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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 m

Metal Foams: A Design Guide

Metal Foams: A Design Guide

M.F Ashby, A.G Evans, N.A Fleck, L.J Gibson,

J.W Hutchinson and H.N.G Wadley

BOSTON OXFORD AUCKLAND JOHANNESBURG MELBOURNE NEW DELHI

Copyright  2000 by Butterworth-Heinemann

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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

vi Contents

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 – N data 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

Contents vii

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 189

14.2 Data for electrical resistivity of metal foams 190

14.3 Electrical conductivity and relative density 191

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

viii Contents

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

Preface and acknowledgements

Metal foams are a new class of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties This Design Guide is

a contribution to the concurrent development of their science and exploitation

It seeks to document design information for metal foams even as the scientific research and process development are evolving This should help to identify promising industrial sectors for applications, guide process development and accelerate take-up

This work is supported by the DARPA/ONR MURI Program through Grant

No N00014-1-96-1028 for Ultralight Metal Structures and by the British Engineering and Science Research Council through a Research Grant Many individuals and groups have contributed to its contents They include Professor

B Budiansky, Professor H Stone, Professor R Miller, Dr A Bastawros, Dr

Y Sugimura of the Division of Engineering and Applied Sciences, Harvard University; Dr T.J Lu, Dr Anne-Marie Harte, Dr V Deshpande of the Micromechanics Centre, Engineering Department, Cambridge University; Dr E.W Andrews and Dr L Crews of the Department of Materials Science and Engineering, MIT; Professor D Elzey, Dr D Sypeck and Dr K Dharmasena

of the Department of Materials Science and Engineering, UVA; Dr John Banhart of the Fraunhofer Instit¨ut Angewandte Materialsforschung, Bremen; Professor H.P Degisher and Dr Brigdt Kriszt of the Technical University of Vienna, Dr Jeff Wood of Cymat Corp Mississauga, Canada; and Mr Bryan Leyda of Energy Research and Generation Inc Oakland, CA

Although the compilers of this Guide have made every effort to confirm the validity of the data and design information it contains, the compilers make no warranty, either expressed or implied, with respect to their quality, accuracy or validity

List of contributors

M.F Ashby

Cambridge Centre for Micromechanics

Engineering Department

University of Cambridge

Cambridge CB2 1PZ

UK

mfa2@eng.cam.ac.uk

A.G Evans

Princeton Materials Institute

Bowen Hall

70 Prospect Avenue

Princeton, NJ 08540

USA

anevans@princeton.edu

N.A Fleck

Cambridge Centre for Micromechanics

Engineering Department

University of Cambridge

Cambridge CB2 1PZ

UK

naf1@eng.cam.ac.uk

L.J Gibson

Department of Materials Science and Engineering Massachusetts Institute of Technology

Cambridge, MA 02139

USA

ljgibson@mit.edu

J.W Hutchinson

Division of Engineering and Applied Sciences Harvard University

xii List of contributors

Oxford Street

Cambridge, MA 02138

USA

Hutchinson@mems.harvard.edu

H.N.G Wadley

Department of Materials Science and Engineering School of Engineering and Applied Science University of Virginia

Charlottesville, VA 22903

USA

haydn@virginia.edu

Table of physical constants and

conversion units

Physical constants in SI units

Absolute zero temperature

Acceleration due to gravity, g

Avogadro’s number, NA

Base of natural logarithms, e

Boltzmann’s constant, k

Faraday’s constant, k

Gas constant, R

Permeability of vacuum, 0

Permittivity of vacuum, ε0

Planck’s constant, h

Velocity of light in vacuum, c

Volume of perfect gas at STP

Conversion of units

273.2°C

9.807 m/s2 6.022 ð 1023 2.718 1.381 ð 10
23 J/K 9.648 ð 104 C/mol 8.314 J/mol/K 1.257 ð 10
6 H/m 8.854 ð 10
12 F/m 6.626 ð 10
34 J/s 2.998 ð 108 m/s 22.41 ð 10
3 m3/mol

Angle, 1 rad 57.30°

Density, 1 lb/ft3 16.03 kg/m3

Diffusion coefficient, D 1 cm3/s 1.0 ð 10
4m2/s

Force, F 1 kgf 9.807 N

1 lbf 4.448 N

1 dyne 1.0 ð 10
5 N Length, l 1 ft 304.8 mm

1 inch 25.40 mm

1 ˚A 0.1 nm Mass, M 1 tonne 1000 kg

1 short ton 908 kg

1 long ton 1107 kg

1 lb mass 0.454 kg Specific heat, Cp 1 cal/g.°C 4.188 kJ/kg.°C

Btu/lb.°F 4.187 kJ/kg.°C

xiv Conversion units

Conversion of units

Stress intensity, KIC 1 ksipin 1.10 MN/m3/2

Surface energy,  1 erg/cm2 1 mJ/m2

Temperature, T 1°F 0.556°K

Thermal conductivity,  1 cal/s.cm.°C 418.8 W/m.°C

1 Btu/h.ft.°F 1.731 W/m.°C Volume, V 1 Imperial gall 4.546 ð 10
3 m3

1 US gall 3.785 ð 10
3 m3

Viscosity,  1 poise 0.1 N.s/m2

1 lb ft.s 0.1517 N.s/m2

Conversion of units – stress and pressureŁ

MN/m 2 dyn/cm 2 lb/in 2 kgf/mm 2 bar long ton/in 2

MN/m2 1 107 1.45 ð 102 0.102 10 6.48 ð 10
2 dyn/cm 2 10
7 1 1.45 ð 10
5 1.02 ð 10
8 10
6 6.48 ð 10
9

lb/in2 6.89 ð 10
3 6.89 ð 104 1 703 ð 10
4 6.89 ð 10
2 4.46 ð 10
4 kgf/mm 2 9.81 9.81 ð 10 7 1.42 ð 10 3 1 98.1 63.5 ð 10
2

bar 0.10 10 6 14.48 1.02 ð 10
2 1 6.48 ð 10
3

long ton/in2 15.44 1.54 ð 10 8 2.24 ð 10 3 1.54 1.54 ð 10 2 1

Conversion of units – energyŁ

J 1 10 7 0.239 6.24 ð 10 18 9.48 ð 10
4 0.738 erg 10
7 1 2.39 ð 10
8 6.24 ð 1011 9.48 ð 10
11 7.38 ð 10
8 cal 4.19 4.19 ð 10 7 1 2.61 ð 10 19 3.97 ð 10
3 3.09

eV 1.60 ð 10
19 1.60 ð 10
12 3.38 ð 10
20 1 1.52 ð 10
22 1.18 ð 10
19

Btu 1.06 ð 103 1.06 ð 1010 2.52 ð 102 6.59 ð 1021 1 7.78 ð 102

ft lbf 1.36 1.36 ð 10 7 0.324 8.46 ð 10 18 1.29 ð 10
3 1

Conversion of units – powerŁ

kW (kJ/s) erg/s hp ft lbf/s

kW (kJ/s) 1 10
10 1.34 7.38 ð 102

erg/s 10
10 1 1.34 ð 10
10 7.38 ð 10
8

hp 7.46 ð 10
1 7.46 ð 109 1 5.50 ð 102

ft lbf/s 1.36 ð 10
3 1.36 ð 107 1.82 ð 10
3 1

Ł To convert row unit to column unit, multiply by the number at the column–row intersection, thus 1MN/m 2 D 10 bar

Chapter 1

Introduction

Metal foams are a new, as yet imperfectly characterized, class of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties They offer potential for lightweight structures, for energy absorp-tion, and for thermal management; and some of them, at least, are cheap The current understanding of their production, properties and uses in assembled in this Design Guide The presentation is deliberately kept as simple as possible Section 1.1 expands on the philosophy behind the Guide Section 1.2 lists potential applications for metal foams Section 1.3 gives a short bibliography

of general information sources; further relevant literature is given in the last section of each chapter

At this point in time most commercially available metal foams are based on aluminum or nickel Methods exist for foaming magnesium, lead, zinc, copper, bronze, titanium, steel and even gold, available on custom order Given the intensity of research and process development, it is anticipated that the range

of available foams will expand quickly over the next five years

1.1 This Design Guide

Metallic foams (‘metfoams’) are a new class of material, unfamiliar to most engineers They are made by a range of novel processing techniques, many still under development, which are documented in Chapter 2 At present metfoams are incompletely characterized, and the processes used to make them are imperfectly controled, resulting in some variability in properties But even the present generation of metfoams have property profiles with alluring potential, and the control of processing is improving rapidly Metfoams offer signifi-cant performance gains in light, stiff structures, for the efficient absorption of energy, for thermal management and perhaps for acoustic control and other, more specialized, applications (Section 1.2) They are recyclable and non-toxic They hold particular promise for market penetration in applications in which several of these features are exploited simultaneously

But promise, in today’s competitive environment, is not enough A survey

of the history of development of new material suggests a scenario like that sketched in Figure 1.1 Once conceived, research on the new material accel-erates rapidly, driven by scientific curiosity and by the often over-optimistic

eV 1. 60 ð 10
19 1. 60 ð 10
12 3.38 ð 10
20 1. 52 ð 10
22 1. 18 ð 10
19

Btu 1. 06 ð 10 3 1. 06 ð 10 10 2.52 ð 10 2... kgf/mm 9. 81 9. 81 ð 10 1. 42 ð 10 98 .1 63.5 ð 10
2

bar 0 .10 10 14 .48 1. 02 ð 10
2 6.48 ð 10
3

long ton/in2 15 .44 1. 54 ð 10 2.24... ð 10 11 9.48 ð 10
11 7.38 ð 10
8 cal 4 .19 4 .19 ð 10 2. 61 ð 10 19 3.97 ð 10
3 3.09

eV 1. 60