Metal Foams: A Design Guide

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190 Metal Foams: A Design Guide P1 I V I Equipotential surface s1 s2 s3 P2 P3 P4 Semi-infinite sample Medium Current flow line Figure 14.1 A four-point probe method for measuring the electrical conductivity of metal foams Relative electrical conductivity (s/s s) 1.0 0.8 0.6 0.4 0.2 0.0 0.0 Duocel open-cell al foam Alulight closed-cell al foam α = 0.33 α = 0.05 0.2 0.4 0.6 0.8 1.0 25 Relative density (ρ/ρs ) Figure 14.2 The relative electrical resistivity and conductivity of open- and closed-cell aluminum foams of differing relative density. The lines are plots of equation (14.4) with ˛ D 0.33 and ˛ D 0.05 14.2 Data for electrical resistivity of metal foams Little data for the electrical resistivity of metal foams has been reported. Figure 14.2 shows measurements of the conductivity of open (ERG-Duocel) and closed (Mepura-Alulight) cell aluminum foams as a function of relative 1 2 5 10 Relative electrical resistivity (q/q s )
Electrical properties of metal foams 191 density, normalized by the conductivity of the fully dense alloy. The conductivity varies in a non-linear way with relative density. Additional data for nickel foams can be found in patents referenced as Babjak et al. (1990), at the end of this chapter. 14.3 Electrical conductivity and relative density Figure 14.3 shows an idealization of a low-density open cell foam. The cell edges have length ℓ and cross-section t ð t, meeting at nodes of volume t 3 . The relative density of an open-cell foam is related to the dimensions of the cells (omitting terms of order ⊲t/ℓ⊳ 4 )by Potential gradient s ³ 3t2 ℓ 2 t t ⊲14.4⊳ Figure 14.3 An idealized open-cell foam consisting of cell edges of length ℓ and cross-section t 2 , meeting at nodes of volume t 3 . In real foams the nodes are larger (‘Plateau borders’) and the edges thinner at their mid-points, because of the effects of surface tension The dependence of electrical conductivity on relative density can be understood in the following way. The cell edges form a three-dimensional network. If a potential gradient is applied parallel to one set of cell edges, the edges which lie parallel to the gradient contribute to conduction but those which lie normal to it do not, because there is no potential difference between their ends. The network is linked at nodes, and the nodes belong to the conducting path. At low relative densities the volume of the nodes is negligible compared
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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
Page 151 and 152: Sandwich structures 139 Note that,
Page 153 and 154: where D � 2⊲1 Eft 2 f ⊳GcR Sa
Page 155 and 156: Weight index ψ = W/2πR 2 ρ s W c
Page 157 and 158: Sandwich structures 145 plastic yie
Page 159 and 160: Sandwich structures 147 within the
Page 161 and 162: Sandwich structures 149 Shuaeib, F.
Page 163 and 164: Energy management: packaging and bl
Page 167 and 168: Energy/Unit cost (kJ/£) 10 1 0.1 0
Page 171 and 172: ys crushes axially at the load Ener
Page 179 and 180: peak pressure MPa Impulse/(mass of
Page 183 and 184: Chapter 12 Sound absorption and vib
Page 185 and 186: Sound absorption and vibration supp
Page 189 and 190: 0 Sound absorption and vibration su
Page 193 and 194: Chapter 13 Thermal management and h
Page 195 and 196: Thermal management and heat transfe
Page 197 and 198: Thermal management and heat transfe
Page 199 and 200: ~ P ~ Re 2.6 1000 800 600 400 200 0
Page 201: Chapter 14 Electrical properties of
Page 205 and 206: Electrical properties of metal foam
Page 207 and 208: 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
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http://www.seac.nl/english/recemat/
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(b) (continued) Appendix: Catalogue
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(f) Vibration-limited design Append
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Index (Company and trade names are
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Heat transfer 4, 182 Heat transfer
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Surface strain mapping 36 Syntactic
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Metal Foams: A Design Guide

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