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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
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Copyright
2000 by Butterworth-Heinemann
All rights reserved.
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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
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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
5.4 Where might metal foams excel?
61
58
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

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