Metal Foams: A Design Guide

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248 Index Creep of metallic foams 105 Creep of sandwich beams 109 Creep testing 35 Creep under multiaxial stresses 109 Crush-bands 92 Cutting of metal foams 194 Cyclic creep 90 Cyclic loading 89 Cyclic loading of fasteners 199 Cylinder with internal pressure 243 Cylindrical shells 140, 157 CYMAT Corporation 234 Damping 176 Damping capacity 43, 177 Data sources 42, 234 et seq, 239 Decibel scale 172 Densification strain 43, 46 Design analysis 55 Design formulae 62 et seq Design objectives 57 Deviatoric strain-rate 81 Diffusional flow 103 DUOCEL 235 DURALCAN 234 Effect of strain rate on plateau stress 161 Effective strain-rate 80 Effective stress 80 Elastic bending 67, 113 Elastic hinges 244 Electrical conductivity 189 et seq Electrical properties 44, 48, 189 et seq Electrical resistivity 4.7 Electrical resistivity 44, 48, 189 et seq Electrical screening 4 Electrodeposition 4 Electrodes 225 Endurance limit 89 Energy absorbers 151 et seq Energy density 153 et seq Energy management 4, 150 et seq Entrapped gas expansion 14 Equivalent stress 80 ERG 222 et seq, 235 Evans, A.G. 5 Evaporation 14 Exchange constants 210 Expansion coefficient 44, 54 Explosives 168 Face sheet wrinkling in sandwich panels 128 Face yield in sandwich panels 116 Failure of beams and panels 69, 120 Fasteners 196 Fatigue 88 et seq Fatigue limit 89 Fatigue terms 88 Fatigue testing 34, 88 Filters 4 Filtration media 5 Finishing of metal foams 194 Fire walls 4 Flame Arresters 4 Fleck, N.A. 5 Flexural vibrations 77 Flywheels, rotating disks 244 Foam properties 42 FRANUHOFER-DELAWARE 235 FRAUNHOFER-INSTUTUTE 235 Fully plastic moment 69, 117 Function 55 et seq Furniture 225 Gas–metal eutectic solidification 21 Gas-releasing particle decomposition in semi-solids 12 Gas-releasing particle decomposition in the melt 9 GASARS 237 GEORGIA INSTITUTE OF TECHNOLOGY 237 Gibson, L.J. 5 H2/metal eutectic solidification 7, 21 Hardness testing of foams 35 Heat exchangers 4, 224, 246 Heat shields 4 Heat sinks 4, 246
Heat transfer 4, 182 Heat transfer and pressure drop 231 Heat transfer coefficient 182, 229 Helical spring 73 Hollow sphere consolidation 17 Hollow sphere structures 17, 237 Housings for electronic devices 5 HYDRO ALUMINUM 237 Hydrodynamic contribution to strength 164 IFAM 235 ILLICHMANN 219 Impact energy absorption 163 et seq Impact velocities 163 Impedance tube 173 Imperfection sensitivity 144 Impulse 163 INCO Limited 225, 238 Indentation 35 Indentation hardness 35 Indentation of sandwich panels 117 Inertial loading effects 165 Introduction 1 Investment casting 6, 12 J2 flow theory 80 et seq JAM Corp 237 Joining of metal foams 194 et seq KARMANN GmbH 217 Kinetic energy 165 Kinetic energy absorber 165 Kronecker delta symbol 81 Light weight machine castings 220 Lightweight panels 3, 113 et seq Lightweight structures 3, 113 et seq Limiting g-factor 151 Literature on metal foams 5 LKR 236 Load ratio, R 89 Loss coefficient 43, 177 Low-weight vehicle 217 Index 249 Making metal foams 6 Material damping 176 Material indices 60, 242 et seq Mechanical Damping 4, 43, 46 Mechanical properties 42, 43, 53 Mechanical response 423 et seq Mechanical testing 27 et seq Melt gas injection 8 Melting point 47 MEPURA 219, 237 MEPURA-SLOVAKIA 219, 237 Metal deposition on cellular preforms 14 Minimising cost 209 Minimising weight 58, 124 Mirrors 223 Models for steady-state creep 106 Modulus 43, 48, 53 Modulus of rupture (MOR) 43 MOLECULAR GEODESICS Inc 238 Moments of sections 64 Molded foam parts 219 Multi-objective optimisation 206 Multiaxial testing of foams 31 Multifunctionality 216 Natural vibration frequencies 76 NEUMAN ALU FOAM 237 Nomenclature and designation 42 Non-dominated solutions 207 Notch sensitivity 97 Nusselt number 186 Objective 55 et seq Optical microscopy 24 Optical systems 222 Optimization 58, 133 et seq Optimized sandwich construction 133 et seq Packaging 4, 150 et seq. Panel 59, 215, 242 Panel, minimum weight 59 Pareto set 206 Particle decomposition in melts 6, 9
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Metal Foams: A Design Guide
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Copyright © 2000 by Butterworth-He
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vi Contents 4.3 Foam property chart
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viii Contents 17 Case studies 217 1
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List of contributors M.F. Ashby Cam
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Table of physical constants and con
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Chapter 1 Introduction Metal foams
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Activity Research Industrial take-u
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Application Comment Introduction Bi
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Cell size (cm) Making metal foams 7
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Making metal foams solidify. The th
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Making metal foams 11 2.4 Gas-relea
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a) Preform Polymer ligaments d) Rem
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a) Vapor deposition of Nickel b) Bu
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Process Steps a) Powder / Can prepa
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Making metal foams 19 flight in a t
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a) Metal - Hydrogen binary phase di
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Entrapped gas expansion Making meta
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(a) (b) (c) 100µm Characterization
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E/E bulk σ peak /σ bulk 1.2 1.0 0
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Stress (MPa) Characterization metho
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Characterization methods 31 foam sp
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Characterization methods 33 ž Prop
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F/2 F/2 F/2 F/2 τ Core Characteriz
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Characterization methods 37 40 40 4
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Characterization methods 39 Gioux,
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(a) (b) (c) Properties of metal foa
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Table 4.1 (a) Ranges a for mechanic
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Stress, σ Schematic Young's modulu
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Properties of metal foams 47 foams.
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Properties of metal foams 49 show t
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Modulus 0.5 /Density (GPa 0.5 /(Mg/
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elations take the form P Ł � Ł
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Chapter 5 Design analysis for mater
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Table 5.1 Design requirements Desig
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Design analysis for material select
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5.4 Where might metal foams excel?
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Table 6.1 Constitutive equations fo
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h SECTION h o h i d d o a b ;;; QQQ
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6.3 Elastic deflection of beams and
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6.4 Failure of beams and panels (a)
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;; ;;; ;; M ;; ;;; ;; ;;; ;; ;; ;;
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Torsion of shafts T T,q T T,q Yield
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R a 2 Flow field R F R 2a 2 F F s c
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;; ; QQ Q ¢¢ ¢ ;; ;; QQ QQ ¢¢
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; ;; Creep p e p e • Area A u F 2
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and its deviatoric (i.e. shear) com
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Normalized effective stress 1.4 1.2
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A constitutive model for metal foam
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A constitutive model for metal foam
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Stress amplitude, ∆σ + Stress,
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Axial strain (%) 5 4 3 2 1 0 0 σma
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Nominal compressive strain Nominal
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σ max σ pl τ max τ pl σ max σ
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Design for fatigue with metal foams
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the net section stress criterion re
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E σ pl (m) 10 1 0.1 0.01 0.1 Relat
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Chapter 9 Design for creep with met
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Design for creep with metal foams 1
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instead to: � Pε 3 D Pε0 2 s Ł
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Time to failure (hours) 10 2 10 1 1
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Design for creep with metal foams 1
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Chapter 10 Sandwich structures Sand
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Sandwich structures 115 The elastic
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Indentation Sandwich structures 117
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H H Core shear Core shear Collapse
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0.5 10−1 t c t c 10 −2 0.5 10
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Sandwich structures 123 the contact
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Sandwich structures 125 four sectio
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c t p p Figure 10.9 Sandwich panel
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Sandwich structures 129 with k ¾ D
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c/ Face sheet yielding 0.14 0.12 0.
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Weight index, ψ 10 −1 10 −2 10
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Sandwich structures 135 To construc
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Sandwich structures 137 The associa
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Sandwich structures 139 Note that,
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where D � 2⊲1 Eft 2 f ⊳GcR Sa
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Weight index ψ = W/2πR 2 ρ s W c
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Sandwich structures 145 plastic yie
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Sandwich structures 147 within the
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Sandwich structures 149 Shuaeib, F.
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Energy management: packaging and bl
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Energy/Unit cost (kJ/£) 10 1 0.1 0
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ys crushes axially at the load Ener
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peak pressure MPa Impulse/(mass of
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Chapter 12 Sound absorption and vib
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Sound absorption and vibration supp
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0 Sound absorption and vibration su
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Chapter 13 Thermal management and h
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Thermal management and heat transfe
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Thermal management and heat transfe
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~ P ~ Re 2.6 1000 800 600 400 200 0
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Chapter 14 Electrical properties of
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Electrical properties of metal foam
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Electrical properties of metal foam
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15.3 Joining of metal foams Cutting
Page 209 and 210: Pull-out load, F p (N) 10 5 10 4 10
Page 211 and 212: Cyclic loading of fasteners Cutting
Page 213 and 214: Time, material, energy, capital, in
Page 215 and 216: Cost estimation and viability 203 A
Page 217 and 218: $/Unit Melting Schematic of the liq
Page 219 and 220: Performance metric, P2 B Non-domina
Page 221 and 222: Cost estimation and viability 209 t
Page 223 and 224: Cost estimation and viability 211 i
Page 225 and 226: P 2 = 1/Loss coefficient (−) 1000
Page 227 and 228: Cost estimation and viability 215 C
Page 229 and 230: Chapter 17 Case studies Metal foams
Page 231 and 232: Case studies 219 Figure 17.2 A pres
Page 233 and 234: Case studies 221 Figure 17.4 Highwa
Page 235 and 236: Case studies 223 Figure 17.6 DUOCEL
Page 237 and 238: Case studies 225 density and high t
Page 239 and 240: Case studies 227 required for compa
Page 241 and 242: Maximum power density at electronic
Page 243 and 244: q *(MW/m 2) 15 10 Power density fix
Page 245 and 246: Case studies 233 which optimized sk
Page 247 and 248: e-mail: cymat@ican.net Web: www.cym
Page 249 and 250: Tel: C0043 7722 801-2125 Fax: C0043
Page 251 and 252: Chapter 19 Web sites An increasing
Page 253 and 254: http://www.seac.nl/english/recemat/
Page 255 and 256: (b) (continued) Appendix: Catalogue
Page 257 and 258: (f) Vibration-limited design Append
Page 259: Index (Company and trade names are
Page 263: Surface strain mapping 36 Syntactic
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Metal Foams: A Design Guide

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