Metal Foams: A Design Guide

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16 Metal Foams: A Design Guide materials are subsequently heated, the pore pressure increases and the pores expand by creep of the surrounding metal (Figure 2.7). This process has been used by Boeing to create low-density core (LDC) Ti–6A1–4V sandwich panels with pore fractions up to 50%. In the process Ti–6A1–4V powder is sealed in a canister of the same alloy. The canister is evacuated to remove any oxygen (which embrittles titanium) and then backfilled with between 3 to 5 atmospheres (0.3–0.5MPa) of argon. The canister is then sealed and consolidated to a high relative density (0.9–0.98) by HIPing causing an eight-fold increase in void pressure. This is too low to cause expansion of Ti–6AI–4V at room temperature. The number of pores present in the consolidated sample is relatively low (it is comparable to the number of powder particles in the original compact), so a rolling step is introduced to refine the structure and create a more uniform distribution of small pores. In titanium alloys, rolling at 900–940°C results in void flattening and elongation in the rolling direction. As the voids flatten, void faces come into contact and diffusion bond, creating strings of smaller gas-filled pores. Cross-rolling improves the uniformity of their distribution. Various cold sheet forming processes can then be used to shape the as-rolled plates. The final step in the process sequence is expansion by heating at 900°C for 20–30 hours. The high temperature raises the internal pore pressure by the ratio of the absolute temperature of the furnace to that of the ambient (about a factor of four) i.e. to between 10 and 16 MPa, causing creep dilation and a reduction in the overall density of the sample. This process results in shaped Ti-alloy sandwich construction components with a core containing a closed-cell void fraction of up to 0.5 and a void size of 10–300 µm. While it shares most of the same process steps as P/M manufacturing, and the cost of the inert gas is minor, HIPing and multipass hot cross-rolling of titanium can be expensive. This process is therefore likely to result in materials that are more costly to manufacture than P/M alloys. 2.8 Hollow sphere structures Several approaches have recently emerged for synthesizing hollow metal spheres. One exploits the observation that inert gas atomization often results in a small fraction (1–5%) of large-diameter (0.3–1 mm) hollow metal alloy spheres with relative densities as low as 0.1. These hollow particles can then be sorted by flotation methods, and consolidated by HIPing, by vacuum sintering, or by liquid-phase sintering. Liquid-phase sintering may be the preferred approach for some alloys since it avoids the compressive distortions of the thin-walled hollow powder particles that results from the HIPing process and avoids the prolonged high-temperature treatments required to achieve strong particle–particle bonds by vacuum sintering methods. Porous nickel
Process Steps a) Powder / Can preparation Ti − 6Al − 4V powder ENTRAPPED GAS EXPANSION Ti − 6Al − 4V can Powder packing density D 0 Evacuate and backfill with Argon gas to pressure p 0 b) HIP Consolidation (900°C, 100 − 200 MPa, 2 hrs.) Final relative density 0.85 − 0.95 p(t), T(t) c) Hot rolling (approx. 930°C, 6 − 40 passes in air) Internal gas pressure d) Expansion heat treatment (900°C, 4 − 48 hrs.) Sandwich panel Facesheet T(t) Isolated pressurized voids Thinning of facesheet Changes in pore shape, matrix microstructure Isolated porosity (
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: a) Vapor deposition of Nickel b) Bu
Page 31 and 32: Making metal foams 19 flight in a t
Page 33 and 34: a) Metal - Hydrogen binary phase di
Page 35 and 36: Entrapped gas expansion Making meta
Page 37 and 38: (a) (b) (c) 100µm Characterization
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
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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
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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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