Metal Foams: A Design Guide

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Chapter 3 Characterization methods The cellular structure of metallic foams requires that special precautions must be taken in characterization and testing. Structure is examined by optical microscopy, scanning electron microscopy and X-ray tomography. The apparent moduli and strength of foam test samples depends on the ratio of the specimen size to the cell size, and can be influenced by the state of the surface and the way in which the specimen is gripped and loaded. This means that specimens must be large (at least seven cell diameters of every dimension) and that surface preparation is necessary. Local plasticity at stresses well below the general yield of the foam requires that moduli be measured from the slope of the unloading curve, rather than the loading curve. In this chapter we summarize reliable methods for characterizing metallic foams in uniaxial compression, uniaxial tension, shear and multiaxial stress states, under conditions of creep and fatigue, and during indentation. An optical technique for measuring the surface displacement field, from which strains can be calculated, is described. 3.1 Structural characterization A metal foam is characterized structurally by its cell topology (open cells, closed cells), relative density, cell size and cell shape and anisotropy. Density is best measured by weighing a sample of known volume; the rest require microscopy. Optical microscopy is helpful in characterizing metal foams provided that the foam is fully impregnated with opaque epoxy (or equivalent) before polishing. This requires that the foam sample be immersed in a low-viscosity thermoset containing a coloring agent (black or deep blue is best), placed in a vacuum chamber and degassed and then repressurized to force the polymer into the cells. The procedure may have to be repeated for closedcell foams after coarse polishing, since this often opens a previously closed cell. Conventional polishing then gives reliable sections for optical microscopy (Figure 3.1(a)). Scanning electron microscopy (SEM) is straightforward; the only necessary precaution is that relating to surface preparation (see Section 3.2). SEM is
(a) (b) (c) 100µm Characterization methods 25 Figure 3.1 (a) An optical micrograph of a polished section of an Alcan aluminum foam. (b) A SEM micrograph of an INCO nickel foam (Kriszt and Ashby, 1997). (c) An X-ray tomograph of an Alulight foam foam (B Kriszt, private communication, 1999)
Page 1 and 2: Metal Foams: A Design Guide
Page 3 and 4: Copyright © 2000 by Butterworth-He
Page 5 and 6: vi Contents 4.3 Foam property chart
Page 7 and 8: viii Contents 17 Case studies 217 1
Page 9 and 10: List of contributors M.F. Ashby Cam
Page 11 and 12: Table of physical constants and con
Page 13 and 14: Chapter 1 Introduction Metal foams
Page 15 and 16: Activity Research Industrial take-u
Page 17 and 18: Application Comment Introduction Bi
Page 19 and 20: Cell size (cm) Making metal foams 7
Page 21 and 22: Making metal foams solidify. The th
Page 23 and 24: Making metal foams 11 2.4 Gas-relea
Page 25 and 26: a) Preform Polymer ligaments d) Rem
Page 27 and 28: a) Vapor deposition of Nickel b) Bu
Page 29 and 30: Process Steps a) Powder / Can prepa
Page 31 and 32: Making metal foams 19 flight in a t
Page 33 and 34: a) Metal - Hydrogen binary phase di
Page 35: Entrapped gas expansion Making meta
Page 39 and 40: E/E bulk σ peak /σ bulk 1.2 1.0 0
Page 41 and 42: Stress (MPa) Characterization metho
Page 43 and 44: Characterization methods 31 foam sp
Page 45 and 46: Characterization methods 33 ž Prop
Page 47 and 48: F/2 F/2 F/2 F/2 τ Core Characteriz
Page 49 and 50: Characterization methods 37 40 40 4
Page 51 and 52: 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
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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.
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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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