Metal Foams: A Design Guide

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92 Metal Foams: A Design Guide Cumulative strain, ε Cumulative strain, ε 0 0 ε max ε max ε min ε min Log cycles, N Log cycles, N (a) (b) 1 3 2 β ∆σ,(∆ε) Band spreading ∆σ,(∆ε) Sequential discrete bands Figure 8.3 Typical behaviors in compression–compression fatigue of metallic foams at a fixed stress range. (a) Progressive shortening by broadening of a single crush band with increasing cycles; (b) sequential formation of crush bands 3. Type III behavior. A single crush band forms and broadens with increasing fatigue cycles, as sketched in Figure 8.3(a). This band broadening event is reminiscent of steady-state drawing by neck propagation in a polymer. Eventually, the crush band consumes the specimen and some additional shortening occurs in a spatially uniform manner. Type III behavior has been observed for Alulight of composition Al–1Mg–0.6Si (wt%) and of relative density 0.35, and for Alporas of relative density 0.11. Data for the Alporas are presented in Figure 8.4(c). In both materials, the normal to the crush bands is inclined at an angle of about 20° to the axial direction, as sketched in Figure 8.3(a). The strain state in the band consists of a normal strain of about 30% and a shear strain of about 30%. A significant drop in the elastic modulus can occur in fatigue, as shown in Figure 8.4(d) for Alporas. This drop in modulus is similar to that observed in static loading, and is a result of geometric changes in the cell geometry with strain, and cracking of cell walls. The precise details remain to be quantified. A comparison of Figures 8.4(a)–(c) shows that all three types of shortening behavior give a rather similar evolution of compressive strain with the number of load cycles. Large compressive strains are achieved in a progressive manner. We anticipate that this high ductility endows the foams with notch insensitivity in compression–compression fatigue (see Section 8.4 below).
Nominal compressive strain Nominal compressive strain 0.1 0 −0.1 −0.2 −0.3 −0.4 0.1 0 −0.1 −0.2 −0.3 −0.4 1 −0.5 1 10 10 R = 0.1 R = 0.5 0.95 σ max σ pl 10 2 10 2 = 2 10 3 10 4 10 5 10 6 10 7 Number of cycles (a) 1.4 σmax = 0.40 σpl 10 3 10 4 10 5 10 6 10 7 10 8 Number of cycles (b) 1.2 1.1 0.49 Design for fatigue with metal foams 93 1.0 0.58 Figure 8.4 (a) Progressive shortening behavior in compression–compression fatigue for a Duocel Al-6101-T6 foam of relative density 0.08. (b) Progressive shortening behavior in compression–compression fatigue for Alcan foam (relative density 0.057; R D 0.5). (c) Progressive shortening behavior in compression–compression fatigue for Alporas foam (relative density 0.11). (d) Progressive shortening behavior in compression–compression fatigue: comparison of the progressive drop in stiffness of Alporas in a monotonic and fatigue test (relative density 0.11)
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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,
Page 53 and 54: (a) (b) (c) Properties of metal foa
Page 55 and 56: Table 4.1 (a) Ranges a for mechanic
Page 57 and 58: Stress, σ Schematic Young's modulu
Page 59 and 60: Properties of metal foams 47 foams.
Page 61 and 62: Properties of metal foams 49 show t
Page 63 and 64: Modulus 0.5 /Density (GPa 0.5 /(Mg/
Page 65 and 66: elations take the form P Ł � Ł
Page 67 and 68: Chapter 5 Design analysis for mater
Page 69 and 70: Table 5.1 Design requirements Desig
Page 71 and 72: 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: Axial strain (%) 5 4 3 2 1 0 0 σma
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 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
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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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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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