area for the skins, increases the mechanical properties ofthe core by stabilizing the cell walls and increases thermal and acoustic insulationproperties. The following materials are commonly used in honeycomb structures.

• Aluminium - Has been used since 1950, several alloys can be used, but incomparison it is old and heavy.

• Glass fibre reinforced plastic - Has a high temperature resistance and goodinsulating properties, but is denser than other materials.

• Kraftpaper honeycombs - impregnated paper with resin to make it waterresistant. Good strength at low cost.

• Nomex honeycomb which is made from Nomex paper - a form of paper basedon KevlarTM (Aramid fibre), rather than cellulose fibres. High strength andtoughness with a low density makes it the most widely used honeycombcore. The initial paper honeycomb is usually dipped in a phenolic resin toproduce a honeycomb core with high strength and very good fire resistance.It is widely used for lightweight interior panels for aircraft in conjunctionwith phenolic resins in the skins. Nomex honeycomb is becoming increas-ingly used in high-performance non aerospace components due to its highmechanical properties, low density and good long-term stability.

Figure 10.5 shows the shear strength and compressive strength of some of thecore materials described, plotted against their densities. Figure 10.6 shows theprices of some core materials.

Honeycombs can be made with several different cell shapes:

HexagonalThe most common shape is the one shown at Figure 10.4, but this can only

be used in flat components.

OverexpandedThe honeycomb in Figure 10.7 is over expanded, so that the cells are rectan-

gular. This gives better properties in the web direction, but worse in the other, itcan therefore be curved in the ribbon direction only. This shape is used for singlecurvature components.

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Figure 10.5: Compressive strength and shear strength of some of the core materialsplotted against their densities.

Figure 10.6: Comparative prices of some core materials.

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Figure 10.7: Overexpanded honeycomb structure.

Negative Poisson’s RatioHoneycombs can be made with negative Poissons Ratio, when the cell walls

are inverted as in Figure 10.8.

Figure 10.8: Honeycombs with negativ Poisson’s ratio.

10.2.3. Corrugated Cores

A corrugated core is shown in Figure 10.9.

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Figure 10.9: Corrugated core.

10.2.4. Wood Cores

Wood can be described as ’nature’s honeycomb’ because on a microscopic scaleyou find that it consists of closed-cell structure. It has a similar structure tothat of a hexagonal honeycomb, and consequently good mechanical properties.When used in a sandwich structure with the grain running perpendicular to theplane of the skins, the resulting component shows properties similar to those madewith man-made honeycombs. However, despite various chemical treatments beingavailable, all wood cores are susceptible to moisture attack and will rot if not wellsurrounded by laminate or resin. Wood is only used in large projects, as it has arelatively high density, of at least 100kg/m3.

BalsaThe most commonly used wood core is end-grain balsa. Balsa wood cores first

appeared in the 1940’s in flying boat hulls, which were aluminium skinned andbalsa-cored to withstand the repeated impact of landing on water. This perfor-mance led the marine industry to begin using end-grain balsa as a core materialin FRP construction. Apart from its high compressive properties, its advantagesinclude being a good thermal insulator offering good acoustic absorption. Thematerial will not deform when heated and acts as an insulating and ablative layerin a fire, with the core charring slowly, allowing the non-exposed skin to remainstructurally sound. It also offers positive flotation and is easily worked with simpletools and equipment.Balsa core is available as contoured end-grain sheets 3 to 50mm thick on a

backing fabric, and rigid end-grain sheets up to 100mm thick. These sheets canbe provided ready resin-coated for vacuum-bagging, prepreg or pressure-basedmanufacturing processes such as RTM. One of the disadvantages of balsa is its

136

high minimum density, with 100kg/m3 being a typical minimum. This problemis exacerbated by the fact that balsa can absorb large quantities of resin duringlamination, although pre-sealing the foam can reduce this. Its use is thereforenormally restricted to projects where optimum weight saving is not required or inlocally highly stressed areas.Balsa was the first material used as cores in load bearing sandwich structures

and is still often used as a core material.

CedarAnother wood that is used sometimes as a core material is cedar. In marine

construction it is often the material used as the ’core’ in strip-plank construction,with a composite skin on each side and the grain of the cedar running parallel tothe laminate faces. The cedar fibres run along the length of the boat giving foreand aft stiffness while the fibres in the FRP skins are laid at ±45◦ giving torsionalrigidity, and protecting the wood.

10.3. Adhesives

Bonding of sandwich construction involve bonding of two very dissimilar con-stituents, one solid and one softer cellular component, and the requirements con-cerning bonding are therefore somewhat different than normal use. The adhesivemust be stronger than the tensile strength of the core. Some of the requirementsof the adhesives are:

Surface preparationThe core and the face material have to be prepared before bonding, which

involves mechanically or chemically cleaning and sometimes priming.

SolventsCore materials are often very sensitive to certain solvents. For instance: Poly-

styrene foams are sensitive to styrene (polyester and vinylester contains styrene),while epoxies and polyurethanes may be used. Similar combinations needs to beinvestigated before bonding components.

Curing vaporsWhen curing, some adhesives (as phenolics) give off vapor when curing, which

can give rise to several bonding problems.

Bonding pressure

137

When pressure is needed to prevent pores to appear, be careful so that thecore will not fail due to the compression.

Adhesive viscosityThe adhesive must have exactly the right combination of surface wetting and

flow. In the case of foam or balsa core, the viscosity should be low enough toenable the adhesive to fill the surface cells properly and leave as little as possibletrapped air. But the viscosity must not be too low,the adhesive could be squeezedout leaving too thin bonding line.

Bond thicknessIf the bond is too thick, it adds extra unnecessary weight to the part. If it is

too thin, bonding will not be one properly.

StrengthThe bond must be able to transfer the design loads, which means it must have

the desired tensile and shear strength, at the temperatures that might occur.

Thermal stressesA frequent cause of debonding failures are thermal stresses. If for instance one

side is heated from sunlight it will deform due to thermal expansion. Most corematerials are very good insulators, and therefor it will be a very high thermalgradient over the bond line. This lead to very high shear stresses in the bondwhich may lead to debonding. In such environment, very ductile adhesives shouldbe chosen (high strain to failure).

ToughnessToughened adhesives which resist cracks better (improved impact resistance)

are on the market. They are ordinary resins which have elastomer particles added.

Viscoelastic propertiesHighly viscoelastic adhesives may be advantageous for example where there

are high thermal gradients.

Curing shrinkageAs much as 7% decrease in volume can an adhesive (as polyesters) shrink when

its curing. This leads to high interface (bond) shear stresses and may decreasethe strength of adhesive joints.

Curing exothermMost adhesives exhibit an exotherm (curing process gives off heat) curing.

This is seldom a problem in thin bondings spread over a large area.

138

Different types of adhesives are for instance:• Epoxy resins• Modified epoxies• Phenolics• Polyurethanes Urethane acrylates• Polyester and vinylester resins

References:Alulight products:

http://www.alulight.com/en/products/products.html

Composites:http://www.users.globalnet.co.uk/~weeks/

Composite%20Materials.htmhttp://www.netcomposites.com/education.asphttp://www.baltek.com/

Fibreshttp:// www.netcomposites.com/education.asp?sequence=45

Foam cores:http://www.netcomposites.com/education.asphttp://www.polymer-age.co.uk/techlink.htmhttp://www.hexcelcomposites.com

Adhesives:http://www.hexcelcomposites.com/products/honeycomb/

sand_design_tech/hsdt_p04.htmlhttp://www.hexcelcomposites.com/products/

Questions•Why are sandwich constructions used?•What kind of face and core materials are used in sandwich constructions?•What is the essential property of any core material•Is End Grain Balsa used as core material in sandwich construction? If yes,what kind of products, and what are the advantages of this product?(http://www.baltek.com/)

•What requirements must be taken into consideration when it comes to bondingsandwich-constructions with adhesives?

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11. Design of sandwich constructions

When we use sandwich panels in different applications we have to know the me-chanical properties of the face and core materials and the geometry of the panel.Often we formulate the design of a sandwich panel as an optimization problemwhere the goal is to minimize the weight of the panel that meet the constraintson stiffness and strength desired. With respect to the core and skin thickness, orthe materials, or the density of the core, the optimization can be carried out.

11.1. Design of sandwich beams

Design of sandwich beams are the basis for understanding more complicated panelsand constructions. Beams are defines as a long, slender, one dimensional structuralelement that carries load primarily in bending (flexure). In classical engineeringbeam theory where the cross-section of the beam is a homogenous material thetransverse shear deformations are neglected. In sandwich beam theory we cannotneglect the transverse shear deformations.An example of a sandwich beam can be seen in Figure 11.1. Here, the beam

has a given point load P at the middle of the length.l We use the subscripts ”f”,

Figure 11.1: A sandwich beam.

and ”c” which refer to the facings, and core, respectively.

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Figure 11.2: A curved beam.

11.2. Preliminaries

Let us start with recalling the problem of a straight beam subjected to a constantbending moment giving the beam a curvature 1/Rx. The length of the curve, lc atthe neutral axis (N.A.), that has radius Rx and angle α, see Figure 11.2, is foundby the formula

lc = Rxα.

The strain εx in a new curveline at a distance z from the N.A. (where εx = 0) canbe found as follows:

εx =(new curve length)-(old curve length)

(old curve length)=(Rx + z)α−Rxα

Rxα

=Rxα+ zα−Rxα

Rxα=

z

Rx.

The stress σx in the beam is then given by

σx = Eεx = Ez

Rx.

The applied bending moment dMx, with respect to the x-axis, caused by the forcedF acting on a small element, see Figure 11.3, of area dA = dydz at a point x is

dMx = zdF = zσxdA| {z }dF

= zσxdydz|{z}dA

.

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Figure 11.3: A small element dA.

The total moment at the point x of the beam with height h and depth b is

Mx =X

dMx =

Z h/2

−h/2

Z b/2

−b/2dMx =

Z h/2

−h/2

Z b/2

−b/2zσxdydz

=

Z h/2

−h/2

Z b/2

−b/2z

µE

z

Rx

¶dydz =

Z h/2

−h/2

Z b/2

−b/2Ez2

Rxdydz

=1

Rx

Z h/2

−h/2

Z b/2

−b/2Ez2dydz =

1

Rx

Z h/2

−h/2

Z b/2

−b/2Ez2dydz

=1

Rx

Z h/2

−h/2bEz2dz =

1

Rx(EI)eq =

1

RxD,

where

(EI)eq = b

Z h/2

−h/2Ez2dz (11.1)

(often also denoted D) is called the equivalent flexural rigidity, also called thebending stiffness. The general expression for the strain will then be

εx =z

Rx=1

Rxz =

µMx

D

¶z =

ÃMx

(EI)eq

!z. (11.2)

The strain will vary linearly with z over the cross-section. The basic equationsfor the sandwich beam are now established, and this makes it possible to find thecross-sectional properties and stresses in such a beam.

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11.3. The Flexural Rigidity and Shear Rigidity

The theory for engineering stresses in beams is easily adapted to sandwich beamsif we modify it slightly.

Flexural rigidityIn an ordinary beam the flexural rigidity, denoted EI, where E is the modulus

of elasticity (Young’s modulus) and I is the secondmoment of area. The equivalentflexural rigidity of a cross-section of a sandwich (see Allan 1969) is the sum offlexural rigidities of the different parts in the sandwich and can be found from(11.1) and is

(EI)eq = Ef

bt3f6+Ef

btfd2

2+Ec

bt3c12= 2 (EI)f + (EI)o + (EI)c , (11.3)

where d (= tf + tc) (see Figure 11.1) is the distance between the centroids of thefaces. The first term, 2 (EI)f , represents the flexural rigidity of the faces alonewhen they are bending about their own neutral axes, and the third term, (EI)c,represents the flexural rigidity of the core. The first and the third term are smallcompared to the second term, (EI)o , which corresponds to the stiffness of thefaces associated with bending about the centroid axis of the whole sandwich.

The faces in a sandwich are thin compared to the core (tf << tc), hence thefirst term in (11.3) is less than 1% of the second term if

3

µd

tf

¶2> 100 or

d

tf> 5.77 (11.4)

because ⎛⎝ Efbt3f6

Efbtfd2

2

⎞⎠ 100 < 1.The first term can therefor be neglected and (11.3) is the reduced to

(EI)eq = Efbtfd

2

2+Ec

bt3c12= (EI)o + (EI)c .

If the core is weak, then Ec << Ef , the third term of (11.3) is less than 1% ofthe second term if

6Ef tfd2

Ect3c> 100, (11.5)

143

because ÃEc

bt3c12

Efbtfd2

2

!100 < 1.

The third term and can therefore be neglected, and (11.3) is reduced to the ap-proximated simple formula

(EI)eq =Efbtfd

2

2= (EI)o . (11.6)

Shear rigidityThe shear rigidity AG (shear stiffness) for a beam with a homogeneous cross-

section is given by

AG =bhG

k,

where h is the height, G is the shear modulus, and k is a shear factor, which forrectangular homogenous cross-sections equals 1.2.The equivalent shear rigidity (shear stiffness) for a sandwich beamwhenEc <<

Ef and tf << tc is given as

(AG)eq =bd2Gc

tc,

where Gc is the shear modulus of the core. We will come back to this later.

11.4. Tensile and Compressive Stresses

In a sandwich the faces carry bending moments as tensile and compressive stresses,while the core carries the transverse forces as shear stresses as illustrated in Figure11.4. The distribution of stresses and shear stresses in a sandwich is shown inFigure 11.4.

11.4.1. Due to bending (transversal loading)

From (11.2) the tensile and compressive stresses (also called direct stresses) in thesandwich due to bending shown in Figure 11.5 is given by

σ = εE =

ÃMx

(EI)eqz

!E. (11.7)

144

Figure 11.4: Stresses at different approximation levels in a sandwich.

Thus, the stress in the face σf of the sandwich due to bending can be written as

σf =MxzEf

(EI)eqfor

tc2< |z| < tc

2+ tf . (11.8)

Figure 11.5: A sandwich beam exposed to (transversal) bending load.

145

IfMx is positive then the maximum stress in the face appears when z = tc/2+ tf :

σf max =MxzEf

(EI)eq=

Mx

¡tc2+ tf

¢Ef

(EI)eq=

EfMx

¡tc2+ tf

¢³Ef btfd2

2

´=

2Mx

¡tc2+ tf

¢btfd2

=Mxtcbtfd2

+2Mx

bd2

while the minimum stress (in the same face) appears when z = tc/2:

σf min =MxzEf

(EI)eq=

Mx

¡tc2

¢Ef

(EI)eq=

EfMx

¡tc2

¢³Ef btfd2

2

´ =Mxtcbtfd2

.

HenceMxtcbtfd2

≤ σf ≤Mxtcbtfd2

+2Mx

bd2

in that face. When tf << tc this shows that we can use the following approxima-tive formula:

σf ≈Mxtcbtfd2

≈ Mxd

btfd2=

Mx

btfd(11.9)

(in order to see this we just use that

2Mx

bd2

Mxtcbtfd2

= 2tftc≈ 0).

(For the other face we obtain similarly that

σf ≈ −Mxtcbtfd2

≈ −Mxd

btfd2= −Mx

btfd.)

We obtain the opposite signs if Mx is negative.

The stress in the core σc of the sandwich due to bending is

σc =MxzEc

(EI)eqfor |z| < tc

2. (11.10)

146

Figure 11.6: A sandwich beam exposed to (in-plane) axial load F.

If Mx is positive then the maximum stress in the core appears when z = tc/2, i.e.

σcmax =MxzEc

(EI)eq=

Mx

¡tc2

¢Ec

(EI)eq=

Mx

¡tc2

¢Ec³

Ef btfd2

2

´=

2Mx

¡tc2

¢Ec

Efbtfd2=

MxtcEc

Efbtfd2

while the minimum stress in the core appears when z = 0,

σcmin =MxzEc

(EI)eq=

Mx (0)Ec

(EI)eq= 0.

Hence0 ≤ σc ≤

MxtcEc

Efbtfd2≤ MxtcEc

Efbtf t2c=

MxEc

Efbtf tc.

Thus when Ec << Ef we can use the following approximative formula:

σc =MxtcEc

Efbtfd2≤ MxdEc

Efbtfd2=

MxEc

Efbtfd≈ 0. (11.11)

The direct stress will vary linearly within each material constituent, but therewill be a jump in the stress at the interface between the face and the core, seeFigure 11.4.

11.4.2. Due to in-plane loading (axial)

The direct strain and stress in a sandwich due to in-plane loading shown in Figure11.6 is

εx0 =Fx

b (2Ef tf +Ectc),

147

where Fx is the axial load (normal force) and εx0 is the strain at the neutral axis(N.A.) if the two facings are of equal thickness (in order to see this, we note thatthe strain εx0 will be the same in the core and faces so that

Fx = Efεx0| {z }σf

2tfb|{z}Af

+Ecεx0| {z }σc

tcb|{z}Ac

= εx0b (2Ef tf + Ectc)).

The stresses will be

σf = Efεx0 and σc = Ecεx0.

The stresses and strains due to bending and in-plane loading can be superim-posed.

11.5. Shear stresses

Consider a small volume element with sidelengths dx, dy and dz see Figure 11.7.Using that

PF ix = 0 where F i

x are the forces acting on the cell walls i in thex-direction, we obtainX

F ix = −σxdydz + (σx +

∂σx∂x

dx)dydz

−τxydxdz +µτxy +

∂τxy∂y

dy

¶dxdz

−τxzdxdy + (τxzdxdy +∂τxz∂z

dz)dydx

=∂σx∂x

dxdydz +∂τxy∂y

dydxdz +∂τxz∂z

dzdydx

=

µ∂σx∂x

+∂τxy∂y

+∂τxz∂z

¶dxdydz = 0.

Hence,∂σx∂x

+∂τxy∂y

+∂τxz∂z

= 0. (11.12)

Similarly, by using thatP

F iy = 0 and

PF iz = 0, we obtain the other two

equations for equilibrium:XFy =

∂τ yx∂x

+∂σy∂y

+∂τ yz∂z

= 0 (11.13)

148

Figure 11.7: A small element.

and XFz =

∂τ zx∂x

+∂τ zy∂y

+∂σz∂z

= 0. (11.14)

It can also be verified that

τxy = τ yx, τxz = τ zx, τ yz = τ zy. (11.15)

Equations (11.12), (11.13), (11.14), and (11.15) are called the equilibrium equa-tions.

We assume that the shear stress in (11.12) will not vary with y, and therefore∂τxy/∂y = 0 (in fact we assume τxy = 0 in all points). Thus we get thatX

F ix =

∂σx∂x

+∂τxz∂z

= 0

and the shear stress τxz can therefore be found as follows:

∂σx∂x

= −∂τxz∂z

.

This givesZ (d+tf )/2

z

∂σx∂x

dz = −Z (d+tf )/2

z

∂τxz∂z

dz = −(τxz((d+ tf)/2| {z }=0

)− τxz(z)) = τxz(z),

(when using the fact that τxz at (d+ tf)/2 = 0) i.e.

τxz(z) =

Z (d+tf )/2

z

∂σx∂x

dz.

149

From equation (11.7)

σ = εE =

ÃMx

(EI)eqz

!E

and the fact thatdMx

dx= Tx

where Tx is the shear force. We obtain that the shear stress τxz(z)

τxz(z) =

Z (d+tf )/2

z

d³

Mx

(EI)eqzE´

dxdz =

Z (d+tf )/2

z

Ez

(EI)eq

dMx

dxdz =

=

Z (d+tf )/2

z

zE

(EI)eqTxdz =

Tx(EI)eq

Z (d+tf )/2

z

zEdz =Tx

(EI)eqB(z),

where B(z) is the first moment of area

B(z) =

Z (d+tf )/2

z

zEdz.

We observe that for |z| < tc/2

B(z) =

Z (d+tf )/2

z

zEdz =

Z tc/2

z

zEcdz +

Z (d+tf )/2

tc/2

zEfdz

= Ec

∙1

2z2¸tc/2z

+Ef

∙1

2z2¸(d+tf )/2tc/2

=Ec

2

"µtc2

¶2− z2

#+

Ef

2

"µd+ tf2

¶2−µtc2

¶2#

=Ec

2

∙t2c4− z2

¸+

Ef

2

"(d+ d− tc)

2

4− t2c4

#

=Ec

2

∙t2c4− z2

¸+

Ef

2d[d− tc]| {z }

=tf

=Ec

2

∙t2c4− z2

¸+

Efdtf2

.

Thus, the shear stresses in the core of the sandwich is

τ c =Tx

(EI)eq

µEf tfd

2+

Ec

2

µt2c4− z2

¶¶for |z| < tc

2. (11.16)

150

For tc/2 ≤ −z ≤ tc/2 + tf (in the upper face)

B(z) =

Z (d+tf )/2

z

zEdz =

Z −tc/2

z

zEfdz +

Z tc/2

−tc/2zEcdz| {z }=0

+

Z (d+tf )/2

tc/2

zEfdz

= Ef

∙1

2z2¸−tc/2z

+Ef

∙1

2z2¸(d+tf )/2tc/2

= Ef1

2

"µtc2

¶2− z2

#+Ef

1

2

"µd+ tf2

¶2−µtc2

¶2#

=Ef

2

∙t2c4− z2

¸+

Ef

2

"µd+ tf2

¶2− t2c4

#=

Ef

2

õd+ tf2

¶2− z2

!

=Ef

2

õ(tf + tc) + tf

2

¶2− z2

!=

Ef

2

µ1

4t2c + tf tc + t2f − z2

¶.

For tc/2 ≤ z ≤ tc/2 + tf (in the lower face)

B(z) =

Z (d+tf )/2

z

zEdz =

Z (d+tf )/2

z

zEfdz = Ef1

2

"µd+ tf2

¶2− z2

#

=Ef

2

õ(tf + tc) + tf

2

¶2− z2

!=

Ef

2

µ1

4t2c + tf tc + t2f − z2

¶(i.e. the same as for the upper face). Hence, the shear stress in the facings of thesandwich is

τ f =TxEf

2 (EI)eq

µ1

4t2c + tf tc + t2f − z2

¶for tc/2 ≤ |z| ≤ tc/2 + tf . (11.17)

Assume that Tx is positive (otherwise max is replaced by min and vice versa).

Then the maximum shear stress in the core appears when the expression(t2c/4− z2) in (11.16) is maximized, i.e. when z = 0 (the neutral axis N.A.),and is found in the following way:

τ cmax =Tx

(EI)eq

µEf tfd

2+

Ec

2

µt2c4− z2

¶¶=

Tx(EI)eq

µEf tfd

2+

Ec

2

µt2c4− 0¶¶

151

=Tx

(EI)eq

µEf tfd

2+

Ect2c

8

¶=

Tx³Ef btfd2

2

´ µEf tfd

2+

Ect2c

8

¶

=Tx

(Efbtfd2)

µEf tfd+

Ect2c

4

¶. (11.18)

The minimum shear stress in the core appears when the expression (t2c/4− z2)in (11.16) is minimized, i.e. when |z| = tc/2 (the face/core interface), i.e.

τ cmin =Tx

(EI)eq

µEf tfd

2+

Ec

2

µt2c4− z2

¶¶=

Tx(EI)eq

µEf tfd

2+

Ec

2

µt2c4− t2c4

¶¶

=Tx

(EI)eq

µEf tfd

2

¶=

Tx³Ef btfd2

2

´ µEf tfd

2

¶=

Txbd

. (11.19)

The maximum shear stress in the face appears when the expression³t2c4+ tctf + t2f − z2

´in (11.17) is maximized, i.e. when z = tc/2 (the face/core

interface) such that

τ f max =TxEf

(EI)eq 2

µt2c4+ tctf + t2f − z2

¶=

TxEf

(EI)eq 2

Ãt2c4+ tctf + t2f −

µtc2

¶2!=

=TxEf

(EI)eq 2

µt2c4+ tctf + t2f −

t2c4

¶=

TxEf

2 (EI)eq

¡tctf + t2f

¢=

TxEf

2³Ef btfd2

2

´ ¡tctf + t2f¢=

=TxEf

Efbd2(tc + tf) =

Txbd2

(tc + tf) =Txbd

(11.20)

(this also shows that τ cmin = τ f max).

The minimum shear stress in the face appears when the expression³t2c4+ tctf + t2f − z2

´in (11.17) is minimized, i.e. when |z| = tc/2 + tf

τ f min =TxEf

(EI)eq 2

µt2c4+ tctf + t2f − z2

¶=

TxEf

(EI)eq 2

Ãt2c4+ tctf + t2f −

µtc2+ tf

¶2!

152

=TxEf

(EI)eq 2

µt2c4+ tctf + t2f −

µt2f + tf tc +

1

4t2c

¶¶=

TxEf

2 (EI)eq(0) = 0.

The deviation between the maximum and minimum shear stress in the corefrom (11.18) and (11.19) will be less than 1 percent, i.e.

τ cmax − τ cminτ cmin

<1

100,

if

τ cmax − τ cminτ cmin

=

µ|Tx|

(Ef btfd2)

³Ef tfd+

Ect2c4

´¶−Ã

|Tx|µEfbtf d

2

2

¶ ³Ef tfd

2

´!|Tx|µ

Ef btf d2

2

¶ ³Ef tfd

2

´ <1

100.

This means thatEct

2c

4Ef tfd<

1

100,

or

100 <4Ef tfd

Ect2c

which is often satisfied for sandwich beams because we often have that the core isweak i.e. Ec << Ef and the faces are thin i.e. tf << tc. Thus we often use τ cminas an approximation for the shear stress in the core (see Figure 11.4).

11.5.1. Summary of approximations

If we assume weak core i.e. Ec << Ef and thin facings i.e. tf << tc, the stressesin the face and core in the sandwich are

σf,max =Mx

btfd(11.21)

from (11.9) since tc ≈ d, andσcmax ≈ 0 (11.22)

from (11.11).As an approximation for the shear stress in the core τ cmin we can use

153

τ c =Txbd

(11.23)

from (11.20).

154

11.6. Sandwich design: stiffness, strength and weight

The deflection, δ of a sandwich beam in general is the sum of the bending and

Figure 11.8: Deflection of a cantilever sandwich beam with an end point load..

shear components, see Figure 11.8 (subscripts ”b” and ”s” denotes bending andshear, respectively),

δ = δb + δs =PL3

B1 (EI)eq+

PL

B2 (AG)eq

where B1 and B2 are constants which depend on the geometry of the loading andthe boundary conditions (type of support). Moreover, the maximum moment Mx

and the maximum shear (transverse) force Tx are given by

Mx =PL

B3, Tx =

P

B4,

155

where B3 and B4 also are constants which depend on the geometry of the loadingand the boundary conditions. In Table 11.24 you can find the constans for severalloading conditions and boundary conditions.

Mode of loading,(all beams are of length L)

B1 B2 B3 B4

δb= PL3

B1(EI)eqδs= PL

B2(AG)eqMx=PL

B3Tx= P

B4

Cantilever,end load,P

3 1 1 1

Cantilever,Uniformly distributed load,q = P/L

8 2 2 1

Three-point bend,central load,P

48 4 4 2

Three-point bend,Uniformly distributed load,q = P/L

3845

8 8 2

Ends built in,Central load,P

192 4 8 2

Ends built in,Uniformly distributed load,q = P/L

384 8 12 2

(11.24)

In Table 11.24, Mx is the maximun bending moment and Tx is the maximumshear (transverse) force.

156

Figure 11.9: Cantilever beam with end point load.

11.7. Example of beam calculations

A cantilever beam has Gc = 30 MPa (80kg/m3 PVC foam), Ef = 200000 MPa(steel), L = 500mm, tf = 1 mm, tc = 30 mm (d = tc + tf = 31 mm), b = 1 mm,as in Figure 11.9.

a) Find the total deflection, δ, and the deflection due to shear in percentage ofthe total deflection.

The total deflection is described as

δ = δb + δs =PL3

3 (EI)eq+

PL

(AG)eq,

where the bending contribution is

δb =PL3

3 (EI)eq=

P · L3

3³Ef btfd2

2

´ = P · (500)3

3³200000·1·1·(31)2

2

´ = 0.43P (mm/N)

and the shear contribution is

δs =PL

(AG)eq=

PL³bd2Gc

tc

´ = P · 500³1·(31)2·30

30

´ = 0.52P (mm/N).

The total deflection is

δ = δb + δs = 0.43P + 0.52P = 0.95P (mm/N).

157

The deflection due to shear in percentage of the total deflection is

δsδb + δs

100 =0.52

0.95(100) = 54.7% (mm/N).

b) Compare a) with a homogenous steel beam with a rectangular cross-sectionof height h = 30 mm and width b = 1mm.

The total deflection is

δ = δb + δs =PL3

3 (EI)eq+

PL

(AG)eq,

where the bending contribution is

δb =PL3

3 (EI)eq=

PL3

3¡Ebh3

12

¢ = 4PL3

Ebh3=

4P · 5003200000 · 1 · 303 = 0.0926P

and the shear contribution is

δs =PL

(AG)eq=

PL¡bhk

¢ ³E

2(1+ν)

´ = P500¡1·301.2

¢ ³2000002(1+0.3)

´ = 0.00026P,where k is a shear factor. For rectangular homogeneous cross-sections k is 1.2.Poissons ratio ν = 0.3. The total deflection

δ = δb + δs = 0.0926P + 0.00026P = 0.0 929P.

The deflection due to shear in percentage of the total deflection is

δsδb + δs

100 =0.00026

0.0 929(100) = 0.28%.

This explains why elementary beam theory usually neglects the contributionof the transverse shear deformation.

c) Compare a) with a homogenous steel beam with a rectangular cross-section ofheight h = 2tf = 2 mm.

Here, the bending contribution is

δb =PL3

3 (EI)eq=

PL3

3¡Eh3

12

¢ = 4PL3

Eh3=4P · 5003200000 · 23 = 312.5P

158

and the shear contribution is

δs =PL

(AG)eq=

PL¡bhk

¢ ³E

2(1+ν)

´ = P500¡1·21.2

¢ ³2000002(1+0.3)

´ = 0.0039P.The total deflection

δ = δb + δs = 312.5P + 0.0039P = 312.5039P.

The deflection due to shear in percentage of the total deflection is

δsδb + δs

100 =0.0039

312.5039(100) = 0.00125% .

159

Figure 11.10: A simply supported three-point bended beam.

11.8. Strength and stiffness design example

A simply supported three-point bending beam, with uniform load case, has P =qL = 10000N,Gc = 40MPa (80kg/m3 PVC foam), (Ec = 100 MPa), shear strengthτ c,cr = 1.5MPa, Ef = 20000MPa (GRP), strength σf,cr = 100MPa, L = 1000mm,tc = 50mm, b = 100 mm, see Figure 11.10. The maximum allowed deformation ofthe beam is L/50.We assume Ec << Ef and tf << tc.

Find the face thickness, tf .

We know that

(EI)eq =Efbtfd

2

2and (AG)eq =

bd2Gc

tc,

and from Table 11.24 we find that

|Tx|max =P

2and |Mx|max =

PL

8. (11.25)

i) Strength design:Calculate the face thickness, tf , for maximum allowable stress.

160

We have the formulae

σf =MxmaxtcEf

2 (EI)eq=

¡PL8

¢tcEf

2³Ef btfd2

2

´ = ¡10000·1000

8

¢50 · 20000

2³20000·(100)·tf ·502

2

´ =

=

¡10000·1000

8

¢50 · 20000

2³20000·(100)·tf ·502

2

´ =250.0

tf,

here d ≈ tc, thus the face thickness for maximum allowable stress

tf =250

σf=250

100= 2.5 mm.

The maximum shear stress in the core is

τ c =Txmaxdb

=P2

db=

P

2db=

10000

2 · 50 · (100) = 1MPa

(which is satisfactory since τ c,cr = 1.5MPa). Next, we want to check the wrinklingstress 12.1

σcr = 0.53pEfEcGc = 0.5

3√20000 · 100 · 40 = 215 MPa

(which is satisfactory since σcr > σf = 100 MPa ).

ii) Stiffness designFind the face thickness for allowable deformation. Total deflection is

δ = δb + δs.

We find that

δb =PL3

3845(EI)eq

and δs =PL

8 (AG)eq

such that

δ = δb + δs =PL3

3845(EI)eq

+PL

8 (AG)eq=

PL3

3845

³Ef btfd2

2

´ + PL

8³bd2Gc

tc

´ ==

10000 · 100033845

³20000·100·tf ·(50)2

2

´ + 10000 · 10008³100·(50)2·40

50

´ = 52.1

tf+ 6.25.

161

Thus, when allowed deformation δ = L/50

tf =52.08333 3

(δ − 6.25) =52.083333¡100050− 6.25

¢ = 3.8 mmwhich is the thickness we must use to fulfill the requirements!Check the requirements due to the approximations. Since

3

µd

tf

¶2= 3

µ53.8

3.8

¶2= 601.3 > 100

(ord

tf=

53.8

3.8= 14.2 > 5.77)

then the first term of 11.3 is less than 1% of the second, and can therefor beneglected, and since

6Ef tfd2

Ect3c=6 · 20000 · 3.8 · (53.8)2

100 · (50)3= 105. 6 > 100

then the third term of 11.3 is less than 1% of the second , and can therefor beneglected such that we can use the reduced form of 11.3. The assumption

(EI)eq = D =Efbtfd

2

2

is valid!

162

12. Failure modes of sandwich panel

A sandwich panel must have the strength to carry the design loads without failingin one of the possible failure modes. We have to design against and consider allthe failure modes to be sure of that the structure will not fail. Examples on failuremodes is shown in Figure 12.1. A sandwich construction will fail by the failure

Figure 12.1: Some failure modes; a)face yielding/fracture, b) core shear failure, c) andd) face wrinkling, e) general buckling, f) face dimpling, and g) local indentation.

mode which occurs at the lowest load. The optimum design is when two or morefailure modes occur at the same load. The failure modes can be found on the basisof when the mode occur. Some of the failure modes is described in the followingchapter.The skin and core materials should be able to withstand the tensile, compres-

sive and shear stresses induced by the design load. Also the adhesive must becapable of transferring the shear stresses between skin and core. The sandwichpanel should also have sufficient bending and shear stiffness to prevent excessivedeflection.

163

12.1. Failure loads and stresses

(I) Face Yielding/fracture:Face yielding/fracture occurs when the normal stress in the face σf equals orexceeds the (yield) strength of the face material, σyf , such that:

σf =Mx

btfd=

PL

B3btfd≥ σyf .

(II) Face wrinkling:Face wrinkling (local buckling) occurs when the normal stress in the face reachesthe wrinkling stress (the local instability stress). Wrinkling occurs when the com-pressive stress in the face is

σf ≥Mx

btfd=

PL

B3btfd= 0.5 3

pEfEcGc. (12.1)

Hence, the wrinkling load is independent of the sandwich geometry, and is only afunction of the face and core properties. It is the core that has most influence onthe wrinkling load.

(III) Core shear failure:Core shear failure occurs in a foam with a plastic-yield point when the principalstresses satisfy the yield criterion. If the shear stress in the core is large comparedto the normal stress, failure occurs when the shear stress, τ c, equals or exceedsthe yield strength of the foam in shear, τ yc. The core failure is given by

τ cmax =Txbd=

P

B4bd≥ τ yc.

(IV) Failure of the adhesive bond (debonding):Failure of the adhesive bond can occur due to overloading. Debonding (the adhe-sive between the skin and the core fail) is the most difficult of the mechanisms toanalyze. The adhesive must have a strength equal or bigger than the shear stressin the bonding line under loading which is almost the same as τ cmax. To avoiddebonding therefore

τ cmax =Txbd≤ τ ya

164

where τ ya is the yield shear stress in the adhesive. High thermal stresses, fatigue,and aging are some of the reasons to debonding.

(V) Core indentation:Core indentation is only a problem when loads are very localized and can beavoided if we ensure that the load is distributed over a minimum area of at least

A ≥ P

σyc,

where σyc is the compressive strength of the core.

(VI) General buckling:General buckling can occur in sandwich constructions due to the transverse sheardeformation. The transverse shear deformation must be accounted for, since thisdecreases the buckling load compared with the ordinary Euler buckling cases. Thecritical buckling load for sandwich columns with thin faces is given by:

1

Pcr=1

Pb+1

Ps,

where Pb is the buckling load in pure bending, and Ps in pure shear, and they aregiven as follows

Pb =π2(EI)eq

(βL)2and Ps = (AG)eq ,

where β is the factor depending on the boundary conditions in Euler buckling, seeFigure 12.2

(VII) Face dimpling (local buckling, or intercellular buckling):Face dimpling may occur in sandwich structures with honeycomb or corrugatedas core material. For a square honeycomb this buckling stress equals

σf = 2.5Ef

µtfa

¶2for Poissons ratio νf = 0.3,

where a is the length of the side of the cell. For hexagonal honeycombs thebuckling stress equals

σf =2Ef

1− ν2f

µtfs

¶2≤ σyf ,

Ãwhen νf = 0.3 then σf ≈ 2. 2Ef

µtfs

¶2!,

165

Figure 12.2: Different cases for Euler buckling.

where s is the radius of the inscribed circle in the honeycomb cell.

(VIII) Fatigue:Fatigue is said to cause more than 90% of all structural failures. For the facematerial, a conservative way to use the fatigue limit under which the materialcan undergo an infinite number of load cycles without exhibiting any damage bytaking the allowable face stress σyf as the material fatigue stress at the givennumber of load cycles and stress ratio. For the core material the reasoning issimilar; substitute the allowable shear stress τ yc with the fatigue limit. Be awarethat there is not always data for all materials available. Hopefully, more data willbe available in the future.

166

12.2. Failure-mode maps

Failure-mode maps can be used to design sandwich constructions in a way thatwill improve the performance of the sandwich so that no single component is over-designed. The designer can choose the anticipated failure mode, or making twodifferent failure modes equally likely occur. Also, this is an advantage for caseswhere certain failure modes should be avoided.The dominant failure mode mechanism for a given design, is the one giving

failure at the lowest load.A transition in failure mechanism takes place when two or more mechanisms

have the same load. This information can be displayed as a diagram or map(failure-mode map).The most important transitions we get from equating pairsof the failure-mode equations are: face yielding - face wrinkling, face yield - coreshear and face wrinkling - core shear, as shown in Figure 12.4. Failure-mode mapscan be constructed from the failure-mode equations that comes out as a result ofthe analysis of the different failure modes.Some different failure modes with the corresponding failure loads for a rectan-

gular sandwich beam are shown in the table below.

Summary of failure modes and failure loads:

Failure Mode Failure LoadFace Yielding/fracture (I) P ≥ σyf

B3btfd

L

Face Wrinkling (II) P ≥ B3btfd

L0.5 3pEfEcGc

Core shear failure (III) P ≥ B4btcL

Failure of the adhesive bond (debonding) (IV) Tx ≥ τ yabdCore indentation (V) P ≥ σycA

(12.2)

12.2.1. Transition equation between face yielding and face wrinkling

Face yielding/fracture occurs when

σf =Mx

btfd=

PL

B3btfd=

P

B3btfLd= σyf .

hence the failure load P is given by

P = σyfB3bd

µtfL

¶. (12.3)

167

Face wrinkling (local buckling) occurs when

σf =|Mx|btfd

=PL

B3btfd= 0.5 3

pEfEcGc.

Thus the failure load P can be written as

P = 0.5B3

µtfL

¶bd 3pEfEcGc. (12.4)

Putting (12.3) and (12.4) equal to each other, we obtain that

σyfB3bd

µtfL

¶= 0.5B3

µtfL

¶bd 3pEfEcGc, (12.5)

i.eσyf = 0.5E

13f E

13c G

13c = 0.5 3

pEfEcGc. (12.6)

By using the fact that for most foams and honeycombs the mechanical prop-erties vary with the density of the material in the following way

Ec = CEρnc , Gc = CGρ

nc , σyc = Cσρ

mc and τ yc = Cτρ

mc , (12.7)

where the constants CE, CG, Cσ, Cτ , n andm depend on the type of microstructureand the mechanical properties of the micromaterial in the core, we find that

σyf = 0.53pEfEcGc = 0.5

3

qEf (CEρnc ) (CGρnc ) = 0.5

3pEfCECGρ2nc .

Thus the transition between face yielding and face wrinkling is given by the equa-tion

ρc =2n

s³σyf0.5

´3 1

EfCECG, (12.8)

which is independent of tf/L and therefore will appear as a horizontal line in afailure mode map in Figure 12.4, where the variable tf/L is along the horizontalaxis and ρc is along the vertical axis.

168

12.2.2. Transition equation between face yield and core shear

Core shear failure occurs when

τ cmax =Txbd=

P

B4bd≥ τ yc,

whereP = τ ycB4bd = (Cτρ

mc )B4bd. (12.9)

by the use of (12.7).

Face yielding/fracture occurs when

σf =Mx

btfd=

PL

B3btfd= σyf .

Thus, we find that the failure load

P = σyfB3b

µtfL

¶d. (12.10)

Putting the two expressions in (12.9) and (12.10) equal to each other

(Cτρmc )B4bd = σyfB3b

µtfL

¶d,

we obtain that

ρmc = σyfB3

CτB4

µtfL

¶.

Thus the transition equation between core shear failure and face yielding will begiven by

ρc =m

rσyf

B3CτB4

µtfL

¶ 1m

. (12.11)

12.2.3. Transition equation between face wrinkling and core shear

Face wrinkling (local buckling) occurs when

σf =Mx

btfd=

PL

B3btfd= 0.5 3

pEfEcGc.

169

Hence,

P = 0.5B3

µtfL

¶bd 3pEfEcGc = 0.5B3

µtfL

¶bd 3

qEf (CEρnc ) (CGρnc )

= 0.5B3

µtfL

¶bd 3pEfCECGρ2nc (12.12)

by the use of (12.7).Core shear failure occurs when

τ cmax =Txbd=

P

B4bd= τ yc.

Hence,P = τ ycB4bd = Cτρ

mc B4bd (12.13)

by (12.7).Putting the two expressions in (12.12) and (12.13) equal to each other, we get

that1

2B3

µtfL

¶bd 3pEfCECGρ2nc = Cτρ

mc B4bd.

i.e.B3 3pEfCECG

2CτB4

µtfL

¶= ρmc

¡ρ2nc¢− 1

3 = ρm−2n

3c .

Thus, the transition equation between face wrinkling and core shear failure willbe

ρc =m− 2n3

sB3 3pEfCECG

2CτB4

µtfL

¶ 1

m− 2n3. (12.14)

Summing up:The Face yield - Face wrinkling transition equation is given by

ρc =2n

s³σyf0.5

´3 1

EfCECG. (1) (12.15)

The Face yield - Core shear transition equation is

ρc =m

rσyf

B3CτB4

µtfL

¶ 1m

. (2) (12.16)

170

The Face wrinkling - Core shear transition equation is given by

ρc =m− 2n3

sB3 3pEfCECG

2CτB4

µtfL

¶ 1

m− 2n3(3) (12.17)

The transitions of failure modes in (12.15), (12.16) and (12.17) are illustratedin the failure mode map in Figure 12.4.

An example of a failure mode map To illustrate that the transition betweenthe failure modes can form a failure mode map, we will have a look at a beam inthree-point bending. The beam has faces with ultimate strength σyf = 150MPaand Ef = 70000MPa. B3 = 4 and B4 = 2. We assume a linear relation betweenthe core properties and the core density, which means that n = m = 1, andthat CE = 1, CG = 0.4 and Cτ = 0.015. Then we obtain the following transitionequations:

The Face yield - Face wrinkling transition equation is given by

ρc = 2n

s³σyf0.5

´3 1

EfCECG= 2

s³σyf0.5

´3 1

EfCECG(1) (12.18)

=2

sµ150

0.5

¶31

(70000) (1) (0.4)= 31.053.

The Face yield - Core shear transition equation is

ρc = (150)(4)

(0.015) (2)= 20000

µtfL

¶. (12.19)

The Face wrinkling - Core shear transition equation is given by

ρc =m− 2n3

sB3 3pEfCECG

2CτB4

µtfL

¶ 1

m− 2n3 (12.20)

=13

s(4) 3p(70000) (1) (0.4)

2 (0.015) (2)

µtfL

¶ 113

=

Ã(4) 3p(70000) (1) (0.4)

2 (0.015) (2)

!3µtfL

¶3= 8.296 4 · 109

µtfL

¶3.

171

Summing up we obtain that:The Face yield - Face wrinkling transition equation is given by

log10 ρc = log10 31.053

The Face yield - Core shear transition equation is

log10 ρc = log10 20000 + log10

µtfL

¶.

The Face wrinkling - Core shear transition equation is given by

log10 ρc = log10¡8.296 4× 109

¢+ 3 log10

µtfL

¶.

Thus, substituting x = log10³tfL

´and y = log10 ρc we obtain that

The Face yield - Face wrinkling transition equation is given by

y = log10 31.053

The Face yield - Core shear transition equation is

y = log10 20000 + x.

The Face wrinkling - Core shear transition equation is given by

y = log10¡8.296 4× 109

¢+ 3x.

The graphs of these expressions are illustrated in Figure 12.3, where we also haveindicated the failure mechanisms which are pairwise dominating on the respectiveside of each graph (1,2 and 3 denote face yield, face wrinkling and core shear,respectively). For each failure mechanism we now find the region for whichthis mechanism is dominating all other mechanisms. This region must be theintersection of the regions where the failure mechanism is pairwise dominatingthe others. The resulting regions are shown in Figure 12.4.

172

Figure 12.3: The graphs of the three transisition equations.

Figure 12.4: Failure mode map for a sandwich beam in three-point bending, which hasfaces made of aluminium and a core with properties that vary with the core density.

173

13. Design Procedures

Designing a sandwich element is very often an integrated process of sizing andmaterial selection in order to get some sort of optimum design with respect tothe objective you have chosen for instance weight, strength, or stiffness. Notethat all material systems have both advantages and disadvantages. Therefore it isdifficult to state some general terms about choosing materials. But, some materialrelated properties can still be considered despite the choice of material, such asdensity of the core material. An optimum design of a sandwich construction isvery difficult to obtain because there are so many different constraints that theproblem becomes complex. But, considering the most important constraints andusing a simple optimization technique could be very useful in the design process.An optimization on strength only does not ensure that the sandwich panel is

stiff enough. In most studies done in optimization they do not take into accountall possible failure modes as they should have.

13.1. The stiffness of sandwich structures and its optimization

We will consider a sandwich beam given a load P in three-point bending see Figure13.1. For several core microstructures it appears that the elastic moduli of the

Figure 13.1: A sandwich beam.

core Ec and Gc vary with the relative density of the core ρc/ρs in the following

174

way

Ec = C1Es

µρcρs

¶2, Gc = C2Es

µρcρs

¶2(13.1)

where ρc is the density of the core, ρs is the density of the solid material (cellwall) in the core, Es is the Youngs modulus of the solid material (cell wall) in thecore, and C1 (≈ 1) and C2 (≈ 0.4) are proportionality constants. We will explainthe concept of relative density ρc/ρs in more detail later.

Recall that for most cases the flexural rigidity

(EI)eq =Efbt

3f

6+

Ecbt3c

12+

Efbtfd2

2

is reduced to

(EI)eq =Efbtfd

2

2, (13.2)

and that the equivalent shear rigidity

(AG)eq =bd2Gc

tc

when d ≈ tc, is reduced to(AG)eq = bdGc. (13.3)

Recall also that the deflection δ

δ = δb + δs =PL3

B1 (EI)eq+

PL

B2 (AG)eq. (13.4)

If we insert (13.2) and (13.3) in (13.4) we obtain that the compliance (the inverseof the stiffness) of the beam

δ

P=

2L3

B1 (Efbtfd2)+

L

B2 (bdGc). (13.5)

In most sandwich design the key issue is to minimize the weight, W , (alsocalled the ”objective function” ) given by

W = mgV = 2ρfgbLtf| {z }facings

+ ρcgbLtc| {z }core

≈ 2ρfgbLtf| {z }facings

+ ρcgbLd| {z }core

, (13.6)

175

for a given bending stiffness P/δ, where m is the mass, V is the volume, g is theacceleration due to the gravity and ρf and ρc is the density of the face and corematerial, respectively. The only free variables are d, tf and ρc. For simplicity weassume that the core density ρc, is fixed. Then the optimization problem is quieteasy. By using (13.5), we find that

tf =2L3

B1Efbd2³

δP− L

B2(bdGc)

´ (13.7)

and by substituting it into (13.6) we have that the objective function (W is to beminimized)

W = 2ρfgL

⎛⎝ 2L3

B1Efbd2³

δP− L

B2(bdGc)

´⎞⎠+ ρcgLd. (13.8)

W =

⎛⎝ 4ρfgL4

B1Efbd2³

δP− L

B2(bdGc)

´⎞⎠+ ρcgLd

We minimize the weight W with respect to the only other free variable, d, by set-ting ∂W/∂d = 0 and then we obtain the optimum core thickness, dopt. Rearranging(13.8) we get that

W =1

B1Ef bδ

4PgρfL4d2 − B1Ef bL

4gρfL4B2(bGc)

d+ ρcgLd =

=1

k1d2 − k2d+ ρcgLd,

where

k1 =B1Efbδ

4PgρfL4, k2 =

B1EfbL

4gρfL4B2 (bGc)

.

Differentiating we get

∂W

∂d= − 2k1d− k2

(k1d2 − k2d)2 + ρcgL = 0

i.e.− (2k1d− k2) + ρcgL

¡k1d

2 − k2d¢2= 0,

176

which is a 4th order equation in d.

If the core density also should be treated as a variable the design optimizationproblem is more complex.

13.1.1. Example of minimum weight design for given stiffness

This is a method for finding the optimum face and core thickness for a givenstiffness, providing the materials included the core properties are predetermined.We assume that the core properties can be varied by choosing different densities.

If the compliance δ/P from (13.5) is denoted C, and solving it with respect totf as a function of d we obtain from (13.7) that

tf =2L3

B1Efbd2³

δP− L

B2(bdGc)

´ = 2L3

B1Efbd2³C − L

B2bdGc

´and by rearranging we get that

tf =2L3

B1Efbd2

⎡⎣ 1³C − L

B2bdGc

´⎤⎦ = 2L3

B1Efb

⎡⎣ 1³Cd2 − dL

B2bGc

´⎤⎦ =

=2L2

B1Efb

⎡⎣ 1³Cd2

L− d

B2bGc

´⎤⎦ = 2L2

B1Efb

∙Cd2

L− d

B2bGc

¸−1which when substituting into the weight equation, we obtain that the total weightW of the beam as a function of d (when d = tc)

W [g] =¡2ρf tf + ρcd

¢L =

Ã4ρfL

2

B1Efb

∙Cd2

L− d

B2bGc

¸−1+ ρcd

!L. (13.9)

A simply supported beam in three-point bending should have a maximummid-point deflection of δ = L/100. B1 is 48 and B2 is 4. Let L = 500mm, thewidth b = 1mm the faces are made of aluminium alloy with ρf = 2700kg/m

3 andEf = 70000MPa and the core has a density ρc = 100kg/m

3 and a shear modulusGc = 40MPa. Assume a point load of 10N is acting in the middle of the beam.

177

50454035302520

2.625

2.5

2.375

2.25

2.125

d [mm]

weight W [g]

d [mm]

weight W [g]

Figure 13.2: Beam weight (g/mm thickness) as function of thickness d.

The weight of the beam per unit thickness (eq. (13.9) times the length L) canthen be plotted versus thickness d as illustrated in Figure 13.2. The weight

W (d) [g] =

⎛⎜⎝4 (2.7 · 10−3) (500)248 (70000)

⎡⎣³

500100

10

´d2

500− d

4 (40)

⎤⎦−1 + 0.1 · 10−3d⎞⎟⎠ 500

simplifying and solving we get that

W (d) [g] =

µ8.0357× 10−4

0.001d2 − 0.00625d + 0.0001d¶500.

The weight of the beam per unit thickness (equation )The curve in Figure 13.2 shows that the optimum design is when d ≈ 29mm.

This value can be found more precisely by solving the equation

W 0(d) = 0

numerically, i.e. solving the equation

1

d22.511 2× 10−3 − 8.035 7× 10−4d

(0.001 d− 0.006 25)2+ 0.05 = 0.

178

The solution of this equation turns out to be i.e. d = 28.617. Thus the minimumtotal weight

W (28.617) =

=

µ8.0357× 10−4

0.001 (28.61729)2 − 0.00625 (28.61729)+ 0.0001 (28.61729)

¶500 =

= 2.058 6g.

Substituting back gives the face thickness

tf =2L2

B1Efb

∙Cd2

L− d

B2bGc

¸−1=

=2 (500)2

48 (70000) 1

⎡⎣³

500100

10

´(28.617)2

500− 28.617

4 (40) 1

⎤⎦−1 == 0.23249mm.

179

Part III

Cellular Solids14. Some definitions of cellular solids

Cellular solids are described by the geometric structure of the cells, that is bothshape and size of the cells and the way the cells are distributed. Foams are three-dimensional cellular solids and are more complex than the two-dimensional struc-tures like honeycomb-structures. But, by studying the two-dimensional structureswe make a basis in understanding the more difficult and complex three-dimensionalstructures of for instance foams.One of the most important feature of a cellular solid is what we call the relative

density, defined by

ρ =ρ∗

ρo(14.1)

where ρ∗ and ρo are the density of the cellular material and the outer (connectedsolid) material (which is the material that the cell-walls are made up of), respec-tively. When the relative density increases, the cell wall gets thicker. Relativedensity of the outer material is the same as the volume fraction of the outermaterial, po, defined by

po =volume of outer material (m3)

volume of foam (m3)=

VoV ∗

(see Figure 14.1). In order to see this, we observe that the density of the foam

ρ∗ =mass of foam (kg)

volume of foam (m3)=

m∗

V ∗

and the density of the outer connected material

ρo =mass of outer (kg)

volume of outer (m3)=

mo

Vo.

For the case when the inner material in Figure 14.1 and 14.2 is air, we have that

m∗ = mo.

180

Figure 14.1: Cellular solids.

Figure 14.2: Volume fraction of square honeycomb cells.

Thus, the volume fraction of the outer material

po =VoV ∗

=

moρom∗

ρ∗=

m∗

ρom∗

ρ∗=

ρ∗

ρo. (14.2)

Moreover, the volume fraction of the inner material is

pI =volume of inner (m3)

volume of foam (m3)=

VIV ∗

.

Note also that

po =VoV ∗

=V ∗ − VIV ∗

= 1− VIV ∗

= 1− pI.

When the cells are square honeycombs, as in Figure 14.2, the volume fractions canalso be expressed in the terms of side length l and wall thickness t in the followingway

181

Materials ρSpecial ultra-low-density foams 0,001Polymeric foams (packaging and insulation) 0,05-0,20Cork 0,14Softwoods 0,15-0,40

Table 14.1: Relative density for some cellular solids.

po = 1− pI = 1−(l − t)2

l2= 1−

µl − t

l

¶2= 1−

µ1−

µt

l

¶¶2=

1−Ã1− 2

µt

l

¶+

µt

l

¶2!= 2

µt

l

¶−µt

l

¶2,

which is approximately 2 (t/l) for small values of t/l. For a closed-cell structure,the relative density ρ∗/ρo can be written as

ρ∗

ρo= po = 2

µt

l

¶.

If the relative density ρ∗/ρo(= po) is is large, say po > 0.3, the structure willlook more like a solid material with isolated pores than a cellular structure (see[5], p. 2). Gibson and Ashby refer to materials with relative density less than 0.3as true cellular solids. Throughout we assume a low density, so that t << l (wallthickness<<wall-length), see Figure 14.3 and that all the walls have the samethickness. Simple beam theory is valid only when t/l < 1/4 (see [5], p. 110).Some examples of the relative density of some cellular solids are given in Table14.1.

In the same way we define the relative Young’s modulus as

E =E∗

Eo

where E∗ and Eo are the Young’s modulus of the cellular material and the solidmaterial, respectively.

182

x

x

x

2

3

1

th

l

Figure 14.3: Honeycomb structure.

14.1. Mechanics of honeycombs

The cells in a honeycomb-structure are usually hexagonal, but they can also betriangular or square or rhombic. We will mainly consider the regular square andregular hexagonal honeycombs. The honeycombs can be made of different typesof materials, such as metal, wood, polymer and ceramics or a combination of twoor more of these materials. For instance, foams of polymer inside the honeycomband thin metal on the outside will give a much more stiff/stabile construction sothat the wall thickness of the metal can be made even thinner to obtain an evenmore light-weight structure.When honeycombs are used in load-bearing structures it is important to un-

derstand the mechanical behavior of these two-dimensional structures, illustratedas hexagonal honeycomb-structures in Figure 14.3.Besides, many natural three-dimensional cellular solids (for instance wood)

that normally are too complex to be treated can be idealized and analyzed ashoneycomb-structures.

14.2. In-plane deformation properties, uniaxial loading of hexagonalhoneycombs

The study of the in-plane (also called transversal) properties will highlight thedifferent deformation and failure mechanisms of the cellular solids. In-plane prop-erties are defined as (the stiffness and strength) properties in the X1 −X2 plane,see Figure 14.4.

183

σ2

σ2

σ1

σ1

Figure 14.4: Honeycombstructure loaded in X1 or X2−direction.

In-plane compression of honeycombs gives us first a bending of the cell wallsand we obtain a linear elastic deformation. If the compression increases beyonda critical strain the cell walls will undergo collapse by elastic buckling, plasticyielding, creep or brittle fracture depending on the type material the cell wall ismade of.If the honeycomb is exposed for tension the cell walls first bend but they will

not obtain elastic buckling. Instead the cell walls will show extensive plasticityand if the cells are brittle it will fracture. The in-plane stiffness and strength arethe lowest ones because in this plane the cell walls will bend. We will study onlythe linear-elastic deformation case of a hexagonal honeycomb in uniaxial loadingin detail.The study of in-plane properties highlights the mechanisms by which cellular

solids deform and fail.

14.2.1. Linear-elastic deformation

If the hexagonal honeycomb is regular (all angles θ are 30◦, and wall thicknessesare equal as Figure 14.5 shows), then the in-plane properties are isotropic. Thismeans that the in-plane properties of the honeycomb can be described by onlytwo independent elastic moduli, for instance by Young’s modulus E∗ and a shearmodulus G∗. The notation ∗ means the effective value. If the honeycomb is notregular, the in-plane properties is described with four moduli (e.g. E∗1,E

∗2,G

∗12

and ν∗12). Here, ν∗12 is the Poisson’s ratio. If the general hexagonal honeycomb

(arbitrary cell wall angle θ) has a low relative density, ρ∗/ρo, (t/l is small) we have

184

Figure 14.5: A regular hexagonal honeycomb.

that

ρ∗

ρo≈

tl(hl+ 2)

2 cos θ(hl+ sin θ)

. (14.3)

When the honeycomb is regular (h = l and θ = 30◦), see Figure 14.5, then (14.3)is reduced to

ρ∗

ρo=

tl(hl+ 2)

2 cos θ(hl+ sin θ)

µ 1l2

1l2

¶=

tl(1 + 2)

2√32(1 + 1

2)=

t

l

2√3

which holds when strains are less than 20% or t/l is small.

The response of the honeycomb when loaded in x1− or x2−direction (seeFigure 14.4), is bending of the cell walls (see Figure 14.6), and is described by fivemoduli: two Young’s moduli E∗1 and E∗2 , a shear modulus G

∗12 and two Poisson’s

ratio ν∗12 and ν∗21. The reciprocal relation (according to Ashby)

E∗1 ν∗21 = E∗2 ν

∗12 (14.4)

where ν∗12 is the negative ratio of the strain in the x2− direction to that in thex1−direction for normal loading in the x1−direction, reduces the five not inde-pendent moduli to four independent moduli. (According to Meidell & Lukkassen,)

ν∗21E1

=ν∗12E2

which gives that ν∗21 E2 = ν∗12 E1

185

x

x

1

2

σ σ

x

x

1

2

σ

σ

1 1

2

2

Figure 14.6: Honeycomb deformed by normal stresss when loaded in X1 and X2.

When loading in x1− or x2− direction, respectively, the four independentmoduli are described as

E∗1Eo

=

µt

l

¶3cos θ¡

hl+ sin θ

¢sin2 θ

, (14.5)

E∗2Eo

=

µt

l

¶3 ¡hl+ sin θ

¢cos3 θ

, (14.6)

ν∗12 = −ε2ε1=

cos2 θ¡hl+ sin θ

¢sin θ

(14.7)

and

ν∗21 = −ε1ε2=

¡hl+ sin θ

¢sin θ

cos2 θ. (14.8)

For regular hexagonal honeycombs, the two Young’s moduli will be reduced to

E∗1Eo

=E∗2Eo

= 2.3

µt

l

¶3,

and the two Poisson’s ratio will be reduced to ν∗12 = ν∗21 = 1. The honeycombexposed to a shear stress is shown in Figure 14.7. It is possible to show that theshear moduli G∗12 to be

G∗12Eo

=

µt

l

¶3 ¡hl+ sin θ

¢¡hl

¢2(1 + 2h/l) cos θ

,

186

x

x

1

2

τ τ

Figure 14.7: Honeycomb deformated by shear stress.

which for regular honeycombs is reduced to

G∗12Eo

= 0.57

µt

l

¶3=1

4

E∗1Eo

which correctly obeys the relation

G =E

2 (1 + ν)

for isotropic solids.

14.3. Out-of-plane deformation properties

Out-of-plane properties are defined as (the stiffness and strength) properties in thex3-plane, see Figure 14.8. The function of a honeycomb core in a sandwich panelis to carry the shear and normal loads in the x3-direction. When honeycombs areloaded either along the x3−plane or in out-of-plane shear they are much stifferand stronger than if they are loaded in in-plane.Out-of-plane tension and compression loading of a honeycomb imply that the

cell walls undergo only axial extension or compression and therefore the moduli,collapse stresses, and strength will be much larger.Also in the out-of-plane case we will only consider the linear-elastic defor-

mation case, as we did in the in-plane case. The out-of-plane analysis gives theadditional stiffness which is needed for the design of honeycomb cores in sandwich-panels, and for the description of the behavior of natural honeycomb-like material,such as wood.

187

Figure 14.8: A honeycomb with out-of-plane loads (faces normal to X3− direction).

14.3.1. Linear-elastic deformation

A total of nine moduli are needed to describe the out-of-plane deformation, thatmeans five new ones in addition to the four already described (E∗1 , E

∗2 , G

∗12 and

υ∗12). We will now find the five new moduli. The Young’s modulus E∗3 , for normal

loading in the x3-direction is obviously the same as the Young’s modulus for theouter material, Eo, scaled by the loadbearing section area

E∗3Eo

=ρ∗

ρo≈ t

l.

The next two Poisson’s ratio are equal to the solid itself

υ∗31 = υ∗32 = υo,

and the Poisson’s ratio υ∗13 and υ∗23 are found from the reciprocal relations (see[5], p. 498)

υ∗13 =E∗1E∗3

υo ≈ 0, υ∗23 =E∗2E∗3

υo ≈ 0.

The shear moduli are more complicated to find because of the non-uniformdeformation in the cell walls due to stress distribution in the honeycomb. Theplane honeycomb may not remain plane, and exact calculations may only be doneusing numerical methods. But, we can obtain upper and lower bounds for the twoshear moduli, with the help of the method in [23], by calculating the strain energy

188

associated first with the strain distribution and next by the stress distribution(see [5], p. 149). If the two coincide, the solution is exact, but if not the truesolution lies somewhere in between the upper and lower bound. We will only givethe results here, for more information see [5], p. 150. The upper and lower boundsfor G∗13, respectively:

G∗13Go≤ cos θ

h/l + sin θ

µt

l

¶,

G∗13Go≥ cos θ

h/l + sin θ

µt

l

¶which are identically, and therefor we have an exact solution. For the regularhexagon we obtain that

G∗13Go

= 0.577

µt

l

¶. (14.9)

The upper and lower bounds for G∗23, respectively:

G∗23Go≤ 12

h/l + 2 sin2 θ

(h/l + sin θ) cos θ

µt

l

¶,

G∗23Go≥ h/l + sin θ

(1 + 2h/l) cos θ

µt

l

¶which are not identically. They will not coincide for a general, anisotropic honey-comb but for a regular hexagon they are reduced to

G∗23Go

= 0.577

µt

l

¶. (14.10)

We see that (14.9) and (14.10) are identical, which confirms that regular hexagonsare isotropic in the x1−x2 plane.The out-of plane shear moduli vary linearly with the relative density (t/l) and

are therefore larger that the in-plane moduli by the factor (t/l)2.Now we have all the parameters describing the orthrotropic structure, and we

can put them into the matrix 18.5 in order to find the compliance matrix (theinverse of the stiffness matrix).

Questions• What is relative density?

189

• Show that relative density is the same as volume fraction. Assume air insidethe cell.• Show that if the hexagonal honeycomb has a low relative density, ρ∗/ρo, (t/l issmall) then

ρ∗

ρs≈

tl(hl+ 2)

2 cos θ(hl+ sin θ)

.

• If the relative density of a square honeycomb is 0.8, what is the wall-thicknessof the honeycomb?• If the volume fraction of a hexagonal honeycomb is 0.8, what is the wall-thicknessof the honeycomb?• When is simple beam theory valid, according to Ashby & Gibson?•What is the difference between in-plane and out-of-plane properties of a honey-comb structure?• If a hexagonal honeycomb is regular (wall thicknesses are equal), are the in-planeproperties isotropic?• What does isotropic mean?• If the honeycomb is irregular and anisotropic, how many moduli for a completedescription of the in-plane properties is needed?• What is the definition of Poisson’s ratio?

190

Part IV

Mechanics and EffectiveProperties of CompositeStructures and Honeycombs15. On effective Properties of Composite Structures

Strongly non-homogeneous structures have fascinated people for a very long time.Archaeological observations in Finland show that fibre- reinforced ceramics weremade about 4000 years ago, and that people already at this time had ideas andtheories for intelligent combinations of materials and structures. Analysis ofthe macroscopic properties of composites was initiated by the physicists Raleigh,Maxwell and Einstein. Around 1970 one managed to formulate the physical prob-lems of material structures and composites in such a way that this field becameinteresting from a purely mathematical point of view. This formulation initiated anew mathematical discipline called homogenization theory. Independently of thisdevelopment scientists within the field of micro-mechanics have developed theirown theory concerning the mechanics of composites and structures.By using these theories we can determine locale and global (effective) proper-

ties of inhomogeneous structures which are too complex to be treated by conven-tional computational methods. The theories make it possible to design materialstructures with optimal properties with respect to weight, strength, stiffness, heatconductivity, electric conductivity, magnetic permeability, viscosity etc.Almost all literature on this field assumes relatively high knowledge in math-

ematics. However, in this paper we give a short introduction to the theory whichrequire physical intuition rather than deep theoretical understanding. We hopethis treatment makes it easier to understand some basic aspects of the theory fora broader audience, especially people with background in engineering.

16. The thermal problem

The heat flow in the direction of decreasing temperature. Moreover, for isotropicmateriels, the velocity v of the heat flow is proportional to the gradient of the

191

temperature, i.e.

v = −λ gradu (= −∙λ∂u

∂x1, λ

∂u

∂x2, λ

∂u

∂x2

¸T= −

⎡⎣ λ ∂u∂x1

λ ∂u∂x2

λ ∂u∂x2

⎤⎦),where u is the temperature and λ is called the conductivity. Assuming no heatsource in the body and no dependence of time, a simple application of the diver-gence theorem (Gauss theorem) shows that

divv = 0, (recall that divv =∂v1∂x1

+∂v2∂x2

+∂v3∂x3

).

Some materials have different effective conductivities in each direction. Thismeans that the velocity v of the heat flow can be written as

v = −∙λ11

∂u

∂x1, λ22

∂u

∂x2, λ33

∂u

∂x2

¸T,

or even more generally asv = −A gradu,

where A a symmetric matrix of the form

A =

⎡⎣ λ11 λ12 λ13λ12 λ22 λ23λ13 λ23 λ33

⎤⎦ .In a composite material we distinguish between the local conductivity A (whichvaries locally) and the effective conductivity

A∗ =

⎡⎣ λ∗11 λ∗12 λ∗13λ∗12 λ∗22 λ∗23λ∗13 λ∗23 λ∗33

⎤⎦(which is constant). This matrix is found as follows. Imagine that the compositeis subjected to a homogeneous temperature-field, that is a temperature-field suchthat the average value hgradui of gradu is constant. Letting hvi be the averagevalue of v = −A gradu we can obtain A∗ from the relation

hvi = A∗ hgradui .

192

The average is taken over some representative domain Y of the composite. Ingeneral this volume should be much larger than the typical length-scale of thematerial (e.g. fiber-diameter), but in the case of periodic materials we can aswell let Y be the cell of periodicity. Roughly speaking the effective conductivitymatrix A∗ is the matrix of a corresponding homogeneous material with the same”effective” thermal properties as the actual composite. In particular, the ”thethermal energy” in Y of the actual composite is equal to ”the thermal energy” inthe corresponding homogeneous material, i.e.Z

Y

1

2(gradu ·A gradu) dv| {z }

thermal energy in the composite

=1

2hgradui ·A∗ hgradui |Y || {z }thermal energy in corresponding

homogenized material.

. (16.1)

For example, if we want to find λ∗11 we impose the thermal field such that hgradui =[1, 0, 0]T then measure the energy W inside Y and obtain λ∗11 from (16.1):

λ∗11 = 2W

|Y | .

17. Isotropic elastic materials

For an isotropic material the shear modulus G and bulk modulus K in planeelasticity (plane strain) are related to the well known Young’s modulus E andPoisson’s ratio ν as follows:

K =E

2 (1 + ν) (1− 2ν) ,

G =E

2 (1 + ν).

The bulk modulus k of the three-dimensional theory is given by

k =E

3

1

1− 2ν .

Thus the plane strain bulk modulus K can be expressed as

K = k +G

3.

193

If the material is a thin plate, we consider the plane-stress problem. In this casethe plane stress bulk modulus is expressed as

K =E

2

µ1

1− ν

¶.

The shear modulus G is independent of the dimension and also independent ofwhether we are dealing with the plane-strain -or plane stress problem.

18. Orthotropic composites

Consider a linear elastic composite material in R3 which is locally orthotropic,and globally orthotropic. This means that in each point of the structure we havethat the stress-strain relation is given as⎡⎢⎢⎢⎢⎢⎢⎣

σ11σ22σ33σ12σ23σ13

⎤⎥⎥⎥⎥⎥⎥⎦| {z }

σ

=

⎡⎢⎢⎢⎢⎢⎢⎣C1111 C1122 C1133 0 0 0C2211 C2222 C2233 0 0 0C3311 C3322 C3333 0 0 00 0 0 C1212 0 00 0 0 0 C2323 00 0 0 0 0 C1313

⎤⎥⎥⎥⎥⎥⎥⎦| {z }

C

⎡⎢⎢⎢⎢⎢⎢⎣e11e22e33γ12γ23γ13

⎤⎥⎥⎥⎥⎥⎥⎦| {z }

e

and the average stress-strain relation of the form

⎡⎢⎢⎢⎢⎢⎢⎣hσ11ihσ22ihσ33ihσ12ihσ23ihσ13i

⎤⎥⎥⎥⎥⎥⎥⎦| {z }

hσi

=

⎡⎢⎢⎢⎢⎢⎢⎣C∗1111 C∗1122 C∗1133 0 0 0C∗2211 C∗2222 C∗2233 0 0 0C∗3311 C∗3322 C∗3333 0 0 00 0 0 C∗1212 0 00 0 0 0 C∗2323 00 0 0 0 0 C∗1313

⎤⎥⎥⎥⎥⎥⎥⎦| {z }

C∗

⎡⎢⎢⎢⎢⎢⎢⎣he11ihe22ihe33ihγ12ihγ23ihγ13i

⎤⎥⎥⎥⎥⎥⎥⎦ ,| {z }

hei

(18.1)

i.e.σ = Ce, hσi = C∗ hei . (18.2)

194

Here we assume equilibrium of stresses in each direction:

∂σ11∂y1

+∂σ12∂y2

+∂σ13∂y3

= 0,

∂σ21∂y1

+∂σ22∂y2

+∂σ23∂y3

= 0,

∂σ31∂y1

+∂σ32∂y2

+∂σ33∂y3

= 0.

where σij = σji (obtained by applying Gauss theorem as for the heat problem)These equations follows if we assume that the net force is 0. The symbol h·idenotes the average taken over some representative domain Y of the composite.In general this volume should be much larger than the typical length-scale of thematerial (e.g. fiber-diameter), but in the case of periodic materials we can as welllet Y be the cell of periodicity. Roughly speaking the effective stiffness matrix C∗

is the matrix of a corresponding homogeneous material with the same ”effective”properties as the actual composite. In particular, the actual strain energy stored inY is equal to the strain energy stored in the corresponding homogeneous material,i.e. Z

Y

1

2(e · Ce) dv| {z }

strain energy in the composite

=1

2hei · C∗ hei| {z } |Y |

strain energy in correspondinghomogenized material.

. (18.3)

Example 18.1. If we want to find C∗1111 we stretch the periodic structure in sucha way that average strain hei = [1, 0, 0, 0, 0, 0]T , then measure (or compute) theaverage stress hσi = [hσ11i , hσ22i , hσ33i , hσ12i , hσ23i , hσ13i]T and finally computethe coefficient C∗1111 from (18.1) which gives us that C∗1111 = hσ11i . Equivalently,we can ask the FE-program to compute the strain energy W (the left side of(18.3)) and then compute C∗1111 from (18.3), i.e. we obtainZ

Y

1

2(e · Ce) dv| {z }

strain energy in the composite

=1

2[1, 0, 0, 0, 0, 0]T · C∗ [1, 0, 0, 0, 0, 0]T |Y | = 1

2C∗1111 |Y | ,

thus

C∗1111 =2(strain energy)

|Y | .

195

The stiffness matrix is symmetric and the elements may be expressed as follows(see e.g. [32]):

C∗1111 =1− ν∗23ν

∗32

∆E∗2E∗3

, C∗1122 =ν∗21 + ν∗31ν

∗23

∆E∗2E∗3

, C∗1133 =ν∗31 + ν∗21ν

∗32

∆E∗2E∗3

C∗2222 =1− ν∗13ν

∗31

∆E∗1E∗3

, C∗2233 =ν∗32 + ν∗12ν

∗31

∆E∗1E∗3

, C∗3333 =1− ν∗12ν

∗21

∆E∗1E∗2

(18.4)

C∗1212 = G∗12, C∗2323 = G∗23, C∗1313 = G∗13,

where∆ =

1− ν∗12ν∗21 − ν∗23ν

∗32 − ν∗31ν

∗13 − 2ν∗21ν∗32ν∗13

E∗1E∗2E

∗3

.

Here, ’E∗i ’ are the effective Young’s moduli, ’G∗ij’ are the effective shear moduli

and ’ν∗ij’ are the effective Poisson’s ratios. The inverse of the effective stiffnessmatrix (the compliance matrix) which (certainly) also is symmetric is given by⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1E∗1

−ν∗12E∗2−ν∗13

E∗30 0 0

−ν∗21E∗1

1E∗2

−ν∗23E∗3

0 0 0

−ν∗31E∗1−ν∗32

E∗2

1E∗3

0 0 0

0 0 0 1G∗12

0 0

0 0 0 0 1G∗23

0

0 0 0 0 0 1G∗13

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦. (18.5)

19. Square symmetric unidirectional two-phase structure

In the case of square honeycombs with locally isotropic material properties (localshear moduli Go and GI and local plane strain bulk moduli Ko and KI withcorresponding volume fractions po and pI , respectively, where the subscript o andI denote outer and inner material, respectively (see Figure 19.1), the stiffnessmatrix reduces to a matrix of the form:⎡⎢⎢⎢⎢⎢⎢⎣

K∗ +G∗T K∗ −G∗T l∗ 0 0 0K∗ −G∗T K∗ +G∗T l∗ 0 0 0l∗ l∗ n∗ 0 0 00 0 0 G∗T,45 0 00 0 0 0 G∗L 00 0 0 0 0 G∗L

⎤⎥⎥⎥⎥⎥⎥⎦ . (19.1)

196

Figure 19.1: The structure of square honeybombs with locally isotropic material prop-erties.

Figure 19.2: The 4 moduli measure resistence against the indicated average strains.

Here, K∗ is the effective transverse (also called ”in-plane”) bulk modulus, G∗T ,G∗T,45 are the effective transverse shear moduli and G∗L is the longitudinal (alsocalled ”out-of plane”) shear modulus, see Figure 19.2. In this case the compliancematrix reduces to

197

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1E∗T

− ν∗TE∗T− ν∗L

E∗L0 0 0

− ν∗TE∗T

1E∗T

− ν∗LE∗L

0 0 0

− ν∗LE∗L− ν∗L

E∗L

1E∗L

0 0 0

0 0 0 1G∗T,45

0 0

0 0 0 0 1G∗L

0

0 0 0 0 0 1G∗L

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦. (19.2)

Using (18.4) and the symmetry we obtain the relations

G∗T =E∗T

2 (1 + ν∗T )(19.3)

4

E∗T=

1

G∗T+1

K∗ +4 (ν∗L)

2

E∗L. (19.4)

l∗ = ν∗L2K∗, n∗ = E∗L + 4 (ν

∗L)2K∗ (19.5)

Moreover, it has been proved by Hill [11] that

E∗L = poEo + pIEI +4(νo − νI)

2³1Ko− 1

KI

´2 (po 1Ko+ pI

1

KI− 1

K∗ ), (19.6)

ν∗L = poνo + pIνI −νo − νI1Ko− 1

KI

(po1

Ko+ pI

1

KI− 1

K∗ ). (19.7)

These two formulae were proved in [11] for the case of transverse isotropy. How-ever, by following the proof in [11] it is easy to check that the same facts hold inour case.

19.1. Calculation of stiffness and compliance matrix

We remark that (19.3), (19.4), (19.5), (19.6) and (19.7) hold for all two-componentunidirectional fiber composite (orientated in the direction x3) satisfying the prop-erty of square symmetry, i.e. the case when the stiffness matrix is of the form(19.1) (we say that the composite satisfies the property of transverse isotropy ifG∗T = G∗T,45, see Figure 19.3). In order to compute all components stiffness ma-trix (19.2) we only have to compute (e.g. numerically by using the finite elementmethod) the four components G∗L, G

∗T , G

∗T,45, and K∗. The other two moduli

198

Figure 19.3: Hexagonal honeycomb. Exampel of structure satisfying the property oftransverse isotropy (i.e G∗T = G∗T,45).

l∗and n∗ are the found by inserting the values of E∗L (19.6) and ν∗L (19.7) into(19.5). If we also want to know E∗T and ν∗T we can evaluate these values by firstevaluating E∗T from (19.4) and finally ν∗T from (19.3).It is possible to show thatG∗L can be found exactly as the effective conductivity

in the similar 2-dimensional problem by letting Go and GI play the same role asthe local conductivity for that problem.

Exercise 19.1. Consider square symmetric unidirectional two-phase compositewith volume-fractions pI = po = 1/2, Poissons ratios νI = νo = 0.3 and Youngsmodulus EI = 0.5, Eo = 1.(no units)

1. Find KI , Ko, GI , Go.

2. By performing a FE-calculation it is possible to find the following effectivemoduli:

K∗ = 0.658455,

G∗T = 0.273775,

G∗T,45 = 0.259418,

G∗L = 0.274426.

Find the effective stiffness matrix C∗

3. Find also ν∗L, E∗L, E

∗T and ν∗T . and find the effective compliance matrix.

199

20. Numerical methods for periodic structures

In order to use conventional software to solve displacement field numerically forperiodic structures, e.g. by the finite element method, it is often necessary to”translate” the information of the average strain hei into equivalent boundaryconditions for the on the cell of periodicity

Y = h0, y1i h0, y2i h0, y3i

for the displacement

u =

⎡⎣ u1u2u3

⎤⎦ .This is obtained by letting each pair of points (xl−, xl+) (the latter point with

the largest coordinates) on opposite faces with normal vector nl be coupled toeach other in such a way that⎡⎣ u1(xl+)

u2(xl+)u3(xl+)

⎤⎦ =⎡⎣ u1(xl−)

u2(xl−)u3(xl−)

⎤⎦+⎡⎣ c1l

c2lc3l

⎤⎦ , (20.1)

where ⎡⎣ c1lc2lc3l

⎤⎦is a constant vector. By integrating along the normal vector nl we obtain that¿

∂uk∂xl

À=

uk(xl+)− uk(xl−)

yl=

cklyl,

thus, recalling that

ekk =∂uk∂xk

γkl =∂uk∂xl

+∂ul∂xk

we obtain the following useful relation

ckkyk= hekki

200

Figure 20.1: The Y -cell in the symmetric case.

cklyl+

clkyk= hγkli . (20.2)

Henceckk = yk hekki .

Observe that ckl and clk are not uniquely determined by this relation when k 6= l.Thus in this case these constants can be chosen independently (as long as (20.2)is satisfied). E.g. we can choose

ckl = clk =hγkli1yl+ 1

yk

. (20.3)

If the material properties are symmetric in each coordinate with respect tothe midpoint ((1/2)y1, ..., (1/2)yn) of the Y -cell problem (see Figure 20.1) thenwe can often use simpler boundary conditions than (20.1).For example, in the case when all average shear strains hγkli = 0, we can in

(20.1) use the Dirichlet condition

ul(xl−) = 0, ul(xl+) = cll(= yl helli), l = 1, 2, 3, (20.4)

and drop all the other boundary conditions. The latter is equivalent with settinga Neumann condition, ∂ui/∂xl = 0, i 6= l on the same faces. It is easy tosee physically that these simplified boundary conditions hold by considering thedeformation of the whole periodic structure, since it is obvious that the solution(which indeed represents the deformed body) must inherit the same symmetryas the material itself (see Figure 20.2). Moreover, in the case when all averagenormal strains hekki = 0, we can in (20.1) use the Dirichlet condition

ui(xl−) = 0, ui(xl+) = cil(=hγili1yl+ 1

yi

), i 6= l (20.5)

201

Figure 20.2: Deformation of the periodic structure in the symmetric case.

and drop all the other boundary conditions. The latter is equivalent with settinga Neumann condition, ∂ui/∂xi = 0, i 6= l for l = 1, 2, 3 on the same faces.The boundary conditions for the conductivity case can be simplified in the

same way.

20.1. Coordinate transformation

For the computation of effective moduli it is sometimes convenient to rotate theoriginal coordinate system. Consider an orthonormal coordinate system with basisvectors

n1 = [n11, n12, n13]

n2 = [n21, n22, n23]

n3 = [n31, n32, n33] .

A vector with coordinates x = (x1, x2, x3) (relative to the usual coordinate system)will have coordinates x0 = (x01, x

02, x

03) (relative to the new coordinate system) given

by the relation ⎡⎣ x01x02x03

⎤⎦ =⎡⎣ n11 n12 n13

n21 n22 n23n31 n32 n33

⎤⎦⎡⎣ x1x2x3

⎤⎦(see Figure 20.3). It is possible to show that the following relation between thestrain e =

£e11, e22, e33,γ12, γ23,γ13

¤T, γij = 2eij (in the usual coordinate system)

and e0 =£e011, e

022, e

033,γ

012, γ

023, γ

013

¤T, γ0ij = 2e

0ij (in the new coordinate system):

e0 = Te,

202

Figure 20.3: The two coordinate systems.

where

T =

⎡⎢⎢⎢⎢⎢⎢⎣n211 n212 n213 n11n12 n12n13 n11n13n221 n222 n223 n21n22 n22n23 n21n23n231 n232 n233 n31n32 n32n33 n31n33

2n11n21 2n12n22 2n13n23 n11n22 + n21n12 n12n23 + n22n13 n11n23 + n21n132n21n31 2n22n32 2n23n33 n21n32 + n31n22 n22n33 + n32n23 n21n33 + n31n232n11n31 2n12n32 2n13n33 n11n32 + n31n12 n12n33 + n32n13 n11n33 + n31n13

⎤⎥⎥⎥⎥⎥⎥⎦ .

Moreover, we can obtain a similar relation between the corresponding stresses σand σ0 :

σ0 = T−Tσ,

where T−T is obtained from T by changing the factors of 2 in T symmetricallyabout the diagonal, i.e.

T−T =

⎡⎢⎢⎢⎢⎢⎢⎣n211 n212 n213 2n11n12 2n12n13 2n11n13n221 n222 n223 2n21n22 2n22n23 2n21n23n231 n232 n233 2n31n32 2n32n33 2n31n33

n11n21 n12n22 n13n23 n11n22 + n21n12 n12n23 + n22n13 n11n23 + n21n13n21n31 n22n32 n23n33 n21n32 + n31n22 n22n33 + n32n23 n21n33 + n31n23n11n31 n12n32 n13n33 n11n32 + n31n12 n12n33 + n32n13 n11n33 + n31n13

⎤⎥⎥⎥⎥⎥⎥⎦ .

The stress-strain relation in the new coordinate system can therefore be writtenas:

σ0 = C 0e0,

203

whereC = TTC 0T.

Concerning these facts we refer to e.g. [3, p. 212].In the plane strain case we put all strains related to the x3-variable equal to

0. If we also assume that the new coordinate system is obtained from the stan-dard one by a rotation in the x1-x2-plane then we obtain the following simplifiedrelations:

C =

⎡⎣ C1111 C1122 C1112C2211 C2222 C2212C1211 C1222 C1212

⎤⎦ ,T =

⎡⎣ n211 n212 n11n12n221 n222 n21n22

2n11n21 2n12n22 n11n22 + n21n12

⎤⎦ ,T−T=

⎡⎣ n211 n212 2n11n12n221 n222 2n21n22

n11n21 n12n22 n11n22 + n21n12

⎤⎦ .As an example, let us consider the square symmetric case, i.e. when the stiffness

matrix is of the form

C∗ =

⎡⎣ K∗ +G∗T K∗ −G∗T 0K∗ −G∗T K∗ +G∗T 00 0 G∗T,45

⎤⎦(c.f. (19.1)). Performing a rotation of 45◦, i.e. [n11, n12] =

h√22,√22

iand [n21, n22] =h

−√22,√22

i, the corresponding stiffness matrix in the rotated coordinate system

becomes

C∗0 = T−TC∗T−1 =

⎡⎣ K∗ +G∗T,45 K∗ −G∗T,45 0K∗ −G∗T,45 K∗ +G∗T,45 00 0 G∗T

⎤⎦ , (20.6)

i.e. C∗0 is the same as C∗ except that the shear moduli G∗T,45 and G∗T have changed

place. This explains the use of the index ”45” and shows that we can calculateG∗T,45 exactly as we calculate G

∗T except by rotating the coordinate system 45

◦.

204

Exercise 20.1. Verify (20.6) by calculating C∗ = TTC∗0T

Exercise 20.2. Let

C∗0 =

⎡⎣ K∗ +G∗ K∗ −G∗ 0K∗ −G∗ K∗ +G∗ 00 0 G∗

⎤⎦By matrix-multiplication it is possible to obtain that

TTC∗0T =C∗0. (20.7)

for any orthonormal coordinate system [n11, n12] = [cosφ, sinφ] , [n21, n22] =[− sinφ, cosφ] This is done by simplifying each of the elements of the matrix.For example we find that¡

TTC∗0T¢11= n411K

∗ + n411G∗ + 2n211n

221K

∗ + 2n211n221G

∗ + n421k + n421G∗

Verify that (20.7) holds for this element. (Note that (20.7) explains why compos-ites with this type of effective stiffness matrixes are called transversely isotropic).

Solution:

¡TTC∗0T

¢11

= (K∗ +G∗)¡n411 + 2n

211n

221 + n421

¢= (K∗ +G∗)

¡n211 + n221

¢2=

= (K∗ +G∗)¡cos2 φ+ sin2 φ

¢2= (K∗ +G∗) 12 = (K∗ +G∗) .

Exercise 20.3. Consider the same square symmetric unidirectional two-phasecomposite in Exercise 19.1. Suppose that the composite is used as core materialin a sandwich construction. How should we direct the fibres in order to maximizethe stiffness of the sandwich (compare the three alternatives in Figure 20.4).

Solution: The deflection of the sandwich due to shear deformation in thecore is dependent of G∗L (in alternative 1), G

∗T (in alternative 2) and G∗T,45 (in

alternative 3), where these parameters correspond ti the same coordinate system asin 19.1). Using the values we see that alternative 1 is (insignificantly) better thanalternative 2 which is better than alternative 3. (For example when calculatingthe deflection of a sandwich beam of type alternative 1 we use the same formulaeas in the isotropic case by using G = G∗L as the shear modulus of the core and thesame goes for alt. 2 and alt. 3).

205

Figure 20.4: Sandwich plate with three alternative cores.

21. A computational example

In the case of square honeycombs with locally isotropic material properties (seeFigure 19.1) the structure is symmetric with respect to the midpoint of the Y -cellY = [−1, 1]3 in all the coordinates x1, x2, x3, and also in the coordinates x01, x02, x3in the coordinate system obtained by a rotation of 45◦ in the x1-x2-plane. Theeffective stress/strain-relation (18.1) reduces in this case to⎡⎢⎢⎢⎢⎢⎢⎣

hσ11ihσ22ihσ33ihσ12ihσ23ihσ13i

⎤⎥⎥⎥⎥⎥⎥⎦ =⎡⎢⎢⎢⎢⎢⎢⎣

K∗ +G∗T K∗ −G∗T l∗ 0 0 0K∗ −G∗T K∗ +G∗T l∗ 0 0 0l∗ l∗ n∗ 0 0 00 0 0 G∗T,45 0 00 0 0 0 G∗L 00 0 0 0 0 G∗L

⎤⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣he11ihe22ihe33ihγ12ihγ23ihγ13i

⎤⎥⎥⎥⎥⎥⎥⎦ . (21.1)

In order to compute the effective in-plane moduli K∗ and G∗T we solve the cellproblem for hei = [1, 1, 0, 0, 0, 0, ]T and hei = [1,−1, 0, 0, 0, 0, ]T and compute thecorresponding valuesK∗ = hσ11i /2 andG∗T = hσ11i /2, respectively. Alternativelywe can compute the strain energy W and compute K∗ and G∗T from the identity

W =1

2hei · C∗ hei |Y | (21.2)

206

(discussed in (18.3)). For the computation it is enough to solve the two-dimensionalcell problem using plane strain. This is due to the fact that the solution of thethree dimensional cell problem in both cases will be independent of the x3-variableand we do not use any information of the strain or stresses in x3-direction for thecomputation ofK∗ andG∗T . Because of the symmetries it suffices to solve the prob-lem on 1/4 of the Y -cell, e.g. on the square Y = [0, 1]2. Since |Y | = 1, we obtainfrom (21.2) that K∗ = W/2 and G∗T = W/2. We can use uniform boundary con-ditions on each face of this square (see Section 20), i.e. for hei = [1, 1, 0, 0, 0, 0, ]Tthe boundary conditions are :

u1(0, x2) = u2(x1, 0) = 0,

u1(1, x2) = u2(x1, 1) = 1

and for hei = [1,−1, 0, 0, 0, 0, ]T :

u1(0, x2) = u2(x1, 0) = 0,

u1(1, x2) = 1

u2(x1, 1) = −1

(this follows from (20.4)). Due to symmetries the module G∗T,45 can be foundexactly as G∗T except that we must rotate the coordinate system 45

◦ (see the lastpart of Section 20.1).Alternatively we can compute G∗T,45 more directly by solving the cell problem

for hei = [0, 0, 0, 1, 0, 0]T and computing the corresponding value G∗T,45 = hσ12i ·1,or equivalently, compute the strain energy W and find G∗T,45 from the identity(21.2) (with |Y | = 1), which gives G∗T,45 = 2W . In this case we use the followingboundary conditions on each face of the square ( according to (20.5))

u2(0, x2) = u1(x1, 0) = 0,

u2(1, x2) = u1(x1, 1) =1

2.

The module G∗L can be found by using hei = [0, 0, 0, 0, 0, 1]T and computing

the corresponding value G∗L = hσ13i . The problem with doing this is that it oftenrequires a full 3D FE-computation regardless of the fact that the solution of thecell problem is independent of the x3-variable. Therefore it is often easier tosolve the corresponding 2D heat-conductivity problem (see Subsection 19.1) with

207

boundary conditions

u(0, x2) = 0

u(1, x2) = 1

using Go and GI as ”thermal conductivities” and computing G∗L from the thermalenergy W (16.1), which gives

G∗L = 2W.

Once we have computed the 4 moduli K∗, G∗T , G∗T,45, and G∗L we can easily

obtain all the other moduli (see Subsection 19.1).

As an example, consider a square honeycomb structure (see Figure 19.1) withvolume fractions pI = po = 1/2 and locally isotropic material properties νI =νo = 0.3, EI = 0.5, Eo = 1 (or equivalently KI = 0. 48076923, Ko = 0. 96153846,GI = 0. 19230769, Go = 0.38461538). By performing a FE-calculation accordingto the above method we obtain the following effective moduli:

K∗ = 0.658455,

G∗T = 0.273775,

G∗T,45 = 0.259418,

G∗L = 0.274426.

Hence, by using (19.3), (19.4), (19.6) and (19.7) we obtain that

ν∗L = 0.3,

E∗L = 0.75,

E∗T = 0.70779659,

ν∗T = 0.29266111,

and by (19.5)

l∗ = 0. 39507,

n∗ = 0.98704.

Thus the effective stiffness matrix is written as

208

⎡⎢⎢⎢⎢⎢⎢⎣0.932226 0.384677 0.39507 0 0 00.384677 0.932226 0.39507 0 0 00.395072 0.395072 0.98704 0 0 0

0 0 0 0.259418 0 00 0 0 0 0.274426 00 0 0 0 0 0.274426

⎤⎥⎥⎥⎥⎥⎥⎦ .

and the effective compliance matrix (19.2) takes the form

⎡⎢⎢⎢⎢⎢⎢⎣1.41284 −0.413482 −0.4 0 0 0−0.413482 1.41284 −0.4 0 0 0−0.4 −0.4 1.33333 0 0 00 0 0 3.8548 0 00 0 0 0 3.64397 00 0 0 0 0 3.64397

⎤⎥⎥⎥⎥⎥⎥⎦ .

In this example we used the same Poisson’s ratios in both phases. Let us considerthe case when νI = 0.4, νo = 0, EI = 0.5, Eo = 1 or equivalentlyKI = 0. 89285714,Ko = 0.5, GI = 0.17857143, Go = 0.5. In this case we obtain the following effectivemoduli:

K∗ = 0.66335 ν∗L = 0.22386372G∗T = 0.3038805 E∗L = 0.79338859G∗T,45 = 0.269322 E∗T = 0.79193337G∗L = 0.307502 ν∗T = 0.3030342

.

Remark 1. In the first example (where the Poisson’s ratios are the same in bothphases) ν∗L and E∗L equals the arithmetic mean of the corresponding phase prop-erties (usually referred to as ”the law of mixtures”). From the last example weobserve that this may not be true when the Poisson’s ratios of the phases aredifferent.

Exercise 21.1. Verify the above values for K∗, G∗T , G∗T,45, and G

∗L by performing

a FE-calculation according to the above method. Use e.g. the Finite ElementMethod programme ANSYS. For the calculation of K∗, G∗T , G

∗T,45 use Structural

problem, element type PLANE 82, element size 0.015, plane strain. For thecalculation of G∗L use thermal problem, element type PLANE 77, element size0.015.

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Part V

Fabrication processesIn this part we will study some of the fabrication processes concerning the mate-rials and structures studied in Part I. In particular we consider the processes offabricating polymers, plastics and composites. Moreover, we study some of theadvanced manufacturing techniques of layer manufacturing technology (LMT).From [4], we have the rough definition of what a material processing is: ”all

that is done to convert stuff into things”. Figure 21.1 gives an picture of thedifferent general materials processing types (independent of the material types).

Fabrication of an acceptable product involves the selection of bothi) an appropriate material andii) a companion method of processing,such that the resulting combination can provide the desired shape, properties,

precision and finish.

22. Fabrication of plastics

The fabrication method depends on what raw material we have. Polymers areformed by many low temperature processes. It is important to know for instancewhether the material is a thermoplastics or thermosetting. Thermoplastics canbe heated and then formed by either a formable solid or a liquid. Thermoset-tings have far fewer options, because once the polymerization has occurred, theframework structure is established and no further deformation can occur. Thusthe polymerization and the shape-forming are usually accomplished at the sametime. We will have a closer look at some of most used fabrication processes:

CastingIn casting, no fillers or no pressure is required. The liquid polymer is poured

into a container having the shape of the desired part. It is an inexpensive process,dimensional precision is quite high, but quality problems can occur due to inade-quate mixing, air entrapment, gas evolution, and shrinkage.Typical products: sheets, plates, rods and tubes as well as small objects such

as jewelry.

210

Figure 21.1: Materials processes.

211

Figure 22.1: Pressure die casting.

Pressure die castingPressure die casting (also called compression molding) is used for net-shape

forming (dimensional accuracy and surface details) of high-quality parts with com-plex shapes. Thanks to the high pressures involved, very thin walled parts can beobtained, see Figure 22.1. Preformed thermosettings (now also thermoplastics)are introduced into an open, heated cavity. Pressure are applied. Products are:gaskets, seals, exterior automobile panels, aircraft fairings , and a wide variety ofinterior panels.

Blow moldingIn blow molding, thermoplastics are converted into bottles or other hollow-

shape containers. The melted polymer is put into a mold, then compressed airis used to spread the polymer into the mold, see Figure 22.2.It is used to makemany containers such as plastic soda containers and milk jugs.

Cold moldingIn cold molding, raw thermosetting is pressed to shape while it is cold. Cured

in a separate oven. It is a low cost process, but neither surface finish nor dimensionprecision is good.

Injection molding

212

Figure 22.2: Blow molding.

Injection molding is the most widely used process for high-volume productionof thermoplastics parts. The resulting form is usually a finished product, no needfor other work before assembly or use. If the process is applied to thermosettings,the process must be modified to provide the temperature and pressure requiredfor curing (which is additional time in a heated mold).Similar to extrusion, the polymer is heated to the liquid state, but it is prepared

in metered amounts, and the melt is forced into a mold to create the part, seeFigure 22.3. This is not a continuos process. Many toys are made by injectionmolding.

Transfer moldingTransfer molding combines elements from compression and injection molding.

Preformed raw thermosetting material is placed into a cavity, where it is heateduntil molten which is forced into the channels in the die. Thin sections canbe made, with excellent detail, and good tolerance and finish. Inserts can beincorporated into the product.Products: switchgear and wiring devices, household appliances that require

heat resistance, structural parts that require hardness and rigidity under load.

213

Figure 22.3: Injection molding.

Reaction injection moldingIn reaction injection molding, two or more highly reactive liquid monomers are

mixed and immediately injected into the mold cavity where the chemical reactionsleading to solidification, occur, see Figure 22.4.Heating is not required. Polyurethane (thermosettings urethane-groups), polyamides

(thermoplastics amids-group), composites with short fibers and flakes can bemolded. Different formulations result in elastomeric or flexible, structural foam(foam core with a hard, solid outer skin), solid (no foam core), or composite prod-ucts. The shapes can be quite complex (with variable wall thickness), and surfacefinish is excellent.Products: automobile products; steering wheels, instrument panels, door pan-

els, armrests, household; refrigerators, water-skis.

Insert moldingInsert molding is an injection molding process whereby plastic is injected into

a cavity and around an insert piece placed into the same cavity just prior tomolding. The result is a single piece with the insert encapsulated by the plastic.The insert can be made of metal or another plastic.Like injection molding in general, insert molding can be accomplished with

a wide variety of materials, including polyethylene, polystyrene, polypropylene,

214

Figure 22.4: Reaction injection molding.

polyvinyl chloride, thermoplastic elastomers, and many engineering plastics. Theprimary factors that restrict the use of insert molding are not process related,but are determined by the strength and other properties required for the moldedproduct.Processing Parameters: One of the chief causes of failure in an insert-

molded part is the cleanliness of the insert. It is absolutely imperative that theinsert be as clean as possible prior to molding. When molding with large metalinserts, the inserts may need to be preheated to minimize the stresses caused bydifferential thermal expansion and contraction. When inserts are manually loadedit is important that the operator maintain a consistent cycle time.

ThermoformingIn thermoforming, thermoplastic sheet material is heated to a working tem-

perature and then formed into a finished shape by heat, pressure, or vacuum, seeFigure 22.5. There are two main steps in the process: heating and forming.Products: range from panels for contoured skylights, large items such as bath-

tubs, to pages of text for the blind.The size of Thermo Pressure Formed parts is limited by the size of the thermo-

forming machines now in use and the size of plastic sheet stock which is available.

215

Figure 22.5: An example of thermoforming.

Commercially available sheet stock is attainable in sizes of 120 inches wide andas long as required in thicknesses of up to .500 inches. Larger, thicker sheet stockis available in special cases.To date, the largest commercially available Thermo Pressure Formed parts are

in the size range of 48 inches long by 24 inches wide and 18 inches deep. However,the size capabilities of the process increase almost daily.

Rotational moldingRotational molding produce hollow, seamless products of a wide variety of

sizes and shapes, including storage tanks, bins, and refuse containers, doll parts,footballs, helmets, and even boat hulls. Gravity is used inside a rotational moldto achieve a hollow form, see Figure 22.6. The polymer is heated and due to therotation, distributed in the form of a uniform thickness all over the moldThe process is principally for thermoplastics (thermosets and elastomers are

more and more common).

ExtrusionBy extrusion, long plastic products with uniform cross section are produced.

Thermoplastic pellets or powder are the raw material. The polymer is heated tothe liquid state and forced through a die under pressure resulting in an endlessproduct of constant cross section, see Figure 22.7. Extrusion is a cheap and rapidmethod.Products: tubes, pipes, window frames, sheet and even coated wires and cables.

60% of polymers are prepared in this way.

216

Figure 22.6: Rotational molding.

Film BlowingFilm blowing uses the same method as extrusion: the material coming out of

the die is blown into a film. An example is plastic wrap.

Foam moldingIn foam molding, plastic foam is fabricated. Foaming agent is mixed with

the plastic resin and releases gas or volatilizes when the combination is heatedduring molding. The materials expand to 2-50 times their original size. Theprocess produce open-cell foams and closed-cell foams. Open cell-foams haveinterconnected pores that permit the permeability of gas or liquid. Closed-cellfoams have the property of being gas- or liquid-tight. Both thermoplastics andthermosettings can be foamed.Polyurethane is one of the most versatile polymers in use today. It’s chemistry

is based on the reaction of an isocyanate with a polyhydroxy compound (polyol).Therefore, a polyurethane foam-in-place system is a combination of the abovetwo components which have been preformulated so they need to only be mixedand dispensed to make polyurethane foam, see Figure 22.8. North Carolina FoamIndustries (NCFI) was awarded a Mission Success Medal on July 29, 1998 byLockheed Martin Michoud Space Systems for production and delivery of a light-weight spray-applied foam insulation system that Lockheed Martin applies on thesurface of the new super lightweight external fuel tank.

217

Figure 22.7: Extrusion.

Figure 22.8: Foaming in-place. From: http://www.ncfi.com/foam-in-place.htm

Products: Rigid foams are useful for structural applications, packaging, ship-ping containers, interiors of thin-skinned metal components, and flexible foamsare primarily used for cushioning.

22.1. Processing of Rubber and elastomers

The simplest of the fabrication processes is dipping, where a master form of metalis first produced, which is dipped into the molten liquid of elastomers.Dipping produce relatively thin parts with uniform thickness, such as boots,

gloves, balloons, swim caps, toys, and fairings.Adaptions of the previously discussed processes for plastics are also used to

produce the shapes (injection, compression, and transfer molding, and extrusion).

218

Figure 22.9: Glovedipping, picture from: http://www.accautomation.com/prodsysc.htm.

References:Fabrication Processes:http://islnotes.cps.msu.edu/trp/toc.htmlhttp://www/designinsite.dk

Fabrication of plastics:http://www.mse.cornell.edu/courses/engri111/polymer4.htm

Foam molding:http://www.ncfi.com/foam-in-place.htm

Videos:http://www.gwplastics.com/capabilities/amto.html3D Body scanner, see http://www.tc2.com/RD/RDBody.htm

Designhttp://www.machinedesign.com/

Application of plastics:http://www.stug.com.au/Applications/Common.html

Questions•What kind of main groups, subgroups and processes of fabrication processes arethere?• How does the fabrication of a thermoplastic polymer differ from the processingof a thermosetting polymer?

219

• What are some of the ways that plastic sheets, plates and tubes can be fabri-cated?• What types of polymers are most commonly blow molded?• What type of products are produced by rotational molding?• How do we produce long plastic products with uniform cross-section?• How are foamed plastics produced?• What is the difference between open-cell foams and close-cell foams?

220

23. Fabrication of Fiber-Reinforced Composites (FRC)

Taking composite materials as a whole, there are many different material optionsto choose from in the areas of resins, fibres and cores, all with their own uniqueset of properties such as strength, stiffness, toughness, heat resistance, cost, pro-duction rate etc. However, the end properties of a composite part produced fromthese different materials is not only a function of the individual properties of theresin matrix and fibre (and in sandwich structures, the core as well), but is also afunction of the way in which the materials themselves are designed into the partand also the way in which they are processed. In this section we compare a fewof the commonly used composite production methods.

23.1. Manufacturing processes of Reinforcements

Individual fibres or fibre bundles can only be used on their own in a few processessuch as filament winding. For most other applications, the fibres need to bearranged into some form of sheet, known as a fabric, to make handling possible.Different ways for assembling fibres into sheets and the variety of fibre orientationspossible lead to there being many different types of fabrics, each of which has itsown characteristics. These different fabric types and constructions are explainedlater.Glass filaments are supplied in bundles either strands, rovings or yarns. A

strand is a collection of more than one continuous glass filament. Roving generallyrefers to a bundle of untwisted strands wound in parallel to form a cylindrical,flat-ended package, similar to thread on a spool. Single-end roving contains onlyone continuous strand of multiple glass filaments. Multiple-end roving containsnumerous wound strands. Yarns are collections of filaments or strands (usuallysmaller than rovings) that are twisted together.

Carbon Fiber: Fiber produced by carbonizing precursor fibers based on PAN(polyacrylonitrile), rayon and pitch to eliminate non-carbon atoms. The term car-bon fiber is often used interchangeably with graphite. Carbon fibres are producedby the PAN or the pitch methods.

Pitch method pulls out graphite threads through a nozzle from hot fluidpitch.The PAN method separates a chain of carbon atoms from polyacrylnitrile

(PAN) through heating and oxidation. The polymer is stretched into alignmentparallel with what will eventually be the axis of the fiber. Then, an oxidation

221

Figure 23.1: Woven mat.

treatment in air between 200 and 300◦C transforms the polymer into a nonmeltableprecursor fiber. This precursor fiber is then heated in a nitrogen environment. Asthe temperature is raised, volatile products are given off until the carbon fiber iscomposed of at least 92% carbon. The temperature used to treat the fibers variesbetween 1000◦C and 2500◦C depending on the desired properties of the carbonfiber.

Aramid: A high strength, high stiffness fiber derived from polyamide. Kevlar R°and Nomex R° are examples of aramids.

Fiberglass: Filaments made by drawing molten glass, commonly used to reinforcecomposite materials.

Woven mats: For applications where more than one fibre orientation is required,a fabric combining 0◦ and 90◦ fibre orientations is useful.Woven fabrics, see Figure 23.1, are produced by the interlacing of warp (0◦) fi-

bres and weft (90◦) fibres in a regular pattern or weave style. The fabric’s integrityis maintained by the mechanical interlocking of the fibres. Drape (the ability ofa fabric to conform to a complex surface), surface smoothness and stability of afabric are controlled primarily by the weave style.

Filament winding: This is the automated process of wrapping resin impreg-nated filaments, see Figure 23.2, (rovings or tows) in a geometric pattern over arotating male mandrel. The component is then cured under high pressure andtemperature.

Rovings: Rovings consist of one or more glass strands made up of varying num-bers of continuous glass fibers of a specific filament diameter. These fibers arecoated with a sizing designed to protect the fiber during processing and to couplewith the customer’s resin to optimize laminate performance.

222

Figure 23.2: Filament winding rovings.

Rovings, the most common form of glass, can be chopped, woven or processedto create secondary fiber forms for composite manufacturing, such as mats, wovenfabrics, braids, knitted fabrics and hybrid fabrics. Rovings are supplied by weight,with a specified filament diameter. The term yield is commonly used to indicatethe number of yards in each pound of glass fiber rovings.

Mats: Mats are nonwoven fabrics that provide isotropic or equal strength inall directions. They come in two distinct forms: chopped and continuous strand.Chopped mats contain randomly distributed fibers cut to lengths typically rangingfrom 1.5 to 2.5 inches and held together with a chemical binder. Inherently weakerthan continuous-strand mats, chopped-strand mats provide low-cost polymer re-inforcement primarily in hand layup, continuous laminating and some closed-molding applications.

Chopped Strand Mat: The chopped strand mats, see Figure 23.3, are madefrom cut fibers laid in a random pattern and bonded with a powdered, highlysoluble resin binder.

Continuous Filament Mat: In a different production step, strands formedbelow the bushings are treated with a binder and formed into a swirl pattern tomake continuous filament mat.

23.2. Prepregs, Preforms and Compounds

A prepreg is an intermediate composite form made by preimpregnating the rein-forcement with resin prior to molding. Molding compounds prepared in this way

223

Figure 23.3: Chop strand mat.

are mostly glass fiber mats or glass filament cloths processed to form molded partsor semi-finished products by hot-press moldingPreforming is an intermediate molding process whereby the reinforcement is

assembled in the shape of the part to be molded. This helps to ensure uniformproperties in a composite product and speed the molding cycle.Glass fiber-reinforced thermoplastic compounds are typically in the form of

pellets consisting of resin with fibers in it. They can have several different forms,i.e. sheets and billets/bulk form, also called bulk molding compounds (BMC) andsheet molding compound (SMC).The pre-mixed material has the consistency of molding clay and is injected

into a mold cavity or placed on the bottom of two mold halves for compressionmolding.

23.3. Fabrication processes of FRC

There are several processes that manufacture fiber-reinforced composites. Someof the processes are almost the same as we studied for manufacturing plastics, butsomewhat modified in order to incorporate the reinforcements. We will considersome of the most widely used processes in manufacture FRCs.

Centrifugal CastingThis process makes cylindrical, hollow shapes such as tanks, pipes and poles.

Chopped strand mat is placed into a hollow, cylindrical mold, or continuous rovingis chopped and directed onto the inside walls of the mold. Resin is applied to theinside of the rotating mold.

Cold press molding

224

Cold press molding is a semi-open molding process. Reinforcements, usuallycontinuous filament mats (CFM), are placed into the tool and a highly filledpolyester resin is poured onto them. The press is closed and the part is cured.The process requires lower pressures, 15 - 100 lb/in2, and temperatures averaging55◦C. Cycle times are in the range of 10 - 20 minutes. Other glass fiber fabrics,mats, veils and preforms are also used. Parts usually have a fair-to-poor surface,so uses are under-hood auto and truck components like fan shrouds, brackets andbattery supports.

Compression Molding (hot press molding)The composite is formed under pressure between matching male and female

mold halves, at temperatures between 130 and 170◦C. The material that is com-pressed is typically one of several combinations of glass fibers and resin. Thesecombinations are: sheet molding compound, bulk molding compound, preform orglass fiber-reinforced thermoplastic sheet.

Continuous LaminationThis is a process for making composite in sheet form such as composite glaz-

ing, corrugated or flat construction panels, and electrical insulating materials.Reinforcement is combined with resin and sandwiched between two plastic carrierfilms. The sheet takes shape under forming rollers, and the resin is cured to formthe composite.

Filament WindingThis process makes high strength, hollow and generally cylindrical products

such as pipe, storage tanks, pressure vessels and rocket motor cases. The fiberis impregnated in a resin bath and pulled by the force of a rotating mandrelwhich gives the part its shape, see Figure 23.4.Veils are used for inner and/orouter surfaces to create a resin-rich surface for better corrosion resistance andaesthetics.

Hand Lay-UpThis process is suited for making large, high strength parts at low to medium

volumes. A combination of reinforcements in roll form is laid into an open moldand impregnated with resin. When the resin cures, the surface of the mold isreplicated on the side of the composite facing the mold.Resins are impregnated byhand, see Figure 23.5, into fibres which are in the form of woven, knitted, stitchedor bonded fabrics. This is usually accomplished by rollers or brushes, with an

225

Figure 23.4: Filament winding.

Figure 23.5: Hand lay-up.

increasing use of nip-roller type impregnators for forcing resin into the fabrics bymeans of rotating rollers and a bath of resin. Laminates are left to cure understandard atmospheric conditions.

Infusion moldingIn infusion molding processes a single-sided mold which is covered with rein-

forcements and sealed with a flexible vacuum bag or film is used. A vacuum isdrawn on the space between the mold and the seal containing the reinforcements,and a thermoset resin is allowed to infiltrate the reinforcements. The resin flowsthrough the reinforcements and cures to form the finished composite. Large partscan be produced; such as boat hulls and windmill blades.

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Figure 23.6: Pultrusion.

Injection MoldingA thermoplastic or thermoset molding compound made of glass fibers and

resin is fed by a screw or plunger into a mold cavity. The mold halves are heldunder pressure until the resin cures. Short glass fibers are commonly used asreinforcements.

PultrusionThis is a continuous process for making a lineal profile with a constant cross

section (such as rod stock, beams, channels and tubing) of fibre reinforced profiles.After the reinforcement is impregnated with resin, the material is pulled througha heated die that gives the part its cross sectional shape, see Figure 23.6.The resincures to create the composite profile.

Reaction Injection Molding (RIM)This process uses a two-component resin system, see Figure 23.7. The two resin

components are combined and mixed together, then injected into a mold cavitycontaining reinforcement. In the mold cavity, the resin rapidly reacts and cures toform the composite part. The reinforcement is added to both resin componentsbefore those components are reacted. The fiber-reinforced resin combination isinjected into the mold cavity where the resin rapidly reacts and cures to form thecomposite part.

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Figure 23.7: Reaction injection molding.

RIM uses liquid raw materials unlike other methods (including injection andcompression) where plastic raw materials are in solid forms must first be melted,then molded.

Resin Transfer Molding (RTM)The reinforcement is placed in the bottom half of matching molds. After the

mold is closed and clamped, resin is pumped under pressure into the mold cavity.The resin wets the reinforcement and cures to form the composite part.

Figure 23.8: Resin transfer molding.

Spray-UpThis is similar to and often combined with hand lay-up. With spray-up, glass

fiber roving is fed into a chopper ”gun” that chops the roving into fibers of pre-determined length. The fibers are directed to a resin stream. The combination

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Figure 23.9: 3D woven sandwich fabric.

material is directed to the mold cavity when the composite part takes shapes.

23.4. Fabrication of Functionally Gradient Materials

Various techniques have been employed to the fabrication of FGMs, includingChemical Vapor Deposition (CVD) / Physical Vapor Deposition (PVD), powdermetallurgy, plasma spraying, electro-plating and combustion synthesis.

23.5. Fabrication of sandwich constructions

3D woven sandwichNew methods makes it possible to braid, weave or knit sandwich structures,

as shown in Figure 23.9.The new research in this techniques and structures fo-cuses on integrated core sandwich panels, based on 3D-Woven sandwich fabrics.Intensive research on the 3D woven sandwich panels has been carried out, provingthe advantages of this material. The very high skin-core debonding resistanceof the panels is in theory very beneficial in increasing the lifetime and damagetolerance of the structure. The application of 3D woven sandwich composites in(semi-) structural composites depends on the long-term behavior and the damagetolerance of the panels. These properties have not yet been investigated. Threeload cases are considered to be essential for the further applicability of the panels:fatigue, impact and static concentrated loads.

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gluehoneycomb material

1) 2)

3) 4)

Figure 23.10: Fabrication of aluminiun honeycombcore.

Manufacturing of honeycomb coresThere are two methods of constructing honeycombs; by Corrugation Process

or by Expansion Process.

• Corrugation Process

Sheets of the material are passed through corrugating rolls, to give them shape,are then cut to length. The sheets are then bonded together to make a completehoneycomb. This process only works for denser materials, which will retain theirshape after corrugation.

• Expansion Process

Sheets of the material are covered in thin strips of adhesive, and are stackedto form a block, see Figure 23.10. The block is sliced to the right thickness, andthen pulled into an expanded form. This method is used for less dense materials.Both of these methods produce a honeycomb in which the original material

runs in one direction. This is known as the web direction. The finished compositematerial will be twice as stiff in the web direction as it is in the other.

Manufacturing of foams

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A new, inexpensive method for manufacturing cellular solids of highly repeat-able and uniform open cell geometry has been developed. Pore sizes as smallas a few microns can be achieved. Materials choices include metals, ceramics,glasses, polymers, semiconductors and composites. A significant advantage tothis method is that the distribution of material at the cell level is readily con-trolled. This creates the possibility for optimally designed cellular structures withexceptional thermophysical and mechanical properties. Multi-functional materi-als are envisioned. These could include load bearing structures which also providefor additional things such as impact/blast absorption, thermal management, con-ductance of electricity and/or shielding of electromagnetic waves, electrical powerstorage, filtering or impeding of fluid flow, retardation of chemical reactions andfire or in-growth of biological tissue.Thermoplastic foams are the result of deliberately adding at least one gas-

generating substance such as a chemical blowing agent, a soluble gas, or volatileliquid under pressure to the polymer melt, then altering the environment to causethe gas-generating substance to yield discrete bubbles. Foams offer unique process-ing challenges, ranging from the technical aspects of controlling bubble nucleationand growth to issues dealing with environmental concerns from diffusing blowingagent gases.Refractory foams can be fabricated from any material or materials combination

(either homogeneously combined or layered) which can be deposited by CVD(chemical vapor deposition). Among the materials that can be deposited are therefractory metals (e.g. niobium, tantalum, tungsten, rhenium) and their ceramiccompounds (e.g. the oxides, nitrides, carbides, borides, and silicides). Depositedmaterial densities of up to 50% of theoretical values can be readily achieved.These materials can be furnished in various sizes and configurations, and are easyto machine. Face sheets of either the same of different material can be applied toenhance the flexural and tensile properties.

References:

Fabrication fiber-reinforced composites:http://www.owenscorning.com/owens/composites/about/fabrication.asphttp://www.advancedcomposites.com/http://www.giplastek.com/rim/http://www.polymerprocessing.com/operations/rim/http://www.raypubs.com/ctyp/ypoverview.html

Composite applications:

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http://www.owenscorning.com/composites/applications/index.asp

About composites:http://www.mdacomposites.org/materials.htmhttp://www.netcomposites.com/http://islnotes.cps.msu.edu/trp/toc.htmlhttp://me.lsu.edu/~composit/

Manufacturing of foams:http://www.uvapf.org/technology/viewInvention.cfm?inventionID=205

Fiber and Powder manufacturinghttp://powdermetinc.com/http://www.reade.com/home_index.htmlhttp://www.wrigley-fibres.com/http://www.claremontflock.com/

Design for Manufacturabilityhttp://www.galorath.com/tools_manuf.shtmhttp://www.npd-solutions.com/dfm.html

Design and analyse of composite materals:Polymer Matrix Composites, http://mil-17.udel.edu/PMC/index.html

3D-woven sandwich:http://www.mtm.kuleuven.ac.be/Research/C2/poly/PhD_hj.htmhttp://www.muratec.net/braider/

Questions• What is Prepreg?• What is Preform?• What is Compound?• How is fiber manufactured?• What are woven mats?• How is carbon fiber manufactured?• What different processes of making fiber-reinforced composites are there?• How can honeycomb-cores be made?

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Figure 24.1: Layer Manufacturing Technology.

24. Layer Manufacturing Technology (LMT)

Layer Manufacturing Technology (LMT), is based on the principle of adding ma-terial in 2D-layers to build a complete 3D-model, that is why it is called additivetechnologies. Figure 24.1 shows how the parts made from LMT looks like in 2Dand 3D and close-up. There are several names of such processes: e.g. Rapid pro-totyping (RP), 3D-printing, solid freeform fabrication (SFF), freeform fabrication(FFF). The different technologies fabricate physical objects directly from CADdata sources. These methods are unique in that they add and bond materials inlayers to form objects. Such systems offer advantages in many applications com-pared to classical subtractive fabrication methods (for instance milling or turning),such as

• Objects can be formed with any geometric complexity or intricacy withoutthe need for elaborate machine setup or final assembly.

• Objects can be made from multiple materials, or as composites, or materialscan even be varied in a controlled fashion at any location in an object.

• Solid freeform fabrication systems reduce the construction of complex ob-jects to a manageable, straightforward, and relatively fast process.

• Small series of parts.

The latter has resulted in their wide use as a way to reduce time to marketin manufacturing. Today’s systems are heavily used by engineers to better un-derstand and communicate their product designs as well as to make rapid tooling

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to manufacture those products. Surgeons, architects, artists and individuals frommany other disciplines also routinely use the technology.The names of specific processes themselves are also often used as synonyms

for the entire field of LMT. Each of these technologies has its singular strengthsand weaknesses.LMT is an acronym for a group of processes capable of producing prototypes

of a complex geometry in various materials (wax, plastic, metal, etc.). The dom-inating types of LMT processes, that will be studied in more detail, are:

• Ballistic particle manufacturing (inkjet)- BPM• Fused deposition modelling - FDM• Laminated object manufacturing - LOM• Selective laser sintering - SLS• Stereo lithography - SLA• Solid ground curing - SGC (cubital)• Three dimensional printing (3DP)• Laser Engineered Net Shaping (LENS)• Inkjets• Powder metallurgy (PM)Price is generally proportional to the time consumption on the machine. This

means that price increases with finer layer thickness, increased volume, as well asincreased part height.The materials used in rapid prototyping are still pretty limited and dependent

on the method chosen. However, the range and properties available are grow-ing quickly. Numerous plastics, ceramics, metals ranging from stainless steel totitanium, and wood-like paper are available. At any rate, numerous secondaryprocesses are available to convert patterns made in a rapid prototyping process tofinal materials or tools.The ever increasing range of materials and processes in the group of additive

material processes make the processes possible to use in also fabrication of finishedproducts and not only prototypes. In for instance the SLS process, metallic powderis the basis and the finished product has very good properties. Therefore, inaddition to prototypes, RP techniques can also be used to make tooling (referredto as rapid tooling) and even production-quality parts (rapid manufacturing).For small production runs and complicated objects, rapid prototyping is often thebest manufacturing process available. Of course, ”rapid” is a relative term. Mostprototypes require from three to seventy-two hours to build, depending on the

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Figure 24.2: Ballistic particle manufacturing.

size and complexity of the object. This may seem slow, but it is much faster thanthe weeks or months required to make a prototype by traditional means such asmachining. These dramatic time savings allow manufacturers to bring productsto market faster and more cheaply.

24.1. Ballistic particle manufacturing (inkjet) BMP

BMP uses CAD-generated three-dimensional solid model data to direct streamsof material (waxes, plastics, photocurable polymers, ceramics, or metals) at atarget, building three-dimensional objects in much the same manner an ink jetprinter produces two-dimensional images. An object is built by a three-axis ro-botic system controlling a piezoelectric ink-jet mechanism ”shooting” particles ofthe material, producing multiple cross sections, onto a target, as shown in Figure24.2.There are different inkjet techniques (deposition systems), but all rely on

squirting a build material in a liquid or melted state which cools or otherwisehardens to form a solid on impact.

24.2. Fused deposition modelling - FDM

FDM, see Figure 24.3 is another deposition method.The Titan machine fromStratasys creates models using high performance engineering materials such aspolycarbonate, ABS and sulfones. Now with Titan, you can create prototypesthat have superior impact strength and also resist heat and corrosive agents such

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Figure 24.3: Fused deposition modelling.

as oil, gasoline and even acids. Multiple materials, coupled with one of the largestbuild chambers in its class, make Titan a smart solution for building, large, strongand durable parts. Parts up to 355 x 406 x 406 mm can be built.

24.3. LOM - Laminated object manufacturing

Laminated object manufacturing, see Figure 24.4 is a process suited for large andheavy parts, e.g. models for metal castings. The process makes use of foils, wherethe undersurface of this foil has a binder that when pressed and heated by theroller causes it to glue to the previous foil. The foil is cut by a laser following thecontour of the slice. To help the removal of the excess material once the parts havebeen built, the exterior of the slice is hatched, as opposed to fluid-based processes(e.g. the SLA process), where the interior is hatched. Fine details cannot beproduced, and surplus material has to be removed manually from the part.Helisys invented this process, but they ceased operation in 2000. However,

there are several other companies with either similar LOM technology, or in earlycommercial stages. Maximum dimension was about 1600 * 1200 * 1200 mm.

24.4. Selective laser sintering - SLS

SLS, see Figure 24.5 produces part from plastic, wax, or metal powders. Advan-tages include the use of industrial plastic types.

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Figure 24.4: Laminated object manufacturing.

Selective Laser Sintering is a thermal process and starts with a thin, evenly-distributed layer of powder. A laser is then used to sinter (fuse) only the powderthat is inside a cross-section of the part. The energy added by the laser heats thepowder into a glass-like state and individual particles coalesce into a solid. Oncethe laser has scanned the entire cross-section, another layer of powder is laid ontop and the whole process is repeated.The hardened layer is lowered, a new layer of powder is spread, and the process

is repeated. Maximum dimensions are about 500 * 500 * 500 mm.The SLS technology is known for its ability to process a variety of prototyping

materials including thermoplastics, investment casting wax, and a powdered metalmaterial for the production of prototype injection molds.

24.5. Laser Engineered Net Shaping (LENS)

Laser-engineered net shaping (LENSTM) builds on the SLS process with a fewnotable exceptions. Instead of bonding material in a bed of powder, the powderis delivered in a gas jet through nozzles. Solid material is formed by solidificationof a molten pool, thus forming a fully dense, free-standing deposit.A variety of materials can be used such as stainless steel, Inconel (a special

nickel material), copper, aluminum etc. Of particular interest are reactive mate-rials such as titanium. Materials composition can be changed dynamically andcontinuously, leading to objects with properties that might be mutually exclusive

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Figure 24.5: Selective laser sintering.

using classical fabrication methods.The strength of the process lies in the ability to fabricate fully-dense metal

parts with good metallurgical properties at reasonable speeds.

24.6. Stereo lithography - SLA

Stereo lithography - SLA is the most common RPT technique, and producesacrylic and epoxy parts from a liquid. Initially, an elevator is located at a distancefrom the surface of the liquid equal to the thickness of the first, bottom-most layer,see Figure 24.7. The laser beam will scan the surface following the contours ofthe slice. The interior of the contour is then hatched using a hatch pattern. Theliquid is a photopolymer that when exposed to the ultra-violet (uv) laser beamsolidifies or is cured. The elevator is moved downwards, and the subsequent layersare produced analogously. Fortunately, the layers bind to each other. Finally, thepart is removed from the vat, and the liquid that is still trapped in the interior isusually cured in a special oven.Almost unlimited geometry possibilities, fine geometric details and high accu-

racy.The required geometry is produced in thin layers (0.0254 mm layer thickness)

that yields a smooth finish. A CNC-controlled laser beam cures a pattern in thesurface of a fluid photosensitive polymer. The hardened layer is then stepwiselowered allowing the fluid to cover the part.

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Figure 24.6: Laser Engineered Net Shaping.

Typical applications are prototypes of injected moulded plastic parts and mod-elling of human bones and skulls. Maximum dimensions are about 500 * 500 *600 mm.

24.7. Solid ground curing - SGC

With the solid ground curing technique, see Figure 24.8, parts are produced fromphotosensitive polymers by hardening them in layers just as the SLA process.However, this is a significantly different process. The vat moves horizontallyas well as vertically. The horizontal movements take the workspace to differentstations in the machine.The light source a uv-lamp (mercury) is used to flood the chamber and expose

and solidify the entire layer at once (instead of using a laser beam as in SLA).This avoids the need for post-curing the parts. To select the areas that shouldbe cured, a mask is built on a glass plate, and subsequently, erased after beginused. The mask is built using a process similar to the one used in laser printers.The glass plate with the mask is placed between the lamp and the surface of theworkspace.Parts are built surrounded by wax, eliminating the need for support structures

(which is needed in SLA). Once a layer has been exposed to the uv-lamp, the un-cured areas-those areas filled with residual, liquid polymer-are replaced by wax.This is done by wiping away the residual polymer and applying a layer of wax.

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Figure 24.7: Stereo lithography.

The wax is hardened by a cold metal plate, and subsequently, the layer is milledto the correct height. The milling station also allows for layers to be removed,i.e. an undo operation is possible. The new layer of polymer is applied when theworkspace moves from the milling station back to the exposure chamber.The process is well suited for large and heavy parts. No separate part support

is required during processing. Compared with SLA, it is more expensive and notas accurate. Machines from Cubital use SGC principle.

24.8. Three dimensional printing (3DP)

Three dimensional printing, see Figure 24.9 was developed at Massachusetts In-stitute of Technology (MIT). It’s often used as a direct manufacturing process aswell as for rapid prototyping.The process starts by depositing a layer of powder object material at the top

of a fabrication chamber. To accomplish this, a measured quantity of powder isfirst dispensed from a similar supply chamber by moving a piston upward incre-mentally. The roller then distributes and compresses the powder at the top ofthe fabrication chamber. The multi-channel jetting head subsequently deposits aliquid adhesive in a two dimensional pattern onto the layer of the powder whichbecomes bonded in the areas where the adhesive is deposited, to form a layer ofthe object.

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Figure 24.8: Solid ground curing.

Once a layer is completed, the fabrication piston moves down by the thicknessof a layer, and the process is repeated until the entire object is formed withinthe powder bed. After completion, the object is elevated and the extra powderbrushed away leaving a ”green” object. No external supports are required duringfabrication since the powder bed supports overhangs.Three dimensional printing offers the advantages of speedy fabrication and low

materials cost. In fact, it’s probably the fastest of all RP methods. Recently coloroutput has also become available. Parts can be made of any material (ceramic,metals, polymers and composites).

24.9. PowderProcessing/PowderMetallurgy

Powder metallurgy is the process where both casting, forming and consolidationare involved. Fine powdered materials are blended, pressed into a desired shape,and then heated in a controlled atmosphere to bond the contacting surfaces of theparticles and establish the desired properties. Some of the advantages with theprocess is that the material waste is very little, unusual materials or mixtures canbe used and the porosity or permeability can be tailored. There are many differentmethods to manufacture products with powder metallurgy processes and in thefuture even more methods will be introduced to the marked. Almost any metal,metal alloy, or nonmetal such as ceramic, polymer or wax or graphite lubricant can

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Figure 24.9: Three dimensional printing.

be converted into powder and can thereby be produced by a powder metallurgymethod.

Powder metallurgy uses sintering process for making various parts out of metalpowder. The metal powder is compacted by placing in a closed metal cavity (thedie) under pressure. This compacted material is placed in an oven and sinteredin a controlled atmosphere at high temperatures and the metal powders coalesceand form a solid. A second pressing operation, repressing, can be done prior tosintering to improve the compaction and the material properties.The properties of this solid are similar to cast or wrought materials of similar

composition. Porosity can be adjusted by the amount of compaction. Usuallysingle pressed products have high tensile strength but low elongation.Powder metallurgy is useful in making parts that have irregular curves, or

recesses that are hard to machine. It is suitable for high volume production withvery little wastage of material. Secondary machining is virtually eliminated.Typical parts that can be made with this process include cams, ratchets,

sprockets, pawls, sintered bronze and iron bearings (impregnated with oil) andcarbide tool tips.FGMs can be fabricated by for instance Powder Metallurgy (PM).

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24.10. Vapor Deposition CVD/PVD

Deposition is a process of depositing a thin layer of film onto the surface of thewafer.Vapor deposition processes usually take place within a vacuum chamber. There

are two categories of vapor deposition processes: physical vapor deposition (PVD)and chemical vapor deposition (CVD). In PVD processes, the workpiece is sub-jected to plasma bombardment. In CVD processes, thermal energy heats the gasesin the coating chamber and drives the deposition reaction.

Chemical Vapor Deposition is done by putting the chemicals into a heatedvacuum chamber containing a wafer. These chemical are fed into the chamber ina gas form. There are a couple of different forms of chemical vapor deposition.Each form has its own advantages and disadvantages. These forms are:APCVD Atmospheric Pressure CVDLPCVD Low Pressure CVDPECVD Plasma Enhanced CVD

Physical vapor deposition does not use a chemical to deposit a film on thewafer but uses physical means. To do this a gas inside a vacuum is excited witha source , like RF (Radio frequency) energy. The molecules of the gas become soenergetic that if they were to collide with some materials they might cause atomsof that material to break free. PVD uses this as a way to deposit layers of materialonto a wafer. A ”target” is placed above the wafer and when the molecules of gasstrike the target and cause the atoms to break free then a layer of atoms will fallonto the wafer.

24.11. Selection of a layered manufacturing process

Selection of a layered manufacturing process depends on the basic application aswell as material and accuracy requirements. Selection rules of thumb have evolved:Applications involving injection molded parts and/or good accuracy, often lead

to stereolithography (SLA) as the best choice.If a prototype part needs to be in final materials and with mechanical proper-

ties that emulate injection molded parts, selective laser sintering (SLS) might bechosen.If the requirement is for large objects that will ultimately be sand cast, lami-

nated object manufacturing (LOM) is often the way to go.

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If the need is for a quick concept model and physical properties are of secondaryimportance, three dimensional printing (3DP) may be most economical.If the requirement is for extreme accuracy and very high resolution, such as

in making jewelry or small parts, a good choice is often an inkjet system such asthe ModelMaker Series from Solidscape, Inc. (formerly Sanders Prototypes).Direct fabrication of metal objects as tools or prototypes will require selective

laser sintering (SLS), or one of the methods based on laser fusing such as laserengineered net shaping (LENS).In order to get the best finish of a product; rotate the geometry such that the

laser "draws" the 2D geometry that is most critical, and not let that surface bestep-wise.

Of course, such rules of thumb risk offending every system manufacturer be-cause there is tremendous overlap in capabilities and specifications. The majorityof applications can probably be accomplished satisfactorily by several of the tech-nologies.

References about additive technologies:

SLS- technology in action:http://www.dtm-corp.com/http://home.att.net/~castleisland/http://lff.me.utexas.edu/sls.html

LMT Processes:http://home.att.net/~castleisland/http://designinsite.dkhttp://www.efunda.com/processes/metal_processing/powder_metallurgy.cfmhttp://www.efunda.com/processes/processes_home/process.cfmhttp://www.efunda.com/home.cfmhttp://www.precitech.ca/pmproc.htmhttp://www.cs.hut.fi/~ado/rp/rp.htmlhttp://home.att.net/~castleisland/rp_int1.htmhttp://www-2.cs.cmu.edu/~rapidproto/manufacturing/mfgresources.htmlhttp://home.att.net/~castleisland/rp_int1.htmhttp://www-2.cs.cmu.edu/~rapidproto/manufacturing/mfgresources.htmlhttp://www-2.cs.cmu.edu/~rapidproto/manufacturing/mfguniversity.htmlhttp://emsh.calarts.edu/~mathart/R_Proto_ref.htmlhttp://home.att.net/~castleisland/com_lks.htmhttp://www.stratasys.com/ (also streaming video on FDM process)

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Figure 24.10: Rapid Prototyping Technologies.

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http://www.acceltechinc.com/nojava/sls.htmlhttp://www.prototype3d.com/http://www.3dsystems.com/http://web.mit.edu/tdp/www/whatis3dp.htmlhttp://www.myb2o.com/myb2ous/RapidPrototyping/Tools/Process/10265.htmhttp://www.mit.edu/~tdp/ (pictures)= next linkhttp://web.mit.edu/afs/athena/org/t/tdp/www/http://www.sandia.gov/media/lens.htmhttp://www.tms.org/pubs/journals/JOM/9907/Hofmeister/Hofmeister-9907.html (LENS)

CVD/PVDhttp://www.corrosion-doctors.org/MetalCoatings/Physical.htmhttp://entcweb.tamu.edu/zoghi/semiprog/deposit.htmhttp://www.darpa.mil/dso/trans/fds_2.htm

Questions• What are the different processes of LMT?• What are the advantages and disadvantages of LMT-processes compared totraditional processes?• How does SLA work?• Explain the powder metallurgy process

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25. Design Considerations

The goals of reducing a large manufacturing cost and improving product qualityhas lead to certain processes and procedures that have come to be known as designfor manufacturability or design for manufacture (DFM). The closely related is alsothe area of design for assembly (DFA).

25.1. Designing for Manufacturability (DFM) )

Design for Manufacturability (DFM) or Design for Fabrication (DFF) is a methodand the theory for designing products that can be produced. In addition thismethod saves time compared to previous methods (or non-methods).In the past, products have been designed that could not be produced. Prod-

ucts have been released for production that could only be made to work in themodel shop when prototypes were built and adjusted by highly skilled technicians.Clearly, there must be some other way to develop a product that is smarter thanthis.A product can be designed in many different ways. The designer’s objective

must be to optimize the product design with the production system. A company’sproduction system includes its suppliers, material handling systems, manufactur-ing processes, labor force capabilities and distribution systems.Generally, the designer works within the context of an existing production

system that can only be minimally modified. However in some cases, the produc-tion system will be designed or redesigned in conjunction with the design of theproduct. When design engineers and manufacturing engineers work together todesign and rationalize both the product and production and support processes, itis known as integrated product and process design. The designer’s consideration ofdesign for manufacturability, cost, reliability and maintainability is the startingpoint for integrated product development.A designer’s primary objective is to design a functioning product within given

economic and schedule constraints. However, research has shown that decisionsmade during the design period determine 70% of the product’s costs while deci-sions made during production only account for 20% of the product’s costs. Fur-ther, decisions made in the first 5% of product design could determine the vastmajority of the product’s cost, quality and manufacturability characteristics. Thisindicates the great leverage that DFM can have on a company’s success and prof-itability.

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However, the application of DFM must consider the overall design economics.It must balance the effort and cost associated with development and refinement ofthe design to the cost and quality leverage that can be achieved. In other words,greater effort to optimize a products design can be justified with higher value orhigher volume products.

Design effectiveness is improved and integration facilitated when:

• Fewer active parts are utilized through standardization, simplification andgroup technology retrieval of information related to existing or preferredproducts and processes.

• Producibility is improved through incorporation of DFM practices.

• Design alternatives are evaluated and design tools are used to develop amore mature and producible design before release for production.

• Product and process design includes a framework to balance product qualitywith design effort and product robustness.

25.2. Product design guidelines

Designers need to understand more about their own company’s production system,i.e., its capabilities and limitations, in order to establish company-specific designrules to further guide and optimize their product design to the company’s pro-duction system. For example, they need to understand the tolerance limitationsof certain manufacturing processes.

DFM Guidelines:• Minimize total number of parts• Standardize components• Use common parts across product lines• Design parts to be multifunctional• Design parts for ease of fabrication• Avoid secondary operations• Utilize the special characteristics of processesIn addition, colors, tolerances and materials also limits the process that should

be used.

Design guidelines

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There has been developed a number of rules for design. Briefly mentioned, thelist looks like this:• Space holes in parts so they can be made in one operation without tooling

weakness. There is a limit in how close holes may be spaced due to strength inthe thin section between holes.• Notes on engineering drawings must be specific and clear.• Dimensions should be made from specific surfaces or points on the parts.• Dimensions should all be from a single datum line.• The design should aim for minimum weight consistent with strength and

stiffness requirements (this means minimized material cost and reduction in laborand tooling costs).• Adjust the design to the manufacture process chosen (wall thickness, fillets,

radii, dies etc.)• Rotation of geometry

25.3. Evaluation of design alternatives

With the traditional approach, the designer would develop an initial concept andtranslate that into a product design, making minor modifications as requiredto meet the specification. DFM requires that the designer start the process byconsidering various design concept alternatives early in the process. At this point,little has been invested in a design alternative and much can be gained if a moreeffective design approach can be developed. Only through consideration of morethan one alternative is there any assurance of moving toward an optimum design.Using some of the previous design rules as a framework, the designer needs tocreatively develop design alternatives. Then alternatives are evaluated againstDFM objectives.

Design guide for composite materials, Part design concernsThe very nature of composites allows designers and manufacturers to tailor

fiber architecture to match performance requirements of a specific part. Fiber ori-entation can be varied to allow wall-thickness variations, development of complexshapes, and production of large parts with integral reinforcing members. Lam-inates may be designed to be isotropic or anisotropic, balanced or unbalanced,symmetric or asymmetric - depending on the in-use forces a component will en-dure.Understanding layered or laminate structural behavior is vital to designing

effective composite components. Adhesion of laminate layers - called plies - is

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critical; poor adhesion can cause delamination under multiple stress, strain, im-pact and load conditions. Ply layup designers must consider adhesion, strength,weight, stiffness, operating temperature and toughness requirements, as well asvariables such as electromagnetic transparency and radiation resistance. Addi-tionally, composite component design must encompass surface finish, fatigue life,overall part configuration, and scrap or rework potential, to name just a few ofthe many applicable factors.The intended fabrication method will also affect design. For instance, manu-

facturers of filament-wound or tape-layed structures use different reinforcementforms and build-up patterns than those warranted for hand laid up laminatepanels or vacuum-bag-cured prepreg parts. RTM accommodates 3-D preformsmore easily than do some other manufacturing techniques. The varying benefitsand limitations of these fabrication techniques provide considerable flexibility toachieve part performance and economies.

25.4. The meaning of colors

Are Colors Significant? Only for the sighted or only if one isn’t color-blind. Forthose of us blessed with sight, we’ve been taught that colors can make us feelgood, excite us, generate fear and joy, or literally make us nauseated. As longas we attach a certain meaning to a particular color, the legends of colors willcontinue to persist.Color is a very important part to web design. As human beings we are very

sensitive to color. We rely heavily on certain colors to give meaning to things. Forexample we associate the color red to love. Like hearts or roses. We also associatered to an emergency like fire trucks or exit signs. As North Americans we associateblack to death however I bet you didn’t know that the Chinese culture associatesblack with happy and joyful. We associate white to purity or wholesomeness likea wedding dress, while in the Chinese culture a bride would never wear whiteon her wedding day because it symbolizes bad luck or death. So you can see bythis simple example that color not only is symbolic for all cultures but NOT allcultures associate color the same way.

How Are Colors Symbolic?Time and tradition have created strong, symbolic color connections. For ex-

ample, we associate red with festivity, blue with distinction, purple with dignity,green with nature, yellow with sunshine, pink with health, and white with purity.

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Context also gives color specific leaning, we know that red means stop, and greenmeans go.

White: White is associated with peace and purity such as in the white cloudsand sparkling snowflakes. Two of the most popular peace symbols are the whitedove and the truce flag.

Red - Vitality, Courage, Self Confidence: When red is featured in adream the tint or shade carries different meanings. A light tint of red - suggeststhe glory of success, hot reds - signify the stress of family quarrels, crimson hues- foretell of happy news from a friend and red hair on a beautiful woman suggeststhat you will receive unexpected good news.

Yellow - Wisdom, Clarity, Self-esteem: Studies show that yellow is mostoften associated with words like cheerful, jovial and sunny, somewhat associatedwith exciting and stimulating and almost never associated with words like respon-dent, dejected, melancholy or unhappy. In short, a wonderful color for lifting thespirits and letting the sun shine in.

Orange - Happiness, Confidence, Resourcefulness: The meaning of or-ange is inexorably linked to the sensations of radiant energy, heat and the glowingpresence of the setting sun. The link between red and yellow, orange takes itstraits from both. It is less passionate and intense than red, incorporating thesunny disposition of yellow. To the human eye, orange is seen as the hottest ofall colors, both in temperature and appearance.

Blue - Knowledge, Health, Decisiveness: The Russian artist Kadinskycaptured the expansive essence of blue when he wrote that blue is ”the infinitepenetration into the absolute essence - where there is, and can be, no end.” Peoplewho are strongly attracted to blue tend to be devoted and deliberate in theiractions and since blue is everywhere, they feel a unity with the world.

Purple - Beauty, Creativity, Inspiration: The purple family is the mostenigmatic of all colors. Purple is a combination of the excitement of red and thetranquillity of blue, the marriage of two diametrically opposed emotions.

Green - Balance, Love, Self control: Green is the most refreshing, restfulcolor to the eye. The word ”green” comes from the same root as ”grow,” so greensymbolizes that which grows: rebirth, regeneration, the renewal of life. Indianmystics see green as the marriage of balance and harmony, the ray that bridgescause and effect.

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References:

Design guidelines:http://www.devicelink.com/mddi/archive/96/04/008.htmlhttp://www.arrem.com/designguide/dgdesvsmat.htmhttp://www.tstar.com/pdf/quadrant-DF.pdfhttp://www.npd-solutions.com/dfmguidelines.htmlhttp://www.geplastics.com/webted/webted.html

Colors:http://crumpledpapers.com/color.htmlhttp://www.wevehadit.com/Publications/Color/page3.htmlhttp://www.srsd.org/~arainone/color.html

Questions• What is DFM?• What is DFF• What do we have to take into consideration when designing for fabrication?•What kind of design-considerations would you take into consideration in general?• How can colors affect our understanding of a product?• If you would like a product to make you feel good, (happy), what color wouldyou choose on your product?

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