Metal Foams: A Design Guide

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212 Metal Foams: A Design Guide 16.5 Applications Two examples of the method follow, each exploring the viability of metal foams in a particular application. In the first, metal foams prove to be nonviable. In the second, despite their present high cost, they prove to be viable. The examples are deliberately simplified to bring out the method. The principles remain the same when further detail is added. Simple trade-off between two performance indices Consider selection of a material for a design in which it is desired, for reasons of vibration control, to maximize the specific modulus E/ (E is Young’s modulus and is the density) and the damping, measured by the loss coefficient . We identify two performance metrics, P1 and P2, defined such that minima are sought for both: and P1 D E P2 D 1 ⊲16.10a⊳ ⊲16.10b⊳ Figure 16.9 shows the trade-off plot. Each bubble on the figure describes a material; the dimensions of the bubble show the ranges spanned by these property groups for each material. Materials with high values of P1 have low values of P2, and vice versa, so a compromise must be sought. The optimum trade-off surface, suggested by the shaded band, identifies a subset of materials with good values of both performance metrics. If high E/ (low P1) is of predominant importance, then aluminum and titanium alloys are a good choice; if greater damping (lower P2) is required, magnesium alloys or cast irons are a better choice; and if high damping is the over-riding concern, tin or lead alloys and a range of polymers become attractive candidates. It is sometimes possible to use judgement to identify the best position on the tradeoff surface (strategy 1, above). Alternatively (strategy 2) a limit can be set for one metric, allowing an optimum for the other to be read off. Setting a limit of >0.1, meaning P2 < 10, immediately identifies pure lead and polyethylenes as the best choices in Figure 16.9. Finally, and preferably (strategy 3), a value function can be determined: 1 V D ˛1P1 C ˛2P2 D ˛1 C ˛2 ⊲16.11⊳ E seeking materials which minimize V. Contours of constant V, likethoseof Figure 16.7, have slope � � ∂P2 D ∂P1 ˛1 ⊲16.12⊳ ˛2 V
P 2 = 1/Loss coefficient (−) 100000. 10000. 1000. 100. 10. 1. 0.1 Cost estimation and viability 213 Performance metrics for stiffness and damping ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Low alloy ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; steels ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Nyoln ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; HDPE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; CTFE PTFE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; LLDPE ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Alcan Tungsten alloys Gunmetal Trade-off surface Bronzes Brasses Alulight Alporas Titanium Melamine UPVC alloys Aluminum PEEK alloys Megnesium alloys Cast irons Tin alloys Sn-Sb alloys Lead alloys Pure lead MDPE Ionomer (IO) LDPE 1. P 1 = Density/modulus (Mg/m 3 /GPa) Figure 16.9 A trade-off plot for the performance metrics P1 D /E and P2 D 1 / . Each bubble refers to a material class. The metal foams are distinguished by filled ellipses (all other materials are fully dense). The shaded band show the optimum trade-off surface. Materials that lie on or near this surface most nearly optimize both performance metrics The point at which one contour is tangent to the trade-off surface identifies the best choice of material. Implementation of this strategy requires values for the ratio ˛1/˛2 which measures the relative importance of stiffness and damping in suppressing vibration. This requires estimates of the influence of each on overall performance, and can, in technical systems, be modeled. Here, however, it is unnecessary. The positions of three classes of metal foams are shown as black ovals. None lie on or near the trade-off surface; all are subdominant solutions to this particular problem. Metal foams, in this application, are non-viable. Co-minimizing mass and cost One of the commonest trade-offs is that between mass and cost. Consider, as an example, co-minimizing the mass and cost of the panel of specified bending stiffness analysed in Chapter 5, Section 5.3. The mass of the panel is given by equation (5.4) which we rearrange to define the performance metric P1: P1 D m ˇ D � � ⊲16.13⊳ E 1/3 10.
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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 183 and 184: Chapter 12 Sound absorption and vib
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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 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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Page 211 and 212: Cyclic loading of fasteners Cutting
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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: Cost estimation and viability 211 i
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
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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