Metal Foams: A Design Guide

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124 Metal Foams: A Design Guide Load (N) Load (N) 800 600 400 200 Finite element 0 0 1 2 3 4 Displacement (mm) 1000 800 600 400 200 0 (Eq. 10.1) (Eq. 10.1) Design 1: Core shear Unload reload Design 2: Indentation Unload reload 0 1 2 3 4 Displacement (mm) Experiment Eq. 10.18 Experiment Eq. 10.13 Finite element Figure 10.8 Load versus displacement curves for two designs of sandwich beams in three-point bending compared with the predictions of a finite-element simulation. In the first, the failure mechanism is core shear; in the second, it is indentation. The details of the geometry and material properties are listed in Table 10.1 Chapter 7. The constitutive model for the foam was calibrated by the uniaxial compressive response, whereas the uniaxial tensile stress–strain response was employed for the solid face sheets. Excellent agreement is noted between the analytical predictions, the finite element calculations and the measured response for both failure modes. 10.5 Weight-efficient structures To exploit sandwich structures to the full, they must be optimized, usually seeking to minimize mass for a given bending stiffness and strength. The next
Sandwich structures 125 four sections deal with optimization, and with the comparison of optimized sandwich structures with rib-stiffened structures. The benchmarks for comparison are: (1) stringer or waffle-stiffened panels or shells and (2) honeycombcored sandwich panels. Decades of development have allowed these to be optimized; they present performance targets that are difficult to surpass. The benefits of a cellular metal system derive from an acceptable structural performance combined with lower costs or greater durability than competing concepts. As an example, honeycomb-cored sandwich panels with polymer composite face sheets are particularly weight efficient and cannot be surpassed by cellular metal cores on a structural performance basis alone. But honeycomb-cored panels have durability problems associated with water intrusion and delamination; they are anisotropic; and they are relatively expensive, particularly when the design calls for curved panels or shells. In what follows, optimized sandwich construction is compared with conventional construction to reveal where cellular metal sandwich might be more weight-efficient. The results indicate that sandwich construction is most likely to have performance benefits when the loads are relatively low, as they often are. There are no benefits for designs based on limit loads wherein the system compresses plastically, because the load-carrying contribution from the cellular metal core is small. The role of the core is primarily to maintain the positioning of the face sheets. Structural indices Weight-efficient designs of panels, shells and tubes subject to bending or compression are determined by structural indices based on load, weight and stiffness. Weight is minimized subject to allowable stresses, stiffnesses and displacements, depending on the application. Expressions for the maximum allowables are derived in terms of these structural indices involving the loads, dimensions, elastic properties and core densities. The details depend on the configuration, the loading and the potential failure modes. Non-dimensional indices will be designated by 5 for the load and by for the weight. These will be defined within the context of each design problem. Stiffness indices are defined analogously, as will be illustrated for laterally loaded panels. The notations used for material properties are summarized in Table 10.2. In all the examples, Al alloys are chosen for which εf f y y /Ef D 0.007. Organization and rationale Optimization procedures are difficult to express when performed in a general manner with non-dimensional indices. Accordingly, both for clarity of presentation and to facilitate comprehension, the remainder of this chapter is organized in the following sequence:
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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 ;; ;;; ;; ;;; ;; ;; ;;
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 and 124: Design for creep with metal foams 1
Page 125 and 126: Chapter 10 Sandwich structures Sand
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: Sandwich structures 123 the contact
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 183 and 184: Chapter 12 Sound absorption and vib
Page 185 and 186: Sound absorption and vibration supp
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Sound absorption and vibration supp
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0 Sound absorption and vibration su
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Sound absorption and vibration supp
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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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