Metal Foams: A Design Guide

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148 Metal Foams: A Design Guide 10.9 Recommendations for sandwich design For those wishing to explore cellular metal core sandwich construction, the following recommendations are pertinent: 1. Determine the constraints that govern the structure and, in particular, whether it is stiffness or strength-limited. 2. If stiffness-limited, the procedure for determining the minimum weights is straightforward, using the formulae summarized in the tables. It is important to realize that there will always be lighter configurations (especially optimized honeycomb or waffle panels). Those configurations should be explicitly identified, whereupon a manufacturing cost and durability comparison can be made that determines the viability of sandwich construction. Other qualities of the cellular metal may bias the choice. It is important to calculate the domains wherein the weights based on elasticity considerations cannot be realized, because of the incidence of ‘inelastic’ modes: face yielding, core yielding, face wrinkling. Some help in assessing these limits has been provided. 3. When strength-limited (particularly when buckling-limited), the rules governing sandwich construction are less well formulated. In general, numerical methods are needed to compare and contrast this type of construction with stiffened systems. Some general guidelines are given in this Design Guide; these give insight into the loadings and configurations most likely to benefit from sandwich construction. Configurations unlikely to benefit are also described. It is recommended that where benefits seem likely, detailed simulations and testing should be used to assess the viability of sandwich construction. References Allen H.G. (1969) Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford. Andrews, E.H., Gioux, G., Onck, P. and Gibson, L.J. (1999) The role of specimen size, specimen shape and surface preparation in mechanical testing of aluminum foams. To appear in Mat. Sci. and Engineering A. Bart-Smith, H. (2000) PhD thesis, Harvard University. Budiansky, B. (1999) On the minimum weights of compression structures. Int. J. Solids and Structures 36, 3677–3708. Deshpande, V.S. and Fleck, N.A. (1999) Isotropic constitutive models for metallic foams. To appear in J. Mech. Phys. Solids. Gerard, G. (1956) Minimum Weight Analysis of Compression Structures, New York University Press, New York. Gibson, L.J. and Ashby, M.F. (1997) Cellular Solids, Structure and Properties, 2nd edition, Cambridge University Press, Cambridge, Ch. 9, pp. 345 et seq. Harte, A.-M. (1999) Private communication. Hutchinson, J.W. and He, M.Y. (1999) Buckling of cylindrical sandwich shells with metal foam cores. Int. J. Solids and Structures (in press).
Sandwich structures 149 Shuaeib, F.M. and Soden, P.D. (1997) Indentation failure of composite sandwich beams. Composite Science and Technology 57, 1249–1259. Soden, P.D. (1996) Indentation of composite sandwich beams. J. Strain Analysis 31(5), 353–360. Tennyson, R.C. and Chan, K.C. (1990) Buckling of imperfect sandwich cylinders under axial compression. Int. J. Solids and Structures 26, 1017–1036. Wilsea, M., Johnson, K.L. and Ashby, M.F. (1975) Int. J. Mech. Sci. 17, 457.
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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
Page 109 and 110: Design for fatigue with metal foams
Page 111 and 112: the net section stress criterion re
Page 113 and 114: E σ pl (m) 10 1 0.1 0.01 0.1 Relat
Page 115 and 116: Chapter 9 Design for creep with met
Page 117 and 118: Design for creep with metal foams 1
Page 119 and 120: instead to: � Pε 3 D Pε0 2 s Ł
Page 121 and 122: Time to failure (hours) 10 2 10 1 1
Page 123 and 124: Design for creep with metal foams 1
Page 125 and 126: Chapter 10 Sandwich structures Sand
Page 127 and 128: Sandwich structures 115 The elastic
Page 129 and 130: Indentation Sandwich structures 117
Page 131 and 132: H H Core shear Core shear Collapse
Page 133 and 134: 0.5 10−1 t c t c 10 −2 0.5 10
Page 135 and 136: Sandwich structures 123 the contact
Page 137 and 138: Sandwich structures 125 four sectio
Page 139 and 140: c t p p Figure 10.9 Sandwich panel
Page 141 and 142: Sandwich structures 129 with k ¾ D
Page 143 and 144: c/ Face sheet yielding 0.14 0.12 0.
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: Sandwich structures 147 within the
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 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
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Cyclic loading of fasteners Cutting
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Time, material, energy, capital, in
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Cost estimation and viability 203 A
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$/Unit Melting Schematic of the liq
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Performance metric, P2 B Non-domina
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Cost estimation and viability 209 t
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Cost estimation and viability 211 i
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P 2 = 1/Loss coefficient (−) 1000
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Cost estimation and viability 215 C
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Chapter 17 Case studies Metal foams
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Case studies 219 Figure 17.2 A pres
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Case studies 221 Figure 17.4 Highwa
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Case studies 223 Figure 17.6 DUOCEL
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Case studies 225 density and high t
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Case studies 227 required for compa
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Maximum power density at electronic
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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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Metal Foams: A Design Guide

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