Metal Foams: A Design Guide

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178 Metal Foams: A Design Guide and the response is minimized by maximizing the material index: Md D ⊲12.15⊳ More generally, the input x is described by a mean square (power) spectral density: � � k ω Sx ⊲ω⊳ D S0 ⊲12.16⊳ ω0 where S0, ω0 and k are constants, and k typically has a value greater than 2. It can be shown (Cebon and Ashby, 1994) that the material index to be maximized in order to minimise the response to x is M 0 d D ωk 1 1 D Mk 1 u ⊲12.17⊳ The selection to maximize M0 d can be performed by plotting a materials selection chart with log⊲ ⊳ on the x-axis and log⊲Mu⊳ on the y-axis, as shown in Figure 12.4. The selection lines have slope 1/⊲1 k⊳. The materials which lie farthest above a selection line are the best choice. Performance index for undamped vibration log ω 1 −1/5 −1/3 −1 Loss coefficient log η k = −∞ k = −6 k = −4 k = −2 Input Lower frequency content White accn White velocity Figure 12.4 Schematic diagram of a materials selection chart for minimizing the RMS displacement of a component subject to an input with spectral density S0 ⊲ω/ω0 ⊳ k If k D 0, the spectrum of input displacement is flat, corresponding to a ‘white noise’ input, but this is unrealistic because it implies infinite power input to the system. If k D 2, the spectrum of the input velocity is flat (or white), which just gives finite power; for this case the selection line on Figure 12.4 has a slope of 1. For larger values of k, the input becomes more concentrated at
Sound absorption and vibration suppression 179 low frequencies, and the selection line is less steep. If k D1, the selection line becomes horizontal and the selection task becomes one of choosing materials with the highest value of ω1, exactly as for the undamped case. Figure 12.5 shows data for metal foams. Metal foam panels and sandwich panels with metfoam cores have attractive values of M0 d , because of their high flexural stiffness and their relatively high damping capacity. The Alporas range of foams offers particularly good performance. For comparison, aluminum alloys have a values of Mu in the range 1.6–1.8 and damping coefficients, , in the range 10 4 2 ð 10 3 in the same units as those of the figure. Material index M u = E 1/3 / ρ (GPa 1/3 /Mg/m 3 ) 8 6 4 2 Material index Mu vs. Damping coefficient Vibes 1 CMS, MFA 14-4-98; Metfoam DB Alporas (0.21) Hydro (0.25) Hydro (0.15) Alulight (0.3) Alulight (0.32) Alporas (0.245) Alulight (0.371) Fraunhofer (0.4) Fraunhofer (0.551) Alulight (0.95) Alulight (0.645) Duocel Duocel (0.235) (0.19) Duocel (0.254) Hydro (0.419) Cymat (0.083) Hydro (0.153) Cymat (0.155) Hydro (0.42) Hydro (0.143) Hydro (0.161) Cymat (0.071) INCO (0.265) INCO (0.31) INCO (0.385) 1.0E-3 0.002 0.004 0.006 0.008 0.01 0.02 0.04 0.06 Material index M d - η Figure 12.5 A selection chart for vibration management. The axes are the index. Mu D E1 /3 / and the damping coefficient Md D . All the materials shown are metal foams, and all have better performance, measured by the index M0 d than the solid metals from which they are made References Asholt, P. (1997) In Banhart, J. (ed.), Metallschäume, MIT Verlag, Bremen, Germany. Beranek, L.L. (ed.) (1960) Noise Reduction, McGraw-Hill, New York. Cebon, D. and Ashby, M.F. (1994) Material selection for precision instruments. Measurement Science and Technology 5, 296–306. Cowan, H.J. and Smith, P.R. (1988) The Science and Technology of Building Materials, Van Nostrand Reinhold, New York.
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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
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 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: 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
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
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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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