Contents

Preface and acknowledgements ix List of contributors xi

Table of physical constants and conversion units xiii

1 Introduction 1

1.1 This Design Guide 1

1.2 Potential applications for metal foams 3

1.3 The literature on metal foams 5

2 Making metal foams 6

2.1 Making metal foams 6

2.2 Melt gas injection (air bubbling) 8

2.3 Gas-releasing particle decomposition in the melt 9

2.4 Gas-releasing particle decomposition in semi-solids 11

2.5 Casting using a polymer or wax precursor as template 11

2.6 Metal decomposition on cellular preforms 14

2.7 Entrapped gas expansion 14

2.8 Hollow sphere structures 16

2.9 Co-compaction or casting of two materials, one leachable 19

2.10 Gas-metal eutectic solidification 20

2.11 Literature on the manufacture of metal foams 20

3 Characterization methods 24

3.1 Structural characterization 24

3.2 Surface preparation and sample size 26

3.3 Uniaxial compression testing 27

3.4 Uniaxial tension testing 29

3.5 Shear testing 30

3.6 Multi-axial testing of metal foams 31

3.7 Fatigue testing 34

3.8 Creep testing 35

3.9 Indentation and hardness testing 35

3.10 Surface strain mapping 36

3.11 Literature on testing of metal foams 38

4 Properties of metal foams 40

4.1 Foam structure 40

4.2 Foam properties: an overview 42

4.3 Foam property charts 48

4.4 Scaling relations 52 References 54

5 Design analysis for material selection 55

5.1 Background 55

5.2 Formulating a property profile 56

5.3 Two examples of single-objective optimization 58

5.4 Where might metal foams excel? 61 References 61

6 Design formulae for simple structures 62

6.1 Constitutive equations for mechanical response 62

6.2 Moments of sections 64

6.3 Elastic deflection of beams and panels 67

6.4 Failure of beams and panels 69

6.5 Buckling of columns, panels and shells 70

6.6 Torsion of shafts 72

6.7 Contact stresses 74

6.8 Vibrating beams, tubes and disks 76

6.9 Creep 78 References 79

7 A constitutive model for metal foams 80

7.1 Review of yield behavior of fully dense metals 80

7.2 Yield behavior of metallic foams 82

7.3 Postscript 86 References 87

8 Design for fatigue with metal foams 88

8.1 Definition of fatigue terms 88

8.2 Fatigue phenomena in metal foams 90

8.3 S-TV^flata for metal foams 94

8.4 Notch sensitivity in static and fatigue loading 97 References 101

9 Design for creep with metal foams 103

9.1 Introduction: the creep of solid metals 103

9.2 Creep of metallic foams 105

9.3 Models for the steady-state creep of foams 106

9.4 Creep data for metallic foams 107

9.5 Creep under multi-axial stresses 109

9.6 Creep of sandwich beams with metal foam cores 109 References 112

10 Sandwich structures 113

10.1 The stiffness of sandwich beams 113

10.2 The strength of sandwich beams 116

10.3 Collapse mechanism maps for sandwich panels 120

10.4 Case study: the three-point bending of a sandwich panel 123

10.5 Weight-efficient structures 124

10.6 Illustration for uniformly loaded panel 126

10.7 Stiffness-limited designs 133

10.8 Strength-limited designs 140

10.9 Recommendations for sandwich design 148 References 148

11 Energy management: packaging and blast protection 150

11.1 Introduction: packaging 150

11.2 Selecting foams for packaging 151

11.3 Comparison of metal foams with tubular energy absorbers 157

11.4 Effect of strain rate on plateau stress 161

11.5 Propagation of shock waves in metal foams 163

11.6 Blast and projectile protection 166 References 169

12 Sound absorption and vibration suppression 171

12.1 Background: sound absorption in structural materials 171

12.2 Sound absorption in metal foams 173

12.3 Suppression of vibration and resonance 175 References 179

13 Thermal management and heat transfer 181

13.1 Introduction 181

13.2 Heat transfer coefficient 182

13.3 Heat fluxes 184

13.4 Pressure drop 186

13.5 Trade-off between heat transfer and pressure drop 187 References 188

14 Electrical properties of metal foams 189

14.1 Measuring electrical conductivity or resistivity

14.2 Data for electrical resistivity of metal foams

14.3 Electrical conductivity and relative density References 193

15 Cutting, finishing and joining 194

15.1 Cutting of metal foams 194

15.2 Finishing of metal foams 194

15.3 Joining of metal foams 195 References 199

16 Cost estimation and viability 200

16.1 Introduction: viability 200

16.2 Technical modeling and performance metrics 201

16.3 Cost modeling 202

16.4 Value modeling 206

16.5 Applications 212 References 216

189 190 191

17 Case studies 217

17.1 Aluminum foam car body structures 217

17.2 Integrally molded foam parts 219

17.3 Motorway sound insulation 220

17.4 Optical systems for space applications 222

17.5 Fluid-fluid heat exchangers 224

17.6 Lightweight conformal pressure tanks 225

17.7 Electrodes for batteries 225

17.8 Integrated gate bipolar transistors (IGBTs) for motor drives 226

17.9 Applications under consideration 232

18 Suppliers of metal foams 234

19 Web sites 239

Appendix: Catalogue of material indices 242 Index 247

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