Metal Foams: A Design Guide

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Appendix: Catalogue of material indices Material indices help to identify the applications in which a material might excel and those for generic components are assembled here. Their derivation and use is illustrated in Chapters 5, 11 and 12. (a) Stiffness-limited design at minimum mass (cost, energy a ) Function and constraints a Maximize b SHAFT (loaded in torsion) Stiffness, length, shape specified, section area free G1/2 / Stiffness, length, outer radius specified; wall thickness free G/ Stiffness, length, wall thickness specified, outer radius free G1/3 BEAM (loaded in bending) / Stiffness, length, shape specified; section area free E1/2 / Stiffness, length, height specified; width free E/ Stiffness, length, width specified; height free E1/3 / COLUMN (compression strut, failure by elastic buckling) E1/2 buckling load, length, shape specified; section area free / a To minimize cost, use the above criteria for minimum weight, replacing density by Cm ,whereCm is the material cost per kg. To minimize energy content, use the above criteria for minimum weight replacing density by q where q is the energy content per kg. b E D Young’s modulus; G D shear modulus; D density. (b) Stiffness-limited design at minimum mass (cost, energy a ) Function and constraints a Maximize b PANEL (flat plate, loaded in bending) E 1/3 / stiffness, length, width specified, thickness free PLATE (flat plate, compressed in-plane, buckling failure) E 1/3 / collapse load, length and width specified, thickness free
(b) (continued) Appendix: Catalogue of material indices 243 Function and constraints a Maximize b CYLINDER WITH INTERNAL PRESSURE elastic distortion, pressure and radius specified; wall thickness free SPHERICAL SHELL WITH INTERNAL PRESSURE E/ elastic distortion, pressure and radius specified, wall thickness free E/⊲1 ⊳ a To minimize cost, use the above criteria for minimum weight, replacing density by Cm ,whereCm is the material cost per kg. To minimize energy content, use the above criteria for minimum weight replacing density by q where q is the energy content per kg. b E D Young’s modulus; G D shear modulus; D density. (c) Strength-limited design at minimum mass (cost, energy a ) Function and constraints a,c Maximize b SHAFT (loaded in torsion) Load, length, shape specified, section area free Load, length, outer radius specified; wall thickness free f/ Load, length, wall thickness specified, outer radius free BEAM (loaded in bending) Load, length, shape specified; section area free Load, length, height specified; width free f/ Load, length, width specified; height free COLUMN (compression strut) Load, length, shape specified; section area free f/ PANEL (flat plate, loaded in bending) Stiffness, length, width specified, thickness free 2/3 f / 1/2 f / 2/3 f / 1/2 f / 1/2 f / aTo minimize cost, use the above criteria for minimum weight, replacing density by Cm ,whereCmis the material cost per kg. To minimize energy content, use the above criteria for minimum weight replacing density by q where q is the energy content per kg. b f D failure strength (the yield strength for metals and ductile polymers, the tensile strength for ceramics, glasses and brittle polymers); D density. cFor design for infinite fatigue life, replace f by the endurance limit e.
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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
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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
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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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
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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
Page 253: http://www.seac.nl/english/recemat/
Page 257 and 258: (f) Vibration-limited design Append
Page 259 and 260: Index (Company and trade names are
Page 261 and 262: Heat transfer 4, 182 Heat transfer
Page 263: Surface strain mapping 36 Syntactic
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Metal Foams: A Design Guide

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