Metal Foams: A Design Guide

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170 Metal Foams: A Design Guide Kenny, L.D. (1996) Mechanical properties of particle stabilised aluminum foams. Materials Science Forum 217–222, 1883–1890. Lankford, J. and Danneman, K. (1998) in Shwartz, D.S., Shih, D.S., Evans, A.G. and Wadley, H.N.G. (eds), Porous and Cellular Materials for Structural Application, Materials Research Society Proceedings, Vol. 521, MRS, Warrendale, PA, USA. Mukai, T., Kanahashi, H., Higashi, K., Yamada, Y., Shimojima, K., Mabuchi, M., Miyoshi, T. and Tieh, T.G. (1999) Energy absorption of light-weight metallic foams under dynamic loading. In Banhart, J., Ashby, M.F. and Fleck, N.A. (eds), Metal Foams and Foam Metal Structures, Proc. Int. Conf. Metfoam’99, 14–16 June 1999, MIT Verlag, Bremen, Germany. Reid, S.R. and Reddy, T.Y. (1983) Int. J. Impact Engng. 1, 85–106. Santosa, S. and Wierzbicki, T. (1998) Crash behavior of box columns filled with aluminum honeycomb or foam. Computers and Structures 68(4), 343–367. Santosa, S., Banhart, J. and Wierzbicki, T. (1999) Bending crush behavior of foam-filled sections. In Banhart, J., Ashby, M.F. and Fleck, N.A. (eds), Metal Foams and Foam Metal Structures, Proc. Int. Conf. Metfoam’99, 14–16 June 1999, MIT Verlag, Bremen, Germany. Seitzberger, M., Rammerstorfer, F.G., Gradinger, R., Degisher, H.P., Blaimschein, M. and Walch, C. (1999) Axial crushing of foam-filled columns. To appear in Int. J. Sol. Struct. Seitzberger, M., Rammerstorfer, F.G., Degisher, H.P. and Gradinger, R. (1997) Crushing of axially compressed steel tubes filled with aluminum foam. Acta Mechanica 125, 93–105. Smith, P.D. and Hetherington, J.G. (1994) Blast and Ballistic Loading of Structures, Butterworth- Heinemann, Oxford. Wierzbicki, T. and Abramowicz, W. (1983) On the crushing mechanics of thin-walled structures. Int. J. Solids Structures 29, 3269–3288.
Chapter 12 Sound absorption and vibration suppression The ability to damp vibration coupled with mechanical stiffness and strength at low weight makes an attractive combination. Automobile floors and bulkheads are examples of structures the primary function of which is to carry loads, but if this is combined with vibration damping and sound absorption the product quality is enhanced. Metal foams have higher mechanical damping than the solid of which they are made, but this is not the same as sound absorption. Sound absorption means an incident sound wave is neither reflected nor transmitted; its energy is absorbed in the material. There are many ways in which this can happen: by direct mechanical damping in the material itself, by thermo-elastic damping, by viscous losses as the pressure wave pumps air in and out of cavities in the absorber and by vortex-shedding from sharp edges. Sound is measured in decibels, and this is a logarithmic measure, in accord with the response of the ear. The result is that – as far as human perception is concerned – a sound-absorption coefficient in the acoustic range of 0.5 (meaning that half the incident energy is absorbed) is not much good. To be really effective, the absorption coefficient must be exceed 0.9. The best acoustic absorbers easily achieve this. Are metal foams good sound absorbers? Data described in this chapter suggest an absorption coefficient of up to 0.85 – good, but not as good as materials such as felt or fiberglass. More significant is that the high flexural stiffness and low mass of foam and foam-cored panels result in high natural vibration frequencies, and this makes them hard to excite. So while metal foams and metfoam-cored panels offer some potential for vibration and acoustic management, their greater attraction lies in the combination of this attribute with others such as of stiffness at light weight, mechanical isolation, fire protection and chemical stability. 12.1 Background: sound absorption in structural materials Sound is caused by vibration in an elastic medium. In air at sea level it travels at a velocity of 343 m/s, but in solids it travels much faster: in both steel
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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
Page 131 and 132: H H Core shear Core shear Collapse
Page 133 and 134: 0.5 10−1 t c t c 10 −2 0.5 10
Page 135 and 136: Sandwich structures 123 the contact
Page 137 and 138: Sandwich structures 125 four sectio
Page 139 and 140: c t p p Figure 10.9 Sandwich panel
Page 141 and 142: Sandwich structures 129 with k ¾ D
Page 143 and 144: c/ Face sheet yielding 0.14 0.12 0.
Page 145 and 146: Weight index, ψ 10 −1 10 −2 10
Page 147 and 148: Sandwich structures 135 To construc
Page 149 and 150: Sandwich structures 137 The associa
Page 151 and 152: Sandwich structures 139 Note that,
Page 153 and 154: where D � 2⊲1 Eft 2 f ⊳GcR Sa
Page 155 and 156: Weight index ψ = W/2πR 2 ρ s W c
Page 157 and 158: Sandwich structures 145 plastic yie
Page 159 and 160: Sandwich structures 147 within the
Page 161 and 162: 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 181: Energy management: packaging and bl
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
Page 205 and 206: Electrical properties of metal foam
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 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
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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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