Metal Foams: A Design Guide

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Preface and acknowledgements Metal foams are a new class of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties. This Design Guide is a contribution to the concurrent development of their science and exploitation. It seeks to document design information for metal foams even as the scientific research and process development are evolving. This should help to identify promising industrial sectors for applications, guide process development and accelerate take-up. This work is supported by the DARPA/ONR MURI Program through Grant No. N00014-1-96-1028 for Ultralight Metal Structures and by the British Engineering and Science Research Council through a Research Grant. Many individuals and groups have contributed to its contents. They include Professor B. Budiansky, Professor H. Stone, Professor R. Miller, Dr A. Bastawros, Dr Y. Sugimura of the Division of Engineering and Applied Sciences, Harvard University; Dr T.J. Lu, Dr Anne-Marie Harte, Dr V. Deshpande of the Micromechanics Centre, Engineering Department, Cambridge University; Dr E.W. Andrews and Dr L. Crews of the Department of Materials Science and Engineering, MIT; Professor D. Elzey, Dr D. Sypeck and Dr K. Dharmasena of the Department of Materials Science and Engineering, UVA; Dr John Banhart of the Fraunhofer Institüt Angewandte Materialsforschung, Bremen; Professor H.P. Degisher and Dr Brigdt Kriszt of the Technical University of Vienna, Dr Jeff Wood of Cymat Corp. Mississauga, Canada; and Mr Bryan Leyda of Energy Research and Generation Inc. Oakland, CA. Although the compilers of this Guide have made every effort to confirm the validity of the data and design information it contains, the compilers make no warranty, either expressed or implied, with respect to their quality, accuracy or validity.
List of contributors M.F. Ashby Cambridge Centre for Micromechanics Engineering Department University of Cambridge Cambridge CB2 1PZ UK mfa2@eng.cam.ac.uk A.G. Evans Princeton Materials Institute Bowen Hall 70 Prospect Avenue Princeton, NJ 08540 USA anevans@princeton.edu N.A. Fleck Cambridge Centre for Micromechanics Engineering Department University of Cambridge Cambridge CB2 1PZ UK naf1@eng.cam.ac.uk L.J. Gibson Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 USA ljgibson@mit.edu J.W. Hutchinson Division of Engineering and Applied Sciences Harvard University
Page 1 and 2: Metal Foams: A Design Guide
Page 3 and 4: Copyright © 2000 by Butterworth-He
Page 5 and 6: vi Contents 4.3 Foam property chart
Page 7: viii Contents 17 Case studies 217 1
Page 11 and 12: Table of physical constants and con
Page 13 and 14: Chapter 1 Introduction Metal foams
Page 15 and 16: Activity Research Industrial take-u
Page 17 and 18: Application Comment Introduction Bi
Page 19 and 20: Cell size (cm) Making metal foams 7
Page 21 and 22: Making metal foams solidify. The th
Page 23 and 24: Making metal foams 11 2.4 Gas-relea
Page 25 and 26: a) Preform Polymer ligaments d) Rem
Page 27 and 28: a) Vapor deposition of Nickel b) Bu
Page 29 and 30: Process Steps a) Powder / Can prepa
Page 31 and 32: Making metal foams 19 flight in a t
Page 33 and 34: a) Metal - Hydrogen binary phase di
Page 35 and 36: Entrapped gas expansion Making meta
Page 37 and 38: (a) (b) (c) 100µm Characterization
Page 39 and 40: E/E bulk σ peak /σ bulk 1.2 1.0 0
Page 41 and 42: Stress (MPa) Characterization metho
Page 43 and 44: Characterization methods 31 foam sp
Page 45 and 46: Characterization methods 33 ž Prop
Page 47 and 48: F/2 F/2 F/2 F/2 τ Core Characteriz
Page 49 and 50: Characterization methods 37 40 40 4
Page 51 and 52: Characterization methods 39 Gioux,
Page 53 and 54: (a) (b) (c) Properties of metal foa
Page 55 and 56: Table 4.1 (a) Ranges a for mechanic
Page 57 and 58: 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
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Pull-out load, F p (N) 10 5 10 4 10
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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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