Metal Foams: A Design Guide

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202 Metal Foams: A Design Guide flux per unit area of structure. In design for the environment, the metric is a measure of the environmental load associated with the manufacture, use and disposal of the material. Each performance metric defines an objective: an attribute of the structure that it is desired to maximize or minimize. Models are developed for the performance metrics following the method of Chapter 5; the resulting performance equations contain groups of material properties or ‘material indices’. The material that maximizes the chosen performance metric has the highest technical merit. But for this to be a viable choice, the performance must be balanced against the cost. 16.3 Cost modeling The manufacture of a foam (or of a component made from one) consumes resources (Table 16.1). The final cost is the sum of these resources. This resource-based approach to cost analysis is helpful in selecting materials and processes even when they differ greatly, since all, no matter how different, consume the resources listed in the table. Thus the cost of producing one kg of foam entails the cost Cm ($/kg) and mass, m, of the materials and feedstocks from which it is made, and it involves the cost of dedicated tooling, Ct ($), which must be amortized by the total production volume, n (kg). In addition, it requires time, chargeable at an overhead rate CL P (with units of $/h or equivalent), power P (kW) at an energy cost Ce ($/kW.h), space of area Table 16.1 The resources consumed in making a material Resource Symbol Unit Materials: inc. consumables Cm $/kg Capital: cost of equipment Cc $/unit cost of tooling Ct $/unit Time: overhead rate CL P $/hr Energy: power P kW cost of energy Ce $/kW.h Space: area A m2 cost of space PCS $/m2 .h Information: R&D Ci royalty payments
Cost estimation and viability 203 A, incurring a rental cost of CS P ($/m2 .h), and information, as research and development costs, or as royalty or licence payments Ci P (expressed as $/h). The cost equation, containing terms for each of these, takes the form [Material] [Tooling] [Time] [Energy] [Space] [Information] # # # # # # � � � � � � � � � � � � mCm Ct CL P PCe ACS P Ci P C D C C C C C ⊲16.1⊳ 1 f n Pn Pn Pn Pn where Pn is the production rate (kg/h) and f is the scrap rate (the material wastage in the process). A given piece of equipment – a powder press, for example – is commonly used to make more than one product, that is, it is not dedicated to one product alone. It is usual to convert the capital cost, Cc, of non-dedicated equipment, and the cost of borrowing the capital itself, into an overhead by dividing it by a capital write-off time, tc (5 years, say) over which it is to be recovered. Thus the capital-inclusive overhead rate becomes [Basic OH rate] [Capital write-off] # # CL P � � �� 1 � � Cc D CL0 P C ⊲16.2⊳ Pn Pn Ltc where CL0 P is the basic overhead rate (labor, etc.) and L is the load factor, meaning the fraction of time over which the equipment is productively used. The general form of the equation is revealed by assembling the terms into three groups: [Material] [Tooling] [Time Capital Energy Space Information] # # # # # # # � � mCm C D C 1 f 1 n [Ct] C 1 � CL0 P C Pn Cc � C PCe C ACS P C PCi ⊲16.3⊳ Ltc The terms in the final bracket form a single ‘gross overhead’, CL,gross, P allowing the equation to be written [Materials] [Dedicated cost/unit] [Gross overhead/unit] # # # � � mCm C D C 1 f 1 n [Ct] C 1 � � CL,gross P ⊲16.4⊳ Pn The equation indicates that the cost has three essential contributions: (1) a material cost/unit of production which is independent of production volume
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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.
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 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
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
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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: Time, material, energy, capital, in
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
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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