Metal Foams: A Design Guide

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180 Metal Foams: A Design Guide Kovacik, J., Tobolka, P. Simancik, F. (1999) In Banhart, J., Ashby, M.F. and Fleck, N.A. (eds), Metal Foams and Foam Metal Structures, Proc. Int. Conf. Metfoam’99, 14–16 June 1999, MIT Verlag, Bremen, Germany. Lu, T.J., Hess, A. and Ashby, M.F. (1999) J. Appl. Phys. 85, 7528–7539. Shinko Wire (1996) Alporas Data Sheets (see Section 17: Suppliers of Metal Foams). Utsuno, H., Tanaka, T. and Fujikawa, T. (1989) J. Acoust. Soc. Am. 86, 637–643. Wang, X. and Lu, T.J. (1999) Optimised acoustic properties of cellular solids. J. Accoust. Soc. Am. 106(2), 1, 1–10. Zop, A. and Kollmann, F.G. (1999) In Banhart, J., Ashby, M.F. and Fleck, N.A. (eds), Metal Foams and Foam Metal Structures, Proc. Int. Conf. Metfoam’99, 14–16 June 1999, MIT Verlag, Bremen, Germany.
Chapter 13 Thermal management and heat transfer 13.1 Introduction The thermal conductivities of metal foams (see Table 4.1(b)) are at least an order of magnitude greater than their non-metallic counterparts, so they are generally unsuited for simple thermal insulation though they can provide some fire protection. The thermal conductivities of closed-cell foams are, however, lower than those of the fully dense parent metal by a factor of between 8 and 30, offering a degree of fire protection in, for instance, an automobile bulkhead between engine and passenger compartment. More important, opencell metal foams can be used to enhance heat transfer in applications such as heat exchangers for airborne equipment, compact heat sinks for power electronics, heat shields, air-cooled condenser towers and regenerators (Antohe et al., 1996; Kaviany, 1985). The heat-transfer characteristics of open-cell metal foams are summarized in this chapter. Examples of the use of metfoams for thermal management can be found in the case studies of Sections 16.4, 16.5, 16.6 and 16.8. Figure 13.1 illustrates a prototypical heat-transfer configuration. Heat sources are attached to thin conducting substrates between which is bonded a layer of open-celled foam of thickness b and length L. A fluid is pumped at velocity vf through the foam, entering at temperature T0 and exiting at temperature Te. An idealization of the foam structure is shown below: the relative density is Q D c/ s and the diameter of the cell edges is d. Thelocal heat-transfer coefficient at the surface of a cell edge is h. There are three guiding design principles. 1. High conductivity ligaments are needed that transport the heat rapidly into the medium: the preference is for metals such as Cu or Al. 2. A turbulent fluid flow is preferred that facilitates high local heat transfer from the solid surface into the fluid. 3. A low-pressure drop is needed between the fluid inlet and outlet such that the fluid can be forced through the medium using a pumping system with moderate power requirements making low fluid viscosity desirable. Heat transfer to the fluid increases as either the ligament diameter, d, becomes smaller or the relative density, / s, increases because the internal
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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
Page 141 and 142: Sandwich structures 129 with k ¾ D
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Page 145 and 146: Weight index, ψ 10 −1 10 −2 10
Page 147 and 148: Sandwich structures 135 To construc
Page 149 and 150: 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 187 and 188: Sound absorption and vibration supp
Page 189 and 190: 0 Sound absorption and vibration su
Page 191: Sound absorption and vibration supp
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 and 202: Chapter 14 Electrical properties of
Page 203 and 204: Electrical properties of metal foam
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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
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q *(MW/m 2) 15 10 Power density fix
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Case studies 233 which optimized sk
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e-mail: cymat@ican.net Web: www.cym
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Tel: C0043 7722 801-2125 Fax: C0043
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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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