Metal Foams: A Design Guide

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112 Metal Foams: A Design Guide and the shear deflection rate at the center of the beam is: Pυs DP c ℓ ⊲9.23⊳ d 2 Both normal and shear stresses are, in general, significant for metal foamcore sandwich beams. For a given loading, material properties and geometry, the shear and normal stresses can be evaluated and substituted into equation (9.21) to obtain the shear strain rate. This can then be substituted into equation (9.23) to determine the creep deflection rate of the beam. Preliminary data for creep of sandwich beams are well described by equations (9.23) and (9.21). References Allen, H.G. (1969) Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford. Andrews, E.W. and Gibson, L.J. (1999) Creep behavior of a closed-cell aluminum foam. Acta Materialia 47, 2927–2935. Andrews, E.W., Ashby, M.F. and Gibson, L.J. (1999) The creep of cellular solids. Acta Materialia 47, 2853–2863. Frost, H.J. and Ashby, M.F. (1982) Deformation Mechanism Maps, Pergamon Press, Oxford. Gibson, L.J. and Ashby, M.F. (1997) Cellular Solids: Structure and Properties, 2nd edition, Cambridge University Press, Cambridge. Hertzberg, R.W. (1989) Deformation and Fracture Mechanics of Engineering Materials, 3rd edition, Wiley, New York.
Chapter 10 Sandwich structures Sandwich panels offer high stiffness at low weight. Their cores, commonly, are made of balsa-wood, foamed polymers, glue-bonded aluminum or Nomex (paper) honeycombs. These have the drawbacks that they cannot be used much above room temperature, and that their properties are moisture-dependent. The deficiencies can be overcome by using metal foams as cores. This chapter elaborates the potential of metal-foam-cored sandwich structures. Competition exists. The conventional way of stiffening a panel is with stringers: attached strips with a profile like a Z, a ? or a top hat. They are generally stiffer for the same weight than sandwich structures, at least for bending about one axis, but they are anisotropic (not equally stiff about all axes of bending), and they are expensive. Metfoam-cored sandwiches are isotropic, can be shaped to doubly curved surfaces, and can be less expensive than attachment-stiffened structures. Syntactic foams – foams with an integrally shaped skin – offer additional advantages, allowing cheap, light structures to be molded in a single operation. Syntactic polymer foams command a large market. Technologies are emerging for creating syntactic metfoam structures. It is perhaps here that current metalfoam technology holds the greatest promise (see Chapter 16). 10.1 The stiffness of sandwich beams The first four sections of this chapter focus on the stiffness and strength of sandwich beams and plates (Figure 10.1). In them we cite or develop simple structural formulae, and compare them with experimental results and with the predictions of more refined finite-element calculations. Later sections deal with optimization and compare metfoam-cored sandwiches with rib-stiffened panels. Consider a sandwich beam of uniform width b, with two identical facesheets of thickness t perfectly bonded to a metallic foam core of thickness c. The beam is loaded in either in a four-point bend, as sketched in Figure 10.2(a), or a three-point bend as shown in Figure 10.2(b). For both loading cases, the span between the outer supports is ℓ, and the overhang distance beyond the outer supports is H. We envisage that the beams are
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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
Page 73 and 74: 5.4 Where might metal foams excel?
Page 75 and 76: Table 6.1 Constitutive equations fo
Page 77 and 78: h SECTION h o h i d d o a b ;;; QQQ
Page 79 and 80: 6.3 Elastic deflection of beams and
Page 81 and 82: 6.4 Failure of beams and panels (a)
Page 83 and 84: ;; ;;; ;; M ;; ;;; ;; ;;; ;; ;; ;;
Page 85 and 86: Torsion of shafts T T,q T T,q Yield
Page 87 and 88: R a 2 Flow field R F R 2a 2 F F s c
Page 89 and 90: ;; ; QQ Q ¢¢ ¢ ;; ;; QQ QQ ¢¢
Page 91 and 92: ; ;; Creep p e p e • Area A u F 2
Page 93 and 94: and its deviatoric (i.e. shear) com
Page 95 and 96: Normalized effective stress 1.4 1.2
Page 97 and 98: A constitutive model for metal foam
Page 99 and 100: A constitutive model for metal foam
Page 101 and 102: Stress amplitude, ∆σ + Stress,
Page 103 and 104: Axial strain (%) 5 4 3 2 1 0 0 σma
Page 105 and 106: Nominal compressive strain Nominal
Page 107 and 108: σ max σ pl τ max τ pl σ max σ
Page 109 and 110: Design for fatigue with metal foams
Page 111 and 112: the net section stress criterion re
Page 113 and 114: E σ pl (m) 10 1 0.1 0.01 0.1 Relat
Page 115 and 116: Chapter 9 Design for creep with met
Page 117 and 118: Design for creep with metal foams 1
Page 119 and 120: instead to: � Pε 3 D Pε0 2 s Ł
Page 121 and 122: Time to failure (hours) 10 2 10 1 1
Page 123: Design for creep with metal foams 1
Page 127 and 128: Sandwich structures 115 The elastic
Page 129 and 130: 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
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Energy management: packaging and bl
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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
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Electrical properties of metal foam
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Electrical properties of metal foam
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15.3 Joining of metal foams Cutting
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Pull-out load, F p (N) 10 5 10 4 10
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Cyclic loading of fasteners Cutting
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Time, material, energy, capital, in
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Cost estimation and viability 203 A
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$/Unit Melting Schematic of the liq
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Performance metric, P2 B Non-domina
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Cost estimation and viability 209 t
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Cost estimation and viability 211 i
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P 2 = 1/Loss coefficient (−) 1000
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Cost estimation and viability 215 C
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Chapter 17 Case studies Metal foams
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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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