Metal Foams: A Design Guide

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214 Metal Foams: A Design Guide with ˇ given by ˇ D � � Ł 2 1/3 12S b ℓ C1 2 ⊲16.14⊳ ˇ is a constant for a given design, and does not influence the optimization. The geometric constant, C1, defined in equation (5.4), depends only on the distribution of loads on the panel and does not influence the subsequent argument. The cost, Cp, of the panel is simply the material cost per kg, C (from equation (16.4)), times the mass m, giving the second performance metric P2: P2 D Cp ˇ D � C E 1/3 � ⊲16.15⊳ Figure 16.10 shows the trade-off plot. The horizontal axis, P1, isthematerial index /E 1/3 . The vertical axis, correspondingly, is the index C /E 1/3 . Cost × density/(modulus) 1/3 [£/m 3 ]/ [GPa 1/3 ] 1000. 100. 10. 1. 0.1 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Al-matrix MMCs ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Titanium ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Beryllium ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; alloys ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Tungsten ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; alloys ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Alporas ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; CFRPs ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Alulight ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Ai-SiC composites ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Stainless ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; steels Alcan ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Lead alloys ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; GFRPs ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; White cast irons Magnesium ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; alloys ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; PP Aluminum alloys Trade-off ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Polystyrene surface Performance metrics for UPVC, Rigid 1.e-002 panel of specified stiffness Low alloy steels Grey cast irons 0.1 1. Density/(Young's modulus) 1/3 , [Mg/m 3 ]/[GPa 1/3 ] Figure 16.10 A trade-off plot for the performance metrics (measured by material indices) for cost and mass of a panel of specified bending stiffness. Each bubble refers to a material class. The metal foams are distinguished by filled ellipses (all other materials are fully dense). The trade-off front, constructed for non-foamed materials, separates the populated section of the figure from that which is unpopulated. Metal foams lie in the unpopulated sector
Cost estimation and viability 215 Conventional alloys (cast irons, steels, aluminum alloys) lie in the lower part of the diagram. Beryllium alloys, CFRPs and Al-based MMCs lie in the central and upper parts. The trade-off surface for conventional, fully dense, materials is shown by the shaded band. Metal foams lie in the unpopulated sector of the diagram – all three classes of foam offer non-dominated solutions to this problem. But even so, they are viable only if the mass/value exchange constant lies in the right range. To explore this question for the panel of specified stiffness we define the value function � V D ˛1P1 C ˛2P2 D ˛1 E 1/3 � � C C E 1/3 � ⊲16.16⊳ (since ˛2, relating value to cost, is unity). Values of ˛1, relating value to mass, are listed in Table 16.2. The equation is evaluated in Table 16.3 for two extreme values of ˛1 for a set of materials including cast irons, steels, aluminum alloys, titanium, beryllium and three metal foams. When ˛1 has the low value of 0.5£/kg, nodular cast irons are the best choice. But if ˛1 is as Table 16.3 The selection of panel materials: stiffness constraint Material E Cm P1 P2 V V Mg/m 3 GPa £/kg ˛1 D ˛1 D £0.5/kg £500/kg Cast iron, nodular 7.30 175 0.25 1.31 0.33 0.99 655 Low-alloy steel (4340) 7.85 210 0.45 1.32 0.59 1.25 660 Al-6061-T6 2.85 70 0.95 0.69 0.66 1.01 345 Al-061–20% SiC, PM 2.77 102 25 0.59 14.8 15.1 309 Ti-6-4 B265 grade 5 4.43 115 20 0.91 18.2 18.7 473 Beryllium SR-200 1.84 305 250 0.27 67.5 67.6 202 Alporasa 0.25 1.0 40 0.23 10.0 10.1 125 Alulighta 0.30 0.8 16 0.3 5.2 5.4 155 Alcana 0.25 0.4 5.8 0.34 2.0 2.2 172 a All three types of metal foam are made in a range of densities, with a corresponding range of properties. These three examples are taken from the middle of the ranges. The costs are estimates only, broadly typical of current prices, but certain to change in the future. It is anticipated that large-scale production could lead to substantially lower costs.
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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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Page 175 and 176: Energy management: packaging and bl
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
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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: P 2 = 1/Loss coefficient (−) 1000
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
Page 245 and 246: Case studies 233 which optimized sk
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 and 254: http://www.seac.nl/english/recemat/
Page 255 and 256: (b) (continued) Appendix: Catalogue
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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