Metal Foams: A Design Guide

263 Pages·2000·4.131 MB·English

by  M. F. Ashby, Tony Evans, N. A. Fleck, Lorna J. Gibson, John W. Hutchinson, H. N. G. Wadley

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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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
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
Index 247
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 Institu¨t 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
[email protected]
A.G. Evans
Princeton Materials Institute
Bowen Hall
70 Prospect Avenue
Princeton, NJ 08540
USA
[email protected]
N.A. Fleck
Cambridge Centre for Micromechanics
Engineering Department
University of Cambridge
Cambridge CB2 1PZ
UK
[email protected]
L.J. Gibson
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
USA
[email protected]
J.W. Hutchinson
Division of Engineering and Applied Sciences
Harvard University
xii List of contributors
Oxford Street
Cambridge, MA 02138
USA
[email protected]
H.N.G. Wadley
Department of Materials Science and Engineering
School of Engineering and Applied Science
University of Virginia
Charlottesville, VA 22903
USA
[email protected]