Handbook of Cellular Metals: Production, Processing, Applications

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

Hans-Peter Degischer, Brigitte Kriszt (Editors) Handbook of Cellular Metals Production, Processing, Applications

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

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Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

Handbook of Cellular Metals Production, Processing, Applications

Edited by Hans-Peter Degischer, Brigitte Kriszt

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

Editors Prof. Dr. Hans-Peter Degischer Technische UniversitaÈt Wien Institut fuÈr Werkstoffkunde und MaterialpruÈfung Karlsplatz 13 A-1040 Wien Austria Dr. Brigitte Kriszt Technische UniversitaÈt Wien Institut fuÈr Werkstoffkunde und MaterialpruÈfung Karlsplatz 13 A-1040 Wien Austria

This book was carefully produced. Nevertheless, authors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Die Deutsche Bibliothek ± CIP-Cataloguing-in-Publication-Data A catalogue record for this book is available from Die Deutsche Bibliothek c WILEY-VCH Verlag GmbH 69469 Weinheim, 2002 All rights reserved (including those of translation in other languages). No part of this book may be reproduced in any form ± by photoprinting, microfilm, or any other means ± nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. printed in the Federal Republic of Germany printed on acid-free paper Composition Hagedorn Kommunikation, Viernheim Printing Strauss Offsetdruck GmbH, MoÈrlenbach Bookbinding J. SchaÈffer GmbH & Co. KG, GruÈnstadt ISBN

3-527-30339-1

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

Preface B. Kriszt and H. P. Degischer

There have been a few international and national research and development programs on cellular metals in recent years: the US Multidisciplinary Research Initiative (MURI) on ultralight metal structures since 1996; a few European research projects funded within the 4th and 5th EU Framework Program; and a focussed research program funded by the German Research Council, which began in 1998. These cooperative activities add to the original research activities at the Fraunhofergesellschaft IFAM in Bremen, the University of Cambridge, Ranshofen and Vienna in Austria, the Slovac Academy of Science in Bratislava, and several other places in Europe. A considerable quantity of data has been produced and presented at international conferences. One of these meetings was organized by the German Society of Materials (DGM) on 28/29 February 2000 at the Vienna University of Technology. The proceedings are mainly in German [1] and the authors wanted another opportunity to publish their results in context with present knowledge. The reader of proceedings might be overwhelmed by very specific research results on selected topics, obscuring a general understanding of this expanding field of research. Besides the classical books dealing with cellular metals [2,3], an overview of the state of the art in the year 2000 was needed, covering primary and secondary processing, characterization of cellular metals, properties, modeling, and exploitation. As a result, some of the contributors to the Vienna symposium ªMetallschaÈume 2000º have been asked to extend their papers, by referring to related results of other researchers and giving a review of their particular topic, whilst maintaining the detailed specialist knowledge of the author. These contributions are introduced by coordinators who describe the state of the art in that field. Foamed metals are described more extensively than other cellular metals because of the actual research activities prevalent in Europe. The European development goal is the application of cellular metals in components for motor vehicles, a field in which price limits and consistent high quality are essential. This handbook aims to give a more detailed overview of the present state of the art in research and development on cellular metals with specific emphasis on processing and characterization of foamed metals than the recent survey [4]. The handbook gives a starting point

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for researchers new to the field, and references to topics adjacent to their own specialty for experts already engaged. Engineers and potential users are encouraged to consider the application of cellular metals, taking into account the specific peculiarities of each material to avoid failures due to miscalculation of processing requirements and performance. A guide to the multitude of different types of cellular metals is provided with an indication of particular differences in properties. Research is ongoing and it is to be hoped that experience with applications, that the book intends to promote and stimulate, is expanding. The editors thank all contributors and acknowledge their assistance in adjusting the content of their contributions in cooperation with each other to produce a concise overview of the state of the art in cellular metals from a European viewpoint.

References

1. H. P. Degischer (ed), ªMetallschaÈumeº 3. M. F. Ashby, A. G. Evans, N. A. Fleck, L. J. Special Issue, Materwiss. Werkstofftechn. 2000, Gibson, J. W. Hutchinson, H. N. G. Wadley, 31(6). Metal Foams: a Design Guide, Butterworth2. L. J. Gibson, M. F. Ashby, Cellular Solids: Heinemann, Oxford 2000. Structure and Properties, 2nd edn., Cambridge 4. J. Banhart, ªManufacture, Characterisation University Press, Cambridge 1997. and Application of Cellular Metals and Metal Foamsº, Progr. Mater. Sci. 2001, 46, 559 632.

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

Foreword T. W. Clyne

Interest in metallic foams dates from the 1940s, when Sosnick filed a patent on a production method involving vaporization of low melting point constituents of metallic alloys [1]. Other publications and patents followed in the subsequent two decades, covering concepts such as that of injecting metal into the interstices around ªspace holderº particles, which are subsequently removed, and the dispersion of particles, which will release gas via chemical reaction or thermal decomposition. However, in general, research on the production and performance of cellular metals remained at a low level until the 1990s, when a substantial acceleration took place. It is now a research topic receiving a high level of attention and various industrial applications are currently being explored. Updated information about these activities is available from certain websites [2] and a comprehensive review has recently been published [3]. Further research is certainly necessary into the development of improved processing methods, since much of the material produced hitherto has been of relatively poor quality and/or inherently rather expensive. However, in this context it is very important to understand the processing-microstructure-property inter-relationships for cellular metals and the relevance of these to the property combinations required for various applications. Making a foam from a metal, as opposed to a polymer, boosts the stiffness, range of operating temperature and resistance to many (organic) solvents, while, in comparison with a ceramic foam, important advantages are expected in terms of toughness, (thermal and electrical) conductivity and formability. However, when considering the detailed characteristics, a clear distinction should be drawn between open-cellular and closed-cellular metal, since, not only are these two materials made by different processing routes, but in general rather separate types of application can be identified for them. Of course, all types of cellular materials tend to be relatively light, and to have a high specific stiffness, but these features usually depend primarily on the pore content, whereas many other properties are much more sensitive to microstructure (cell structure and nature of cell walls).

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Closed-Cell Foams Since the most promising methods for cheap production of bulk material tend to generate closed-cell foams (commonly of aluminum), attention has been concentrated on these for many structural applications. These include various components designed to absorb energy progressively under relatively low applied (compressive) loads. In principle, the reduced constraint on cell walls, compared with solid metal, should mean that large plastic strains can arise throughout via concertina-like deformation, with substantial absorption of energy. However, the performance of such components has often been a little disappointing hitherto, with premature failure commonly occurring within shear bands and such poor tensile ductility exhibited that components tend to fracture readily if any tensile stresses arise, for example under bending moments. It is now becoming clear that these problems are substantially reduced if the cell size can be kept fine and uniform preferably to sub-mm levels. There is thus a strong incentive to develop processing techniques capable of producing such material in bulk. Furthermore, it is commonly the case that the cell walls in these foams contain severely embrittling constituents, such as large ceramic particles and thick oxide films. Some such constituents are often deliberately introduced during processing in order to raise the melt viscosity and thus inhibit cell coarsening and drainage [4]. Recent work has confirmed that such constituents can have highly deleterious effects on the mechanical characteristics of the foam and has outlined the mechanisms responsible for this [5]. Further work is required both on understanding these effects in more detail and on developing processing routes in which these constituents are suitably modified or eliminated. Closed-cell foams are also of interest for other types of application, such as thermal barriers, although ceramic materials would often be preferred for these. Open-Cellular Metals Suggested and actual applications include filters, catalyst supports, heat exchangers, fluid flow damping conduits (including various types of shock wave dissipation devices), biomedical prostheses, internally-cooled shape memory actuators, air batteries, and protective permeable membranes and sheathes. Such functional components tend to incorporate higher added value than those in purely structural applications, which is appropriate in view of the generally higher costs of producing open-cellular metal. The scale of the cell structure is often important for the functional characteristics. This will clearly be a basic specification for filters and fluid flow limiting devices, but a fine cell size would often be preferred for heat exchangers etc. (subject to limitations imposed by any danger of pore clogging), while bone in-growth into prosthetic implants might require relatively coarse pores. However, these properties would often be needed in combination with a minimum strength and ductility requirement, so a relatively fine, uniform cell structure and a defectfree cell struts' microstructure might be beneficial from that point of view. A wide range of metals is being investigated for applications of open-cellular metals, bringing a requirement for improved understanding of process optimization issues in various alloy systems.

Foreword

References

1. B. Sosnick, US Patent 2 434 775, 1948. 4. V. Gergely, H. P. Degischer, T. W. Clyne, 2. http://www.metalfoam.net ªRecycling of MMCs and Production of http://www.npl.co.uk/npl/cmmt/metalMetallic Foamsº in Comprehensive Composite foams/index.html Materials, Vol. 3: Metal Matrix Composites, http://www.msm.cam.ac.uk/mmc T. W. Clyne (ed.), Elsevier, Amsterdam 2000, 3. J. Banhart, ªManufacture, Characterisation p. 797 820. and Application of Cellular Metals and Metal 5. A. E. Markaki, T. W. Clyne, ªThe effect of cell Foamsº Progr. Mater. Sci. 2001, 46, 559 632. wall microstructure on the deformation and fracture of aluminium-based foamsº Acta Mater. 2001, 49, 1677 1686.

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Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

Contents 1 2 2.1 2.1.1 2.1.2

2.1.2.1 2.1.2.2 2.2 2.2.1 2.2.2 2.2.2.1 2.2.2.2 2.2.2.3 2.2.2.4 2.2.2.5 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.4.1 2.3.4.2 2.4 2.4.1 2.4.2 2.4.3 2.5 2.5.1 2.5.2

Introduction: The Strange World of Cellular Metals 1 Material Definitions, Processing, and Recycling 5

Foaming Processes for Al 8 Gas Injection: the Cymat/Alcan and Norsk Hydro Process 8 In-situ Gas Generation: the Shinko Wire Process and the FORMGRIP process 10 The Shinko Wire Process [2] 10 The FORMGRIP Process 12 Industrialization of Powder-Compact Foaming Technique 14 Principles of Foam Production 14 Practical Aspects of Foam Production 17 Powder selection 17 Mixing 18 Densification 18 Further processing of foamable material 19 Foaming 19 State of Commercialization 20 Making Cellular Metals from Metals other than Aluminum 21 Zinc 22 Lead 22 Titanium 22 Steel 25 Powder-Compact Foaming Technique 25 Steel Foams from Powder Filler Mixtures 27 Recycling of Cellular Metals 28 The Remelting of Cellular Metals 28 Recycling of Cellular Metal Matrix Composites 29 Conclusions 32 The Physics of Foaming: Structure Formation and Stability 33 Isolated Gas Bubble in a Melt 34 Agglomeration of Bubbles: Foam 35

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2.6 2.6.1 2.6.2 2.6.2.1 2.6.2.2 2.6.2.3 2.6.3 2.6.3.1 2.6.3.2 2.6.3.3 2.6.3.4 2.6.4 2.7 2.7.1 2.7.1.1 2.7.1.2 2.7.2 2.7.2.1 2.7.2.2 2.7.2.3 2.7.3 2.7.3.1 2.7.3.2 2.7.3.3 2.7.3.4 2.7.4 2.7.4.1 2.7.4.2 3 3.1 3.1.1 3.1.1.1 3.1.1.2

3.1.1.3 3.1.1.4 3.1.2 3.1.3 3.1.3.1 3.1.3.2

Infiltration and the Replication Process for Producing Metal Sponges 43 Replication 44 The Replication Process: General Principles 46 Pattern Preparation 46 Infiltration 48 Pattern Removal 49 Physical and Mechanical Properties of Metal Sponge 51 Continuous Refractory Patterns 51 Discontinuous Refractory Patterns 51 Burnable Patterns 53 Leachable Patterns 53 Conclusions 55 Solid-State and Deposition Methods 56 Formation from Single Cells: Coreless Methods 58 Hollow-Sphere Structures made from Gas Atomized Hollow Powders 58 Hollow-Sphere Structures made from Coaxially Sprayed Slurries 59 Formation from Single Cells: Lost Core Methods 60 Hollow-Sphere Structures made by Cementation and Sintering 60 Hollow-Sphere Structures made from Galvanically Coated Styrofoam Spheres 61 Hollow-Sphere Structures made from Fluidized Bed Coated Styrofoam Spheres 61 Bulk Formation: Coreless Methods 63 Sintered Metal Powders and Fibers 63 Methods Utilizing Special Sintering Phenomena 64 Foaming of Solids 65 Foaming of Slurries 67 Bulk Formation: Lost Core Methods 67 Powder Metallurgical Space Holder Method 67 Deposition Methods 68 Secondary Treatment of Cellular Metals 71

Forming, Machining, and Coating 75 High-Temperature Forming 75 Specific Problems in Foam Forming 75 Process Sequence for Manufacturing 3D Composites with Aluminum Foam Cores 76 Material Behavior at the Solidus 77 Forming of Cellular Metals at High Temperatures 78 Machining 79 Coating 79 Mechanical Properties of Spray Deposits 80 Specific Difficulties in Foam Coating 80

Contents

3.1.3.3 3.2 3.2.1 3.2.2 3.2.2.1 3.2.2.2 3.2.2.3 3.2.2.4 3.2.3 3.2.4 3.2.4.1 3.2.4.2 3.2.5 3.2.5.1 3.2.5.2 3.2.6 3.3 3.3.1 3.3.1.1 3.3.1.2 3.3.1.3 3.3.1.4 3.3.2 3.3.2.1 3.3.2.2 3.4 3.4.1 3.4.2 3.4.2.1 3.4.2.2 3.4.3 3.4.3.1 3.4.3.2 3.4.3.3 3.4.3.4 3.4.3.5 3.4.3.6 3.4.3.7 3.4.3.8 3.4.4 3.4.4.1 3.4.4.2

Thermal Sprayed Composites from Metal Foams 81 Joining Technologies for Structures Including Cellular Aluminum 83 Introduction 83 Feasible Joining Technologies 83 Mechanical Fastening Elements 83 Gluing 84 Welding 84 Soldering and Brazing 85 Foam Foam Joints 87 Foam Sheet Joints 87 Microstructural Investigations 88 Mechanical Properties of Foam Sheet Joints 90 Transferability to Structural Parts 98 Tubes 98 Hat-Profiles 99 Summary 100 Encasing by Casting 103 Foam Cores for Encasing by Casting 103 Core Production 103 Core Attachment 104 Mechanical Properties 105 Coating of the Foam Cores 106 Shell Casting Processes 107 High-Pressure Casting Processes 107 Bonding Between Shell and Foam Core 112 Sandwich Panels 113 Sandwich Foaming Process 114 Industrial Application 116 Technological Benefits 117 Technical Limitations 118 Joining Technology of AFS 119 Laser Welding 120 TIG/MIG Welding 120 Bolt/Pin Welding 121 Punch Riveting 122 Riveting Nuts and Screws 123 Flow Drilling 123 Riveting 123 Bonding 123 Cutting of AFS 124 Laser Beam Cutting 124 Water Jet Cutting 124

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4 4.1 4.1.1

4.1.1.1 4.1.1.2 4.1.2 4.1.2.1 4.1.2.2 4.1.2.3 4.1.2.4 4.1.2.5 4.1.2.6 4.1.3 4.1.4 4.2 4.2.1 4.2.1.1 4.2.1.2 4.2.2 4.2.2.1 4.2.2.2 4.2.2.3 4.2.2.4 4.2.3 4.2.3.1 4.2.3.2 4.2.4 4.2.4.1 4.2.4.2 4.2.5 4.3 4.3.1 4.3.2 4.3.3 4.3.3.1 4.3.3.2 4.3.3.3 4.3.3.4 4.3.4 4.3.4.1 4.3.4.2 4.3.4.3 4.3.5

Characterization of Cellular Metals 127

Characterization of Cellular and Foamed Metals 130 Definition of Structural Features of a Cellular Metal and Influence on Property Profile 130 Density and Volume Fraction of Pores 131 Shape and Size of Pores 133 Characterization Methods and Quantities of Geometric Architecture of Real Metallic Foams 136 Sample Preparation 136 Pore Size 137 Pore Shape 139 Pore Orientation 140 Thickness of Cell Edges and Walls 140 Topological Features 141 Characterization of Microstructure of Massive Cell Material 141 Conclusions 143 Computed X-ray Tomography 145 Principle of the Technique 145 X-ray Radiography 145 X-ray Tomography 146 Set-ups 147 Medium-Resolution Microtomography 147 High-Resolution Microtomography 147 Resolution Required for the Study of Metallic Foams 148 Reconstruction Method 148 Experimental Results 148 Initial Cell Structure 148 Evolution of the Structure During a Compression Test 150 Micromodeling of a Foam by Finite Elements 151 Direct Meshing of the Actual Microstructure 151 Results 152 Conclusions 155 Considerations on Quality Features 156 Introduction 156 Non-Uniformity of Cellular Metals 156 Macroscopic Parameters 159 Type of Cellular Metal 159 Surface and Dimensions 159 Apparent Density 161 Properties 161 Microscopic Features 161 Microstructure of the Metal 162 Geometrical Features 162 Microdefects 164 Mesoscopic Features 165

Contents

4.3.5.1 4.3.5.2 4.3.6 4.3.7 4.3.7.1 4.3.7.2 4.3.7.3 4.3.8

Geometry of Cellular Structure 165 Density Distribution 166 Systematics of Quality Features 166 Approximation of a Cellular Structure by a Continuum 168 Calculation of Density Maps 168 Representation of Non-Uniformity of Densities 172 Mesoscopic Basis for Material Modeling 174 Proposal of Quality Criteria 174

5 5.1 5.1.1 5.1.1.1 5.1.1.2 5.1.1.3 5.1.2 5.1.3 5.1.3.1 5.1.3.2 5.1.4 5.1.4.1 5.1.4.2 5.1.4.3 5.1.5 5.1.6 5.1.6.1 5.1.6.2 5.1.6.3 5.2 5.2.1 5.2.2 5.2.2.1 5.2.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.3.3.1 5.3.3.2 5.3.3.3

Mechanical Properties and Determination 183 Young's Modulus 183 Influence of the Foam Structure 184 Influence of the Foam Density 185 Influence of Deformation 186 Compression Behavior 187 Energy-Absorbing and Impact Behavior 190 Energy Absorbing Capability 190 Impact Behavior 191 Tension Behavior 193 General Tensile Behavior 193 The Influence of Notches 195 Foam-Specific Test Problems in Tension 196 Torsion Behavior 196 Fracture Behavior 197 Crack Initiation and Crack Propagation 197 Fracture Toughness 198 Foam-Specific Test Problems 201 Fatigue Properties and Endurance Limit of Aluminum Foams 203 Literature Survey of Endurance Data 203 High Cycle Fatigue Properties and Endurance Limit 208 Material and Procedure 208 Results 209 Mechanism of Crack Initiation 210 Summary 214 Electrical, Thermal, and Acoustic Properties of Cellular Metals 215 Electrical Properties 215 Thermal Properties 221 Acoustic Properties 225 Materials for Sound Insulation 226 Sound Absorbing Materials 228 Structural Damping 236

Material Properties 179

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6 6.1 6.1.1 6.1.2 6.1.2.1 6.1.2.2 6.1.2.3 6.1.3 6.1.3.1 6.1.3.2 6.1.3.3 6.1.3.4 6.1.3.5 6.1.3.6 6.1.3.7 6.1.3.8 6.1.4 6.1.5 6.1.5.1 6.1.5.2 6.1.6 6.1.7 6.2 6.2.1 6.2.2 6.2.2.1 6.2.2.2 6.2.3 6.2.3.1 6.2.3.2 6.2.4 6.2.5 7 7.1

7.1.1 7.1.2 7.1.3 7.1.4 7.1.5 7.1.5.1 7.1.5.2 7.1.5.3 7.1.5.4

Modeling and Simulation 243

Modeling of Cellular Metals 245 Motivation 246 Micromechanical Modeling of Cellular Materials: Basics 247 Analytical and Numerical Models 247 Classification of Microgeometries 249 Information Obtainable from Micromechanics 251 Selected Results of Micromechanical Simulations 252 Influence of Material Distribution in the Cell Walls 252 Influence of Wavy and Curved Cell Walls 255 Influence of Irregular Vertex Positions 257 Microgeometries Containing Cells of Different Sizes 258 Influence of Holes and Solid-Filled Cells 260 Influence of Fractured or Removed Cell Walls 261 Yield and Collapse Surfaces 262 Fracture Simulations for Metallic Foams 266 Modeling of Mesoscopic Density Inhomogeneities 269 Macroscopic Modeling and Simulation 272 Low Energy Impact on Thin Metallic Foam Paddings 273 Crushing of Foam-Filled Crash Elements 275 Design Optimization for Cellular Metals 276 Outlook 277 Mesomodel of Real Cellular Structures 281 Introduction 281 3D Mesomodel 284 Elastic Regime 285 Plastic Regime 285 Modeling of Uniaxial Compression 288 Deformation Band 289 Mechanical Properties 292 Discussion 294 Conclusions 297 Service Properties and Exploitability 299

The Range of Applications of Structural Foams Based on Cellular Metals and Alternative Polymer Solutions 299 Introduction 299 Potential Areas of Use 300 Material Properties 300 Main Component Configurations 301 Application and Attachment Techniques 304 Casting 304 Thermal Joining Processes 305 Mechanical Joining Processes 306 Three-dimensional sandwich 306

Contents

7.1.5.5 7.1.6 7.1.6.1 7.1.6.2 7.1.6.3 7.1.6.4 7.1.7 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.2.6 7.2.7 7.2.8 7.2.9 7.2.10 7.2.11 7.2.12 7.2.13 7.2.14 7.3 7.3.1 7.3.1.1 7.3.1.2 7.3.2 7.3.2.1 7.3.2.2 7.3.2.3 7.3.3 7.4 7.4.1 7.4.2 7.4.2.1 7.4.2.2 7.4.2.3 7.4.2.4 7.4.3 7.4.3.1 7.4.3.2 7.4.3.3 7.4.3.4

Alternative Cellular Materials Based on Polymers 306 Effectiveness 307 Bending and Torsional Stress 307 Impact Stresses 308 Axial Load 309 Acoustics 310 Outlook 311 Functional Applications 313 General Considerations 313 Biomedical Implants 314 Filtration and Separation 315 Heat Exchangers and Cooling Machines 315 Supports for Catalysts 317 Storage and Transfer of Liquids 317 Fluid Flow Control 317 Silencers 318 Spargers 318 Battery Electrodes 318 Electrochemical Applications 319 Flame Arresters 319 Water Purification 319 Acoustic Control 319 Machinery Applications 320 Parameters 321 Thermal Behavior 321 Pull-Out Strength of Detachable Joints 322 Examples of Application 323 Foamed Steel Pipes 323 Machine Table 327 Cross-Slide 329 Conclusions 330 Prototypes by Powder Compact Foaming 330 Introduction 331 Methods, Machines, and Molds 332 Manufacturing Methods for Precursor Material 333 Foaming Process 334 Foaming Furnaces 334 Foaming Molds 336 Prototypes and their Applications 337 Automotive Applications 338 Construction and Architecture 340 Other Technical Applications 340 Improbable Applications 343

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7.5.4 7.5.4.1 7.5.4.2 7.5.5 7.5.5.1 7.5.5.2 7.5.6

Applying the Investment Methodology for Materials (IMM) to Aluminum Foams 346 Introduction: The Investment Methodology for Materials (IMM) 346 Initial Market Scan for Potential Applications for Al Foams 347 Material Assessment 347 Technical Performance 347 Cost of Production 348 Co-Minimizing Volume and Cost in Energy-Absorbing Applications 349 Market Forecast 350 Market Size for Aluminum Foam 350 Market Timing for Aluminum Foams 350 Value Capture 351 Industry Structure 351 Appropriability of Profits 352 Conclusions: Applying IMM to Aluminum Foams 353

8 8.1 8.2 8.3

Processing 355 Properties 358 Design and Application 360

7.5 7.5.1 7.5.2 7.5.3 7.5.3.1 7.5.3.2 7.5.3.3

Strengths, Weaknesses, and Opportunities 355

Index 365

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

List of Contributors O. Andersen Frauenhofer-Institut fuÈr Fertigungstechnik und Materialforschung (IFAM) Auûenstelle fuÈr Pulvermetallurgie und Verbundstoffe Winterberstr. 28 01277 Dresden Germany M. Arnold Lehrstuhl fuÈr Werkstoffwissenschaften UniversitaÈt Erlangen-NuÈrnberg Martensstr. 5 91058 Erlangen Germany M. F. Ashby Engineering Design Centre University of Cambridge Engineering Department, Trumpington Street Cambridge CB2 1PZ UK J. Banhart Hahn-Meitner-Institute Dept. of Materials ± SF3 Glienicker Str. 100 14109 Berlin Germany

F. BaumgaÈrtner Schunk Sinter Metalltechnik GmbH Postfach 10 09 51 35339 Gieûen Germany C. Beichelt Wilhelm KARMANN GmbH Karmannstr. 1 Postfach 26 09 49084 OsnabruÈck Germany T. Bernard Neue Materialien Bayreuth GmbH UniversitaÈtsstr. 30 94447 Bayreuth Germany H. W. Bergmann² UniversitaÈt Bayreuth Lehrstuhl Metallische Werkstoffe Ludwig-Thoma-Str. 36b 94440 Bayreuth Germany H. J. BoÈhm Institute of Lightweight Structures and Aerospace Engineering Vienna University of Technology Guûhausstr. 27±29 1040 Vienna Austria

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R. Braune Lehrstuhl fuÈr Fertigungstechnologie UniversitaÈt Erlangen-NuÈrnberg Egerlandstr. 11 91058 Erlangen Germany

C. Haberling Firma Audi AG Abteilung Werkstoffe/Verfahren/Recycling I/EG-34 85045 Ingolstadt Germany

T. W. Clyne Department of Materials Science University of Cambridge Pembroke Street Cambridge CB2 3QZ UK

F. Heinrich Lehrstuhl fuÈr Werkstoffwissenschaften UniversitaÈt Erlangen-NuÈrnberg Martensstr. 5 91058 Erlangen Germany

T. Daxner Institute of Lightweight Structures and Aerospace Engineering Vienna University of Technology Guûhausstr. 27±29 A-1040 Vienna Austria

Th. Hipke Frauenhofer Institut fuÈr Werkzeugmaschinen und Umformtechnik (IWU) Reichenhainerstr. 88 09126 Chemnitz Germany

H. P. Degischer Institute of Materials Science and Testing Vienna University of Technology Karlsplatz 13 1040 Vienna Austria B. Foroughi Institute of Materials Science and Testing Vienna University of Technology Karlsplatz 13 1040 Vienna Austria M. C. Hahn Lehrstuhl fuÈr Fertigungstechnologie UniversitaÈt Erlangen-NuÈrnberg Egerlandstr. 11 91058 Erlangen Germany

C. KoÈrner Lehrstuhl Werkstoffkunde und Technologie der Metalle UniversitaÈt Erlangen-NuÈrnberg Martensstr. 5 91058 Erlangen Germany J. Kovacik Institute of Materials and Machine Mechanics Slovak Academy of Science Racianska 75 P.O. Box 95 83008 Bratislava Slovakia A. Kottar Institute of Materials Science and Testing Vienna University of Technology Karlsplatz 13 1040 Vienna Austria

List of Contributors

B. Kriszt Institute of Materials Science and Testing Vienna University of Technology Karlsplatz 13 1040 Vienna Austria R. Kretz ARC Leichtmetallkompetenzzentrum Ranshofen GmbH Postfach 26 5282 Ranshofen Austria E. M. A. Maine Centre for Technology Management Engineering Design Centre Engineering Department University of Cambridge Trumpington Street Cambridge CB2 1PZ UK E. Maire CR1 CNRS GEMPPM Batiment Saint ExupeÂry 23 Avenue Capelle 69621 Villeurbanne cedex France U. Martin Institute fuÈr Metallkunde TU Bergakademie Freiberg Gustuv-Zeuner-Str. 5 09596 Freiberg Germany H. Mayer Institute of Meteorology and Physics University of Agricultural Sciences TuÈrkenschanzstr. 18 1180 Vienna Austria

A. Mortensen Laboratoire de MeÂtallurgie MeÂcanique Ecole Polytechnique FeÂdeÂrale de Lausanne 1015 Lausanne Switzerland U. Mosler Institut fuÈr Metallkunde TU Bergakademie Freiberg Gustuv-Zeuner-Str. 5 09596 Freiberg Germany C. Motz Erich-Schmid-Institute of Material Science Austrian Academy of Science Jahnstr. 12 8700 Leoben Austria R. Neugebauer Frauenhofer Institut fuÈr Werkzeugmaschinen und Umformtechnik (IWU) Reichenhainerstr. 88 09126 Chemnitz Germany A. Otto Lehrstuhl fuÈr Fertigungstechnologie UniversitaÈt Erlangen-NuÈrnberg Egerlandstr. 11 91058 Erlangen Germany R. Pippan Erich-Schmid-Institute of Material Science Austrian Academy of Science Jahnstr. 12 8700 Leoben Austria

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G. Rausch Frauenhofer Institut fuÈr angewandte Materialforschung (IFAM) Lesumer Heerstr. 36 28717 Bremen Germany

R. F. Singer Institut fuÈr Werkstoffwissenschaften UnivertitaÈt Erlangen-NuÈrnberg Martensstr. 5 91058 Erlangen Germany

C. San Marchi Northwestern University Department of Materials Science and Engineering Evanston IL 60202-3108 USA

S. Stanzl-Tschegg Institute of Meteorology and Physics University of Agricultural Sciences TuÈrkenschanzstr. 18 1180 Vienna Austria

F. G. Rammerstorfer Institute of Lightweight Structures and Aerospace Engineering Vienna University of Technology Guûhausstr. 27±29 1040 Vienna Austria

G. Stephani Frauenhofer-Institut fuÈr Fertigungstechnik und Materialforschung (IFAM) Auûenstelle fuÈr Pulvermetallurgie und Verbundstoffe Winterberstr. 28 01277 Dresden Germany

W. Seeliger Wilhelm KARMANN GmbH Karmannstr. 1 Postfach 26 09 49084 OsnabruÈck Germany M. Seitzberger Institute of Lightweight Structures and Aerospace Engineering Vienna University of Technology Guûhausstr. 27±29 1040 Vienna Austria F. Simancik Institute of Materials and Machine Mechanics Slovak Academy of Science Racianska 75 P.O. Box 95 83008 Bratislava Slovakia

M. Thies Lehrstuhl fuÈr Werkstoffwissenschaften UnivertitaÈt Erlangen-NuÈrnberg Martensstr. 5 91058 Erlangen Germany B. Zettl Institute of Meteorology and Physics University of Agricultural Sciences TuÈrkenschanzstr. 18 1180 Vienna Austria

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

List of Abbreviations AFS AVS BET CCD CIP COD CT CTOD CVD DOF 2D or 3D EB-DVD EDM ESRF FE FORMGRIP FPZ HIP IFAM IMM INSA IP IWU LBM LDC LEFM LKR MIG MMC MURI PCF PM PSF

aluminum foam sandwich averaging volume size Brunnauer-Emmett-Teller nitrogen gas absorption method charged coupled device cold isostatic pressing crack opening displacement computer tension specimen crack tip opening dispacement chemical vapour deposition degree of freedom two- or three dimensional electron beam directed vapor deposition process electrodischarge machining European Synchrotron Radiation Facility, Grenoble finite elements foaming of reinforced metals by gas release in precursors fracture-process zone hot isostatic pressing Fraunhofer-Institute for Applied Material Research investment methodology for materials Institut National des Sciences AppliqueÂes de Lyon intellectual property Fraunhofer-Institute for Machine Tools and Forming Technology lattice block materials low density core material linear elastic fracture mechanics Leichtmetallkompetenzzentrum, Ranshofen, Austria metal inert gas arc welding metal matrix composite USA multidisciplinary research initiative powder compact foaming powder metallurgy point spread function

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PVD RV RVE SAS SEM TIG US XCT

physical vapour deposition representative volume representative volume element Slovak Academy of Science scanning electron microscopy tungsten inert gas arc welding ultrasonic X-ray computed tomography

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

1 Introduction: The Strange World of Cellular Metals F. Simancik When Nature builds large load-bearing structures, She generally uses cellular materials: wood, bone, coral. There must be good reasons for it. M. F. Ashby

It is well known that porous structures are good for insulation, packaging, or filtering, but few people believe that they can also be very effective in structural applications. Thousands of scientific publications deal with the minimization of porosity in load-bearing parts. Engineers work hard to eliminate pores from castings, powder metallurgy parts, weld joints, or coatings, thinking that a defect-free part is a pore-free one. With this attitude it is difficult for someone to accept that a loadbearing material can include pores, even quite large ones. However, large natural structures of porous materials have existed for thousands of years, demonstrating how evolution has generated cellular structures that optimize mechanical properties and structural function for minimum weight. Mankind tries to learn from nature. Understanding the benefits of natural structures gives us information to help us produce man-made cellular solids. The cellwall material has to be chosen very carefully if the structure is expected to carry loads. Polymers appear to be insufficiently rigid and ceramics are too brittle. Perhaps metals could be the right choice. Several of the engineering properties of metallic foams are superior to those of polymeric ones: they are stiffer by an order of magnitude, they are stable at elevated temperatures, they possess superior fire resistance, and they do not produce toxic fumes in a fire. Moreover, these materials are fully recyclable without any pollution or waste problems. The latter fact can no longer be ignored, because the production, disposal, and use of stronger and stiffer materials in new products often have negative environmental impacts over the product life cycle. Owing to their pores, cellular metals possess a set of unusual properties compared with bulk structural materials: they are crushable, they exhibit a plateau stress if compressed, and they exhibit a change in Poisson ratio on deformation. The excellent combination of good mechanical properties (mostly strength and stiffness) and low weight is the prime advantage. In addition, cellular metals

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1 Introduction: The Strange World of Cellular Metals

absorb high impact energies regardless of the impact direction, and are very efficient in sound absorption, electromagnetic shielding, and vibration damping. Most of the mechanical properties of foam materials can be achieved with other materials, sometimes more effectively, but foams can offer a unique combination of several (apparently contradictory) properties that cannot be obtained in one conventional material at the same time (e. g., ultra-low density, high stiffness, the capability to absorb crash energy, low thermal conductivity, low magnetic permeability, and good vibration damping). Cellular metals are thus promising in applications where several of these functions can be combined. These properties depend significantly on the porosity, so that a desired portfolio of properties can be tailored by changing the foam density. This is one of the most attractive features of these remarkable materials. Cellular material properties also depend on the pore structure. This influence, imperfectly understood at present, is a topic of intense study. Various constitutive laws have been suggested for the characterization and modeling of this relationship. These laws, originally developed for polymeric foams, are usually based on the relative density of the foam, and therefore suppose uniform cellular structure, at least at a macroscopic level. However, metallic foams are dramatically different from polymeric foams: polymeric foams generally have a regular microstructure, whereas metallic foams may be highly disordered with a wide dispersion of cell size and shape. Moreover, many imperfections exist in a cell structure, such as cracks or holes in the cell walls, corrugated cells etc. These effects are inevitable due to manufacturing at significantly higher temperatures than in the case of polymers. If these features are not taken into account and the properties of the foam are characterized only in relation to apparent density, a higher scatter of properties is to be expected. This is why it is still widely believed that acceptable reproducibility of the properties of metallic foams is questionable. The structure of metallic foams is often non-uniform, especially in the case of complex 3D parts. It should be noted that a uniform structure is not necessary for obtaining acceptable and reproducible properties. Anisotropic or gradient pore structures allow the distribution of load bearing material according to load conditions (simulating the optimum bone-like structure), without a need to increase the overall weight or volume of the component. Therefore, the challenge for manufacturing is not to produce a uniform structure, but to achieve reproducible properties with a controlled non-uniform structure. If the non-uniform structure is optimal, the crucial question ªWhat is the material?º should be answered. It is really difficult to distinguish between material and structure. If a cellular metal is a material, it is very problematic to define geometryindependent material characteristics (the strength or elasticity modulus); if it is a structure made of a certain metal it is almost impossible to define its random geometry. Cellular metals can be prepared by various processing methods. They may all be called ªmetallic foamsº, but they are very different materials, depending on the manufacturing technique. The production method affects the distribution of the

1 Introduction: The Strange World of Cellular Metals

cell-wall material in such a way that the properties of differently manufactured materials are not comparable. Metallic foams result from the nucleation and subsequent growth of gas bubbles in a liquid or semi-liquid metal. They usually have a non-uniform pore structure (variable pore size and sometimes preferred orientation of pores). The pores are initially closed, but some defects always appear on cooling, owing to shrinkage of solidifying metal and gas-pressure reduction in pores. Many solidified cell faces have non-uniform curvature or are corrugated and have occasional broken walls that still hang in place. These are the main features of this kind of cellular solid. Other cellular metals may be manufactured by casting or deposition of the metal onto templates or place holders, which have to be removed from the final product, thus creating a porous structure. These cellular structures usually have adjustable distribution of pore size (according to the template) and their cells are always open. The manufacturing process dictates not only the properties but also the potential applications of the foam. Thus foams prepared by the powder compact foaming (PCF) technique (usually with a dense skin) can be effectively used as net-shape components, stiffening cores in castings, or in complicated hollow profiles, whereas the foams prepared by the ªmolten metal routeº (typically large blocks or panels) can be effectively used as voluminous energy absorbers, cores for sandwiches, or for blast protection. The open cellular structures made by investment casting are good for heat exchangers, sound absorbers, or for electrodes in batteries. The properties arising from the cellular structure produced by a certain manufacturing technique cannot be effectively achieved using another method. This also means that cellular metals manufactured differently are not necessarily competitive materials. The first attempt to foam a metal was performed by B. Sosnik in 1943 [1]. In order to create pores, he added mercury to molten aluminum. In 1956 J. C. Elliot replaced mercury by foaming agents generating gas by thermal decomposition [2], so now modern scientists and engineers can develop metallic foams without having to deal with the toxicity of mercury. In 1959 B. C. Allen [3] invented the PCF route for manufacturing metallic foams and the basic processing techniques were thus completed. The success in the preparation of the first metallic foams and discovery of their remarkable properties started a euphoric enthusiasm for these materials. In 1957 J. Bjorksten stated [4]: ªFoamed metals offer great market potential and might conceivably account for 10 % of all metals produced within 20 yearsº. However he also said: ªA lot of work still remains to bring about production on a large scale, such as closer control of density and dimensions.º Unfortunately, only the second of his statements turned out to be realistic. Although it is many years since the first patents concerning the manufacture of metallic foams appeared, the material has not been put into large-scale commercial production yet. This discouraging fact can be attributed to inadequate design of components, low reproducibility of properties, a lack of testing procedures and calculation approaches, absence of concepts for secondary treatment, as well as the production technologies being too complicated and relatively expensive.

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In spite of disappointments and mistrust, interest in cellular metals is growing. A new era started, at least in Europe, at the end of the 80s thanks to the activities of the Fraunhofer Institute for Advanced Materials in Bremen (IFAM). When J. Baumeister showed his floating aluminum on German TV in the ªKnoff-Hoff showº this remarkable material found a lot of enthusiastic fans. Stabilization of the melt via viscosity-increasing additions significantly improved the quality of the foam structure [5,6]. The development of new foaming techniques enabled reasonable manufacturing costs, and so metallic foams became very attractive to the transport industry, especially for lightweight stiff body structures and crash absorbing elements. The first industrial companies (Shinko-Wire, Cymat, Alulight, Schunk, Karman, Neuman-Alufoam) have already established a group of ªmetfoamº producers and further companies will join them soon. At present metallic foams are still insufficiently characterized, and understanding of the process is incomplete, leading to inadequate control and, hence, variable properties. This gives an impetus for large multilateral scientific activities like the USA Multidisciplinary Research Initiative on ultralight metal structures (MURI) [7] or the German Reasearch Council's focussed research program (DFG) [8]. Better understanding leads to better process control and improved properties. The producers themselves have aggressive development programs for their materials. The next generation of metallic foams will certainly be better. With all these shortcomings, even the present generation has shown excellent performance in many case studies. The structures, though still apparently imperfect, can be acceptable if they are applied properly in a foam-familiar design, because cellular metals have to be used in non-traditional ways. The problem-solving approach, instead of the trial-and-error method, will definitely accelerate the implementation of cellular metals in real products. An intensive and close collaboration among scientists, engineers, producers, and end users is crucial for success. Dr. Bjorksten's: ªNow it's up to industry to decide what to do with itº [4] would have fatal consequences for the future of cellular metals.

References

1. B. Sosnik, US Patent 2 434 775, 1948. 6. J. Iljoon et al., US Patent 5 115 697, 1992. 2. J. C. Elliot, US Patent 2 751 289, 1956. 7. Ultralight Metal Structure Project, MURI 3. B. C. Allen, US Patent 3 087 807, 1963. Grant No. N00014-1-96-1O28, Washington 1996. 4. Modern Metals, 1957, October. 5. S. Akiyama et al., European Patent 0 210 803, 8. Zellulare metallische Werkstoffe, DFG-Priority 1986. Program 1075, Bonn 1999.

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

2 Material Definitions, Processing, and Recycling H. P. Degischer

A great variety of cellular metals is produced by research laboratories and industrial development departments. Established industrial products are Duocel, Incofoam, Alporas, and some others are on the brink of market introduction. The different types of products and prototypes are the result of various combinations of processing, architecture, and metal matrix. The architecture of the cellular structure is the result of the processing technique, which can be classified according to Fig. 2-1, but each process has special features typical of the producing company or laboratory. None of the manufacturing techniques can be applied to any metal; each is appropriate for one or other base metal. Cellular structures are those with a relative

Processing techniques for cellular metals classified according to the state of the metal, the formation of the cellular architecture, and the pore-forming ingredients.

Figure 2-1.

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density of less than 0.3 [1]. Materials with higher relative densities are called porous materials (for instance, powder compact greens), most of which also can be produced by the processing techniques listed in Fig. 2-1. The most widely developed and investigated cellular metals are based on aluminum and its alloys. The general aspects of processing are described elsewhere [1 3] and specific presentations can be found in the proceedings of the conferences dealing with cellular metals [4 10]. The most important processing techniques are described in detail in subsequent chapters. Cellular metals are heterogeneous materials formed by a 3D metallic matrix with gas-containing pores occupying more than 70 vol.-%. Cellular metals are classified according to the following criteria (Fig. 2-1). x

x

x

The metal condition during production of porosity: liquid, solution or emulsion, solid. The forming process involved: casting, foaming, deposition, sintering (including precursor slurry). The method of pore formation: incorporating hollow substrates, removable substrates, or gas (either directly, dissolved, or by means of a dissociating agent).

Open porosity structures can be formed by replication (Duocel [6]), deposition (Incofoam [6]) or by construction of solid ingredients with space between (for instance, the 3D networks of lattice block materials (LBM) [5,6] or those prepared by rapid prototyping techniques [11]). Open-cell solid structures may be called sponges. Closed cells are produced by embedding or cementation of hollow ingredients (ªsyntactic foamsº), or by foaming in the liquid state. The expression ªmetal foamsº, strictly valid only for the liquid phase, is often used to describe the solid product. Mixtures of metal powders and blowing agents are compacted by extrusion or hot pressing providing a precursor material foamed above the solidus temperature, a method called ªpowder compact foamingº (Alulight [5 10], IFAM-Foaminal [3,5 10], Alufoam [5,7]). The Formgrip material [3,7] is made by remelting a stir-cast foamable precursor metal matrix composite. Low-density-core material (LDC [3,6]) is produced by pore formation in the solid state by the high gas pressure of entrapped dissociating blowing agents. A blowing agent powder is mixed into the melt either in a crucible (Alporas [1±7]) or in the gate in pressure die casting (Buehler [10]). Foaming of particle-reinforced metals takes advantage of the stabilization of gas bubbles by the ceramic ingredients producing a cellular metal matrix composite from the melt (Cymat [1 7], COMBAL [10]). The formation of a gas metal eutectic is the principle for the production of Gasar foams [1,2,6]. A slip reaction foam technique based on foaming of precursor slurry by chemical reaction and a reaction sintering process for aluminides has been described [10]. The originally closed cells of foamed metals may not be gas tight after solidification owing to cracks in their walls. The resulting cellular metal products can be differentiated by their structural features. The term ªstructureº is used for the description of cellular materials at different levels of observation (structology): the geometric architecture of the solid (skeleton) in the individual cells and their 3D arrangement, the variations of that

2 Material Definitions, Processing, and Recycling

architecture within a considered sample or part (degree of uniformity), and the microstructure of the solid itself and its surface. The cells are formed by plateau borders (edges and nodes) and, in the case of closed cells, by walls connecting them [12] with a particular microstructure of the metal, eventually containing the remnants of the foaming additives and other microstructural inhomogeneities. The multitude of structural features (see Chapter 4) and their spatial distribution are still subject to investigation in order to correlate them with processing parameters and functional properties, aiming for the development of quality-relevant specifications. Cellular metals are inherently heterogeneous: real samples usually exhibit local non-uniformity like variations in cell architecture and mass distribution. The simplest description of a cellular metal is given by stating the production process, the composition of the metal, and the apparent density: producer/process alloy composition apparent density [g/cm3]. The established symbol for the corresponding heat treatment condition of light metals could be added; for example: Alulight AlSiMgCu 0.45 T1.

References

1. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, 2nd ed., Cambridge University Press, Cambridge 1997. 2. M. F. Ashby, A. G. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: a Design Guide, ButterworthHeinemann, Woburn 2000. 3. J. Banhart, N. A. Fleck, M. F. Ashby (eds), Metal Foams Special Issue, Adv. Eng. Mater. 2000, 2(4). 4. J. Banhart (ed.), Proc. MetallschaÈume, MIT, Bremen 1997. 5. J. Banhart, H. Eifert (eds), Proc. Metal Foam USA Symposium, MIT, Bremen 1998. 6. D. S. Schwartz, D. S. Shih, A. G. Evans, H. N. G. Wadley (eds), Proc. Porous and Cellular Materials for Structural Applications, MRS Symp. Proc. Vol. 521, MRS, Warendale, PA 1998.

7. J. Banhart, M. F. Ashby, N. A. Fleck (eds), Proc. Metal Foams and Porous Metal Structures, MIT, Bremen 1999. 8. T. W. Clyne, F. Simancik (eds) Proc. Metal Matrix Composites and Metallic Foams, Euromat 1999, Vol. 5, Wiley-VCH, Weinheim 2000. 9. H. P. Degischer (ed) Proc. MetallschaÈume, Special Issue, Mater. Wissenschaft Werkstofftechn. 2000, 31(6). 10. J. Banhart, M. F. Ashby, N. A. Fleck (eds), Proc. Cellular Metals and Metal Foaming Technology (MetFoam 2001), MIT, Bremen 2001. 11. A. BuÈhrig-Polaczek, in Proc. Materialsweek 2000, Symposium H3, http://www.materialsweek.org/proceedings. 12. D. Weaire, S. Hutzler, The Physics of Foams, Clarendon Press, Oxford 1999.

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2.1 Foaming Processes for Al

2.1

Foaming Processes for Al

C. KoÈrner and R. F. Singer

The melt route for processing closed-cell metal foams is very attractive since this approach allows economic handling of large quantities of material. Melt-route processes are also well suited to the use of scrap as feedstock. In order to foam the melt properly, gas must be introduced. This can be either done by gas injection or by in-situ gas generation by a chemical decomposition of a foaming agent. For the production of homogenous foams some prerequisites have to be fulfilled. If foaming is by in-situ gas generation uniform dispersion of the foaming agent in the melt within a time that is short compared to the decomposition or reaction time of the additive is required. In addition, the escape of gas during the foaming process has to be prevented. One important step to meet these requirements is to increase the viscosity of the melt. There are several approaches to do this: foaming in the semi-liquid state, incorporation of ceramic particles [1] or oxidation [2]. The effect of the particles added is always twofold: beside increasing the melt viscosity they stabilize the cell walls. Independent of the specific foaming process it is found that porosity, quantified by density, and mean cell size are intimately related. Generally, for a particular alloy or composite the mean cell size can not be chosen independently of the porosity. 2.1.1

Gas Injection: the Cymat/Alcan and Norsk Hydro Process

The Cymat/Alcan and Norsk Hydro melt-foaming process is a continuous, gas-injection method developed simultaneously and independently by Alcan [1] and Norsk Hydro [3] in the late 1980s and 1990s. A sketch of the process developed by Alcan is given in Fig. 2.1-1. The patent is now licensed and exploited by the Cymat Aluminum Corporation [www.cymat.com]. The process employed by Hydro Aluminum, Norway is analogous. A metal matrix composite (Al-wrought or Al-casting alloy matrix ‡ 10 30 vol.-% SiC or Al2O3

Figure 2.1-1. Principle of the melt-foaming route employed by Cymat. The foam casting process for producing flat panels consists of melting and holding furnaces, the foaming box and foaming equipment, and a twin-belt caster [1].

2 Material Definitions, Processing, and Recycling

particles) is used as a starting material. The starting material is molten with conventional foundry equipment and transferred to a tundish where gas, typically air, is injected via small nozzles incorporated into a rotating impeller, thus forming a dispersion of small gas bubbles. The bubble size can be controlled by adjusting the gas flow rate, the impeller design (number of nozzles and their size), and the speed of rotation of the impeller. The gas bubbles rise to the surface where they accumulate. The ceramic particles are trapping gas bubbles owing to the favorable interface energy and serve as stabilizer of the cell walls and delay their coalescence. They also reduce the velocity of the rising bubbles by increasing the viscosity of the melt. That is, the particles reduce the kinetic energy of the rising bubbles and hence the danger of mechanical rupture when they arrive at the surface. The resulting metal foam, which is still liquid, is carried away by means of a conveyor belt where it solidifies and cools. The relative density is predominantly controlled by the process parameters, such as rotor speed, gas flow, and the amount of particles in the melt, and finally the solidification condition. This process of casting aluminum foam is capable of producing slabs with a relative density in the range 2 20 % (0.05 0.55 g/cm3). The average cell size is inversely related to the density (Fig. 2.1-2a) and is in the range 2.5 30 mm [1].

a)

Average cell size as a function of the reciprocal density for: a) Cymat foam [1]; b) FORMGRIP [7] products.

Figure 2.1-2.

b)

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Figure 2.1-3. Optical micrographs of Cymat foam produced by the gas-injection method: left) cell structure (density about 0.3 g/cm3), inhomogeneous and anisotropic; right) foam surface (density about 0.05 g/cm3).

The production facility set up by Cymat is capable of casting foam panels in continuous length at an average rate of 900 kg/h up to 1.5 m wide with a thickness range of 25 150 mm. This shows that the process is relatively straightforward and economical. Challenges that may require more work in the future include the variation in cell size, the density gradient, and the anisotropy of the cell structure, which results from mechanical forces from the conveyor belt (Fig. 2.1-3). Especially earlier prototype have been compressed by the conveyor belt producing flattened pores causing poor stiffness and strength values along the thickness of the slabs. It should also be noted that the preparation of the composite feedstock requires relatively tedious long time stirring processes to achieve the proper homogenous distribution of the particles in the melt. In principle, this foam generation technology also allows the casting of nonrectangular, 2D profiles as well as 3D shapes. 2.1.2

In-situ Gas Generation: the Shinko Wire Process and the FORMGRIP process

The gas-injection method suffers from the fact that a relatively small number of large bubbles is generated, which leads to rather coarse and irregularly shaped pore distribution. Two techniques are described below, in which the foaming gas results from a thermal decomposition of solid ingredient. In this way a huge number of bubble nuclei is created throughout the melt.

The Shinko Wire Process [2] The manufacturing process of the Alporas foam is a batch casting process patented by Shinko Wire Company Ltd., Japan (see Fig. 2.1-4) [2]. The installed manufacturing plant is capable of making large sized blocks of foamed aluminum. For adjusting the viscosity of the molten aluminum 1.5 % Ca is added at 680 hC and stirred for 6 min in an ambient atmosphere. The addition and subsequent agitation of an element with a high oxygen affinity facilitates an oxidation process on the surface of the molten metal and leads to an increase of 2.1.2.1

2 Material Definitions, Processing, and Recycling

Figure 2.1-4.

Manufacturing process for Alporas foams [2].

the viscosity by the formation of oxides: CaO, Al2O3, CaAl2O4. There is an appropriate stirring resistance for optimizing the foaming ratio [4]. The thickened aluminum is poured into a casting mold and stirred with an admixture of 1.6 % TiH2 as a foaming agent. While vigorously stirring, the TiH2 dissociates and H2 -bubbles are formed causing molten material to expand and to fill the mold. Then, the foamed material is cooled by fans to solidify in the casting mold. After removal from the casting mold. An Alporas block 450 mm wide, 2050 mm long, and 650 mm high is sliced into plates. Alporas is an ultra-light material with a closed-cell architecture (Fig. 2.1-5). The density of the product is 0.18 0.24 g/cm3, the mean cell size is about 4.5 mm. Alporas is regarded as the best commercially available aluminum foam in terms of regular cell micro structure. This is to a certain extent because transfer and deformation of the still liquid foam, as in the Cymat/Norsk Hydro process, is avoided. The cell architecture is the outcome of a growing process where bubble expand and coalesce due to cell wall rupture.

Figure 2.1-5. Typical cell structure of an Alporas foam. As a result of the growth process most cells are far from equiaxed. The global homogeneity is superior to other commercially available aluminum foams.

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The FORMGRIP Process The FORMGRIP (Foaming of Reinforced Metals by Gas Release in Precursors) process integrates some of the advantages of melt- and powder-route approaches for foam production into one processing technique [5 7]. It comprises ªbakingº a precursor material with the foaming agent entrapped in a mold to generate foam in-situ by dissociation, which is very similar to the established powder routes. However, the precursor is prepared via melt processing [7]. A diagram of the FORMGRIP process is depicted in Fig. 2.1-6. The precursor preparation comprises dispersion of a mixture of AlSi12 powder and the pre-treated gas-generating TiH2 powder in an Al-9Si/SiCp (particle size 12.8 mm) composite melt by conventional mechanical stirring 1200 rpm for 50 70 s. The critical point is that during this processing step only a limited portion of hydrogen is released from the foaming agent. This is achieved by the following precautions: a low temperature of the melt at the moment of the hydride introduction (T ˆ 620 hC), a high melt viscosity due to SiC particles and a pre-oxidized, retarded foaming agent [8]. The thermal pre-treatment of the foaming agent consists of a two-step thermal oxidation sequence (24 h at 400 hC ‡ 1 h at 500 hC), which slightly reduces the hydrogen concentration of the TiH2. The oxide barrier layer formed on the powder surface slows down the kinetics of gas evolution. The amount of the incorporated hydride is about 1.5 wt.-% of the melt mass. The mixed melt is cast into a mold by cooling and pore growth is suppressed by cooling. The SiCp particles are also important for foam stabilization, which becomes plausible from their distribution in Fig. 2.1-7. The resulting precursor material already exhibits a porosity of 14 24 %. The second stage of the FORMGRIP process comprises heating of the precursor material above the solidus temperature. As a result, hydrogen released from the TiH2 diffuses to the bubble nuclei already present and expands them further. Typical cell structures are depicted in Fig. 2.1-8 [7]. 2.1.2.1

Figure 2.1-6. Diagram of the melt-based FORMGRIP process for production of near net-shape metal foam parts [7].

2 Material Definitions, Processing, and Recycling

Optical micrographs illustrating the distribution of SiC particles in Al-9Si alloy based FORMGRIP foams, showing sections through: a) cell wall, b) a node. A significant fraction of particles is located at the gas/melt interface [5].

Figure 2.1-7.

Figure 2.1-8. Examples of cross sections of aluminum alloy FORMGRIP foams baked under different conditions. Porosity, P, levels and the mean cell sizes, d, are: a) P ˆ 69 %, d ˆ 1.1 mm; b) P ˆ 79 %, d ˆ 1.9 mm; c) P ˆ 88 %, d ˆ 3.1 mm [7].

The relation between relative foam density and average cell diameter fits that derived for Cymat foams. Fig. 2.1-2b shows the mean cell diameter as a function of the reciprocal density (see Section 4.1). The mean cell diameter is inversely proportional to the density indicating that foam expansion is governed by cell coalescence and the mean cell wall thickness is constant. The dependence of the cell diameter on the density is the same for both contents of SiC particles. The influence of particle size has not yet been investigated. Theoretical work of Kaptay [9] and experimental work of Weigand [10] indicate that a reduction of particle size will not lead to a higher stabilization and therefore to a smaller critical cell wall thickness. In terms of geometrical complexity and simultaneous microstructural control, the FORMGRIP process surpasses the Shinko Wire one. There is no need to transfer material from a mold into a die while the foaming process is going on. In addition, the precursor material can be shaped before the final baking step. The economics of the FORMGRIP process, however, are clearly inferior to the other processes discussed in this chapter. This is due to the discontinuous nature of the process as well as its various number of processing steps.

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2.2 Industrialization of Powder-Compact Foaming Technique

References

1. J. T. Wood, ªProduction and Application of Continuously Cast, Foamed Aluminumº in Proc. Fraunhofer USA Metal Foam Symposium, 7 8 October 1997, Stanton, Delaware. 2. T. Miyoshi, M. Itoh, S. Akiyama, A. Kitahara, ªAluminum Foam, Alporas: The Production Process, Properties and Applicationsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 125. 3. P. Asholt, ªAluminium Foam Produced by the Melt Foaming Route Process, Properties and Applicationsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 133 140. 4. L. Ma, Z. Song, ªCellular structure control of aluminium foams during foaming process of aluminium meltº Scripta Mater. 1998, 39(11), 1523 1528. 5. V. Gergely, T. W. Clyne, ªThe FORMGRIP process: foaming of reinforced metals by gas release in precursorsº Adv. Eng. Mater. 2000, 2(4), 175 178.

6. V. Gergely, T. W. Clyne, ªA Novel Melt-Based Route to Aluminium Foam Productionº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 83 89. 7. V. Gergely, ªMelt Route Processing for Production of Metallic Foamsº, Department of Materials Science and Metallurgy, Cambridge 2000. 8. A. San-Martin, F. D. Manchester, ªThe H Ti (hydrogen titanium) systemº Bull. Alloy Phase Diagrams 1987, 8(1), 30 43. 9. G. Kaptay, ªInterfacial Criteria for Ceramic Particle Stabilised Metallic Foamsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 141 146. 10. P. Weigand, ªUntersuchung der Einfluûfaktoren auf die pulvermetallurgische Herstellung von AluminiumschaÈumenº, FakultaÈt fuÈr Bergbau, HuÈttenwesen und Geowissenschaften, RWTH, Aachen, MIT Verlag, Bremen 1999.

2.2

Industrialization of Powder-Compact Foaming Technique

J. Banhart and F. BaumgaÈrtner

There are many different ways to manufacture cellular materials [1]. One of the available processes has become increasingly popular in the past few years and is at the stage of industrial implementation now. The method is sometimes loosely called the ªpowder-metallurgical routeº, but the term ªpowder-compact foaming techniqueº seems more appropriate. 2.2.1

Principles of Foam Production

The technique consists of mixing aluminum or aluminum alloy powders with appropriate foaming agents, which get entrapped by compacting this mix to a dense product called ªfoamable precursor materialª. The powder mix can be compacted directly by hot pressing, conform extrusion, or powder rolling. Alternatively the pow-

2 Material Definitions, Processing, and Recycling

Figure 2.2-1.

Foam production by powder-compact foaming technique.

der may be cold compacted for better handing in conventional extrusion or rolling (Fig. 2.2-1). Heating the precursor above its solidus temperature releases the pressure on the foaming agent allowing decomposition and formation of bubbles. After cooling a low-density foam structure of originally closed cells is obtained [2,3]. The method is not restricted to aluminum and its alloys: tin, zinc, lead, gold, and some other metals and alloys can also be foamed by choosing appropriate foaming agents and process parameters (see Section 2.1.2). The most common alloys for foaming, however, are pure aluminum or wrought alloys such as aluminum 2xxx, 6xxx, or 7xxx alloys, e. g. AA 2014, 6060, 6061, 6082, or 7075. Casting alloys such as AlSi7Mg (A356) and AlSi12 are also frequently used because of their low melting point and good foaming properties, although in principle virtually any aluminum alloy can be foamed by carefully adjusting the process parameters. Quite complex-shaped metal foam parts can be manufactured by expanding the foam inside a mold, thus confining spatial expansion. An example for one such part is shown in Fig. 2.2-2. The part, developed in the framework of a feasibility study, is a novel pantograph horn for an electrical locomotive. This light-weight solution based on aluminum foam replaces traditional cast aluminum parts saving 30 % weight. A nice feature of the technique is that composite structures consisting of an aluminum foam and bulk metal parts can be made without using adhesives. Examples are foam-filled aluminum sections and sandwich panels with an aluminumfoam core and metallically bonded steel, aluminum, or even titanium face sheets. For making such composites the foamable precursor material is first bonded to the solid section or sheet by co-extrusion or roll-cladding, after which the foamable core layer is expanded by heat treatment [4,5] (see also Section 3.3).

15

16

2.2 Industrialization of Powder-Compact Foaming Technique Figure 2.2-2. Aluminum foam part (Schunk Sintermetalltechnik, Giessen).

The advantages of the powder-compact route are obvious and are listed in Table 2.2-1. Beside the first two features already mentioned, the flexibility arising from the preparation of the precursor from powders is important. Alloys can be made simply by mixing inexpensive elementary powders. No ceramic additives are needed to stabilize the foam, in contrast to some of the melt-route foaming processes in which up to 15 % silicon carbide has to be added [1,6]. However, if required, ceramic powders, metal fibers, or ceramic fibers can be added to the powder blend for special applications, such as for reinforcement or to increase wear resistance. Naturally, there are also some disadvantages that are inherent to the process. Metal powder is more expensive than bulk metal and requires effort for compaction. This rules out applications that require very cheap materials. Moreover, the size of aluminum foam parts that can be manufactured is limited by the size of the baking furnace, and is therefore smaller than for some of the competing melt-foaming processes. The largest sandwich components that have been manufactured using the powder-compact foaming technique are about 2 m q 1 m q 1 cm in size (possibly larger in future). At LKR in Ranshofen a part of similar size was produced without face sheets (Fig. 2.2-3). True 3D-volume parts are usually not thicker than 30 cm, a limit which is difficult to shift to higher values. A large aluminum foam column produced at Fraunhofer IFAM was 1 m high and 18 cm in diameter, weighing 13 kg. In contrast, the liquid-metal route allows for making panels 15 m in length [7] and 100 cm thickness [8]. However, as these processes cannot be used for near-net-shape production and only permit very simple geometries, they are appropriate for different fields of application. Continuous foaming of long products is under investigation [9]. The middle column of Table 2.2-1 lists some of the problems that are still encountered when foaming aluminum with the powder-compact melting method but which can, in principle, be solved with further research.

2 Material Definitions, Processing, and Recycling Table 2.2-1. Characteristics of powder-compact foaming method: advantages and disadvantages that are inherent are listed together with points that are presently problematic, but can be solved in principle.

Advantage

Problem

Disadvantage

Net-shape foaming possible

Uniformity of pore structure still not satisfactory

Cost of powders

Composites can be manufactured

Process control must be improved

Very large volume parts difficult to make

Parts are covered by metal skin

Permeable (holes)

Coating process requires sealing

Graded porosity can be achieved

Difficult to control

Flexibility in alloy choice No stabilising particles have to be added Ceramics and fibers can be added

Rear wall of an automobile made of aluminum foam (LKR Ranshofen and DaimlerChrysler AG, see chapter 7.4).

Figure 2.2-3.

2.2.2

Practical Aspects of Foam Production Powder selection The appropriate selection of the raw powders with respect to purity, particle size and distribution, alloying elements, and other powder properties is essential for successful foaming. Commercial air-atomized aluminum powders were shown to 2.2.2.1

17

18

2.2 Industrialization of Powder-Compact Foaming Technique

be of sufficient quality. However, powders from different manufacturers led to notable differences in foaming behavior and empirical criteria have been derived to facilitate the selection of powders. The cost of powders and the ability of a manufacturer to provide sufficient quantity with a constant quality are also crucial. As already pointed out, alloys can be obtained in different ways. The frequently used alloy AlSi7, for example, can be either prepared by atomizing a AlSi7 melt, or by blending pure aluminum powder with 7 wt.-% silicon powder, or, in a third way, by mixing 58 % of standard AlSi12 powders with 42 % aluminum powder.

Mixing The mixing procedure should yield a homogeneous distribution of alloying elements and the foaming agent to ensure that high-quality foams with uniform pore-size distributions are obtained. Powders are mixed in batches of 500 kg at Schunk-Honsel in commercial large-scale tumbling mixers with parameters determined in technological tests. Alternatively, powder mixes can be obtained by aerodynamic mixing. For example, Alulight International GmbH Austria mixes aluminum and titanium hydride in large containers with 50 80 short pulses of pressurized nitrogen gas. 2.2.2.2

Densification Powder consolidation can be carried out by various techniques. It has to be ensured that the foaming agent is completely embedded in the metal matrix and no residual open porosity remains. One way to obtain foamable precursor material with nearly 100 % theoretical density is the combined use of cold isostatic pressing (CIP) and ram extrusion. CIP is first applied to consolidate the powder mix to billets with a relative density of 70 80 % and a mass of typically 50 kg. These billets are used in the subsequent extrusion step. Although CIPping is not absolutely necessary (powders have been filled into thin-walled aluminum cartouches and inserted into the extrusion machine without prior consolidation) it has additional advantages such as the prevention of powder contamination and powder de-mixing. The CIP billets themselves are not foamable because of their large content of residual porosity, which causes massive hydrogen losses when the material is heated. To obtain foamable material, the billets are preheated to 350 hC and extruded as rods or any other profile. For this a horizontal direct extrusion machine is used (25MN Schunk-Honsel). The extrusion machine is operated in cycles with a new billet inserted after each extrusion step. This way rather high outputs can be achieved. Foamable material has also been manufactured by rotary continuous extrusion in the so-called CONFORM process by Mepura (Ranshofen) [10]. Here a rotating wheel is used to drag the powder into the consolidation chamber from which it is pulled off in radial direction as a compacted wire. Foamable wires of about 8 mm diameter were manufactured from wrought alloys containing titanium hydride. 2.2.2.3

2 Material Definitions, Processing, and Recycling

Further processing of foamable material The extruded material can be foamed as it is after consolidation or it can be worked to the required shape. By conventional rolling, foamable sheets with thicknesses down to about 2 mm are produced. Optionally, the foamable raw material can be clad to conventional sheets of metal, of steel or aluminum for example, by attaching two sheets to either side of the foamable precursor before rolling. This way a purely metallic sandwich structure is obtained. By deep drawing, the sheets and the sandwiches may be transformed to 3-D-shaped sheets for special applications. In all cases it is favorable to start from near-net-shape precursors in order to minimize foam flow [11]. 2.2.2.4

Foaming Heat treatment at temperatures above the solidus temperature of the foamable matrix is necessary to produce the foam structure. The gas released by the decomposing foaming agent may form pores in the solid state but only above the solidus are bubbles formed and the matrix expands up to a maximum volume, that is to a minimum density. The density and density distribution of the growing foam can be controlled by several parameters. The foaming agent content in the precursor material is obviously important, but furnace temperatures and heating rates also have an influence [12]. The mold material, the mold shape, and the type of furnace naturally influence the heating rate and have therefore also to be considered. A careful control of the heating conditions during foaming is essential for obtaining high-quality foams. The difficulty is that the liquid foam is thermodynamically unstable and conditions change constantly during foaming. There are various intermediate stages: at first only the mold is heated directly, whereas the foamable material receives heat only indirectly via heat conduction through the mold. Initially there are merely some point contacts between the piece of foamable material in the mold and the mold walls. However, as the temperature increases, the precursor softens and assumes the contour of the mold thus increasing the transfer of heat. Moreover, heat transfer via radiation gains importance with rising temperatures. The reflectivity of the mold and precursor surfaces may change during the process and add a further variable. Finally, after foaming has started, the thermal conductivity of the precursor rapidly decreases thus reducing heat flow. As soon as the mold has been filled with foam it has to be cooled down below its solidus temperature to stabilize the foam structure. The phenomena during cooling are also quite complex and difficult to describe for reasons similar to those mentioned for the heating phase. Typical densities of aluminum foams are in the range 0.4 0.8 g/cm3 including the closed skin around the foam body. The final density of a foamed part can be simply predicted if the volume of the hollow mold and the mass of the inserted precursor material are known. The foaming mold may be loaded with several small pieces or one single piece of precursor. Choosing the latter method (which is preferred by LKR and SAS [13]) one has to take into account that each piece of the expanding precursor material has a dense aluminum oxide layer on its sur2.2.2.5

19

20

2.2 Industrialization of Powder-Compact Foaming Technique

Left) top of aluminum foam part made by inserting various pieces of foamable material into the mold (dark figures indicate original size of the precursor pieces). Right) foam part made of two pieces of precursor without achieving bonding between the two pieces.

Figure 2.2-4.

face, which has to be broken up by expansion of the individual foam pieces. Incomplete foaming may cause the foamed pieces to remain separated even after the foaming process (Fig. 2.2-4b). A relative movement of the foam pieces to each other helps to break up the oxide films. Fig. 2.2-4 shows an example of a successful formation of a foamed body from various pieces of the precursor and an example of failure. In the former case the location of the original individual foam pieces can still be identified from the contrast in gray scales between the various regions: darker gray identifies oxide layers of extruded surfaces, brighter gray is the new (expanded) surface. This effect is currently exploited to create foam panels and other foamed parts for making designer objects. 2.2.3

State of Commercialization

Currently the foaming technique described is still in the stage of industrial implementation. Nevertheless, a number of companies have already made commitments for a future production and are building up facilities [14]. The joint effort of Schunk Sintermetalltechnik (Gieûen) and Honsel GmbH&Co KG (Meschede) is one example. Owing to their collaboration with Karmann the activities are preferentially directed towards foam and foam sandwich parts with a complex 3D geometry (see Section 3.3). Alulight International GmbH is another example. It is a joint venture of SHW (Germany) and Eckart Austria. The company offers aluminum foam panels in sizes up to 625 mm q 625 mm, with thickness of 8 25 mm. Neuman Alufoam, another Austrian company, also offers foamable precursor material (extrusions) and foamed parts.

2 Material Definitions, Processing, and Recycling

References

1. J. Banhart, ªManufacture, characterisation and application of cellular metals and metal foamsº Prog. Mater. Sci. 2001, 46, 559 632. 2. J. Baumeister, German Patent DE 40 18 360, 1990. 3. J. Banhart, ªFoam metal: the recipeº Europhysics News 1999, 30, 17. 4. J. Baumeister, J. Banhart, M. Weber, German Patent DE 44 266 27, 1994. 5. H.-W. Seeliger, ªApplication Strategies for Aluminium-Foam-Sandwich Parts (AFS)º in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 23. 6. P. Asholt, ªAluminium Foam Produced by the Melt Foaming Route Process, Properties and Applicationsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 133. 7. Cymat Corp. (Canada), Product information sheets, http://www.cymat.com 1999.

8. T. Miyoshi, M. Itoh, S. Akiyama, A. Kitahara, ªAluminum Foam, Alporas: The Production Process, Properties and Applicationsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 125. 9. G. Stengele, H. MuÈcke, A. SchoÈne, German Patent DE 197 34 394 A 1, 1998. 10. H. P. Degischer, H. WoÈrz, DE Patent 4206303, 1992. 11. F. BaumgaÈrtner, H. Gers, ªBauteile aus AluminiumschaÈumenº Ingenieur Werkstoffe. 1998, 3, 42. 12. I. Duarte, J. Banhart, ªA study of aluminium foam formation kinetics and microstructureº Acta. Mater. 2000, 48, 2349. 13. R. Kretz, F. Simancik, private communication. 14. http://www.schunk-group.com, http:// www.alulight.com, http://www.neuman.at

2.3

Making Cellular Metals from Metals other than Aluminum

G. Rausch and J. Banhart

The previous section was dedicated exclusively to aluminum foams. For many applications one would like to use cellular materials made from metals or alloys other than aluminum. There have been some attempts to manufacture metal foams by simply adapting the powder-compact process originally developed for aluminum to other metals by adjusting the properties of the foaming agent and the process parameters. This procedure was successful in some cases. However, for high-melting alloys the powder-compact foaming technique is difficult to implement and especially for titanium no promising results could be obtained. Here alternative routes based on advanced powder metallurgy yielded better results. Therefore, in the current section the topic will be slightly extended from ªfoamedº to ªcellular or porous metalsº in a more general sense.

21

22

2.3 Making Cellular Metals from Metals other than Aluminum

2.3.1

Zinc

Zinc can be foamed by a straight-forward modification of the powder-compact technique. The foaming agent used for aluminum (TiH2) can be used, although ZrH2 seems to yield slightly better results. Powder properties and mixing procedures are quite similar to aluminum. Only the pressing and foaming temperature has to be chosen slightly lower than for aluminum due to the melting temperature of zinc at 419 hC. Foamed zinc shows a very uniform pore structure. This can be attributed to the fact that the decomposition temperature of the foaming agents TiH2 matches with the melting temperature of the metal. Therefore, melting and pore formation occur simultaneously and round bubbles are created from the very beginning. In contrast to aluminum, there is no solid state expansion range with corresponding crack formation. Fig. 2.3-1a shows an example of a zinc foam. 2.3.2

Lead

Lead and lead alloys such as Pb Sn and Pb Sb can be foamed by another modification of the process. TiH2 and ZrH2 cannot be used as foaming agents because of the low melting temperatures of pure lead (327 hC) and even lower solidus temperature of the alloys. Quite good foams have been obtained by using lead(II) carbonate as a foaming agent: it decomposes above about 275 hC and releases CO2 and water, which act as foaming gas. Fig. 2.3-1b shows an example of a lead foam 2.3.3

Titanium

Owing to its high melting temperature (1670 hC) and relatively low density (4.51 g/ cm3), titanium and its alloys are excellent materials for lightweight applications at elevated temperatures and are widely used in aeronautical applications. Porous ti-

a) Figure 2.3-1.

b)

Zn and Pb foams (width of sample is about 5 cm).

2 Material Definitions, Processing, and Recycling

tanium structures have an additional potential for weight reduction and could even be suitable for functional applications if the pore structure were open. In principle, there are many possible production methods for cellular materials based on titanium (see Section 2.4), most of them starting from metal powders. 1. 2. 3. 4.

Consolidation of slurry-saturated plastic foam. Foaming and sintering of powder slurries. Reaction sintering of elemental powder mixtures. Foaming of powder compacts containing foaming agents (powder-compact melting process). 5. Hot isostatic pressing and creep expansion of titanium compacts with entrapped inert gas. 6. Sintering of hollow spheres. 7. Sintering of compacted or loose powder filler mixtures. While some of these methods (1 3) have not yet been investigated very intensively, the feasibility of the foaming agent process (4) for titanium has been demonstrated [1]. However, owing to the high temperatures during foaming titanium, the reactivity of this metal with practically any non-inert gas and the lack of appropriate foaming molds, this method is not suitable for producing shaped titanium foam components. Hot isostatic pressing of titanium powder with gas entrapment (5) has been successfully developed for some aircraft applications [2]. Metal hollow spheres (6) can be produced using wet chemical methods for coating Styrofoam spheres [3]. Shaping and sintering of these hollow structures typically result in materials with very low porosity. One of the most promising methods for manufacturing open porous titanium materials is the sintering of compacted or extruded mixtures of powders and fillers that contain removable space-holder materials. The materials are mixed and shaped by conventional PM techniques. After removal of the space holder the green samples are sintered at temperatures of 1100 1400 hC. Bram and coworkers use urea and ammonium hydrogen carbonate as space holders [4], which can be removed by thermal treatment below 200 hC. Depending on the size and shape

Figure 2.3-2. Open porous titanium made by space-holder technique: left) pore size 1 4 mm; right) pore size about 500 mm, porosity 55 80 %.

23

24

2.3 Making Cellular Metals from Metals other than Aluminum

Figure 2.3-3.

Pore structure of open porous titanium with 67 % porosity.

Figure 2.3-4. Strength and Young's modulus as a function of density obtained from bending and tension tests [5].

2 Material Definitions, Processing, and Recycling

of the space-holder powder, spherical and angular pores in the range 0.1 2.5 mm can be obtained, resulting in overall porosities of 70 80 %. It was found that the sintering activity can be increased by partially substituting titanium by titanium hydride, thus yielding an increased compression strength. At Fraunhofer IFAM, polymer granules were used as the space holder. They were removed by a chemical process at temperatures around 130 hC, after pressing. After space-holder removal, samples are sintered in vacuum at temperatures of 1100 1250 hC. Depending on the particle size of the granules, average pore diameters in the range 200 3000 mm can be obtained. Fig. 2.3-2 shows some typical samples. Fig. 2.3-3 shows the typical pore structure of samples based on spherical space-holder granules. Beyond the primary pore structure, some microporosity (secondary pores) inside the sintered network is visible. It was shown that the secondary porosity has a strong influence on the overall strength of the samples and can be reduced by either changing the sintering parameters and/or partially replacing titanium powder by titanium hydride [4]. As for all porous materials, the mechanical properties of cellular titanium are a function of density. Fig. 2.3-4 shows the strength and Young's modulus obtained from bending and tension tests as a function of density. 2.3.4

Steel Powder-Compact Foaming Technique The long experience in making aluminum foams from powder metallurgy (PM) precursors encouraged researchers to transfer this process to higher-melting materials such as iron-based alloys and steels. The major requirements for an adaptation of the foaming agent process to this group of materials are the following. 2.3.4.1

x x x x

Selection of suitable foaming agents. Development of alloys qualified for good ªfoamabilityº. Evaluation of compaction methods. Adaptation of the foaming process.

The basic requirements for foaming agents are: point of gas emission above 1000 1200 hC (depending on the alloy composition), broad temperature range of gas emission (up to 1550 hC for nearly pure iron), and sufficient volume of gas release. It was found that especially metal nitrides and certain carbonates show a significant gas emission and qualify for being useful as foaming agents. Examples are manganese nitride, chromium nitride, molybdenum nitride, calcium carbonate, strontium carbonate, and barium carbonate [5,6]. Theoretical investigations [5,7] have shown that both the iron carbon and the iron boron system [7] are able to meet the basic requirements for being foamed to iron-based metallic foams, namely: a low melting point matching the decomposition temperature of the foaming agent, and a broad two-phase semisolid region in the phase diagram, thus creating a wide foaming interval. As for the production of Al based foamable pre-

25

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2.3 Making Cellular Metals from Metals other than Aluminum

Iron-based foams obtained from the foaming agent process.

Figure 2.3-5.

cursor material, extrusion has been successfully used for compacting iron powder mixtures. The resulting samples are shown in Fig. 2.3-5. Experiments with powder mixtures of iron and carbon have shown that free carbon without any additional foaming agent already leads to a certain degree of porosity. Carbon is oxidized during the foaming process and the resulting gaseous CO and CO2 creates pores. However, pore size distributions are not uniform and pore shape is usually rather irregular. The porosity mainly results from large, isolated pores (Fig. 2.3-6). Adding 0.25 % SrCO3 leads to an increase of porosity to 55.5 % (Fig. 2.3-7). The pore structure at this composition appears to be more homogeneous and the average pore size is obviously lower. Increasing the amount of SrCO3 results in a further increased porosity (64.3 %). From that it can be concluded that SrCO3 has a significant influence on the achievable porosity and the maximum expansion. The foaming agent technique has therefore been shown to be feasible for steel. However, foaming of stainless steel or even superalloys has not yet been successful and the general state-of-the-art of foaming steel with the foaming agent method is still far behind the aluminum foaming technology.

Iron-based metal foams made from extrusion-pressed powder mixtures of Fe ‡ 2.5 % C: left) 0.0 % SrCO3, middle) 0.25 % SrCO3, right) 0.50 % SrCO3.

Figure 2.3-6.

2 Material Definitions, Processing, and Recycling

Figure 2.3-7.

Average porosity as a function of foaming agent content (SrCO3).

Steel Foams from Powder Filler Mixtures All foamed metals have essentially closed cells. For certain applications (filters, membranes, biomedical applications) open porosity is required. For this class of materials the space-holder technique (see also Section 2.3) can be used. The process used for steel is very similar to the one described in the titanium section. The process starts with a mixture of metal powders and the filler powder. The mixture is compacted, usually by axial compression in a conventional powder press. If necessary, an additional bonding agent is used in order to achieve a better strength of the green samples. After pressing an additional drying step is optional. After this the filler/bonding agent phase is removed from the samples, in a chemical (catalytic) or thermal process. After complete filler removal the samples are sintered in a furnace under hydrogen atmosphere. Either urea [4] or plastic granules [8] can be used as space holders. In Fig. 2.3-8 examples of porous 316L and Inconel 600 materials are given, developed by Forschungszentrum JuÈlich GmbH. The porosity of these materials is about 70 % with an average pore size of 1.0 1.4 mm. 2.3.4.2

SEM images of sintered specimen: left) stainless steel 316L, 1100 hC, 1 h, particle size I16 mm; right) Inconel 600, 1250 hC, 1 h, particle size 100 200 mm [4].

Figure 2.3-8.

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2.4 Recycling of Cellular Metals

References

1. G. Rausch, T. Hartwig, M. Weber, O. Schultz, ªHerstellung und Eigenschaften von TitanschaÈumenº Materwiss. Werkstofftechn. 2000, 31, 412 414. 2. R. L. Martin, R. J. Lederich, Metal Powder Rep. 1992, Oct, 30. 3. O. Andersen, U. Waag, L. Schneider, G. Stephani, B. Kieback, ªNovel metallic hollow sphere structuresº Adv. Eng. Mater. 2000, 2, 192 195. 4. M. Bram et al., ªPreparation and Characterization of High-Porosity Titanium, Stainless Steel and Superalloy partsº in Metal Foams and Porous Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 197 202.

5. B. Kriszt, A. Falahati, H. P. Degischer, ªMachbarkeitsstudie zur Herstellung von Eisenbasisschaumº in MetallschaÈume, J. Banhart (ed), MIT Verlag, Bremen 1997, p. 59 70. 6. C.-J. Yu, H. Eifert, M. KnuÈwer, M. Weber, ªInvestigation for the selection of foaming agents to produce steel foamsº Mater. Res. Soc. Symp. Proc. 1998, 521, 145 150. 7. M. KnuÈwer, Herstellung von Eisenschaum nach dem pulvermetallurgischen Treibmittelverfahren, Dissertation, UniversitaÈt Bremen, Fraunhofer IRB Verlag, Stuttgart 1999. 8. G. Rausch, M. Weber, M. KnuÈwer, ªNeue Entwicklungen zur Herstellung von StahlschaÈumenº Materwiss. Werkstofftechn. 2000, 31, 424 427.

2.4

Recycling of Cellular Metals

H. P. Degischer

Cellular metals compete with polymers for some applications. The recyclability of metals is one of their benefits, enabling ecologically sustainable product life cycles [1]. Compared to bulk metal products, there are two complications to be tackled in remelting cellular metals: x

x

The high surface-to-volume ratio of the order of 100/length unit increases the extent of surface adsorptions and reactions. The low average density, due to the high porosity filled with gas, makes the cellular material float on its melt.

2.4.1

The Remelting of Cellular Metals

Heating cellular aluminum in air enhances the growth of the oxide film not only in open cellular structures, but also in those foamed by formation of closed pores in the liquid, or semi-solid state, which usually become permeable to gas after solidification and cooling. When heating the cellular aluminum up to the melting point in a short time, about 1 h, the thickness of the oxide film may reach about 10 mm and any cracks formed will be covered quickly by

2 Material Definitions, Processing, and Recycling

ongoing oxidation. The growth will slow down after prolonged heating, when the thickness reaches about 100 mm [2], which is similar to the cell-wall thickness. The dehydrated oxide is stable up to about 2000 hC, so the cellular aluminum part is slowly converted to a cellular alumina structure, which may maintain its macroscopic shape if it does not break up under its weight, or an external force. It is difficult to submerge a cellular part in a melt because it tends to float and contains a lot of air, which would have to be replaced by melt. Therefore the cellular structures have to be compressed as much as possible, as is done with packaging foils, or shredder scrap before melting [1,3]. Cellular metals can be shredded too and treated as normal shredder scrap. Nevertheless, the high content of surface oxides reduces the efficiency of metal reclamation. The only experience is from small batch laboratory trials on scrap from powder-compact foamed aluminum [4], in which efficiencies up to 80 % have been reached. Oxides and other impurities have to be removed by the usual cleaning process for melts to the extent necessary for the later production process [3]. The purity requirements may be very low for the production of cellular metals. Impurities in precursor material prepared for powder-compact foaming, as well as for foaming in the melt, might be advantageous, as long as they act as nuclei for the formation of pores. There might be even an up-grading of lowquality scrap when used for the production of foamed metals [5]. The Ti remaining from the blowing agent (usually I0.5 wt.-%) is soluble below 0.12 wt.-% at the peritectic temperature of the binary aluminum melt [1] and does not degrade the quality of the alloy, but provides a grain-refining effect during solidification. ALPORAS foam contains about 2 wt.-% Ca, which is an element to be restricted below 0.1 wt.-% in all cast alloys. Ca will be partly oxidized and thus transferred into the dross, but some care has to be taken in the mix of ingredient scrap for not exceeding the specified impurity levels for the secondary alloy. The impurity levels of secondary aluminum cast alloys are not as stringent [1,3], so that scrap of the common types of cellular aluminum can be added to the remelting furnace. 2.4.2

Recycling of Cellular Metal Matrix Composites

Cellular aluminum produced by foaming particulate-reinforced melts, like the Cymat process [6] (formerly developed by Alcan [7] and Hydro [8]), the FORMGRIP process [9], and the shape foaming technique COMBAL [10] may be collectively named MMC foams. It might be of interest to recycle the MMC matrix of the foam without significant reduction of the particle content, because of the economic value of reclaimed MMC based on the primary processing cost to overcome the nonwettability. Any reuse of MMC saves the effort necessary to bond the two components together during processing. Originally, this type of foam was a spin-off of particulate-reinforced aluminum processing, consequently it has been proposed to reuse particle-reinforced aluminum alloys in the production of aluminum foam [11]. One advantage of this recycling route is that the specification requirements

29

30

2.4 Recycling of Cellular Metals

for the production of metallic foams, may not be as stringent as placed on MMC for bulk components, thus higher quantities of oxide skins and other impurities may be tolerated, or are even advantageous in foamable aluminum. Figure 2.4-1 shows the material flow cycle for discontinuously reinforced metals and cellular metals made from MMC indicating the possible interactions between these two cycles: x

x

x

Remelted MMC, with, or without cleaning treatments, can be used as a base material for the melt foaming processes and for FORMGRIP. Any secondary alloy, including that reclaimed from MMC melts, can be used for production of cellular structures by any of the known production methods. Scrap from MMC foams can be introduced into the MMC cycle, if quality requirements are met.

The same rules have to be obeyed for the recycling of MMC foams as for the MMC matrix [11] in addition to the pretreatment (compaction and drying) to reduce gas evolution. Two main problems have to be tackled when remelting MMC. x x

The reactivity of the reinforcement with the melt increases with temperature. The dewetting tendency of the reinforcement limits conventional melt cleaning methods.

Figure 2.4 -1. Recycling of discontinuously reinforced metals and of metal foams based on MMC, indicating the reuse of secondary MMC for the processing of foamed metals either by the powdercompact method, or by the melt-foaming technique.

2 Material Definitions, Processing, and Recycling

The reaction between 6xxx type wrought alloys and alumina reinforcements is driven by the Mg content forming MgAl2O4, spinel. An original level of approximately 2 vol.-% spinel seems to stabilize at just above 3 vol.-% after several remelting cycles; this does not influence the mechanical properties significantly [12], but may increase wettability and, consequently, reduce foamability. SiC-reinforced wrought alloys cannot be remelted without severe aluminum carbide formation at the interfaces. The formation of Al4C3 would be detrimental as it significantly reduces the corrosion resistance of the component. Furthermore, it affects the foamability by increasing the viscosity of the melt and above all by providing wettability. Nonwettability of the additives is necessary for the trapping of gas bubbles. In the case of Al casting alloys containing 7 12 wt.-% Si reinforced by SiC, there is the chance to conserve the integrity of SiC by keeping the melt temperature below 750 hC as recommended for primary foundry technology [13]. A detailed study of the recycling of SiC-particle reinforced Al Si casting alloys is given elsewhere [14], where the quality criteria of the melt are given and remelting, recycling, and holding practices are described. x x

x x x

x x

Dry, pre-heated scrap can be added to the melt between 700 and 750 hC. During a rest period, usually more dross is formed than on primary material. It contains mainly oxides and SiC-particles without reducing significantly their content in the melt. The dross has to be skimmed. An impeller is introduced to produce strong movement under the surface skin. Fluxing and degassing with argon (SF6 may also be used) to remove oxides and reduce the hydrogen content. The melt is allowed to sit and then skimmed. The melt is mechanically agitated, without forming a vortex, to distribute the SiC particles homogeneously.

No loss in particle content was reported and the removal of porosity, oxide films, and hydrogen were efficient. The amount of dross generated is relatively high and may amount to more than 10 % of the total weight. If the ceramic particles should be removed from the aluminum melt, conventional salt addition, or fluxing techniques (as are executed to remove oxide films [14]) can be applied. Gravity settling allows the fluxed ceramic ingredients to float to the dross at the top of the aluminum melt. Rotary salt furnace technology is an established reclamation process to recover aluminum from various mixtures, including particle reinforced metals; however, this requires 20 50 wt.-% salt [13]. Both wrought and foundry alloys and even machining chips can be recovered using this technique. Recovery of about 80 % of the available aluminum can be expected [15]. The efficiency of particle removal by fluxing is related to the probability of contact between the ceramic constituent and the flux. Duralcan, a supplier of particulate-reinforced aluminum, proposes to incorporate the salt into a melt agitated by gas injection [16]. Thus dewetting is achieved with much smaller salt additions (I1 wt.-% for alumina and about 1.5 wt.-% for SiC) and in combination with

31

32

2.4 Recycling of Cellular Metals

the adsorption of gas to the reinforcement also accelerates particle separation by floating, where it can be skimmed off. 2.4.3

Conclusions

There are the following possibilities for recycling, or reuse of cellular metals (especially cellular aluminum). x

x

x

x

Recycling of unreinforced cellular metals can be carried out as for packaging material (foils), or shredder scrap, by remelting, with an efficiency probably reduced to 80 % to produce bulk cast products from the secondary metal. In the case of recycling ALPORAS, the impurity level of Ca has to be controlled. Recycling of MMC foams can be done by extracting the matrix metal for conventional secondary products. The reinforcement may be segregated to the dross and deposited. Recycling of MMC foams can alternatively be achieved by remelting according to the precautions for MMC recycling, but at a reduced efficiency due to the increased oxide content to produce MMC foams again. The foam production itself may be based on an up-grading of secondary material with higher contents of impurities that increase foamability. In particular, the cycles for MMC and MMC foams can be closely related.

References

1. Grundlagen und Werkstoffe, Aluminium Taschenbuch, Vol. 1, Aluminium Verlag, DuÈsseldorf 1995. 2. American Society of Materials, Proc. 4th ASM Int. Conf. Recycling of Metals, 17 18 June 1999, Vienna, ASM International, Metals Park, OH. 3. K. Krone, Aluminium Recycling, Verein Deutscher Schmelzhuetten e. V., DuÈsseldorf 2000. 4. M. Strini, Private communication, ARCLeichtmetall Kompetenzzentrum Ranshofen, Austria 1996. 5. H. P. Degischer, F. Simancik, ªRecyclable Foamed Aluminium as an Alternative to Compositesº in Environmetnal Aspects in Materials Research, H.Warlimont (ed), DGM, Oberursel 1994, p. 137 140. 6. Cymat Corporation, Mississauga, Canada 2000, http://www.cymat.com.

7. I. Jin, L. D. Kenny, H. Sang, US Patent 5 112 697, 1992. 8. W. W. Ruch, B. Kirkevag, NO Patent 1989, World Patent wo 91/01387, 1991. 9. V. Gergely, T. W. Clyne, ªA Novel MeltBased Route to Aluminium Foam Productionº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 83 89. 10. D. Leitlmeier, H. Flankl, ªDevelopment of a New Processing Technique Based on the Melt Route to Produce Near Net Shape Foam Partsº in Proc. METFOAM 2001, MIT Verlag, Bremen 2001, p. 171 174. 11. V. Gergely, H. P. Degischer, T. W. Clyne, ªRecycling of MMC and Production of Metallic Foamsº in Comprehensive Composite Materials, Vol. 3, T. W. Clyne et al. (eds), Elsevier, London 2000, p. 797 820.

2 Material Definitions, Processing, and Recycling 12. D. M. Schuster, M. D. Skibo, R. S. Bruski, and Fabrication of Light Metals and Metal R. Provencher, G. Riverin, ªThe recycling and Matrix Composites, Montreal, TMS, 1992, p. 598 604. reclamation of metal-matrix compositesº 15. T. F. Klimowicz, ªThe large scale commerJ. Metals 1993, 45(May), 26 30. cialization of aluminum natrix compositesº 13. Duralcan, Duralcan Composite Casting J. Metals 1994, Nov, 49 53. Guidelines, Duralcan USA, San Diego, CA 16. Duralcan, Aluminium Recovery from Metal 1990. Matrix Composite Scrap, Duralcan USA, Novi, 14. R. Provencher, G. Riverin, C. Celik, Michigan 1996. ªRecycling of Duralcan Aluminium Metal Matrix Compositesº in Proc. Adv. Production

2.5

The Physics of Foaming: Structure Formation and Stability

C. KoÈrner, M. Arnold, M. Thies, and R. F. Singer

A foam is a dispersion of gas bubbles in a liquid in which the bubbles are deformed due to their mutual interaction. Cellular metals produced via gas bubbles in liquid metal are commonly named metal foams although they do not strictly meet the definition above after solidification. Owing to the surface energy necessary to form the metal±gas interface a foam is never in equilibrium and hence permanently trying to lower the internal energy by reducing the internal surface. That is, the cellular structural state of a foam evolves with time and its actual structure is a function of its history including all thermal and mechanical influences. The foam structure is normally strongly disordered and evolves by some combination of three basic mechanisms: bubble coalescence via film rupture; bubble coarsening via diffusion of gas from smaller to larger bubbles; and drainage downwards and out from the foam in response to gravity [1]. It is only in recent years that some progress has been made towards an understanding of the basic mechanisms governing the temporal evolution of foams [1±5]. Owing to their opacity and the high temperatures, in-situ observation of the structure evolution of metal foams is difficult [6]. Fortunately, the solidification process is in general much faster than the evolution processes at least as far as the evolution is not caused by expansion. That is, nearly full information of the foam formation process can be extracted from ex-situ investigation of foamed samples in different stages of expansion.

33

34

2.5 The Physics of Foaming: Structure Formation and Stability

2.5.1

Isolated Gas Bubble in a Melt

Since a foam consists of interacting gas bubbles it is helpful to consider in a first step an isolated gas bubble in an infinitely extended fluid. The dynamics of a spherical bubble with radius R is described by the Rayleigh equation [7,8] S RR

R_ 3 _2 1 2s (Pbubble s s PT ) R S 4v ˆ R 2 r R

(1)

where Pbubble ˆ bubble pressure, PT ˆ equilibrium pressure in the liquid, s ˆ surface energy, n ˆ kinematic viscosity, r ˆ density. The left hand side of Eq. (1) describes the inertia and viscous forces that both delay bubble growth. Neglecting viscous effects the time for the formation of a bubble in aluminum with radius R ˆ 1 mm at a bubble overpressure of DP ˆ 10 4 bar is given by [7] r r (2) ˆ 0:015s t ˆ 0:915 R DP That is, inertia effects delaying bubble expansion can be neglected if foam formation is on a time scale of seconds. The contribution of viscous forces for liquid metals is normally very small, for example about 4nr(R/RÇ) z 10 6 bar with RÇ ˆ 1 mm/ s; R ˆ 100 mm; n ˆ 1 mm2/s. On the other hand, if foaming takes place in the semi-liquid state, where the viscosity of the metal is several orders of magnitude higher than in the liquid state, viscous forces might delay bubble expansion. Bubble expansion takes generally more than one second for commercially known foaming methods for metals [9]. In this case, the viscous and inertia forces can be neglected and the Rayleigh equation reduces to pressure equilibrium at the gas±liquid interface Pbubble ˆ PT S 2

s s ˆ P0 S rgh S 2 R R

(3)

where g ˆ gravity constant, P0 ˆ ambient pressure, h ˆ depth. The pressure contribution resulting from the surface energy (s ˆ 0.2 N/m for Al) is 0.04 bar and 4 bar for bubble diameters of 100 mm and 1 mm, respectively. For h ˆ 100 mm the hydrostatic pressure is about 0.02 bar. Owing to gravity there is a pressure gradient present in the melt that deforms the bubble and makes it move. The bubble is accelerated until a stationary velocity, v, is reached where the resulting viscous forces balance the buoyant forces (Fig. 2.5-1). For nearly spherical bubbles the rising velocity v can be calculated from Stokes' law [7] s rgR2 Q v ˆ for R II (4) 3h rpg where h ˆ nr ˆ dynamic viscosity.

2 Material Definitions, Processing, and Recycling Figure 2.5-1. Velocity field around a rising bubble in a liquid. The velocity and deformation of the bubble depends on the viscosity of the melt, the surface tension, and the bubble size.

For a pure aluminum melt and bubble radii R of 100 mm and 10 mm the rising velocity is about 1 cm/s and 100 mm/s, respectively. Additives in the fluid like SiC or Al2O3 particles influence the movement of the bubbles and are able to stabilize them [10±12]. They have an effect on both the viscosity of the melt and the surface tension. How these particles actually operate and how their action can be optimized is not yet understood and still a matter of research. A gas bubble grows or shrinks due to gas exchange with the surrounding melt [13]. There is a gas flow from the liquid into the bubble if the concentration of dissolved gas in the liquid, as a result of the decomposition of a foaming agent for example, is higher than the equilibrium concentration in the liquid given by Henry's law for a given gas pressure in the bubble. Since hydrogen, which is preferentially used as foaming gas, dissociates when dissolved in aluminum the equilibrium hydrogen concentration, ceq, at the gas±liquid interface is governed by Sievert's law, a special form of Henry's law [14] ceq ˆ 1:4 q 10s3 q 10s

2760 T

p Pbubble

mol p cm3 bar

(5)

where T ˆ temperature of the melt. 2.5.2

Agglomeration of Bubbles: Foam

A foam is an agglomeration of many gas bubbles taking a polyhedral form due to their mutual interaction (Fig. 2.5-2). Usually, the volumes separated by thin walls are named cells. As mentioned before a foam is not a static structure but always evolving towards a lower internal energy. That is, already during the formation of a foam there are processes going on which try to alter the structure. In a pure liquid these processes are so fast that the development of a foam is not possible. For this reason additives have to be added to stabilize the foam. Foams made without a suitable additive boil, that is, the development of long-lasting membranes is not possible and the

35

36

2.5 The Physics of Foaming: Structure Formation and Stability Figure 2.5-2. Cell structure of an aluminum foam produced by the FORMGRIP process foamed under different conditions: a) porosity, 79 %; mean cell diameter, 1.9 mm; b) porosity, 88 %; mean cell diameter, 3.1 mm. The arrow marks a residual portion of a ruptured cell wall [30].

2D-lattice Boltzmann simulation of the growth of bubble nuclei by in-situ gas generation. The cell walls are not stabilized, so two bubbles coalesce if the cell wall reaches a

Figure 2.5-3.

critical lower value. The melt boils, the number of bubbles decreases, and gas is lost to the environment. The structure collapses once a critical expansion factor is reached [31].

structure is unstable (Fig. 2.5-3). In order to obtain a foaming material additives have to be added to the liquid, which slow down cell-wall rupture [15]. Consequently, a metal foam never consists of a pure metal. There must always be additives like SiC or Al2O3 present [11,16]. These additives are either added deliberately from outside [11], produced during processing by oxidation [17], or are already present in form of oxides if metal powders are used [18]. There are two different strategies to introduce the cell forming gas into the melt: by injection through a nozzle [11,19] or by in-situ gas segregation or generation [9,17]. The latter can be achieved by a chemical decomposition of a foaming agent or by creation of a supersaturation of gas in the melt. If foaming is realized by gas injection the gas bubbles are directly created without bubble nucleation and growth. The bubble size is determined by various parameters such as the nozzle geometry, the gas flow rate, and the impeller speed. Experience shows that the bubbles generated are relatively large. The bubble shape depends on the viscosity of the melt, the bubble size etc. Foaming by in-situ gas generation starts with homogeneous or heterogeneous bubble nucleation followed by bubble growth by gas diffusion into the nuclei [13] (Fig. 2.5-4). The rate at which bubbles nucleate homogeneously, NÇ0, is given by [20] N_ 0 ˆ c0 f0 es

DGhom kT

with DGhom ˆ

16ps 3 3DP2

(6)

2 Material Definitions, Processing, and Recycling

Figure 2.5-4. Expansion stages of an AlMg1 foam with 0.4 % TiH2 produced by powder compaction. By applying a high ambient pressure of 100 bar during heating bubble nucleation was suppressed until the sample was

completely liquid. Already at the very beginning of foam expansion coalescence occurs frequently indicating that the initial number of nuclei will not have much influence on the residual foam structure.

where c0 ˆ concentration of gas molecules, f0 ˆ frequency factor of gas molecules joining the nucleus, k ˆ Boltzmann constant, DGhom ˆ activation energy for homogeneous nucleation, DP ˆ gas pressure resulting from the dissolved gas following Sievert's law. Heterogeneous nucleation occurs when a bubble forms at an interface between two phases, between a ceramic particle and the melt, for example. The rate for heterogeneous nucleation, NÇ1, is given by [20] N_ 1 ˆ c1 f1 es

DGhet kT

(7)

where c1 ˆ concentration of heterogeneous nucleation sites, f1 ˆ frequency factor of gas molecules joining the nucleus, DGhet ˆ activation energy for heterogeneous nucleation. In the presence of heterogeneous nucleation sites this type of nucleation will be favored over homogeneous nucleation because of its lower energy barrier. Potential nucleation sites are the foaming agent particles and the particles present for foam stabilization and alloying [18]. For polymers it is known that the nucleation rate can be influenced by the processing parameters [20±22]. A systematic investigation of the nucleation rate for metals as a function of the processing parameters is yet missing but it is expected that the mechanisms are very similar to those in polymers. Owing to the presence of additional particles in the melt, heterogeneous nucleation is probably the main nucleation mechanism. The shape of the starting gas bubbles changes during growth from spherical to polygonal (Fig. 2.5-4). From a pure energetic point of view one would expect the formation of Kelvin or Weaire±Phelan cells [3], which minimize the total internal surface and hence the total internal energy. Actually, most of the cells are far away from these ideal structures. That is, the complex formation process of the foam does not necessarily lead to the energetically preferred structure. When two cells coalesce due to cell-wall rupture the resulting cell is strongly deformed (Fig. 2.52b). It is hampered to take an energetically more suitable form due to the presence of the other cells. As a result, the cell geometry is in general not equilateral and the

37

38

2.5 The Physics of Foaming: Structure Formation and Stability

cell walls are curved due to the pressure difference of neighboring cells. One effective way to characterize the cell structure is by the shape factor, F, calculated from a 2D cut through the foam [23] (see also Section 4.1) F ˆ

n 4p X ai n i li2

(8)

where n ˆ total number of cells, i ˆ cell number, li ˆ cell-boundary length, ai ˆ cell area. The shape factor describes the deviation of the cell geometry from a circle with F ˆ 1. It is found that F decreases much more with decreasing foam density than expected from the transition of spherical to polygonal cells (Fig. 2.5-5) [23]. That is, the deformation of the cells and the occurrence of bent cell walls increases continuously during foam expansion. Thus, polygonal cell structures for different densities are not self-similar. A further mechanism that might lead to a structural change of the foam is coarsening analogous to Ostwald ripening. As a result of the pressure difference of about 10 3 bar of neighboring cells with different size, there is a concentration gradient (see Eq. 5) and therefore a flow of dissolved gas from smaller to larger cells. Hence, small cells shrink and large cells grow, so the foam structure coarsens [24]. This effect is very pronounced for aqueous foams due to the small cell wall thickness (about 100 nm). Numerical calculations [25] confirm the experimental finding that this kind of coarsening is an effect of secondary importance on the relevant time scale for the production of aluminum foams with a typical cell wall thickness of 50±300 mm. On the other hand, gas loss by diffusion to the environment can be substantial for long holding times if the hydrogen partial pressure in the ambient atmosphere is zero (Fig. 2.5-6). The formation of an aluminum foam by in-situ gas generation is from the very beginning intimately correlated with cell coalescence (Fig. 2.5-4). If foam expansion would be a mere enlargement of the structure without cell coalescence, so the number of cells is constant during foaming, one would expect the mean pore diameter, D, to be proportional to rrel1/3 (rrel ˆ relative foam density). The

Mean shape factor, F, of the cell structure as a function of the foam density for an AlSi10Mg0.6 foam produced by powder compaction [23]. Energetically optimized cell structures would show a form factor equal to that of a pentagon.

Figure 2.5-5.

2 Material Definitions, Processing, and Recycling Figure 2.5-6. Cell structure of an Alulight foam after heating to 670 hC under an ambient pressure of 100 bar and subsequent foaming by pressure reduction to 11 bar. The thick metal layer at the surface is the result of gas loss to the environment during the 15 min in the liquid state.

last expression is deduced from a simple cubic plate model for the cells with the assumption that the volume of the cell-forming material per cell is constant. Actually, the experimental data (see Fig. 2.5-7) is much better fitted by D ˆ

1s

d 3d   p for rrel II 1 3 1 s rrel rrel

(9)

which follows from a cubic plate model assuming a constant mean cell-wall thickness, d. That is, the mean cell-wall thickness is constant during expansion. It depends on the alloy and is found between 50 mm and 300 mm for aluminum foams. Consequently, given a fixed alloy cell size and relative density are intimately related and can hardly be influenced by processing parameters [23]. In order to generate aluminum foams with a lower density and smaller cells the mean cellwall thickness has to be reduced. How the cell walls of metal foams are stabilized by the particles and which properties of them (quantity, size, form) determine the mean cell-wall thickness is not yet understood and a matter of flow research [18]. Coalescence, rupture of a cell wall, is a mechanical process that depends on the mechanical stability of the membrane. It has statistical character and occurs if a local fluctuation of the film thickness leads to faster local thinning because it is not compensated by restoring forces. The different physical mechanisms that are responsible for the mechanical stability of a membrane have been extensively investigated for aqueous films [5,15]. Experimental studies of the stability of metal membranes are not known in literature. Physical forces between the two surfaces of the film like the van der Waals or electromagnetic interaction are only relevant

Figure 2.5-7. Mean pore diameter as a function of the reciprocal foam density for a wrought alloy (open symbols) and a cast alloy (full symbols) foam produced by powder compaction. The samples were foamed at various ambient pressures. The full lines give the results for a cubic plate model (Eq. 9) with constant mean cellwall thickness of 180 mm for the wrought alloy and 130 mm for the cast alloy [31].

39

40

2.5 The Physics of Foaming: Structure Formation and Stability

for very thin films (I1 mm). For thicker films, as it is the case for metal foams, there are two effects that might lead to a kind of elasticity of the membrane. The Gibbs' effect [15] takes into account that a local thinning of the membrane leads to a local thinning of the surfactants. As a result, the surface energy increases at this point leading to a restoring force. The Marangoni effect [15] describes that a gradient of the surface energy leads to a flow of surfactants taking with it a thin film of fluid in the direction of lower concentration. In order to maximize both effects the surfactant should minimize the surface energy. At the moment, it is not clear whether the stability of metal membranes is based on one of these two mechanisms. In metals, melt surfaces are covered with oxides and other particles that might have the required effects on the surface energy. The origin for cell-wall instability is cell-wall thinning, which can be traced back to different mechanisms. The first one is simply related to foam expansion itself. If a cell expands the cell-wall thickness decreases due to mass conservation. During foam expansion the principal mechanism for cell-wall thinning is by growth. The second mechanism of cell-wall thinning is drainage due to gravity and capillary forces. Drainage determines the foam stability in the absence of further expansion due to gas release, that is, the time that a given foam structure is maintained without destruction. Gravity induces a melt flow from the top to the bottom of the foam and generates a density gradient [4,5]. Neglecting capillary forces, the draining velocity, vD, can be estimated in a first approximation by the balance of gravity and viscous stress from shear flow within the Plateau borders [1] vD Z

grd2edge h

(10)

That is, the draining velocity increases with the cell-edge thickness, dedge. Capillary forces arise due to the different curvature of the interfaces. They force the melt from the cell membranes to the cell edges (Fig. 2.5-8). The rate of cell-wall thinning due to this pressure gradient can be modeled using a Reynolds-type equation for the flow between two circular parallel discs with immobile wall surfaces [5] x_ ˆ s

2sx 3 3hR2 RPB

(11)

where x ˆ cell-wall thickness, 1/RPB ˆ curvature of the Plateau border, R ˆ radius of the disc. Integration of the last equation shows that cell walls of 100 mm in pure aluminum reduce to 1 mm in I1 s. This result is in contrast to experimental observations where metal foams are held in the liquid state for several minutes without a structural change. How a metal foam attains this high stability is not yet understood. From a practical point of view foam collapse is very important. Foam collapse usually proceeds from the outer surface to the interior and is closely related to the appearance of a dense metal layer at the bottom (Fig. 2.5-9).

2 Material Definitions, Processing, and Recycling Cellular automaton simulation of the material transport from regions with lower curvature to higher curvature due to capillary forces.

Figure 2.5-8.

Figure 2.5-9. Collapse of an aluminum foam (powder route precursor AlSi10Mg0.6). Collapse proceeds from the outer surface to the interior, the metal of the collapsed cells drains down to the bottom. Left) the sample was heated to 665 hC at 1 bar ambient pressure and further expanded at constant temperature by pressure reduction to 500 mbar. Right) the sample was heated to 665 hC at 1 bar ambient pressure and held at constant temperature for 30 min.

Collapse happens if the amount of gas loss to the environment by diffusion or by cell-wall rupture is substantial and not compensated by in-situ gas generation. One has to distinguish between collapse by growth and collapse by aging, due to a long holding time. Foam collapse by growth occurs when a critical expansion factor is reached. In this case, cell-wall rupture on the foam surface leads to a pronounced loss of gas to the environment. Collapse by aging results from gas loss to the environment by diffusion and cell-wall rupture due to drainage by gravity and capillarity. For the production of foam parts foam rheology plays a crucial role. The rheological bearing is important when mechanical forces are present. During foam formation there are always mechanical forces acting on the foam. These might result from a spatial restriction like a mold, from an injection molding process [26], or a conveyer belt on which the foam is transported before solidification [11]. The mechanical response of foams to applied forces is very complex. Foams show wall slip, compressibility, and non-Newtonian viscoelasticity [27]. They exhibit a nonzero shear modulus although made out of gas and liquid, which both individually display a vanishing shear modulus. Consequently, a foam shows a very complex rheological behavior including bubble deformation, rearrangement, and avalanche processes [28,29]. The resulting pore structure is in general not isotropic but orientated in foaming direction. This behavior is even more pronounced if the foam fills a complicated mold with dimensions of the same order as the mean pore dia-

41

42

2.5 The Physics of Foaming: Structure Formation and Stability Figure 2.5-10. AlSi10Mg0.6 foam produced by powder compaction. Since heating was not homogenous, the internal structure represents different stages of the foaming process. The expansion of the central region leads to a compression of the exterior cells that were formed before.

meter. As a result, pores are deformed and also destroyed during mold filling by mechanical forces or a non-uniform foaming velocity (Fig. 2.5-10). Hence, the internal foam structure is strongly influenced by the particular production procedure.

References

1. A. Saint-Jalmes, M. U. Vera, D. J. Durian, ªUniform foam production by turbulent mixing: new results on free drainage vs. liquid contentº Eur. Phys. J. B 1999, 12, 67±73. 2. S. A. Koehler, S. Hilgenfeld, H. A. Stone, ªLiquid flow through aqueous foams: The node-dominated foam drainage equationº Phys. Rev. Lett. 1999, 82(21), 4232±4235. 3. A. M. Kraynik et al. ªFoam Micromechanicsº in Proc. Foams and Emulsions, Cargese, Corsica; Kluwer, Dordrecht 1999. 4. S. Hutzler, ªThe Physics of Foamsº, Department of Physics, University of Dublin 1998. 5. A. E. Bhakta, E. Ruckenstein, ªDecay of standing foams: drainage, coalescence and collapseº Adv. Colloid Interface Sci. 1997, 70, 1±124. 6. J. Banhart, et al. ªMetal foam evolution studied by synchrotron radioscopyº Appl. Phys. Lett. 2000. 7. L. D. Landau, E. M. Lifschitz, Hydrodynamik, 3rd ed, Akademie-Verlag, Berlin 1974. 8. S. F. Edwards, K. D. Pithia, ªA model for the formation of foamsº Physica A 1995, 215, 270±276.

9. I. Duarte, J. Banhart, ªA study of aluminium foam formation ± kinetics and microstructureº Acta Met. 2000, 48, 2349±2362. 10. V. Gergely, T. W. Clyne, ªThe FORMGRIP process: foaming of reinforced metals by gas release in precursorsº Adv. Eng. Mater. 2000, 2(4), 175±178. 11. J. T. Wood, ªProduction and Application of Continuously Cast, Foamed Aluminumº in Proc. Fraunhofer USA Metal Foam Symp. 7±8 October 1997, Stanton, DW. 12. G. Kaptay, ªInterfacial Criteria for Ceramic Particle Stabilised Metallic Foamsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 141±146. 13. A. Arefmanesh, S. G. Advani, ªDiffusioninduced growth of a gas bubble in a viscoelastic fluidº Rheologica Acta 1991, 30, 274±283. 14. P. Lutze, J. Ruge, ªWasserstoff in Aluminium und seinen Legierungenº METALL 1990, 65, 649±652. 15. H. Lange, SchaÈume und ihre StabilitaÈt, VDI-Berichte, 1972, 182, 71±77.

2 Material Definitions, Processing, and Recycling 16. S. W. Ip, J. Wang, J. M. Toguri, ªAluminium foam stabilization by solid particlesº Canad. Metall. Q. 1999, 38, 81±92. 17. T. Miyoshi et al. ªAluminum Foam, ALPORAS: The Production Process, Properties and Applicationsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999. 18. P. Weigand, ªUntersuchung der Einfluûfaktoren auf die pulvermetallurgische Herstellung von AluminiumschaÈumenº, FakultaÈt fuÈr Bergbau, HuÈttenwesen und Geowissenschaften, RWTH, Aachen 1999. 19. P. Asholt, ªAluminium Foam Produced by the Melt Foaming Route Process, Properties and Applicationsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 133±140. 20. J. S. Colton, N. P. Suh, ªNucleation of microcellular foam: theory and practiceº Polym. Eng. Sci. 1987, 27(7), 500±503. 21. H.-Y. Kwak, Y. W. Kim, ªHomogeneous nucleation and macroscopic growth of gas bubble in organic solutionsº Int. J. Heat Mass Transfer 1998, 41(4±5), 757±767. 22. C. B. Park, L. K. Cheung, ªA study of cell nucleation in the extrusion of polypropylene foamsº Polym. Eng. Sci. 1997, 37(1), 1±10. 23. C. KoÈrner et al., ªInfluence of processing conditions on morphology of metal foams produced from metal powderº Mater. Sci. Technol. 2000, July-August, 781±784.

24. C. Monnereau, M. Vignes-Adler, ªDynamics of 3D real foam coarseningº Phys. Rev. Lett. 1998, 80(23), 5228±5231. 25. C. KoÈrner, R. F. Singer. ªNumerical Simulation of Foam Formation and Evolution with Modified Cellular Automataº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999. 26. F. Schorghuber, F. Simancik, E. Hartl, US patent 5 865 237, 1999. 27. W. Hanselmann, E. Windhab, ªÛber das Flieûen von Schaum in Rohren; Foam flow in pipesº Appl. Rheol. 1996, Dezember, 253±260. 28. D. J. Durian, ªFoam mechanics at the bubble scaleº Phys. Rev. Lett. 1995, 75(26), 4780±4783. 29. D. J. Durian, ªBubble-scale model of foam mechanics: Melting, nonlinear behaviour, and avalanchesº Phys. Rev. E 1997, 55(2), 1739±1751. 30. V. Gergely, ªMelt Route Processing for Production of Metallic Foamsº, Department of Materials Science and Metallurgy, Cambridge 2000. 31. M. Arnold et al., ªExperimental and Numerical Investigation of the Formation of Metal Foamº in Proc. Materials Week 2000 [http://www.materialsweek.org/proceedings/ index.htm].

2.6

Infiltration and the Replication Process for Producing Metal Sponges

C. San Marchi, A. Mortensen

The process of replicating a structure has been known to the metallurgist for centuries. For example, casting can be thought of as a replication procedure in which a metal is used to reproduce the negative form of the mold. In the study of porous materials, however, replication refers to a process used to replicate the open-pore architecture of a porous material.

43

44

2.6 Infiltration and the Replication Process for Producing Metal Sponges

2.6.1

Replication

More specifically, this process can be defined as a general three-step procedure for the production of highly porous materials (Fig. 2.6-1). The three steps are: 1. preparation of a removable pattern; 2. infiltration of the pattern followed by solidification (or an alternative process, such as curing or cross-linking, which rigidifies the infiltrate); and 3. removal of the pattern. In some cases, a fourth step, such as pyrolysis, may be required to transform the porous network into the desired phase. In this text, we focus on the use of the replication process for the production of cellular metals with open porosity. Several

Figure 2.6-1.

Diagram of the replication process.

2 Material Definitions, Processing, and Recycling

authors have noted that metal (or metallic) sponge is perhaps the most appropriate terminology for these materials as both the term ªfoamº and ªcellularº imply a closed-cell architecture [1,2], while porous metals produced by replication must have an open-pore network. We will thus refer to metals with open porosity of any density I0.8, produced by replication, as metal sponge. This process is distinct from deposition techniques, such as those used by Inco Limited (Swansea SA6 5QR, Wales, UK) to produce porous nickel substrates, called Incofoam [3]. In that process, a temporary pattern is used, but the pore space is not replicated: instead, the pattern is coated and the pore space only partially filled. Sintering methods that utilize a space holder are also not considered replication for two reasons: the micro-architectural features of the pores are determined by the metal powder size in addition to the space-holding material and infiltration is not one of the processing steps. The so-called lattice block materials (LBM) are prepared using polymer patterns of truss structures and investment techniques; thus the lattice block is rather an engineered structure and cannot really be considered a metal sponge, which can be ªshapedº and ªformedº while maintaining the statistics of its properties, as long as the cell sizes are of millimeter or more dimensions. For more details on lattice block materials contact JAMCORP (17 Jonspin Road, Wilmington, MA 01887-1020 USA). Although we limit this discussion to metals, we note in passing that the polymeric sponge technique used to produce porous ceramics also does not replicate the pattern and should not be considered a replication process. In a metallurgical context, the replication technique can be used to produce metal sponge that is difficult or impossible to produce by other processing methodologies. Replicated metal sponge, for example, by necessity has an open-pore structure, which is a fundamental difference compared to most commercially available foamed metals. The structure or architecture of metal sponge produced by replication is flexible and determined by the pattern: porosity as high as 98 % [4] and as low as 55 % [2] for different pattern materials have been reported and pore sizes as small as 10 mm have been achieved [5]. In addition, metal sponge can be produced from virtually any alloy that can be cast (provided a suitable pattern material exists). The replication process has been used extensively for the production of various porous materials including carbon [6], silicon carbide [7], aluminum alloys [2,4,5,8±13], magnesium alloys [14,15] and alloys based on iron and nickel [4,16]. In the following sections we provide details about the production of metal sponges by replication techniques. We first describe the important physical phenomena that govern each of the three basic steps of the replication process (with some emphasis on sponge produced from salt patterns for which the most information exists in the literature). We then provide some physical and mechanical properties of metal sponge produced in this manner.

45

46

2.6 Infiltration and the Replication Process for Producing Metal Sponges

2.6.2

The Replication Process: General Principles Pattern Preparation The primary requirements of the pattern material are that it be sufficiently refractory at the casting temperature and that it be chemically stable when in contact with the melt. Additionally, after infiltration an open network must exist between the metal ligaments such that the pattern material can be removed. The choice of the pattern material necessarily determines the range of architectures that can be produced. Four types of pattern materials are described below: continuous refractory (investment), discontinuous refractory (pelleted casting sands), burnable (polystyrene and resin), and leachable (sodium chloride). Refractory investment casting material (continuous refractory pattern) is emerging as perhaps the most common space-holder for replication processing of lowdensity metal sponges [4,12±15]. A slurry of an appropriate investment is infiltrated into a preform that has the form of the desired metal sponge and that can be easily removed. Commercial polyurethane sponges (generally referred to as a foam) are typically used, as they are available with variegated properties in terms of porosity, pore size, and strut size (thickness of the ligaments or beams that make up the sponge) and can be easily burned out in air. Other preform materials can also be employed, provided that they can be removed without damaging the architecture of the investment. The main restriction here is that the investment must have a particulate size that is significantly smaller than the architecture to be replicated; also, its relative density must be sufficiently low that the solid investment grains can be removed from the metal±refractory composite. Investment casting is a well-developed technology that can be applied to almost any castable metal. Another conventional type of space holder is pelleted casting sand, or other granulated mineral (discontinuous refractory pattern) [16]. In this method casting sand is mixed with an organic binder to form comparatively coarse agglomerates that can then be filled into a mold to form the pattern. The porosity of the pattern is limited by the packing efficiency of the pellets, which are typically spherical. Maximum random packing efficiency of mono-sized spheres is about 0.64 [17] and can be greater for mixtures of different-sized pellets, although practical limits are determined by the necessity to remove the pattern after infiltration with the melt. Moreover, patterns of packed, discrete elements of this sort (as opposed to the continuous nature of investment pattern) must be infiltrated such that these space-holders can still be removed, that is they must not be completely embedded in the infiltrating metal; this is discussed below. In principle, pelleted casting sands can be used with any sand-castable alloy. A rather unusual pattern material is polystyrene [11] (burnable pattern), although any burnable space-holder can potentially be used in the same manner. Polystyrene spheres are coated with a resin and then filled into a mold before the resin is hardened. The resin acts to form the connected network between the spheres; this network is necessary for removal of the pattern. The pore size 2.6.2.1

2 Material Definitions, Processing, and Recycling

is determined by the size of the initial spheres (or particles) and the ratio of polystyrene to resin. This type of pattern has the advantage that it is not necessary to physically remove solid grains from the structure after infiltration, as the pattern is essentially burned away at the end of the process. On the other hand, this pattern must be infiltrated relatively cold to avoid burning of the pattern during infiltration (i. e., while the metal is still liquid) and is thus limited to low-melting alloys such as aluminum, magnesium, and zinc. The fourth class of pattern material is leachable: these patterns are removed by dissolution in an appropriate solvent. The process of dissolution (or leaching) is less restrictive on size and density than insoluble refractory materials. In practice however, patterns of leachable material are created from granules or powder, thus the density is related to the packing efficiency of the granules, which itself depends on the size (and size distribution) of the granules. Sodium chloride (NaCl) has been employed most extensively as a leachable pattern, because it is inexpensive and easy to handle. Sodium chloride patterns used for the production of porous aluminum were first reported [8,9] and patented [10] in the 1960s, and have advanced more recently [5] (there are also reports of their use for carbon sponge [6] and for SiC sponge [7], both with a pyrolysis step). Salt patterns are limited by their melting point; NaCl, for example, is limited to aluminum and lower-melting alloys, while NaF could potentially be used at temperatures greater than 900 hC. Additionally, highly concentrated saline solutions are generated during dissolution and can cause significant corrosion in some alloys. Salt grains also have the advantage that they can be sintered to enhance the connectivity of the salt, change the structure of the pattern, and create a free standing preform that can be handled and subsequently infiltrated [5±7]. The sintering step is not necessary, however, for two reasons: transient bonding of the grains (perhaps due to humidity in the salt [8]) may occur during preheating the salt prior to and during infiltration, and incomplete penetration of the melt locally where individual grains meet, provides the necessary open-network for salt removal. Sintering processes depend on a number of parameters, including particle size, temperature, atmosphere, residual stresses, and time. Such numerous process parameters might explain some of the varying observations in the literature with regard to the sintering of sodium chloride. Incidentally, these varying observations point to the fact that sodium chloride may be a good choice for a pattern material because of flexibility in controlling the sintering mechanisms and thus the microarchitectural features of the pattern. There is a consensus in the literature that large sodium chloride particles sinter predominantly by an evaporation±condensation mechanism, in which the necks between the particles grow without densification of the salt compact. Small particle compacts, on the other hand, can densify significantly during sintering, due to the predominance of other mechanisms where the center-to-center distances between particles can decrease, such as bulk diffusion [18±21]. The minimum particle size that can sinter without densification has been estimated to be about 150 mm [19,20]. Sintering in vacuum may promote the evaporation±condensation mechan-

47

48

2.6 Infiltration and the Replication Process for Producing Metal Sponges

ism for smaller particles [22] as supported by the pressure dependence that was noted for the rate of neck growth when non-densifying sintering mechanisms are dominant [23]. There are advantages to both classes of sintering mechanisms with respect to producing metal sponge. Non-densifying mechanisms, such as evaporation±condensation should develop a structure dictated by capillary equilibrium: these are well known [24]. The pore architecture in such a case is expected to be similar to the regular structures of polymeric sponge. Densifying mechanisms, on the other hand, provide a means to achieve relative densities significantly greater (and thus significantly lower for the sponge) than those attainable by packing and pressing of particles. Sintered salt densities as high as 90 % have been reported with nearly all the pores as open porosity, although for a particle size of 1 mm, which would pose challenges in the subsequent processing steps [25].

Infiltration Ideally, infiltration under the influence of gravity is preferred as it does not require special equipment or procedures. In most cases, however, the metal does not wet the pattern and some additional force must be applied to the melt to promote (or assist) infiltration and effect a uniform distribution of metal within the pattern. Vacuum and low-pressure assisted casting procedures are standard foundry technologies and, in many cases, these are sufficient for infiltration. Indeed, it has been reported that spontaneous infiltration is possible when infiltrating salt grains greater than 4 mm in size. Vibration slightly reduces the size of salt grains that can be infiltrated under gravity, while vacuum applied to the pattern with a slight overpressure on the melt has also been used to infiltrate grains as small as a few hundred micrometers in diameter [8]. The specific pressure required to initiate infiltration (the threshold pressure, P0) depends to a large extent on the size of the pores to be infiltrated and the volume fraction of these pores. A detailed physical description of infiltration is beyond the scope of this work; more detailed information is available elsewhere [26±28]. To the authors' knowledge, the pressure required to initiate infiltration has not been explored with specific emphasis on patterns used for replication processes; however, expressions derived for the threshold pressure in the infiltration of packed ceramic beds with pure aluminum should be directly relevant. Garcia-Cordovilla et al. offer a simple semi-empirical relationship [27] 2.6.2.2

P0 ‰MPaŠ z 16

f s 0:09 (1 s f )D

where f is the volume fraction solid (or in this context the fractional density of the pattern) and D is a characteristic diameter of the solid in micrometers. This relationship is based on data for particles in the range 10±100 mm packed to a density of 50±60 % and infiltrated with pure aluminum, but it should provide reasonable magnitude estimates of the pressures required for infiltration over a broader range

2 Material Definitions, Processing, and Recycling

of conditions since it contains the functional dependencies on f and D expected from theory [26±30]. This relation predicts that particles with an average diameter of 100 mm and packed to 75 vol.-% will require an applied pressure of a couple of atmospheres to initiate infiltration, while D ˆ 4 mm and f ˆ 0.98 requires the application of about one atmosphere of pressure to the melt, such that infiltration can be achieved by evacuating the pattern and taking advantage of atmospheric pressure. The degree to which the metal penetrates the pattern, particularly at the local level, is also an important consideration and obviously depends on the applied pressure. When the pattern material is porous, a very high applied pressure will cause the space between individual grains of investment to be infiltrated, such that these then cannot be removed. In a system with a wetting angle greater than ninety degrees, a low (yet finite) pressure will cause infiltration of larger pores within the pattern, yet cannot force the metal into small channels against adverse capillary forces. Thus, in patterns created from granulated materials such as pelleted sand, the regions near contacts between individual grains may remain uninfiltrated if the pressure is low enough. These open channels between adjoining discontinuous grains are necessary for the removal of the pattern. Control of the infiltration then is important to effect a uniform distribution of metal in the large channels of the pattern without penetrating the microstructural elements of the pattern when it is porous. Few details have been given in the literature about infiltration in the context of replication processing, although generally the techniques appear to be some form of vacuum or low-pressure assisted casting methods [4,12±16]. A modified die-casting method has also been used [11] and any other high-pressure casting methods such as squeeze casting should be appropriate. For example, gas-pressure infiltration at pressures up to 80 bar has been used to infiltrate patterns with small pores [5]. After infiltration is complete, the metal must, of course, solidify, which is an integral part of any casting process. Methods utilized to control solidification shrinkage depend on the specifics of the casting process, but generally consist of directional solidification in the case of gas-pressure infiltration or some type of riser or reservoir in general foundry methods.

Pattern Removal The pattern removal step depends on the characteristics of the pattern. Patterns from fine-grained ceramic powders such as investment casting compound and agglomerated silica pellets are typically removed by spraying water on the pattern± metal composite [12±16], such that the water physically breaks down the pattern into the small grains from which it is made. This requires penetration of the porous network by the spray, or at least that the fluid can ªwickº into the grain structure of the pattern so that it breaks down. For relatively fine (I1 mm) and dense sponges i10 %), however, it is unclear how efficient this process would be for sections many times the pore size. Additional methods such as (ultrasonic) vibration may also prove useful for removal of solid grains. 2.6.2.3

49

50

2.6 Infiltration and the Replication Process for Producing Metal Sponges

Polymer pattern materials can be removed by burning in air as is the case for polystyrene-resin patterns [11]. The cleanliness of this burning is an important issue in an industrial setting. These patterns, however, have the advantage that complex parts can be machined before removal of the pattern and without significant damage to the structure of the sponge. In some cases, leachable patterns can also be machined to complex geometries prior to leaching and without damaging the architecture of the sponge. In the case of salt, removal of the pattern is by immersion in water, causing dissolution of the salt. Dissolution is primarily a diffusive process, as the dissolved salt ions diffuse from their place-holding position into the water bath through the narrow channels in the sponge where the water is essentially stagnant. Thus, the rate and total time of dissolution depend strongly on the size of the specimen. Salt is more difficult to remove from small pores, particularly if gas is entrapped in the pores; this is the so-called ªgas lockº phenomenon, which can block the penetration of fluid into the porous network [8]. Corrosion of metal sponge during leaching of the pattern can be a problem due to the large surface area of the porous network, thus the salt concentration and the immersion time must be minimized. This is accomplished by simply changing the water periodically, however, it is important that the sponge is not drained at this point, as this will cause gas to be entrapped in pores and promote ªgas lock.º Additionally, impurities in the water should be controlled to avoid precipitation of other salts in these concentrated solutions. Aluminum alloys (the metals for which salt patterns are most applicable) tend to be relatively corrosion-resistant in salt solutions. The aluminum±copper alloys are among the least corrosion-resistant in salt solutions, but sponge can still be prepared from these alloys without degradation by corrosion. Electrochemical protection could also offer additional protection from corrosion. A large volume of water is not necessary as salt-saturated water is denser than distilled water, and hence falls to the bottom of the container where it remains in the absence of convection. As a result, during the dissolution process a large concentration gradient is maintained between the outer surface of the salt±metal composite suspended near the surface of the dissolution bath (but completely immersed) and the bottom of the container. For large pores and low-density sponge, mixing may modestly enhance dissolution if the velocity of the fluid in the porous network is affected. In most cases, however, this condition is not met and mixing the water primarily distributes the salt concentration and reduces the diffusion gradient in the water bath, in turn slowing the leaching process. The final stage of salt removal from the sponge is rinsing. This can be accomplished by flowing water through the structure, or simply by changing the water several times to incrementally remove the saturated fluid; this process is greatly facilitated by the higher density of salt solutions. Pressurized gas is also effective for removing the residual fluid in the sponge such that dissolved salts are not left in the structure when this water evaporates. Other methods may contribute to more efficient (faster) removal of salt, but these must enhance the rate of diffusion of the salt in the fluid. For example, ul-

2 Material Definitions, Processing, and Recycling

trasonic vibration has been proposed as a useful method as it should increase the rate of diffusion with the added benefit of freeing gas bubbles entrapped in the porous network [8]. 2.6.3

Physical and Mechanical Properties of Metal Sponge

Published reports of metal sponge produced by replication techniques are summarized in Table 2.6-1. Relevant details of the processes and properties of the resulting metal sponge are briefly described below in the context of the basic pattern technologies: continuous refractory, discontinuous refractory, burnable, and leachable.

Continuous Refractory Patterns A variety of metal sponges have been produced from commercial polyurethane preforms: aluminum alloys [4,12,13], magnesium alloys [14,15] and several alloys having melting points up to 1500 hC [4]. Infiltration has been conducted with vacuum or pressure-assisted investment casting techniques. The investment is removed by means of a water spray, although additional specifics have not been supplied in the literature. Metal sponge with volumes up to 1500 cm3 have been prepared in this way; in addition, components, such as modules for heat exchangers integrally cast with plates and tubes, have been demonstrated [4]. The porous metals produced with this methodology have porosity in the range 92±98 % and pores sizes as small as 0.85 mm, Table 2.6-1. Practical limits of replication with investment patterns, however, have yet to be clearly identified and may include a wider range of structural parameters than reported to date. Although size effects (including density) have not been systematically explored, compressive strength (plateau stress) of aluminum and magnesium sponge with about 97 % porosity have been reported to be less than 0.25 MPa and in accordance with prediction based on phenomenological relationships [12±15]. Strain rate sensitivity has also been reported for these materials although a complete interpretation of these data has not yet been offered [31,32]. 2.6.3.1

Discontinuous Refractory Patterns Cast-iron sponge has been produced using pelleted silica sand [16]. The size of the pellets can be varied from about 1 mm to over 5 mm. The porosity of the sponges is reported to be about 60 %, Table 2.6-1. It appears that gravity casting methods were used, perhaps assisted with vacuum. The pattern is removed with pressurized water, but it is unclear if the pellets can be removed from a material several centimeters in depth. Preliminary mechanical data in compression have been reported and feature a significant drop in load carrying capacity after about 2 % strain. Permeability tests have also been reported though no systematic conclusions have been drawn. Incidentally, a similar sponge-like material (from aluminum) was produced as early as the 1930s in Germany, except that the pattern was not removed [33]. 2.6.3.2

51

Al (SG91A)

Al (Cu, Zn, Fe, Ni, Co)

pig Fe

Al

Al

Investment of polyurethane sponge

Investment of polyurethane sponge

Pelleted casting sand

Polystyrene and resin

NaCl

Al alloys

* Represents range of properties as reported.

NaCl (presintered)

Mg (AZ91)

Investment of polyurethane sponge

Al

Metal

gas-pressure infiltration

gravity, vibration assisted, pressure assisted by vacuum

modified die casting

vacuum assisted

vacuum or pressure assisted

vacuum assisted

vacuum assisted

Infiltration technique

leaching

leaching

burning

pressurized water

(not reported)

water spray

water spray

Pattern removal

Summary of replication techniques used for the production of metal sponge.

Pattern material

Table 2.6-1.

0.01±3

0.45±1.45

0.15±5

1.2±3.7

1±5

0.85±2.5

4.5

4.5

Pore size (mm)

65±81

55±67

(60±63) full range not reported

73±86

60±63

92±98

93±96

97

Porosity (%)

Metal sponge characteristics*

[5]

[2]

[8]

[11]

[15]

[4]

[12, 13]

[14, 15]

Reference

52

2.6 Infiltration and the Replication Process for Producing Metal Sponges

2 Material Definitions, Processing, and Recycling

Burnable Patterns Aluminum sponge has been prepared from resin-bonded polystyrene spheres (Table 2.6-1) with porosity in the range 73±86 % and pore sizes in the range 1±4 mm [11]. Infiltration was conducted with a modified die-casting technique and the pattern was removed by burning in air. Properties of these metal sponges have not been reported. 2.6.3.3

Leachable Patterns Aluminum sponge was produced from NaCl as early as 1961 [8]. The patterns were prepared by packing salt grains in a mold and infiltrating by one of several techniques depending on the size of the salt grains: by gravity (i 3.4 mm), on a vibrating table (i 1.7 mm), or with an overpressure and simultaneous application of pressure (j 0.15 mm). The compressive strength of an A356 aluminum alloy sponge was observed to depend on the heat treatment and at 10 % strain varied in the range 20±30 MPa for porosity in the range 60±63 %. The porosity undoubtedly varied depending on the size (and distribution of sizes) of the salt grains. In an independent study, Banhart reports a range in porosity between 55 and 67 %; however, he does not provide any details about the processing other than that the pattern was leachable [2]. Some basic property indicators (mechanical response to compression, pressure drop and sound adsorption) are given in this latter report. Detailed analysis of properties is not given in either reference. Recently, gas-pressure infiltration techniques have been used to infiltrate sintered NaCl with grain sizes as small as 10 mm [5]. Porosity was in the range 68±81 % depending, in part, on the size of the salt grains. A SEM micrograph of an aluminum sponge prepared by replication of sintered NaCl is shown in Fig. 2.6-2. The mechanical response of a metal sponge depends on the microstructure of the metal (Fig. 2.6-3), as with any fully dense alloy; however, the properties of the metal sponge are further influenced by the level of porosity. The shape of the flow curves in Fig. 2.6-3 are somewhat different from what is generally observed with commercially available closed-cell metal foams. This is due to the inherently higher ductility of most of the base metals used to produce the sponges represented in Fig. 2.6-3 in comparison to commercial cellular metals, as well as the higher regularity of the architecture of these metal sponges, and the comparatively low porosity. The stiffness was found to be about half that expected from simple phenomenological relationships [5]. The processing limits for replication from leachable patterns, like the other pattern technologies, have not been clearly evaluated and there is some divergence in the literature. The range of available pore sizes and porosity, however, is clearly considerable. 2.6.3.4

53

54

2.6 Infiltration and the Replication Process for Producing Metal Sponges

Figure 2.6-2. Scanning electron micrograph of aluminum sponge produced by replication from sintered NaCl patterns.

Figure 2.6-3. Compressive response of several aluminum-alloy sponges produced by replication from sintered NaCl patterns. The salt has grains approximately 0.5 mm in diameter and the fraction solid is noted as f.

2 Material Definitions, Processing, and Recycling

2.6.4

Conclusions

Replication processing provides a versatile and attractive method for the production of metal sponge (often called open-celled metal foam). Advantages of this process comprise considerable control of the pore size, density, and internal architecture of the sponge, the capacity for net or near-net shape component production, and the potential for production of components that are part dense, part porous. Also, the open-porosity that is intrinsic to metal sponge can be put to advantage in several applications that require fluid flow through the porous metal, such as filters and heat-exchangers. The replication process exists in a few variants, which differ mostly according to the nature of the pattern: continuous refractory, discontinuous refractory, burnable, and leachable patterns are four classes of patterns that have been employed to date. The range of density and pore size that can be achieved in replicated metal sponges depends largely on the pattern material and also on the infiltration process. With leachable patterns, in particular, these ranges have been shown to be comparatively wide; at present these also seem to be complementary to what can be achieved with the methods utilizing insoluble patterns. There is, though, significant room for innovation in replication technology as related to the production of metal sponge and there exists perhaps even opportunities for cross-pollination between the methods described here.

References

1. D. Weaire, M. A. Fortes, Adv. Phys. 1994, 43, 685. 2. J. Banhart, Adv. Eng. Mater. 2000, 2, 188. 3. J. Babjak, V. A. Ettel, V. Paserin, US Patent 4 957 543, 1990. 4. I. Wagner, C. Hintz, P. R. Sahm, in Metal Matrix Composites and Metallic Foams, Proc. Euromat 99, Munich, Germany, T. W. Clyne, F. Simancik (eds), DGM/Wiley-VCH, Weinheim 2000, p. 40. 5. C. San Marchi, J.-F. Despois, A. Mortensen, in Metal Matrix Composites and Metallic Foams, Proc. Euromat 99, Munich, Germany, T. W. Clyne, F. Simancik (eds), DGM/WileyVCH, Weinheim 2000, p. 34. 6. R. W. Pekala, R. W. Hopper, J. Mater. Sci. 1987, 22, 1840. 7. T. J. Fitzgerald, V. J. Michaud, A. Mortensen, J. Mater. Sci. 1995, 30, 1037.

8. L. Polonsky, S. Lipson, H. Markus, Modern Castings 1961, 39, 57. 9. H. Seliger, U. Deuther, Freiburger Forschungshefte 1965, 103, 129. 10. H. A. Kuchek, US Patent 3 236 706, 1966. 11. L. Ma, Z. Song, D. He, Scripta Mater. 1999, 41, 785. 12. Y. Yamada, K. Shimojima, Y. Sakaguchi, M. Mabuchi, M. Nakamura, T. Asahina, T. Mukai, H. Kanahashi, K. Higashi, Mater. Sci. Eng. 1999, A272, 455. 13. Y. Yamada, K. Shimojima, Y. Sakaguchi, M. Mabuchi, M. Nakamura, T. Asahina, T. Mukai, H. Kanahashi, K. Higashi, Mater. Sci. Eng. 2000, A280, 225. 14. Y. Yamada, K. Shimojima, Y. Sakaguchi, M. Mabuchi, M. Nakamura, T. Asahina, T. Mukai, H. Kanahashi, K. Higashi, J. Mater. Sci. Lett. 1999, 18, 1477.

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2.7 Solid-State and Deposition Methods 15. Y. Yamada, K. Shimojima, Y. Sakaguchi, M. Mabuchi, M. Nakamura, T. Asahina, T. Mukai, H. Kanahashi, K. Higashi, Adv. Eng. Mater. 2000, 2, 184. 16. U. Mohr, W. Bleck, in Metal Matrix Composites and Metallic Foams, Proc. Euromat 99, Munich, Germany, T. W. Clyne, F. Simancik (eds), Wiley-VCH, Weinheim 2000, p. 28. 17. R. M. German, Particle Packing Characteristics, Metal Powder Industries Federation, Princeton, NJ 1989. 18. C. S. Morgan, L. L. Hall, C. S. Yust, J. Am. Ceram. Soc. 1963, 46, 559. 19. A. A. Ammar, D. W. Budworth, Proc. Br. Ceram. Soc. 1965, 3, 185. 20. W. J. Tomlinson, G. Astle, J. Mater. Sci. 1976, 11, 2162. 21. R. J. Thompson, Z. A. Munir, J. Am. Ceram. Soc. 1982, 65, 312. 22. W. D. Kingery, M. Berg, J. Appl. Phys. 1955, 26, 1205. 23. J. B. Moser, D. H. Whitmore, J. Appl. Phys. 1960, 31, 488.

24. P. J. Wray, Acta Metall. 1976, 24, 125. 25. R. W. Davidge, Proc. Br. Ceram. Soc. 1969, 12, 245. 26. A. Mortensen, I. Jin, Int. Mater. Rev. 1992, 37, 101. 27. C. Garcia-Cordovilla, E. Louis, J. Narciso, Acta Mater. 1999, 47, 4461. 28. A. Mortensen, in Metal Matrix Composites, A. Kelly, C. Zweben (eds), Vol. 3 of Comprehensive Composite Materials, T. W. Clyne (ed.), Pergamon, Oxford, UK 2000, Ch. 21. 29. A. Mortensen, J. A. Cornie, Metall. Trans. 1987, 18A, 1160. 30. A. Mortensen, T. Wong, Metall. Trans. 1990, 21A, 2257. 31. T. Mukai, H. Kanahashi, Y. Yamada, K. Shimojima, M. Mabuchi, T. G. Nieh, K. Higashi, Scripta Mater. 1999, 41, 365. 32. H. Kanahashi, T. Mukai, Y. Yamada, K. Shimojima, M. Mabuchi, T. G. Nieh, K. Higashi, Mater. Sci. Eng. 2000, A280, 349. 33. W. Thiele, Metal Mater. 1972, 6, 349.

2.7

Solid-State and Deposition Methods

O. Andersen and G. Stephani

In this chapter, solid-state and deposition methods for the manufacturing of cellular metals are reviewed with regard to their most important processing features. Discussion will be limited to methods producing predominantly 3D structures. Typical values of the cell size, cell wall thickness, and obtainable relative densities are cited wherever available. Earlier overviews including both methods of manufacturing are available [1,2]. The term ªsolid-state methodº means that directly before the formation of the cellular structure, the metal is in the solid state. However, in some cases limited amounts of liquid phase appear in the process: during liquid-phase sintering or brazing of single cells. Except for foaming of solids, all solid-state methods require a sintering step before the final cellular metallic structure is obtained. Naturally, powder metallurgical methods play a dominant role in this area.

2 Material Definitions, Processing, and Recycling

Porosity in cellular structures made from powders often exhibits two different size scales: a macroporosity of the order of the targeted cell size, and a microporosity in the order of the primary particle or, in case of reactive sintering, the grain size. For all powder metallurgical processes, the cost of the powders is a major concern. Some of the methods, especially those using slurries of metal powders dispersed in a dissolved binder, are capable of using cheap oxides and thus have the potential for a significant cost reduction. Deposition methods need to mobilize the metal in order to transport it onto a porous substrate. This is normally done by transforming the metal into the ionic or vapor state. From the method of manufacture, it can be deduced that the deposition methods are only capable of generating an open-cell morphology. Usually, they also imply a heat treatment for the removal of the precursor on which the metal is deposited. A practical differentiation between the methods in question can be made with the help of two manufacturing parameters, as is shown in Fig. 2.7-1. The chosen criteria, ªformation of cellular structureº and ªformation of cellsº have direct implications for the processing itself, as well as for the resulting properties of the structure. According to this classification, the formation of the cellular structure can be accomplished by building it up from single cells, which do not necessarily have to be in the final metallic state. Alternatively, the structure can be built up from bulk. The formation of the cells themselves can either be carried out with the help of a lost core, or in a coreless manner. Within this framework the deposition methods, for example, constitute a small subset of the lost core bulk processes.

Solid state and deposition methods from single cell

from bulk

coreless methods structures from hollow powders

sintered metal powders and fibers

structures from hollow

special sintering effects

spheres made by coaxial

foaming of solids

spraying of slurries

foaming of slurries

lost core methods

Classification of solid-state and deposition methods from a manufacturing point of view. Figure 2.7-1.

cementation process

p/m space holder methods

galvanic hollow spheres

deposition methods

IFAM hollow spheres

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2.7 Solid-State and Deposition Methods

Generally, formation from single cells has the potential of a very close control of the cellular properties. However, in most cases the single cell processes require more processing steps than bulk formation processes. Processes using lost cores usually are prone to introducing unwanted interstitials like carbon and oxygen into the base material, since the cores are predominantly hydrocarbons, which have to be removed thermally. Another disadvantage compared to coreless processes is the additional time required for the removal of the core. Generally speaking, there is a remarkable variety of solid-state and deposition methods for making cellular metals, which all have their specific strengths and weaknesses. It therefore depends very much on the final application, which method may be best suited in a given situation. 2.7.1

Formation from Single Cells: Coreless Methods Hollow-Sphere Structures made from Gas Atomized Hollow Powders It is known that gas atomization often generates a small amount (typically 1±5 %) of hollow particles owing to gas entrapment in the liquid ligaments. By appropriate separation methods, these hollow particles can be separated from the solid ones 2.7.1.1

a) Surface

b) Cross section

1.0 mm

1.0 mm

Figure 2.7-2. HIP-bonded hollowsphere structure made from alloy 625 (courtesy IPML, University of Virginia, Charlottesville).

2 Material Definitions, Processing, and Recycling

and consolidated to yield hollow-sphere structures. Typical sphere diameters are 500±1000 mm with wall thicknesses about 100±300 mm [3]. Different methods for consolidation are reported: sintering, transient liquid phase sintering with the help of a powdered additive, and hot isostatic pressing (HIP). Best results with regard to specific stiffness were achieved with HIP bonding, Fig. 2.7-2. This was attributed to the predeformation of the cells and enlarging of the contact zones. Structures were made from TiAlV 64 as well as from a nickel-based superalloy (alloy 625). Relative densities of 0.3±0.12 were achieved. Other methods of producing hollow metal powders without using lost cores have been reported, such as coaxial atomization of melts [4], atomization of melts containing a dissolved gas [5], and plasma treatment of powder particles containing an absorbed gas [6]. However, nothing is known about cellular structures made thereof.

Hollow-Sphere Structures made from Coaxially Sprayed Slurries Hollow spheres can be produced by spraying a powder slurry containing a solvent and a polymer binder through the outer orifice of a coaxial nozzle [7]. By hydrodynamic interaction with the gas passing through the inner orifice, single bubbles are formed. In flight, they are spherodized by surface tension, and dried. The resulting hollow spheres can have diameters in the range 1±6 mm with close control (e4 %) of the dimensions. Wall thickness is typically around 100 mm and can be varied between 40 and 200 mm [8]. Subsequently, the powder shells are heat treated to remove the organic binder and, at a higher temperature, to sinter the metal powder particles to form a closed metallic shell. In order to obtain cellular structures, the single hollow spheres are filled in molds and either diffusion bonded or sinter bonded with the help of a metal powder slurry. The use of slurries leads to an undesirable reduction in overall void space of the structure. Nonetheless, values of the relative density of 0.12 were 2.7.1.2

Figure 2.7-3. FeCr hollow spheres bonded together with magnetite slurry and reduced (courtesy Georgia Institute of Technology).

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2.7 Solid-State and Deposition Methods

achieved with stainless steel structures made from reduced iron and chromium oxide powders [9], Fig. 2.7-3. 2.7.2

Formation from Single Cells: Lost Core Methods Hollow-Sphere Structures made by Cementation and Sintering If spherical iron particles are immersed in a stirred CuSO4 solution, the so-called cementation reaction 2.7.2.1

Cu2‡ ‡ Fe () Cu ‡ Fe2‡ leads to deposition of pure copper on the particles while simultaneously the iron core is being dissolved. The process can be carried out until the iron is completely dissolved in the electrolyte and only hollow copper shells remain [10]. Hollow copper powders were prepared using reduced iron oxide powders as the lost core. The resulting copper particles had diameters of about 500±750 mm. The walls are very rough and porous, having a thickness of a few hundred microns. The hollow copper particles need further heat treatment to give them sufficient strength for handling. Cellular metallic structures are achieved by packing the hollow particles in ceramic molds and bonding them by sintering. Good results were achieved by coating the copper particles with tin, thus enabling liquid-phase sintering. The resulting cellular bronze structures exhibit good interparticle bonding, dense cell walls, and relative densities of about 0.2 [11], Fig. 2.7-4.

Cross section of a bronze hollow-sphere structure made by cementation and sintering (courtesy Institute for Chemical Technology of Inorganic Materials, Technical University of Vienna).

Figure 2.7-4.

2 Material Definitions, Processing, and Recycling

Figure 2.7-5. Brazed nickel hollow-sphere structures with sphere diameter of 4.5 mm made from galvanically manufactured hollow spheres (courtesy ATECA, Montauban, France).

Hollow-Sphere Structures made from Galvanically Coated Styrofoam Spheres Hollow spheres can be made by galvanic coating of Styrofoam spheres, which act as a lost core [12]. The Styrofoam is thermally removed. Sphere diameters may range from 2 to 10 mm. The sphere walls show excellent uniformity in thickness, which is typically in the few micron range. Thick walls are very expensive to manufacture. Material choice is limited to a few metals suitable for galvanic deposition (typically copper and nickel). For making purely metallic structures, the single spheres can be joined by brazing [13] or diffusion bonding. Sphere sizes are in the range of a few millimeters and relative densities can be smaller than 0.05 since the galvanic process is able to produce very thin and uniform coatings [14]. With suitable sorting methods for the Styrofoam cores, very uniform spheres can be obtained, which allow for the manufacturing of ordered structures, Fig. 2.7-5. 2.7.2.2

Hollow-Sphere Structures made from Fluidized Bed Coated Styrofoam Spheres According to previously published work [15], commercially available Styrofoam spheres can be coated in a fluidized bed process with a suspension containing metal powder and a binder. The resulting green spheres may be debindered and sintered to obtain single metallic hollow spheres. Alternatively, the green spheres can be subjected to a suitable forming process to obtain green parts made up of single cells [16], Fig. 2.7-6. The resulting green parts 2.7.2.3

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2.7 Solid-State and Deposition Methods Figure 2.7-6. Process scheme for making hollow-sphere structures (courtesy IFAM, Dept. of Powder Metallurgy and Composite Materials, Dresden).

are heat treated in the same way as the single spheres. In principle, this allows for the production of hollow-sphere structures from arbitrary metals and alloys. In order to enhance the mechanical properties of the resulting structures, large contact areas between the spheres are achieved by applying a slight pressure to the green spheres during the forming step. In this stage, the elastic Styrofoam core helps to prevent buckling and leads to a more uniform distribution of the cell pre-deformation. A typical example of the resulting structure is shown in Fig. 2.7-7. The attainable range of the sphere diameters is 0.5±10 mm. Wall thicknesses have been made from 10 to 1000 mm. Relative densities can be as low as 0.03. Recent overviews of the processing and properties of such structures are given elsewhere [17,18]. Materials currently under investigation are numerous, with a focus on stainless steel 316L [19] and low-cost hollow-sphere structures made from iron oxides [20].

Figure 2.7-7. IFAM 316L hollow-sphere structure. Left hand side: computer tomography images of cross sections (courtesy IFAM, Department of Powder Metallurgy and Composite Materials, Dresden).

2 Material Definitions, Processing, and Recycling

2.7.3

Bulk Formation: Coreless Methods Sintered Metal Powders and Fibers Porous metals made from sintered particulates are already in widespread use for predominantly functional applications. A good overview of classical commercial processes and products relying on plain sintered metal powders is available [21]. The powders are sifted to narrow size fractions, die compacted, and sintered. Bronze, stainless steels, titanium, and nickel-based alloys are common in commercial production. Depending on the particle morphology and packing density, the relative density of the resulting parts can reach values as low as 0.4, while pore sizes are from 0.5 to 200 mm. However, usually the relative density is quite high (0.8±0.6). Much lower relative densities can easily be achieved by using particles with large length-to-diameter ratios: metal fibers. Depending on the length-to-diameter ratio and the processing route, relative densities of 0.01 can be obtained. Very fine fibers down to diameters of a few microns can be produced by the bundle drawing technique [22]. Fibers are available in many corrosion and heat resistant alloys: 316 and 302-type, Inconel 601, FeCrAlloy, Hastalloy X, Nichrome, and some titanium alloys. Diameters of bundle drawn fibers can be as small as a few microns. Using broken fiber bundles or short fibers, highly porous structures can be manufactured by applying textile or other dressing techniques with subsequent sintering to get a rigid structure. Depending on the application, the mean pore size of such structures can be made as small as a few microns. The relative density typically is in the range 0.35±0.1, but can also be much smaller. There are other mechanical technologies for making fibers, such as shaving from either wire, foils, or bars. These fibers have irregular cross sections, either triangular or rectangular with a certain surface roughness and equivalent diameters of 25±100 mm. These shaving methods have been recently improved by introduction of superimposed vibrations, which results in a more homogeneous cross section [23]. 2.7.3.1

Figure 2.7-8. Cross-sectional cut of sintered fiber structure made from melt-extracted short fibers from FeCrAl 23.15. From left to right: relative density 0.3, 0.2, 0.1 (courtesy IFAM, Department of Powder Metallurgy and Composite Materials, Dresden).

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2.7 Solid-State and Deposition Methods

Using the melt extraction process for making short fibers directly from the melt, the materials limitations of the mechanical fiber manufacturing routes can be overcome [24,25]. Highly porous sintered structures from intermetallics such as Ni3Al [26] and FeAl, as well as from many other ferrous and nonferrous alloys have been made. Equivalent fiber diameters are 50±150 mm, fiber length may vary between 3 and 25 mm. This allows for relative densities between 0.5 and 0.03 in the final structure, Fig. 2.7-8.

Methods Utilizing Special Sintering Phenomena In common powder metallurgical production, the formation of pores is an unwanted by-product of the sintering process. Many origins of pore formation have been explained theoretically and attributed to a variety of different physical phenomena. Some of these effects are capable of generating a very large amount of porosity and thus lend themselves to making cellular metals. An early example is the so-called Kirkendall effect, in which in a diffusion couple pores are generated in the component with higher diffusivity [27]. Aldinger [28] has evaluated the potential of an extreme Kirkendall effect for making porous structures. Cellular structures were obtained by using coated particles where the core consists of the component with higher diffusivity. The powders are then pressed and sintered. Experiments with nickel and cobalt coated beryllium powders showed a maximum volume increase of 262 %, corresponding to an absolute density of 0.47 g/cm3 and a relative density in the order of 0.2. The structures exhibit a mixture of closed-cell porosity with diameters of 50 to 100 mm and wall thicknesses around 10 mm, depending on the size of the starting powders and the thickness of the coatings. Theoretical considerations lead to the conclusion that under ideal conditions, relative densities can be made arbitrarily small. In reality, this is hindered by a number of different effects, such as incomplete or non-uniform coating of the particles. In reactive sintering, elemental powders are used instead of pre-alloyed powders in order to enhance sinterability and reduce cost. Especially in intermetallic systems, an unwanted swelling of the sintered parts is noticed under certain processing conditions. A general treatment of the different mechanisms for swelling in the system Ti-Al was given elsewhere [29]. KnuÈwer exploited the swelling effect for manufacturing FeAl structures with open porosity [30]. Relative densities down to 0.5 were reported. In contrast to the cell morphology obtained via the Kirkendall effect, these structures exhibit an almost exclusively open porosity. Due to the different effects taking place during swelling, a macro- and a microporosity are generated, both being of an open type (Fig. 2.7-9). Macroscopic porosity is in the order of the primary particle sizes, typically in the range 50±150 mm. The size range of the microscopic porosity is determined by the grain size of the intermetallic phase generated, and is typically smaller than the macroscopic porosity by one or two orders of magnitude. 2.7.3.2

2 Material Definitions, Processing, and Recycling

Porous TiAl3 structure prepared from elemental powder mixture. Large pores correspond to primary Al particles (courtesy IFAM, Department of Powder Metallurgy and Composites).

Figure 2.7-9.

Foaming of Solids Kearns et al. first described a solid-state foaming process where porosity in metals is generated by expanding a hot-isostatically pressed mixture of argon gas and metal powder at elevated temperatures and ambient pressure [31]. More recent work utilizes this principle for making TiAlV 64 sandwiches with a porous core [32]. This is achieved by canning TiAlV 64 powder in canisters of the same material. After HIP, the resulting billet can be isothermally forged or hot rolled to achieve sheets. Subsequently, an expansion annealing treatment (typically at temperatures i0.6Tm for 4±48 h) generates the porous core, Fig. 2.7-10. This method, which is known as the low-density core (LDC) process, uses creep expansion due to the internal gas pore pressure to generate the desired porosity. Queheillalt et al. have carried out a thorough analysis of the process kinetics and morphological evolution of the pores [33]. The resulting porosity in the core region is largely unconnected and shows pore diameters of 10±100 mm. The relative density lies in the range 0.65±0.5. One advantage is the capability of producing very large sheets (up to 2000 mm q 1200 mm q 4 mm). A slightly different approach described previously utilizes the transformation superplasticity found in allotropic materials [34]. Transformation superplasticity occurs at all grain sizes by biasing with a deviatoric stress (from the entrapped gas) of internal stresses (from the allotropic mismatch during thermal cycling about the allotropic temperature range). Hence, the rather lengthy expansion annealing can be replaced by a significantly shorter thermal cycling treatment. 2.7.3.3

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2.7 Solid-State and Deposition Methods

Low Density Core Process Steps a) Powder / Can Preparation

Ti-6Al-4V can

Powder packing density D0

Ti-6Al-4V powder

Evacuate and backfill with Argon gas to pressure p 0

b) HIP Consolidation (1040oC, 100 - 200MPa, 2h) Isolated pressurized voids

Final relative density 0.85 - 0.95

p(t), T(t)

c) Hot Rolling (approx. 850oC, 6-20 passes) Thinning of facesheet Internal gas pressure

Changes in pore shape, matrix microstructure

d) Expansion Heat Treatment (900oC - 1200˚C, 4 - 48 h) Vacuum furnace Sandwich panel

Isolated porosity (<40%)

Facesheet

Figure 2.7-10.

LDC process scheme (courtesy IPML, University of Virginia, Charlottesville).

2 Material Definitions, Processing, and Recycling

Foaming of Slurries There are only few reports on the foaming of slurries, and work has not been very successful up to date owing to low strengths of the resulting structures. According to Banhart et al., metal powder slurries containing a foaming agent can be poured into molds and foaming occurs due to decomposition of the foaming agent [2]. Stabilizing the resulting liquid foam is essential and in some cases is accomplished by adding a stabilizer capable of polymerization on contact [1]. After foaming, the organic contents have to be removed thermally, followed by a sintering step. Relative densities as low as 0.05 have been reported [35]. 2.7.3.4

2.7.4

Bulk Formation: Lost Core Methods Powder Metallurgical Space Holder Method The use of space holders in powder metallurgy is a well-known technique to create different pore sizes and achieve relative densities lower than 0.4. The space holder is mixed with the metal powder and, depending on the final shape of the product, several methods are used for forming of the powder mixture: die compaction, extrusion, and rolling. A general difficulty of these methods is the need to remove large quantities of organic or inorganic space holder material from the parts. Good results can be achieved with carbamide (urea), which can be thermally removed below temperatures of 200 hC. Porous structures from stainless steel 316L, nickel based superalloys, and titanium (Fig. 2.7-11) have been made this way (see Section 2.3) [36,37]. Pore sizes are typically in the range of a few hundred microns up to a few millimeters, and relative densities of 0.4±0.2 are reported. 2.7.4.1

Figure 2.7-11. Titanium sample with relative density of 0.3 made by space holder method (courtesy Research Centre Ju È lich, Institute for Materials and Processes in Energy Systems).

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2.7 Solid-State and Deposition Methods

Deposition Methods Deposition techniques always need a parent structure on which to deposit the metal. Most common is the use of polymeric (polyurethane) foams. In order to ensure the penetration of the structure by the mobilized metal, a thermophysical shock treatment (reticulation) for the removal of residual membranes is needed. After deposition, the parent structure is removed thermally or chemically. If the metal is deposited from the ionic state (either galvanically or electroless), a pretreatment is necessary that assures either electrical conductivity or, in the case of electroless plating, a sufficiently rough surface of the parent structure. Materials choice is limited to nickel, nickel±chromium, silver, copper, and tin. Relative densities are typically less than 0.1 with average cell sizes from 400 mm up to a few millimeters. In order to overcome the limitations in materials choice, it is also possible to deposit the metal from the vapor state. Albeit being a nickel foam, INCOFOAM made by Inco Ltd., Canada, is an example of a commercially available product made by chemical vapor deposition. A recent development in this area is the electron beam directed vapor deposition process (EB-DVD), which was used to evaporate and deposit an Inconel alloy 625 onto an open celled, reticulated structure [38], Fig. 2.7-12. The EB-DVD technology uses a combination of an electron beam gun and an inert gas carrier jet of controlled composition to create thick coatings with high deposition rates (i10 mm/min) and could thus overcome the economical limitations encountered to date by vapor deposition methods. 2.7.4.2

Figure 2.7-12. As-deposited Inconel 625 structure made by EB-DVD, relative density 0.01 (courtesy IPML, University of Virginia, Charlottesville).

2 Material Definitions, Processing, and Recycling

References

1. V. Shapovalov, MRS Bull. 1994, 19(4), 24 2. J. Banhart, J. Baumeister, in Porous and Cellular Materials for Structural Applications, D. S. Schwartz, D. S. Shih, A. G. Evans, H. N. G. Wadley (eds), Materials Research Society Proceedings, Vol. 521, Warrendale, Pennsylvania, USA, 1998, p. 121. 3. D. J. Sypeck, P. A. Parrish, H. N. G. Wadley in Porous and Cellular Materials for Structural Applications, D. S. Schwartz, D. S. Shih, A. G. Evans, H. N. G. Wadley (eds), Materials Research Society Proceedings, Vol. 521, Warrendale, Pennsylvania, USA, 1998, p. 205. 4. J. M. Beggs, T. G. Wang, D. D. Elleman, US Patent 4 344 787, 1982. 5. C. P. Ashdown, J. G. Bewley, G. B. Kenney, US Patent 5 024 695, 1991. 6. G. D. Cremer, US Patent 4 162 914, 1979. 7. L. B. Torobin, US Patent 4 671 909, 1987. 8. K. M. Hurysz, J. L. Clark, A. R. Nagel, C. U. Hardwicke, K. J. Lee, J. K. Cochran, T. H. Sanders in Porous and Cellular Materials for Structural Applications, D. S. Schwartz, D. S. Shih, A. G. Evans, H. N. G. Wadley (eds), Materials Research Society Proceedings, Vol. 521, Warrendale, Pennsylvania, USA, 1998, p. 191. 9. J. L. Clark, K. M. Hurysz, K. J. Lee, J. K. Cochran, T. H. Sanders in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 171. 10. H. Danninger, S. Strobl, R. GuÈrtenhofer in Proc. PM `98: Powder Metall. World Congress Exhib., Grenada, V. Arnhold, A. Romero (eds), EPMA, Shrewsbury, Vol. 1, 1998, p. 185. 11. S. Strobl, M. Kupkova, H. Danninger, M. Kupka, E. Dudrova, L. Kovac, R.GuÈrtenhofer in Proc. Int. Conf. FRACTOGRAPHY 2000, Slovak Republic, L. Parilak(ed.), IMR SAS Kosice, 2000, p. 446. 12. M. JaÈckel, German Patent 3 210 770, 1982. 13. A. Rousset, J.-P. Bonino, Y. Blottiere, C. Rossignol, French Patent 8 707 440, 1987. 14. Product data sheet, MECAPROTEC Industries, Muret, France, 1998. 15. M. Jaeckel, H. Smigilski, German Patent 3 724 156, 1987.

16. O. Andersen, L. Schneider, G. Stephani, Ingenieur-Werkstoffe 1998, 7(4), 36. 17. U. Waag, L. Schneider, P. LoÈthman, G. Stephani, Metal Powder Rep. 2000, 55(1), 31. 18. G. Stephani, U. Waag, P. LoÈthman, O. Andersen, L. Schneider, F. Bretschneider, H. Schneidereit in Advances in Powder Metallurgy & Particulate Materials, Proc. 2000 World Congress Powder Metall. Particulate Mater. MPIF, Princeton 2000, p. 12 119. 19. O. Andersen, U. Waag, L. Schneider, G. Stephani, B. Kieback, Adv. Eng. Mater. 2000, 2(4), 192. 20. L. Schneider, U. Waag, P. LoÈthman in Proc. 2000 Powder Metall World Congress, p. 510 21. W. Schatt, K.-P. Wieters, Powder Metallurgy: Processing and Materials, EPMA, Shrewsbury 1997, p. 344. 22. J. A. Roberts in Handbook of Fillers and Reinforcements for Plastics, H. S. Katz, J. V. Milewski (eds), Van Nostrand Reinhold, New York 1978, p. 579. 23. R. De Bruyne, I. Lefever, J. Saelens, J. Vandamme in Advances in Powder Metallurgy & Particulate Materials, Proc. 1996 World Congress on Powder Metall. Particulate Mater., MPIF, Princeton 1996, p. 16±99. 24. G. Lotze, G. Stephani, W. LoÈser, H. Fiedler, Mater. Sci. Eng. A 1991, 133, 680. 25. O. Andersen, G. Stephani, Metal Powder Rep. 1999, 54(7/8), 30. 26. S. Steigert, Z. Li, O. Andersen, G. Stephani, T. Schrooten in Proc. Materials Week 2000 [http://www.materialsweek.org/proceedings/ index.htm]. 27. A. D. Smigelskas, E. O. Kirkendall, Trans. AIM 1947, 171, 130. 28. F. Aldinger, Acta Met. 1974, 22, 923. 29. A. BoÈhm, B. Kieback, Z. Metallkd. 1998, 89(2), 90. 30. M. KnuÈwer, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 203. 31. M. W. Kearns, P. A. Blenkinsop, A. C. Barber, T. W. Farthing, Int. J. Powder Metall. 1988, 24(1), 59.

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2.7 Solid-State and Deposition Methods 32. D. S. Schwartz, D. S. Shih, R. J. Lederich, R. L. Martin, D. A. Deuser in Porous and Cellular Materials for Structural Applications, D. S. Schwartz, D. S. Shih, A. G. Evans, H. N. G. Wadley (eds), Materials Research Society Proceedings, Vol. 521, Warrendale, Pennsylvania, USA, 1998, p. 225. 33. D. T. Queheillalt, B. W. Choi, D. S. Schwartz, H. N. G. Wadley, Metall. Mater. Trans. A 2000, 31, 261. 34. D. C. Dunand, J. Teisen in Porous and Cellular Materials for Structural Applications, D. S. Schwartz, D. S. Shih, A. G. Evans, H. N. G.

Wadley (eds), Materials Research Society Proceedings, Vol. 521, Warrendale, Pennsylvania, USA, 1998, p. 231. 35. S. B. Kulkarni, P. Ramakrishnan, Int. J. Powder Metall. 1973, 9(1), 41. 36. M. Bram, C. Stiller, H. P. Buchkremer, D. StoÈver, H. Baur, Adv. Eng. Mater. 2000, 2(4), 196. 37. G. Rausch, T. Hartwig, M. Weber, O. Schulz, Materialwiss. Werkstofftechn. 2000, 31(6), 412. 38. D. T. Queheillalt, D. D. Hass, D. J. Sypeck, H. N. G. Wadley, J. Mater. Res. 2001, 16(4), 1028.

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

3 Secondary Treatment of Cellular Metals F. Simancik

The introduction of new materials into practice requires suitable technologies for their machining, forming, surface coating, or joining. Many papers in the literature deal with the preparation of cellular metals and with the evaluation of their mechanical and physical properties, but only limited attention is paid to their secondary treatment. There is no doubt that the following unusual features of cellular metals require specific approaches for shaping and fabrication. x x x x

x

Crushability of the structure (difficult forming and machining). High sensitivity to tensile loading (difficult forming). Defects in cell walls and in surface skin (difficult coating). Outer surface that is usually covered with oxides (difficult coating, brazing, welding). Presence of the melt stabilizing ceramic particles (difficult machining).

Components made of metallic foam are usually prepared in near-net-shapes by foaming in the mold. These porous components are always covered with a compact surface skin. However, the skin usually contains various defects like small holes or microcracks, so it cannot be considered fully dense. The skin significantly improves the properties and the appearance of the foamed part, so it is undesirable to remove it. In addition, removing the skin would be expensive. There are other cellular metals made using various templates or placeholders. They have open-cell structures and no outer skin (the template must be removed from the structure after solidification). It is obvious that the secondary treatment of these two kinds of structures will be very different. Machining Machining of net-shape foams breaks the dense surface skin and reveals the inner structure of the pores. Machining is best avoided at the design stage. Nevertheless, even well-designed components will need to be cut and drilled. Cellular metals can, in principle, be cut by all conventional methods, but achieving a high-quality surface is substantially more costly than for traditional materials. If ceramic particles are used for stabilizing the liquid foam, the excessive wear on the machine tools

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has to be taken into account, especially if SiC particles are present. Conventional machining causes bending of thin pore walls in ductile alloys and fracture in brittle alloys. Pore walls yield or fracture at their thinnest point, which is often out of the cutting plane. This leads to poor quality of the cutting surface and low precision. The accuracy and quality of the cutting plane are significantly affected by partial melting of the thin pore walls and their subsequent diffusion bonding to the cutting tool. High porosity and the resultant low thermal conductivity do not allow for efficient cooling by transport of heat into the surroundings. On the other hand, melting and bending of pore walls can be utilized for the strengthening of the cutting surface (bent pore walls are pressed into the surface pores, which improves their apparent density). If high precision and a good quality machined surface is required, traditional methods of machining cannot be used. Electric discharge machining was demonstrated to be most suitable, as it avoids the mechanical effect on the pore walls and thus their bending and failure. Material in the cutting plane simply burns out. The result is a clean cutting plane (without material pressed into the surface pores) and good dimensional accuracy. The speed of electric discharge machining is substantially greater in porous materials than with dense ones. The main disadvantage of the process is the need to use dielectric fluid, which penetrates into the porous structure and needs to be removed after machining by burning: this is environmentally harmful. If a simple cut is required, wire electric discharge machining in water can be used to overcome this disadvantage. A water beam with abrasive can also be used for the precise cutting of cellular metals. The quality of the cutting plane is substantially better than in the case of classical band saws (the bending of pore walls does not take place). As the cutting speed and the thickness of the plate increases, the quality of the bottom edge of the cutting plane deteriorates owing to scatter of the beam. The same effect takes place in plasma or laser cutting. If the component is foamed, its final shape derives from the mold and forming is usually not necessary. From the practical point of view, forming can be considered with respect to flat plates. Sometimes bending or roll-bending of these panels is required. During bending, cracks initiate in the tensile surface and then they rapidly propagate across the whole section. The bending that can be achieved without damage is limited by the plasticity of the thin surface skin and the thickness of the plate (as the thickness of the plate grows, the deformation of the tensile loaded part of the sample for a given bending radius increases). Panel bending is therefore possible only for foams made of ductile alloys and/or at higher temperatures (see Section 3.1). Surface coating For surface coating the same basic principles can be applied as for the bulk cellwall material, but ªsoakingº of the porous structure should be taken into account as it significantly restricts those surface treatment procedures in which components are immersed (acid pickling, anodizing, etc.). Aluminum foam can be anodized like aluminum, but removal of the electrolyte from the structure is required to avoid corrosion. Owing to the microporosity of the surface skin, painting with

3 Secondary Treatment of Cellular Metals

viscous paints is not problematic. Baking of the paint can result in the formation of bubbles (blisters in the surface paint) caused by the expansion of gases in pores and their attempts to escape through surface microcracks. For this reason it is recommended to leave some bare areas to enable the foam to ªbreatheº on temperature changes. If the foam has to be sealed completely, the coating process should be performed in vacuum until the coating solidifies. Joining For practical applications of cellular metals, joining techniques are required. As the structure of cellular metals is similar to that of wood, methods used for joining wooden parts, especially gluing and bolting, can also be used with cellular metals. Moreover, methods of joining metal parts, such as welding and soldering, are also possible. Joining cellular metal parts with bolts is simple, quick, flexible, and cost effective: the joint is also detachable. The strength of the joint depends primarily on the density and pore size of the foam and increases if foam with a surface skin is used. Higher strength is achieved with foams having finer porosity (finer porosity provides a larger contact surface for the thread of the bolt). The strength of the joint can be significantly improved if the drilled hole is filled with a suitable adhesive. Brazing and Soldering The brazing or soldering of metallic foams is still questionable. The metal surface is always coated with various oxides, depending on the alloy used. Oxides impede the formation of brazed or soldered joints and therefore they must be removed before or during the soldering. They can be removed either mechanically (scraping) or chemically (using fluxes). Scraping of oxides usually takes place under a layer of melted solder to avoid subsequent oxidation. However, this is a laborious operation demanding a skilled worker and it is costly. The strength of the soldered joint is usually lower than the tensile strength of the foamed sample owing to the negative effect of solder on the strength of the basic alloy near the joint. Flux can be used only for foams with a compact surface skin, otherwise there is a danger of it penetrating into the porous structure. It cannot be fully removed from the pores, which increases the danger of subsequent corrosion. As small cracks always appear on the foam's surface, soldering with premature fluxing can be used for sandwich structures. Foams without a surface skin can be soldered without fluxing, but the strength of the joint is substantially lower than for samples with the surface skin (oxides cannot be fully removed from the surface of open pores by scraping). Glued Joints Metallic foams can be glued with all types of adhesive recommended for gluing the cell-wall metal. These joints can be quickly and easily made and their strength often exceeds the strength of the basic foam structure. Because of the simplicity and flexibility, glued joints can be recommended for preparation of permanent joints.

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However, glued joints also have disadvantages: low thermal stability, different coefficients of thermal expansion for the adhesive and the bonded material, decreasing strength of the glued joint due to aging of the adhesive, and formation of an insulating layer (thermal and electrical) are some of them. Moreover, if foams without a surface skin are glued together, a greater consumption of adhesive (weight increase, cost) has to be expected because of the significantly enlarged surface area. Welding Metallic foams can be also welded, if the weldability of the cell-wall material is good. Welded joints are very promising, but the techniques need further development and the costs are still relatively high for practical application. Welding problems arise mainly from the very low and variable thickness of the surface layer. This obstacle can be partially overcome using controlled heat input into the joint, by laser-welding for example. Good joints can be obtained if the foamable material is used as filler. Welding in combination with such a filler can provide a method for repair of foamed parts. Another possibility for joining cellular metals is the use of integral foams containing the parts made from bulk material, which are built into the foamed structure and if possible diffusion bonded to the foam during foaming. These parts provide the contact counterparts of the foam for a joint. The bulk material can be either locally placed inside the foam if the position of joint is known before foaming (Fig. 3-1a), or it can create a large portion of the foam's surface (Fig. 3-1b). The material of the built-in element should be compatible with the cell-wall alloy with respect to corrosion resistance and thermal expansion. Locally distributed elements need precise positioning and suitable fastening to avoid displacement due to foam motion during foaming, which makes the foaming procedure more expensive. The use of various coversheets that are diffusion bonded to the foam during foaming can eliminate the higher costs and lower flexibility of the built-in elements, on the other hand the higher overall weight must be taken into account.

a)

b)

Joints made using bulk aluminum parts diffusion bonded to the AlSi12 foam as: a) locally placed element, b) 3 mm thick Al coversheet.

Figure 3-1.

3 Secondary Treatment of Cellular Metals

Further Reading

4. C. Born, H. Kuckert, G. Wagner, D. Eifler, 1. H. P. Degsicher, A. Kottar, ªOn the Nondestructive Testing of Metal Foamsº in Metal MetallschaÈume, Wiley-VCH, Weinheim 2000, Foams and Porous Metal Structures, J. Banhart, p. 547. [Ultrasound soldering.] M. F. Ashby, N. A. Fleck (eds), MIT Verlag, 5. R. Neugebauer, T. H. Hipke, in Porous and Cellular Materials for Structural Applications, Bremen 1999, p. 213 D. S. Schwartz, D. S. Shih, A. G. Evans, 2. O. B. Olurin, N. A. Fleck, M. F. Ashby, J. H. N. G. Wadley (eds), Materials Research Mater. Sci. 2000, 35, 1079. [Joining using Society Proceedings, Vol. 521, Warrendale, wood screws.] Pennsylvania, USA, 1998, p. 265. [Water jet 3. K.-J. Matthes, H. Lang, MetallschaÈume, cutting, joining.] Wiley-VCH, Weinheim 2000, p. 558. [Soldering of foams.]

3.1

Forming, Machining, and Coating

M. C. Hahn, R. Braune, and A. Otto

Cellular metals are a new class of materials with low densities and novel physical, mechanical, thermal, electrical, and acoustic properties, which offer potential for lightweight structures, for energy absorption, and for thermal management [1]. In order for their outstanding material properties to be used, they have to be machined and processed to build structural components. The relevant techniques are described in this section. 3.1.1

High-Temperature Forming

At present cellular metals produced from the melt, by deposition, and by solid-state processes are available. They have very valuable properties in terms of density, stiffness, and energy absorption, but their potential usefulness is limited by the difficulty of forming or fabricating finished parts. A forming process is necessary for the manufacture of 3D structural parts and a joining technique is required to fabricate such parts into composite components.

Specific Problems in Foam Forming Today it is possible to make 3D composites with cellular aluminum cores from rollplated foamable semi-finished products, as described in Section 3.3. This method, however, is based on the powder-compact foaming technique and is quite costly. 3.1.1.1

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Foams produced from melts, in contrast, are much less expensive but there are problems with the forming properties of foamed cellular metals. At ambient temperature, forming the foams gives rise to fractures or to the collapse of the pore structure in the deformed zone. Local stress and strain concentrations can occur causing failure at the weakest parts of the cellular structure [2]. Forming at elevated temperatures facilitates the shaping of metallic foams without failure and with the pore structure being retained. At high temperatures the yield stress and the deformation limits can be significantly reduced so that yielding can occur. Local stress concentrations can be reduced by creep relaxation. The details of the process are described in the following section.

Process Sequence for Manufacturing 3D Composites with Aluminum Foam Cores The process sequence for manufacturing 3D composites with core structures of foamed aluminum is shown in Fig. 3.1-1. The cover sheets of the sandwich panel are formed in a first process step to serve as forming tools for the cellular core material in the subsequent integrated forming and joining process. The result is a complex near-net-shape composite part. The aluminum foam is formed at temperatures closed to the solidus temperature. As an example, the working area in the Al Si phase diagram and a workpiece made from the alloy AlSi12 are shown in Fig. 3.1-2. 3.1.1.2

Figure 3.1-1.

Process sequence [3].

Figure 3.1-2.

Left) working area in Al Si phase diagram [3]. Right) workpiece formed in a steel

mold [3].

3 Secondary Treatment of Cellular Metals

The workpiece in Fig. 3.1-2 was formed using a steel mold in a chamber furnace in the temperature range of the solidus. The forming force in this case was gravity. The mold was reproduced well, including the corrugations, but a disadvantageous temperature management and locally higher stresses at the beginning caused a collapse in contact areas at the edges.

Material Behavior at the Solidus The behavior of the material in the temperature range of the solidus is important for the later forming process of the different foamed metals. Besides the alloying elements, the production process also influences the thermal behavior. Materials produced by the powder-compact foaming technique have a surface skin, which impedes heat transfer from the furnace atmosphere into the foam. Materials produced from the melt mostly have open pores outside and therefore, because of the large surface, heat transfer into the material is accelerated. Consequently, the temperature range of the working area for high-temperature forming is reached earlier. Another important factor is the foaming agent. Up to the solidus temperature metallic foams do not show any permanent changes in the cell structure, but on reaching the solidus temperature foams that are produced with titanium hydride (TiH2) as the foaming agent show the formation of new pores in the cell walls. This results from TiH2 remaining from the production process that releases hydrogen when the dissociation temperature is surpassed and the alloy starts to melt. The cell structure changes as the temperature rises, and on exceeding the solidus a combination of pores is possible (Fig. 3.1-3, left). Foams that are produced by gas injection into the melt do not show such a behavior; the pore structure remains stable even above the solidus, as shown in Fig. 3.1-3, right. It is obvious that a high-temperature forming process should take place below the solidus of cellular aluminum to avoid weakening the formed parts by additional coalescence of pores. 3.1.1.3

Figure 3.1-3. TiH2 (left) and gas injection foamed (right) foams: influence of temperature and foaming agent on cell structure.

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Forming of Cellular Metals at High Temperatures The temperature at which the forming process takes place is important. To form structural parts of titanium hydride aluminum foams it is necessary to work below the solidus temperature to prevent the cell structure from collapse because the main factor of this procedure is the forming force. Above this temperature threshold value a controlled forming process is not feasible using this material because even very small forming forces destroy the cellular structure. Thus, temperature management is quite difficult. On the one hand, the yield stress has to be reduced to allow high deformation, and on the other hand the solidus temperature must not be exceeded. The foams produced by gas injection, which are often stabilized by particles, show a different behavior at temperatures above the solidus. The particles, for example silicon carbide (SiC), added to raise the viscosity in the production process [4] keep the structure stable even in this temperature range because the particles stabilize the aluminum matrix and the cellular structure. In the temperature region above the solidus the temperature is the main factor because the material starts to melt into a semi-solid state. The yield force can be reduced again, whereas the respective solidus temperature depends on the alloy of the foam. Besides the temperature, time is an important factor in the forming process because the procedure is diffusion controlled and thus time dependent. The longer the forming process lasts the larger are, for example, the resulting bending angles. In addition, variation decreases, which is reflected in improved reproducibility at slow forming velocities. Some examples of high-temperature forming of cellular metals are shown in Fig. 3.1-4. Foam samples made from the melt by gas-injection with about 15 wt.-% SiC particles, were bent at temperatures of 5 (top), 10 (middle), and 15 hC above solidus (bottom) with a constant forming force. In this case the force was the 3.1.1.4

Figure 3.1-4. Samples of aluminum foam bent by high-temperature forming.

3 Secondary Treatment of Cellular Metals

weight of the bending wing. As can be seen the material can be formed without collapse of the cell structure, and relatively large bending angles are possible. Owing to the properties mentioned above, the temperature range and with it the working area and the process window can be expanded. Thus, this material is very well suited to high-temperature forming process in contrast to the TiH2 foamed materials, which only show a small process window. 3.1.2

Machining

Conventional cutting and machining techniques like sawing, milling, or drilling all are suitable for processing metal foams. But using conventional machine tools causes surface distortion or damage to low-density metal foams [5]. Nevertheless, the conventional methods are satisfactory for most applications in which metal foams have to be machined [6, 7]. For accurate cutting electrodischarge machining (EDM), chemical milling, waterjet cutting, high speed cutting, or diamond sawing are recommended [5]. This is especially necessary for machining metallic foam specimens for testing, to avoid cell damage that would influence the properties of the samples. Owing to the cellular structure of metal foams there are different methods of machining the material. The appropriate technique should be selected according to the required quality of the cutting surface. For cutting of metallic foams reinforced with hard particles like SiC, a diamond cutting tool might be required. 3.1.3

Coating

Owing to their properties, metal foams have great potential in lightweight construction. At present there are few applications for metallic foams because foams with open surfaces show relatively low mechanical strength and are difficult to join to other parts. So metallic foams are not yet well suited to structural applications [8]. To further enhance the stiffness and strength of the foams they are often used as composites with roll-plated or adhesive bonded cover sheets. The cut surface of metal foam displays open cells and a rough texture, and is vulnerable to local damage [5]. It can be filled with an epoxy or other resin, or, in the case of syntactic structures that have a natural skin, the surface can be coated by conventional methods. These manufacturing methods are mostly limited to plane surfaces and do not allow complex shaped parts. By using thermal spraying techniques almost any desired form of foam-spray-deposit composites can be produced. Furthermore, there are considerable advantages concerning recycling and usage at elevated temperatures compared with adhesive-bonded composites [8].

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3.1 Forming, Machining, and Coating Figure 3.1-5.

Spray deposition diagram [8].

Mechanical Properties of Spray Deposits Thermal spraying is a surface technique using powder or wire materials melted by an energy source. The molten materials are accelerated and set onto the surface to be coated by a gas jet (Fig. 3.1-5). The energy source can be a wire arc or an inert gas plasma. Spraying materials can be metals, ceramics, or plastics. The mechanical properties of spray deposits are not the same as those of the bulk material, because there are differences in the structure. Spray deposits show anisotropic behavior determined by their lamella structure. During the rapid cooling process of the molten spray particles residual stresses develop, which, together with impurities or brittle phases like oxides inside the layer, may cause the lamellae to slide under load. Thus, normally the strength of the spray deposit is less than that of the intrinsic bulk material [8]. There are methods for improving the mechanical properties of the spray deposits. By preheating the substrate the cooling velocity, and with it the shrinkage stresses, can be reduced. The use of inert gas instead of compressed air for spraying decreases the proportion of brittle phases in the spray deposits. Furthermore, specific thermal treatment leads to significant improvements of the spray deposit properties. Metallurgical and positive substance joints between deposit and substrate result from diffusion and increase the adhesion of the deposit. In addition, diffusion causes an increase of cohesion of the lamellae inside the spray deposit [8]. The boundary layer between the foam core and the spray deposit is of essential importance for the properties of the composites. This layer has to transmit the maximum shear stress. If the adhesion of the spray deposit is not strong enough, this will cause delamination due to the shear stress. The deposit peels off by crack propagation in the boundary layer and so the whole component fails. Consequently, in the selection of the deposit materials both high specific strength and favorable spray characteristics have to be taken into account to get an optimum for the construction of structure parts. 3.1.3.1

Specific Difficulties in Foam Coating To get a stable boundary layer that is able to transmit the shear stress between foam core and spray deposit it is necessary to allow the sprayed particles to interlock with the substrate. To achieve this, the surface to be coated has to be pre3.1.3.2

3 Secondary Treatment of Cellular Metals

treated to roughen and to activate it. This is generally done by corundum blasting [8]. Currently available foamed semi-finished products made via the powder-metallurgical route have a thin smooth surface skin. This surface is often damaged during the blasting process, which opens the underlying pores. Thus, a surface treatment that is more suitable for foams is required because the spraying process is not able to fill the open cells and form a new plane surface. A suitable approach may be microblasting, in which the semi-finished foam products are blasted with low pressure and with particles less than 100 mm in diameter. Although the process parameters have not been fully investigated yet, the first results of the microblasting technique have been very satisfying.

Thermal Sprayed Composites from Metal Foams Currently aluminum foam is coated by wire arc spraying. By bringing the wires together in a strong electric field inside a spray gun, an arc is formed which causes the wire to melt. Then the molten particles are sprayed on the substrate by an accelerating gas jet. This is a widespread industrial process because it is economical and easy to use [8]. But using compressed air as accelerating gas has a negative effect on the formation of the spray deposit because of the oxides that arise in the different layers. In addition, the commercial wires are developed for corrosion protection and not for high strength and outstanding mechanical properties as required for metallic foam coating. An obvious improvement in the formation of the spray deposit can be achieved by the use of nitrogen (N2) as the acceleration gas, thereby causing significantly less oxides than compressed air (Fig. 3.1-6). The important process parameters are spraying distance, gas pressure, and arc power. The usual spray materials are AlSi6 and NiAl5. AlSi6 is normally used to repair damaged aluminum components and shows good properties regarding specific strength and hardness. A thermal treatment to improve the adhesion of the layers, on the other hand, reduces the mechanical properties of the deposit. NiAl5 is a typical spraying material used for its excellent adhering properties. It is easy to spray and facilitates the production of deposits with a very low proportion of oxide when used with an inert gas for spraying. Thermal treatment reduces the residual stres3.1.3.3

Figure 3.1-6.

High (left) and low (right) oxide NiAl5 layers [8].

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3.1 Forming, Machining, and Coating

ses and leads to a relatively small reduction of the hardness of the spray deposit. One disadvantage is the high density of NiAl5 compared with aluminum alloys. The use of highly tensile solidifiable aluminum alloys as spray materials is the subject of investigations at the present time [8]. Another technique more complicated than wire arc spraying but producing much better spray deposits is plasma spraying (Fig. 3.1-7). The spraying material is injected into an inert gas plasma as a powder and then heated and accelerated in the direction of the substrate. The material is an AlSi30 powder, which in conjunction with suitable process parameters leads to relatively hard deposits when sprayed. A practical thermal treatment of these spray deposits and their further mechanical properties are currently being investigated. Thermal spraying is a suitable and flexible method of producing composites with metallic foam cores. But investigations are still necessary with regard to the enhancement of the mechanical properties of the deposits as well as the pretreatment of the metallic foams.

Figure 3.1-7.

Left) spray deposit on aluminum foam [8]. Right) plasma sprayed deposit [8].

References

1. M. F. Ashby, A. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: A Design Guide, ButterworthHeinemann, Boston, MA, USA, 2000, Ch. 1. 2. M. Hahn, A. Otto, in MetallschaÈume, H. P. Degischer (ed), Wiley-VCH, Weinheim 2000, p. 432 433. 3. M. Hahn, A. Otto, in MetallschaÈume, H. P. Degischer (ed), Wiley-VCH, Weinheim 2000, p. 538 540. 4. M. F. Ashby, A. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: A Design Guide, ButterworthHeinemann, Boston, MA, USA, 2000, Ch. 2.

5. M. F. Ashby, A. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: A Design Guide, ButterworthHeinemann, Boston, MA, USA, 2000, Ch. 15. 6. Shinko Wire. Technical description: ALPORAS, Shinko Wire Co. Ltd., Amagasaki, Japan 1998. 7. MEPURA. Technical description: Alulight, Metallpulvergesellschaft mbH, Ranshofen, Austria 1996. 8. M. Maurer, E. Lugscheider, in MetallschaÈume, H. P. Degischer (ed), Wiley-VCH, Weinheim 2000, p. 523 526.

3 Secondary Treatment of Cellular Metals

3.2

Joining Technologies for Structures Including Cellular Aluminum

T. Bernard and H. W. Bergmann

Products of cellular aluminum are on the brink of widespread application. Various research projects concentrate on the characterization and simulation of the mechanical properties of the cellular structures, others target the reduction of the cost of production of cellular metals. However, until feasible joining technologies are not available, mass production of components is impossible. Though there are already well-known processes for the production of foam sheet composites like the roll-cladding process [1], other technologies have to be investigated for the partial stiffening of hollow extruded profiles. 3.2.1

Introduction

The aim of this contribution is to give an overview of feasible conventional joining technologies. Section 3.2.2 summarizes common techniques that are regarded as suitable for cellular metals according to the literature, ensuing an overview of feasible joining technologies for foam foam joints. The main focus however, is put on foam sheet joints and their properties in different loading cases as this is of greater interest for structural applications. The structure of the joints and their properties are described in Section 3.2.3 and Section 3.2.4. 3.2.2

Feasible Joining Technologies

This section summarizes conventional joining techniques that are feasible for compound structures utilizing aluminum foams.

Mechanical Fastening Elements There is a huge variety of mechanical fastening elements available. The possibilities range from hollow spheres- to metal-plugs, as well as nails, screws, and rivets. Experiments show that there are only a few suitable technologies in which the strength of the joint is approximately the strength of the applied cellular material [2]. With nails, only a frictional-fitting joining mechanism can be achieved with the consequence that the strength of the joint is too low for technical applications. In contrast to this, fasteners using not only a frictional-, but a form-fitting mechanism as well, are preferable. Screws, as well as some types of blind rivets, show this combined fitting mechanism. The application of wood screws is described in the literature [3]. Additionally self-drilling screws were investigated, 3.2.2.1

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3.2 Joining Technologies for Structures Including Cellular Aluminum

which have the advantage that no additional hole has to be drilled into the sheet material. The performance of the mechanical joints can be improved if the fastening elements are additionally smeared with epoxy adhesives before driving them into the foam [4,5]. A further possibility for joining foams with mechanical fasteners is the application of integral foams [3], where the foam contains parts made from bulk material. These parts, screw sockets for example, are integrated into the foamed structure and bonded to it during the foaming process. However, the locally distributed elements need precise positioning and suitable fastening in order to avoid a displacement caused by the foam motion during foaming. Consequently, not only is the weight of the cellular structure increased by integrating these parts, but the cost of production as well.

Gluing Gluing has been described as a feasible joining technology for aluminum foams [6]. Different gluing systems have to be distinguished. One-component systems are, for instance, epoxy-based and cure for approximately 30 min at 180 hC. The process conditions of these adhesives make them very interesting for car manufacturers, as the glue can cure during cathodic electrocoating and no further working steps are necessary. Epoxy-based systems are available as conventional glues or as expanding glues. The latter ones are very convenient for bridging high tolerances and for integrating foam bodies into hollow extruded profiles. In case a thermal curing process is undesired, two-component systems are available that cure at room temperature. By combining riveting and gluing it is easily possible to fix the foam body in the structure while the curing of the glue takes place. Additionally, the properties of the composite are improved in certain loading cases. 3.2.2.2

Welding Welding processes that have been shown suitable for joining aluminum foams are laser-beam welding [6] and ultrasonic (US) welding [7]. With the latter process, various geometries of the joining area are possible. They reach from quadratic joints with a maximum area of 100 mm2 to roller seam welds with a width of 1 5 mm and a maximum length of 500 mm. Finally circular bonding areas with typical diameters of 18 mm are producible. A characteristic of the US welding process is that it is a joining process in the solid state based on friction and consequently not a real welding process, where both joining partners are transferred into the liquid state for joining [7]. Laser-beam welding has been shown as a viable joining technology for aluminum foams [6]. Owing to its characteristics such as the keyhole effect and the minimal heat input, deeper parts of the structure can be integrated into the joint as well. Fig. 3.2-1 shows the principle mechanism of surface welding and the key-hole welding effect for bulk and foam material. 3.2.2.3

3 Secondary Treatment of Cellular Metals

Figure 3.2-1.

Surface welding and keyhole effect during laser-beam welding.

Soldering and Brazing Soldering and brazing of aluminum foams is impeded by their oxide layer, which has to be removed before or during the soldering process. There are two ways of removing the oxide layer: one is mechanical destruction by scratching, brushing, or ultrasonics, the other is the application of flux. The latter causes serious corrosion problems if it is not removed properly. In consequence, the joint requires good accessibility so that the flux can be washed out after the soldering process. This makes soldering with flux unsuitable for sheet foam composites, where a connection along the whole surface is desired. When removing the oxide layer mechanically, the use of foams with a casting skin is advantageous, as the oxide layer is easier to remove. 3.2.2.4

Soldering Various Sn- and Zn-based solders can be used for fabricating structures using Al foams [3]. Reliable joints are said to be possible without the use of fluxes, just by scratching the oxide layer. Another suitable technology is the S-Bond process, developed by Euromat [8]. This solder has a chemical composition of SnAg4Ti4 (wt.-%) and a melting range of 220 229 hC. The S-Bond process is a flux-free soldering process that is characterized by the mechanical ripping of the oxide layer that has formed around the molten soldering material. The oxides of the substrate layer are partially ripped during the soldering process, so that a metallurgical interaction of the soldering material and the substrate can take place. Additionally, the soldering material creeps below the oxide layer of the substrate and wets its surface totally. S-Bond is available as wire, rod or foil, which makes this process an interesting alternative for extensive joints. Though flux-free soldering technology can be transferred to aluminum foams, corrosion preventing measures have to be taken as the Sn- and Zn-based alloys can cause corrosion problems in combination with aluminum.

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3.2 Joining Technologies for Structures Including Cellular Aluminum

Brazing Brazing (Ti450 hC) is a feasible joining process for aluminum foams [9]. Though noncorrosive fluxes are available for brazing, it is advisable to coat the structure to protect it from humidity. The brazes are preferably Al-based and the furnace atmosphere should be inert. An alternative is the use of a porous filler material [9], which expands during the brazing process (Fig. 3.2-2). Thus a sudden change in porosity from foam to bulk material is prevented. The working temperature of the filler material has to be low enough that the porous base material does not deform during the expansion of the filler material. As outlined, there is a variety of suitable joining technologies available for fabricating structures utilizing aluminum foams. However, for a practical investigation the number of technologies has to be limited to one or two processes per category. Table 3.2-1 gives an overview and some characteristic properties of relevant joining technologies.

Figure 3.2-2.

Joining of Al foam and solid Al by brazing with a filler that expands to a foam [9].

Table 3.2-1. Characterization and classification of the joining technologies

Joining technology

Formation of the joint

Joining temperature

Joining class

Detachability

Riveting

point-contact

RT

mechanical

±

Screwing

point-contact

RT

mechanical

I

Gluing

area-contact

RT to 180 hC

adhesive

±

Riveting/Gluing

area/pointcontact

RT to 180 hC

mech./ adhesive

±

Flux-free soldering

area-contact

250 hC

thermal

±

Laser-beam welding

line-contact

Melting Point

thermal

±

3 Secondary Treatment of Cellular Metals

3.2.3

Foam Foam Joints

As the main requirement of industrial appliers are feasible technologies for foam sheet composites, the joining of foam±foam structures is shown only schematically. The authors have carried out feasibility studies for all joining technologies mentioned in Table 3.2-1 except for laser-beam welding. Laser-beam welding of aluminum foams is described in [10]. Though Al-foam joints can be made by this technique there are still many problems. Owing to the collapse of the cellular structures during welding, large amounts of filler material have to be used, which increases the density of the structure in the area of the seam. Another problem is the thickness of the foam structures, because they will not be welded through the whole cross section. Additionally, the number of joining geometries is limited when welding Al-foams. Only butt-joints have been investigated so far and it will be difficult to produce other joining geometries like T-joints and overlap joints. In contrast, most joint geometries can be realized with area contact joints. Table 3.2-2 shows the relevant joining techniques and the corresponding joining geometries.

Table 3.2-2.

Feasibility of the joining technologies for various foam-foam joining geometries Butt-joint

T-joint

Overlap-joint

Blind riveting

±

±

I

Screwing

±

I

I

Gluing

I

I

I

Riveting/gluing

±

±

I

Soldering

I

I

I

Welding

I

with restrictions

with restrictions

3.2.4

Foam Sheet Joints

The following text concentrates on processes for producing foam sheet composites [2,11]. Though there are other processes, such as the roll-bonding process [1], further technologies have to be investigated, for integrating foam bodies into hollow extruded profiles or for the partial stiffening of structural parts. In most

87

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3.2 Joining Technologies for Structures Including Cellular Aluminum

cases, foam sheet composites offer only one-sided accessibility. This has to be taken into consideration when selecting a feasible joining technology. Under these circumstances, all joining technologies listed in Table 3.2-1 are feasible.

Microstructural Investigations Figure 3.2-3 shows micrographs of the investigated foam sheet joints. 3.2.4.1

Screwing (Figure 3.2-3a) A form-fitting joining mechanism can not only be made by the bulge of a rivet, but also by the thread of a screw. As the foam material is compressed when the screw is driven in, enough material is present to fill the single parts of the thread, thus creating a form-fitting joining mechanism. Its strength, however, is highly dependent on the density of the foam and will decrease with it. Riveting (Figure 3.2-3b) Owing to the smooth surface of the rivet, there is only a friction-fitting mechanism in the area of the shank, whose peculiarity is basically defined by the number of cell edges adjacent to the hole. As already described (Section 3.2.2.1) a friction-fitting mechanism is not sufficient for metal foams and has to be combined with a form-fitting mechanism. In case of the displayed rivet, this is made by forming a bulge at the bottom of the structure, whose diameter is significant bigger than the pre-drilled hole. Gluing (Figure 3.2-3c) Gluing belongs to the group of joining technologies generating a material-fitting joining mechanism. This is caused by adhesive forces between the surface of the substrate and the glue. Consequently, well-glued samples should not fail at the interface, as the adhesive forces should be higher than the cohesive forces in the glue

Figure 3.2-3.

a) Screwing

3 Secondary Treatment of Cellular Metals

b) Riveting

c) Gluing

d) Soldering

e) Laser-beam welding Figure 3.2-3.

Micrographs of the investigated foam sheet joints.

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3.2 Joining Technologies for Structures Including Cellular Aluminum

or the substrate. The bonding of the glue and the surface might either be caused by ionic bonding or polar interactions [12]. Gluing is a feasible joining technology for foamed metals, independent of the presence of a casting skin. Though the area in direct contact with the sheet material is drastically reduced in the absence of a casting skin, the viscosity of the glue is low enough to fill the pores. The loss of surface can be compensated for by an additional form-fitting joining mechanism. Soldering (Figure 3.2-3d) Like gluing, soldering can be used as a joining technology generating an area-contact joining mechanism. In spite of the extensive oxide layer on the metal foam, interdiffusion zones form between solder and substrate materials, when applying S-bond. For soldered samples, the presence of a casting skin is advisable. As already described, relative movement between the parts is necessary during joining with a flux-free solder like S-bond [8]. Consequently, both surfaces have to be as plane as possible, so that the wetting of the substrate can take place everywhere. If there is no casting skin, the solder flows into the pores, but in contrast to glued samples does not form a material-fitting joint with the cell walls, as the oxide layer of the molten solder in the pores cannot be torn properly during the relative movement of the parts. Consequently, the remaining joining area would be limited to the number of the present cell edges, which would result in a reduced strength of the structure. Laser-Beam Welding (Figure 3.2-3e) The connection of the sheet to the foam with a laser is based on two principal joining mechanisms: a material one and a shape-related one. The heat input of the laser causes the melting of the sheet material and the underlying foam structure. After resolidification a metallic connection is created. However, this connection exists only between the molten sheet material and the molten material of several cell structures located close to the interface. The keyhole effect supports this mechanism. Because of the deep penetration of the laser beam, additional cells that are located in close proximity to the sheet surface can be included in the joining zone. Additionally, the concentrated heat input of the laser beam causes only minimal melting of foam structures outside the original joining zone. On the other hand, the molten material from the cover sheet and filler material flows into the pores of the foam structure during the welding process and fills them partially. The additional material prevents the formation of a seam groove and is responsible for the shape related connection mechanism.

Mechanical Properties of Foam Sheet Joints The load-carrying capability of the joints is highly dependent on the manner in which the joint is loaded. For this reason the joining technologies have to be tested in different loading cases. 3.2.4.2

3 Secondary Treatment of Cellular Metals

Geometry of the Samples and Testing Parameters Figure 3.2.4 shows sketches of the samples used for pull-out and tensile-shear testing. The geometries of the sandwich structures for bend tests and the corresponding testing conditions that were selected according to the given standards are listed in Table 3.2-3.

Figure 3.2-4.

Table 3.2-3.

Geometry of the samples for tensile-shear and pull-out testing.

Geometry of the samples for bend tests Dimensions (L q W q H) [mm]

Testing speed

Distance of the bending die/stamp

Four-point bend test DIN 53 293

240 q 25 q 10

5 mm/min

200 mm / 100 mm

Three-point bend test DIN 50 111

145 q 25 q 10

5 mm/min

free distance: 45 mm

Dynamic bend test

145 q 25 q 10

5.7 km/h

105 mm

91

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3.2 Joining Technologies for Structures Including Cellular Aluminum

Pull-Out Tests Pull-out tests were carried out with structures utilizing mechanical fastening elements. After preliminary investigations with a selection of conventional fastening elements, all fasteners were excluded that form the joint according to a frictionalfitting joining mechanism. Though good results with frictional-fitting fastening elements could be measured with large volume samples [5], the thickness of foams for technical applications such as the partial stiffening of structures should be limited to less than 10 mm. In this case however, there is not enough material left for the frictional interaction between cell edges and the fastening element, so that it will be torn out at low loads. Figure 3.2-5 shows some characteristic load deflection curves of joints utilizing mechanical fasteners with an additional form-fitting joining mechanism. Riveted samples show a larger range of deformation as the bulge has to be pulled through a hole of smaller diameter. This means that a great amount of deformation work has to be done. In contrast to this, the diameter of the investigated screws reduces to the tip of the screw. As a consequence, not much deformation work can be done when pulling out the screw, after the maximum load has been reached. Obviously, the pull-out load is dependent on the density of the foam material. The effect of relative density on the maximum pull-out load, Fr, is nonlinear with a power of about 1.5 [5] Fr ˆ Ar3=2

Figure 3.2-5.

loading.

(1)

Qualitative load deflection curves for screwed and riveted samples in tensile-shear

Tensile-Shear Tests Tensile-shear tests were carried out for the joining technologies listed in Table 3.2-1. The maximum shear loads for the joining technologies are given in Table 3.2-4. There are two different failure mechanisms that apply to point-contact joining technologies or area/line-contact joining technologies. Laser-beam welded and

3 Secondary Treatment of Cellular Metals Table 3.2-4.

Influence of the joining technology on the maximum load in tensile-shear loading

Joining method Riveting

Maximum tensile shear load 997 e 91.12 N

Screwing

1282 e 130 N

Riveting/gluing

1548 e 182 N

Gluing

2043 e 220 N

Flux-free soldering

2112 e 596 N

Laser-beam welding

580 e 116 N

glued samples tend to fail in the foam close to the joining zone. Consequently, the mechanical properties of the cellular structure influence the behavior under tensile shear loading. This is observable at a maximum load that represents the mechanical properties of the foam. After the maximum load is passed, the foam tears almost brittle. Laser-beam welded samples show a lower maximum load than glued samples as their joining area is smaller. Consequently the failure load is highly dependent on the number of welding seams. In contrast, riveted and screwed samples show ductile failure behavior under tensile-shear loading. The fastening element compresses parts of the cellular structure during the deformation. When the remaining cross section of the foam body is too small, the foam breaks, which is shown by an abrupt decrease of the load. Influence of the Foam Density on the Joint Strength for Line-Contact Joints Figure 3.2-6 shows that the strength of welded samples is highly dependent on the relative density of the foam [2], i. e. the number of the cell walls in the area of the joint. In these experiments the casting skin was removed before joining so that the resulting joining mechanism is based on a fusion of the sheet with the cell structures as well as by form-fitting due to a flow of the melt into the porous structure. The failure of the joint is observed to start close to the welding seam. The failure behavior can be described by a correlation between the foam density and the strength of the joint. s Metalfoam ˆ Cr2 max

(2)

ˆ rmin S ar s Metalfoam max

(3)

There are two ways of assessing the dependence of the strength of laser-beam welded composites on the foam density. For example, the strength of massive sheet sheet joints of about 210 N/mm2 (Fig. 3.2-6) would result in a relationship according to a power law (Eq. 2). In this study however, the joining partner is not a massive material but a powder-metallurgic produced aluminum. As a consequence, the values of the massive material cannot be reached with a density of

93

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3.2 Joining Technologies for Structures Including Cellular Aluminum

a)

b) Figure 3.2-6.

Influence of the density of the Al foam on the strength of laser-beam welded joints.

2.7 g/cm3. The values of composites utilizing a metal foam with a casting skin indicate a linear relationship between the foam density and the strength of the joint. Here, the casting skin must be assessed as a massive joining partner and the resulting density of the casting skin is 1.8 g/cm3 (linear regression of Eq. 3). The solution of the power law equation gives a lower value of 1.1 g/cm3. Bend Tests Influence of the Joining Technology on the Properties in Four-Point Bending With the help of the slopes in the linear section of the load deflection curves in four-point bending, it is possible to calculate the effective bending stiffness (EJ)eff of a sandwich element according DIN 53 293. The optimum joint is an area joint, so glued sandwich structures show the highest effective bending stiffness, which is equal to the theoretical bending stiffness (EJ)theo. Further results show that a decrease of the joining area by utilizing other joining techniques leads to a reduction of the stiffness of the structure. Therefore, riveted samples show the worst properties due to the puncture joint. The stiffness of the structure is additionally reduced by the holes that are necessary

3 Secondary Treatment of Cellular Metals

Influence of the joining technology on the energy absorbing behavior of a sandwich structure in four-point bending after a deflection of 10 mm (see Table 3.2-3).

Figure 3.2-7.

for integrating the rivets. Welded and riveted/glued samples show an average stiffness, like soldered specimens. As the integral of the load deflection curve (equal to the energy absorbed during the deformation) increases with rising stiffness, the stiffness of the composites is mirrored in the values of energy absorption up to a deflection of 10 mm (Fig. 3.2-7). Related to their mass, structures utilizing a steel sheet (applied joining technology: gluing) show the worst properties owing to the high weight of the sheet material. Composites utilizing a tissue on the tensile side of the structure are the lightest, but they have a low stiffness owing to the tissue. In consequence, the amount of energy that can be absorbed is comparatively low. Four-point bend tests with a constant bending moment along the sample serve for evaluating the stiffness of a sample. In the case of a three-point bend test the maximum bending moment is in the area of the bending stamp. Thus, three-point bend tests serve for evaluating the strength of the structure. Influence of the Joining Technology on the Properties in Three-Point Bending As in four-point bending, the joining technology has a strong influence on the properties of the composite. In contrast to the four-point bend tests, glued/riveted samples show the best properties in this loading case. Structures that were simply glued failed owing to cracks in the foam core. By combining the processes, the rivet relieves the foam core from high stresses and makes the structure less dependent on inhomogeneities of the foam. This is confirmed by the comparatively low variance of the results. Apart from the structures utilizing a tissue, all samples vary around the same value for the maximum load. For realizing a good energy absorbing behavior a ductile deformation behavior is necessary as well as a high maximum load. According to Fig. 3.2-8, which shows the amount of energy absorbed during three-point bending after a deformation of 10 mm against the mass of the structure, glued, riveted/glued, soldered, and laser-beam welded structures

95

96

3.2 Joining Technologies for Structures Including Cellular Aluminum

Influence of the joining technology on the energy absorbing behavior of a sandwich structure in three-point bending after a deflection of 10 mm (see Table 3.2-3).

Figure 3.2-8.

meet this requirement. Though the strength of the tissues is high enough, it fails after a comparatively low deformation owing to catastrophic fracture. Displaying the amount of absorbed energy in Fig. 3.2-7 to 3.2-10 shows that all key figures located on the same straight line through the origin of the diagram have the same mass specific value. With an increasing slope of the line, the mass-related properties increase as well. The goal of optimization is therefore to increase the slope of the line on which the values are located. This cannot only be achieved by a variation of the joining technology, but also by the density of the foam core. Influence of the Density of the Foam Core on the Properties in Three-Point Bending The results of three-point bend tests with structures utilizing a foam body without casting skin and an average density from 0.3 to 1.1 g/cm3 show that there is an almost linear dependence of the maximum load on the density of the foam core in the investigated density range.

Figure 3.2-9. Influence of the weight of the sandwich structure on the value of the absorbed energy up to a deflection of 10 mm (see Table 3.2-3)

3 Secondary Treatment of Cellular Metals

Comparing the performance of sandwich panels where the casting skin was still on the core material to those without casting skin reveals that the sandwich panels with core material without casting skin have a higher specific energy absorption (Fig. 3.2-9). As the foam is compressed in the area of the bending stamps during three-point bending, the loading mode in this area is consequently similar to a compression test. However, the casting skin is orientated perpendicular to the load and cannot enhance the energy absorbing properties. Thus the casting skin just decreases the mass-related energy absorbing properties in bending. Influence of the Joining Technology on the Properties in Dynamic Three-Point Bending Dynamic three-point bending of sandwich structures serves for simulating sudden impact, like in crash situations. The goal is to absorb an impact energy that is as high as possible. This can only occur if the sheets stay bonded well to the foam core during the whole deformation. Figure 3.2-10 shows the influence of the different joining technologies on the impact energy that can be absorbed against the mass of the structure. The results of the dynamic three-point bend tests basically confirm the results of the quasi-static tests. Glued and glued/riveted samples show the best properties, followed by soldered specimens, owing to the ductile deformation behavior of the joint in bending. Welded samples show a high variance. The high dependence of this joining technology on the porosity of the foam increases with the testing speed. If some parts of the structure are not joined well, owing to an uneven surface of the foam or because of big pores in the area of the welding seam, and if these areas are orientated unfavorably during the deformation, the composite structure fails almost without absorbing any energy. Under optimum conditions however, most of the kinetic energy can be absorbed. In this case, continuous seams show better results than step-welded seams. Step-welded seams are usually used in order to stop cracks propagating through the seam. However, in

Figure 3.2-10. Influence of the joining technology on the energy absorbing behavior of a sandwich structure in dynamic three-point bending (see Table 3.2-3).

97

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3.2 Joining Technologies for Structures Including Cellular Aluminum

the case of step-welded foam-sheet composites the share of insufficient joined areas is increased artificially by not joined areas, which leads to a decrease of the properties. 3.2.5

Transferability to Structural Parts

The basic fields of application of aluminum foams are energy absorbing structures and stiffening of structural elements. The following sections show the transferability of the described joining technologies to structural elements.

Tubes The integration of foam bodies in tubes for energy absorbing structures is well described elsewhere [13,14]. The results show that gluing as well as laser-beam welding are feasible joining technologies for this application. Figure 3.2-11 shows an X-ray of a crash-absorbing element partially filled with Al foam and a detail of the joining area. Regarding the triggering of the sequential buckling process, laser-beam welding shows some synergetic effects in axial loading, as shown previously [13,15]. The initial peak load of the characteristic load deflection curve in axial loading can be reduced, which leads to an increase in the effectiveness of the composite structure in axial loading. 3.2.5.1

Figure 3.2-11. Foam body integrated in an Al tube by laser-beam welding for an application as a crash element in the front side member of a vehicle [13].

3 Secondary Treatment of Cellular Metals

3.2.5.2

Hat-Profiles

Dynamic Three-Point Bend Tests All joining technologies listed in Table 3.2-1 are feasible for integrating a rectangular foam tube into a hat-profile. Figure 3.2-12 shows the single parts of the structure and the resulting composites after testing. The various joining strategies that were investigated included one-sided joining and three-sided joining, as shown in Fig. 3.2-12. Not only the selected joining technology, but also the joining strategy has significant influence on the properties of the composite structure. The properties were investigated in torsion tests and dynamic three-point bend tests. In the latter experiments, the impact mass was 600 kg, which hit the structure at a speed of 10 km/h. Figure 3.2-13 shows load deflection curves for three-sided glued and laser-beam welded structures.

Figure 3.2-12. Integration of a foam body into a hat profile for improving the torsion, bending, and energy absorbing behavior of the structure.

Figure 3.2-13. Influence of the joining strategy (one- or three-sided) and the joining technology on the deformation behavior of a hat-profile in dynamic three-point bending.

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3.2 Joining Technologies for Structures Including Cellular Aluminum

Owing to the optimum contact area of glued samples, the sheet material stays in contact with the foam during the whole deformation of the composite structure. In the welded sample, however, the sheet can deform independently of the foam in large areas, which reduces the energy-absorbing potential of the structure in a defined interval of deformation. Independently of the joining technology, three-sided joining improves the energy-absorbing properties of the structure. Torsion Tests The torsion tests shown in Fig. 3.2-14 show that glued samples have better properties than welded ones. Fewer folds form during the deformation process, which means that more deformation energy can be absorbed by the porous structure. In laser-beam welded samples, the welding seams that fix the foam core are the weakest part of the structure and tear during the loading process. Corresponding to the bend tests, the experiments with foam-filled hat profiles show that with increasing area of the joint, the properties of the composites increase.

Figure 3.2-14. Influence of the joining strategy (one- or three-sided) and the joining technology on the deformation behavior of a hat-profile in torsion.

3.2.6

Summary

In a final overview, Table 3.2-5 and Table 3.2-6 show the properties of the investigated joining technologies for different cases of loading, including a technological assessment of the joining technologies.

3 Secondary Treatment of Cellular Metals Table 3.2-5. Summary of the properties of the investigated joining technologies in the different loading cases (++ very good; + good; o overage; ± bad;/ not carried out)

Tensile shear test

Pull out test

Four-point bend test

Three-point bend test

Dynamic bend test

Riveting

+

++

±

±

±

Screwing

+

+

±

±

±

Gluing

+

/

++

+

+

Riveting/ Gluing

++

/

o

++

++

Laser beam Welding

o

/

+

+

o

Table 3.2-6. Final evaluation of the investigated joining technologies (++ very good; + good; o overage; ± bad)

Accessibility

Costs

Recycling

Functionality

Freedom of design

Transferability on structural parts

Riveting

++

++

++

+

o

+

Screwing

++

++

++

+

+

+

Gluing

o

o

o

o

++

++

Riveting/ gluing

±

o

o

++

o

+

Soldering

o

±

+

+

++

+

Laser-beam welding

+

±

++

o

o

++

101

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3.2 Joining Technologies for Structures Including Cellular Aluminum

References

1. H.-W. Seeliger, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 29. 2. T. Bernard, J. Burzer, H. W. Bergmann, in Sheet Metal 2000, B. Shirvani et al. (eds), Proc. 8th Int. Conf. Sheet Materials, 17 19 April 2000, University of Central England, Birmingham 2000, p.561. 3. N. SedliakovaÂ, F. SimaÂncik, J. KovaÂcik, in MetallschaÈume, J. Banhart (ed.), MIT Verlag, Bremen 1997, p. 177. 4. Information material of IWU Chemnitz, Germany. 5. O. B. Olurin, N. A. Fleck, M. F. Ashby, Adv. Eng. Mater. 2000, 2, 521. 6. J. Burzer, T. Bernard, H. W. Bergmann, in Porous and Cellular Materials for Structural Applications, D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS Symp. Proc. Vol. 521, MRS, Warrendale, PA 1998, p. 159. 7. C. Born, H. Kuckert, G. Wagner, D. Eifler, Materwiss. Werkstofftechn. 2000, 31, 547.

8. D. Pickart-Castillo, F. Hillen, I. Rass, Materwiss. Werkstofftechn. 2000, 31, 553. 9. K.-J. Matthes, H. Lang, Materwiss. Werkstofftechn. 2000, 31, 558. 10. I. Burmester, M. Goede, J. Bunte, Materwiss. Werkstofftechn. 2000, 31, 436. 11. T. Bernard, H. W. Bergmann, Materwiss. Werkstofftechn. 2000, 31, 440. 12. W. Bergmann, Werkstofftechnik, Teil 2: Anwendung, 2nd ed., Hanser Verlag, Munich 1991. 13. C. Haberling, H. G. Haldenwanger, T. Bernard, J. Burzer, H. W. Bergmann, Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 37. 14. R. Gradinger, M.Seitzberger, F. G. Rammerstorfer, H. P. Degischer, M. Blainschein, Ch. Walch, Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 313. 15. J. Burzer, Beitrag zur Einsetzbarkeit von MetallschaÈumen in der Verkehrstechnik, H. W. Bergmann, G. Ziegler (eds), Herbert Utz Verlag Wissenschaft, Munich 2000.

3 Secondary Treatment of Cellular Metals

3.3

Encasing by Casting

C. KoÈrner, F. Heinrich, and R. F. Singer

Foam parts prepared by expansion in a mold show a closed surface skin with a thickness comparable to the cell-wall thickness of about 200 mm. Even in cases where the surface near cells are compressed yielding a few layers of cell walls along the outer skin, it is not suitable for carrying high loads, as required for structural applications. Casting aluminum around a foam can create components where a low density foam core is completely surrounded by a massive outer shell. The shell can be designed in such a way that additional functions besides its load carrying ability can be fulfilled. As only one processing step is required to produce such a foam core component, production is expected to be very economical. Potential applications for this kind of foam core castings are space frame nodes, knuckles, control arms, cross-members, and stiffness providing structural components. The described method also offers the potential to produce quasi-hollow castings where conventional salt or sand cores are replaced by permanent foam cores in complex geometries. The various casting methods for the massive outer shell differ by the acting pressures, the die-filling time, and the solidification time, which is mainly determined by the temperature of the die. Generally, casting of the shell is not completely straightforward due to the limited compressive strength of the foam cores and the very thin surface skin, which is not without flaws [1]. A further difficulty results from the fact that methods have to be developed for fixing the cores. The following text is based on three publications: squeeze-casting, Kretz and Kaufmann [2]: high-pressure die-casting, Heinrich, KoÈrner, and Singer [3,4]; and gravity die-casting, Simancik and Schoerghuber [5]. 3.3.1

Foam Cores for Encasing by Casting Core Production A prerequisite for encasing by casting is a dense foam surface. At the moment there are two production routes resulting in a solid surface skin, the powder compact foaming, like Alulight and the FORMGRIP process. Both processes comprise baking of a foamable precursor material in a mold. They differ in the way the precursor material is produced (Section 2.1). Up to now the aluminum foam cores used for encasing were exclusively produced via the powder compact technique. There are two different methods: the furnace baking method and the injectionmolding technique [5]. It depends on the core geometry whether the first or the second method is more suitable. Generally, for very complex cores the injection molding technique is particularly suitable. Another difference between the two methods is the fact that the surface skin of the foams produced via the injec3.3.1.1

103

104

3.3 Encasing by Casting Foam core inserts produced by compaction of aluminum powder mixed with TiH2: a) for sand casting (ca. 300 cm3, baking furnace) [2], b) for squeeze casting (baking furnace) [2], c) for die casting (baking furnace) [3,4], d) for gravity casting (injection molding) [5]. Figure 3.3-1.

tion-molding technique is thicker than that of the furnace baking method. This is an advantage for encasing but it also increases the weight of the core. Figure 3.3-1 shows several core geometries used for different encasing techniques.

Core Attachment A suitable core attachment system has to perform two functions: first it has to keep the core in place in the die when the die is open and during the movement of die closing. The more important second function is to maintain the desired distance between the foam core and the die wall during the casting process because this distance determines the wall thickness of the castings. One method to realize a suitable attachment of the core is by creating elongated wedge-shaped spacers during the foaming process of the cores (Fig. 3.3-2). These spacers have to be long enough to transfer the acting forces to the foam core without damage. It is very important to place the spacers corresponding to the melt flow to avoid flow barriers resulting in ªdead zonesº. This is especially true for die- and squeeze casting, where the melt freezes quickly. 3.3.1.2

Figure 3.3-2. Al foam core insert with spacers to prevent movement in the die during casting of the shell [4].

3 Secondary Treatment of Cellular Metals

Mechanical Properties The aluminum alloys used for the foam cores are wrought or casting alloys. Generally, the porosity of the surface, from the appearance of cracks or open cells, is higher for the casting alloys. On the other hand, due to their smaller cell size, casting alloys are more tolerable against penetration of melt. This is especially true for small samples. Besides defects already present there are two important properties of the cores that determine the processing parameters during high-pressure casting: the foam compression strength (global strength s CG) and the compression strength of the surface skin (local strength s CL). The global strength s CG (Fig. 3.3-3) defines the maximum allowed pressure in the process without foam compression [3]. The samples prepared of the wrought alloy (Fig. 3.3-3) show a significantly higher scatter of the values compared to the casting alloy. This is a result of the small sample thickness of 10.5 mm and the coarser pore structure of the wrought alloy foams in the present case. It is observed that infiltration of foam cores already occurs at pressures that are much lower than s CG. This is either the result of open pores in the surface or the product of a local fracture of the surface skin. As a consequence, an indefinite pore volume is infiltrated. The local compressive strength s CL can be measured by a compression test where a liquid (water) exerts a homogenous pressure on a foam surface of 25 mm q 25 mm (Fig. 3.3-4) [4]. From simple mechanical considerations one finds that the maximum bending stresses acting in the cell walls that make up the surface are proportional to 3.3.1.3

p(D2/d2) t p(1/d2r2) where p ˆ pressure, D ˆ cell diameter, d ˆ cell-wall thickness, r ˆ foam density. As a result, the local compressive strength s CL increases with increasing density.

Figure 3.3-3. Global compressive strength s CG versus density of several Al foam samples from plates produced via the furnace-baking method [4].

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3.3 Encasing by Casting

Figure 3.3-4. Average values of the local compressive strength versus density of several foam samples produced via the furnace-baking method [4].

There is a strong scatter of strength values due to the inhomogeneous cell structure of the foams. The results in Fig. 3.3-4 demonstrate that the strength of the foam surface skin has to be improved for squeeze and die casting, which are characterized by a very high pressure. For gravity die casting the global strength as well as the local strength are not so important.

Coating of the Foam Cores In order to obtain reproducible and sound castings, foam infiltration has to be avoided. That is, for high-pressure casting s CL has to be improved. This can be achieved by reinforcing the foam surface by an additional coating. The coating method has to meet two requirements: it has to be applicable to complex geometries and in reasonable thickness. This is fulfilled by a plasma-sprayed coating of Al99.5 or a coating made from a ceramic slurry. By increasing the thickness of the coating the local compression strength is increased until the global compression strength is reached. For even higher thicknesses the foam is no more damaged by local breakage of cell walls but by global compression (Fig. 3.3-5). Experimentally it was found, that for coatings with a thickness higher than 350 mm local damage is completely suppressed and foam damage is by global compression. Since both, the local and the global strength show the same dependence on the foam density the critical thickness of the coating is supposed to be independent of the foam density. 3.3.1.4

3 Secondary Treatment of Cellular Metals

a)

Optical micrographs showing foam inserts after the local compressive test: a) no coating, surface damage occurs at low pressure level preferentially at locations with large cells; b) ceramic coating with d ˆ 300 mm,

Figure 3.3-5.

b)

c)

breakage of the surface at high pressure levels; c) Al plasma sprayed coating, d ˆ 200 mm, local damage and overall collapse by compression deformation, d ˆ 400 mm, compression [4].

3.3.2

Shell Casting Processes

Depending on the used casting process, different requirements have to be fulfilled by the foam cores and the processing conditions. The difficulty lies in producing sound casting shells without infiltration or deformation of the foam core. In addition, local melting of the surface skin has to be avoided. It was found in former experiments made in sand and permanent mold casting, that melting of the skin may occur in particular in the gate area where incoming hot metal can cause damage to the thin foam skin by heat and erosion [2]. This effect can be avoided by surface coatings or by use of foam cores with a thicker skin. Available coatings are lubricants or die coatings, which are in use in the foundry industry to cover molds and sand cores before casting. In the following two different approaches are described in more detail: pressureless casting and high-pressure casting.

High-Pressure Casting Processes The difficulty during high-pressure casting processes is to avoid infiltration and deformation of the foam cores. For this reason, controlled solidification and pressure build-up are necessary to ensure that the melt solidifies on the surface of the aluminum foam core and that growth of a cast skin occurs before the maximum pressure is applied so that the cast shell itself is able to bear the load of casting pressure. 3.3.2.1

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3.3 Encasing by Casting

Squeeze Casting [2] The squeeze-casting process (Fig. 3.3-6) is characterized by slow, high-pressure bottom-up filling of the die and provides similar die-filling conditions as in low pressure permanent mold casting. The clamping unit of a squeeze-casting machine is similar to that of a conventional high-pressure die-casting machine. The shot unit is placed below the machine and fills the die vertically. The shot speed is very slow compared to the high-pressure die-casting process. The shot pressures can be varied from 300 to 1200 bar. This controlled filling is ideal for sensitive inserts such as foam cores. Figure 3.3-7 shows the arrangement of the foam core in the die. The casting trials were performed with three foam alloys (Al99.5, AlMgSi1, AlSi10) and two different materials for the casting of the shell: AlSi9Cu3 and AZ91. Figure 3.3-8 shows the cross section of an AZ91 magnesium casting with an aluminum foam core. The gate speed was approximately 0.5 m/s. The melt pressure had to be reduced to a very low level to avoid foam core deformation and core infiltration. In most trials infiltration occurred due to the small range of possible parameter variation of the squeeze-casting machine. By casting with suitable machine parameters, the UBE squeeze-casting machine allows the production of castings with wall thickness of 3 23 mm in which the

Figure 3.3-6.

Schematic representation of the squeeze-casting process [2].

Figure 3.3-7. Arrangement of the foam core insert in the squeeze-casting die [2].

3 Secondary Treatment of Cellular Metals Figure 3.3-8. Cross section of a AZ91 squeeze-casting part with AlMgSi1 aluminum foam core [2] (150 x 60 x 39 mm3).

cores are not infiltrated and not deformed. However, the processing window for achieving good samples without core infiltration or core deformation is a very narrow one. Die Casting [3] [4] Essential for die casting is controlling dwell pressure with the help of a real-time control system [3,4]. In the first phase of the conventional die-casting process the die is filled with melt as fast as possible. In the second phase very high dwell pressures are applied to balance the shrinkage and to minimize porosity of the castings by compressing the entrapped gases. Because of the high velocity of the castingpiston a high pressure peak appears at the end of the first phase when the die is completely filled resulting in massive foam infiltration and collapse (Fig. 3.3-9). In order to avoid this peak, a real-time controlled die-casting machine is indispensable. With real-time control it is possible to control the casting velocity and the casting pressure at every step of the casting process. That is, the piston can be decelerated at the end of the filling phase to prevent the pressure peak. To use a real-time controlled machine an accurate dosage system is required. The castings were performed with the standard casting alloy AlSi9Cu3. The melt temperature was about 720 740 hC, die temperature about 250 270 hC. Casting investigations were carried out on two demonstration parts (Fig. 3.3-10).

Figure 3.3-9. Comparison of dwell pressure with and without real-time controlled die-casting machine [4].

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3.3 Encasing by Casting

Figure 3.3-10. Two different demonstration parts with foam core inserts encased by die casting: a) trapezoid, b) plate [4].

As core materials the casting alloy AlSi10 and the wrought alloy AlMg1 were used. The upper bound of the pressure inside the die is limited by the global compression strength of the foam core. It is about 60 100 bar and can only be raised by increasing the foam density.

a)

b)

Figure 3.3-11. a) Infiltrated pore volume versus specific casting pressure of several casting experiments with coated and uncoated foam cores. b) Porosity in the cast outer skin versus specific casting pressure of several casting experiments with coated and uncoated foam cores [4].

3 Secondary Treatment of Cellular Metals

Casting experiments with coated and uncoated foam cores were performed for a plate-like geometry with different specific casting pressures pNS. The specific casting pressure is the operating dwell pressure in the casting chamber. It has to be taken into account that the actual acting pressure inside the die is much lower because of friction. Figure 3.3-11 shows the infiltrated pore volume VI and the porosity in the skin versus pNS. As expected infiltration increases with increasing pNS whereas porosity in the skin decreases. By using coated foam cores a significant reduction of core infiltration is possible. In accordance with the tests to determine the local compression strength, the plasma-sprayed plates show the best results. More recent results achieved with optimized die design and process conditions (evacuation of the die) demonstrate that the porosity of the skin can be reduced even to less than 5 % without infiltration of the core. The minimum skin thickness is about 2 mm for die geometries evaluated so far. Gravity Casting [5] The foam core samples (AlSi12 and AlMg1Si0.6) used had a density of 0.8 0.9 g/cm3 and were prepared by injection of the foam into sand molds (Fig. 3.3-12) using the injection-molding technique. They were inserted into an existing gravity casting die (steel) with conventional gating and risering. The casting alloy AlSi9Cu3 at 740 hC was used to cast the outer shell around the foam cores. In contrast to die- or squeeze casting the acting pressures during gravity casting are insignificant and much smaller than the local compressive strength of the foam cores. That is, as long as there are no large cracks in the foam surface infiltration or compression due to high pressures is not observed during gravity casting. No melting of the foam core could be detected in the experiments performed (Fig. 3.3-13). Pouring liquid metal around the foam core results in heating up and consequent expansion of the gas inside the pores. In contrast to the high-pressure casting methods the gas is not prevented from diffusing from the core into the melt where it forms bubbles. That is, the expanding gas can cause porosity in the shell or even destroy the integrity of the casting because of gas bubble formation. This expansion of the gas and the deterioration of the shell can be minimized by preheating the cores before insertion.

Figure 3.3-12. Pressure-less casting: Foam core, encased core, and cross section with foam core (height of the foamed part 25 cm, maximum width of the cross section 12 cm) [5].

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3.3 Encasing by Casting

Figure 3.3-13. Aluminum casting with different foam cores: left, AlSi12 foam; right, AlMg1Si0.6 foam (diameter of the foam filled tubes 6 cm) [5].

Another advantage of preheating the cores is that cold shuts, which appear in regions of the castings with the lowest thickness of the shell, can be avoided. The preheating of the cores leads to a lower heat flow from the melt into the core, thus enabling reduction of the wall thickness in comparison to usual sand cores, which can not be preheated. With preheating temperatures of 400 hC the minimum shell thickness is found to be about 1.5 mm.

Bonding Between Shell and Foam Core Generally, no bonding develops between the core and the shell during casting because of the continuous aluminum oxide layer that prevents the core surface from reaction with the molten metal [5]. The same effect occurs using aluminum cores in magnesium squeeze castings [2]. The contact time appears to be too short for significant reactions between the aluminum oxide skin and the magnesium melt. There are two possible ways to improve the bonding [5]. 3.3.2.2

x

x

Mechanical bonding by flow of liquid metal into the outer foam structure supported by intentional weakening of the surface skin, e. g., by sand-blasting. Disadvantage are that the weight of the casting increases and the bonding occurs only locally and is difficult to control. Metallurgical bonding by coating the cores with various agents supporting diffusion through the aluminum oxide layer. With a suitable metallic coating a metallurgical bonding can be achieved. On this point, however, further research is necessary.

The shrinkage of the cast shell during solidification leads to a pressure fit of the inserted core. For most applications metallurgical bonding will not be necessary to achieve the required component properties such as improved energy absorption behavior or improved damping properties. The absence of bonding may sometimes even improve structural damping of the part due to additional energy dissipation at the shell/core interface [5].

3 Secondary Treatment of Cellular Metals

References

1. H. P. Degischer, A. Kottar, Metal Foams and Druckgieûverfahrenº in MetallschaÈume 2000, Vienna, Wiley-VCH, Weinheim 2000. Porous metal Strutures, J. Banhart, M. F. Ashby, A. Fleck (eds), MIT Verlag, Bremen 4. F. Heinrich, C. KoÈrner, R. F. Singer, ªEncasing of Al Foams by Die Casting as 1999, p. 213 Manufacturing Process for Light Weight 2. R. Kretz, H. Kaufmann. ªFabrication of Componentsº in Proc. Materials Week 2000. Squeeze Castings with Permanent Aluminum Foam Coresº in EUROMAT, Metal Ma- 5. F. Simancik, F. Schoerghuber, ªComplex Foamed Aluminum Parts as Permanent trix Composites and Metallic Foams, Munich Cores in Aluminum Castingsº in Porous and 1999. Wiley-VCH, Weinheim 1999. Cellular Materials for Structural Applications, 3. F. Heinrich, C. KoÈrner, R. F. Singer. MRS, San Francisco, CA 1998. ªHerstellung flaÈchiger Leichtbauteile durch Umgieûen von Aluminium-SchaÈumen im

3.4

Sandwich Panels

J. Banhart, W. Seeliger, and C. Beichelt

For structural applications metal foams are often used in combination with conventional dense metal structures such as sheets, columns, or more complex-shaped hollow metal structures. This allows for optimized mechanical properties in a given loading situation [1]. It also facilitates ªhidingº the metal foam inside a closed and dense structure, which again is advantageous for corrosion protection. Such composites containing aluminum foam may be manufactured in various ways. The most obvious and straightforward one is achieved by adhesive bonding of pre-fabricated aluminum foams and flat face sheets. However, this approach has certain disadvantages and is not feasible in all cases. An alternative and preferable method consists in establishing composites during the foaming process. Foamfilled columns can be produced by inserting foamable precursor material into a column and then heating. The foam will eventually rise and fill the column. Another possibility is to start with a foamed part and to coat it with aluminum by thermal spraying [2] thus establishing a dense outer skin. Yet another way is to use the foam as a core for die-casting [3,4]. Aluminum foam sandwich (AFS) panels may be manufactured very elegantly by roll-cladding face sheets to a sheet of foamable precursor material, then creating the desired shape in an optional working step, and by finally foaming the entire composite [5,6] (Fig. 3.4-1). Foaming will create a highly porous core structure without melting the face sheets if the melting points of the foam and the face sheets are different and process parameters are chosen appropriately.

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3.4 Sandwich Panels

Figure 3.4 -1.

Process steps for making sandwich panels with aluminum foam cores.

3.4.1

Sandwich Foaming Process

The formation of a metal foam sandwich may be visualized by making use of an X-ray technique that has been developed recently [7] and allows for the monitoring of the internal structure of expanding metal foams. Since the technological implementation of the production process for aluminum foam sandwiches still suffers from occasional flaws that can be traced back to inadequate process parameters and defects in the foamable material, the X-ray investigations may also help to identify such problems. One example of this is shown in Fig. 3.4-2. The foaming of this particular sandwich panel was carried out at a furnace temperature of 750 hC. The first frame corresponds to an early stage of foaming. The foamable core layer already shows a slight absorption contrast to the face sheets, indicating that some porosity has already formed at this stage. Moreover, a crack may be seen on the right upper side running right through the foamable layer. The second frame, showing the situation just 5 s later, reveals that the foaming of the core layer takes place in a highly non-uniform way. The restricted heat flux through the face sheets leads to a temperature gradient and triggers the foaming process near the interface of face sheet and core layer. As can be seen from Fig. 3.4-2, the crack in the precursor material has deepened after the initiation of the foaming process and still extends over the entire foam layer. After 22 s of ongoing foaming, however, the core layer is fully expanded and the crack has disappeared. Therefore, this type of defect does not lead to an obvious defect in the foam sandwich. In order to obtain a complementary view of expanding metal sandwich structures, metallographic images have been made of samples that were foamed to a given expansion stage and were then quenched. Three of these images are shown in Fig. 3.4-3. The unfoamed sample shows a sharp boundary between the foamable core (characterized by the angular-shaped gray silicon particles embedded in the light aluminum matrix) and the dense face sheets to the right. The foamed sample in the middle, which is at a stage corresponding approximately to that of full expansion, shows the typical microstructure of an under-eutectic aluminum-silicon alloy. The light aluminum-rich grains surrounded by the eutectic phase can be easily identified. The dense face sheet is virtually pore-free and

3 Secondary Treatment of Cellular Metals Series of radioscopic images of an expanding AlMn1/AlSi7-foam/AlMn1 sandwich [8]. Foamed at a furnace temperature of 750 hC.

Figure 3.4 -2.

shows no structure in the low magnification chosen. The interface of foam and face sheet lies on a straight line and is well defined. Finally, the foamed sample on the right hand side of Fig. 3.4-3 represents an even later stage of expansion. It exhibits a notably coarser grain size distribution in the foam and a slightly diffuse boundary between foam and face sheet. The eutectic phase has grown into the former face sheet material by diffusion processes and has locally amalgamated with the face sheet alloy: one reason for the excellent bonding between foam cores and face sheets in properly manufactured aluminum foam sandwich parts and the explanation of the absence

Figure 3.4 -3. Metallographic images of sandwich structures with an AlSi7 core. Three different expansion stages are shown: left) unfoamed precursor material; middle) sandwich

shortly before maximum expansion; right) sandwich at the onset of face sheet melting. The width of each image is 0.75 mm.

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3.4 Sandwich Panels

of face sheet delaminations in tests of the tensile strength of sandwich structures. 3.4.2

Industrial Application

On the basis of technological advantages and limitations, application strategies have to be developed in order to simplify the decision whether or not AFS components should be used in a certain production process and to avoid unrealistic decisions. The application of light-weight materials often implies higher costs and, compared to steel, eventually a loss of stiffness and an increase of manufacturing problems. For a technically and economically successful application of AFS components, a new approach to vehicle body architecture is required [9]. For an application in the ªBody in Whiteº technique (BIW) about 90 % of the current design concept requires a complete change. The space frame, for instance, should be designed considering the stiff AFS components in a way that the special properties of AFS may be optimally exploited. A simple replacement of steel parts by AFS parts will not suffice since the benefit of the stiffened planar surfaces are not employed efficiently. Therefore, a new BIW architecture must be developed. Examples for such new concepts are shown in Fig. 3.4-4 and Fig. 3.4-5. Whenever replacing conventional materials by AFS, it must be taken into consideration that the range of AFS properties includes some characteristics that have previously been achieved by additional parts. For example, the use of AFS for the fire wall could imply the elimination of heat shields and the associated connect-

Figure 3.4 -4. ªDetroit Show Car 1998º developed by Karmann (Osnabru Èck) for demonstrating potential uses of aluminum foam sandwich panels. The rear bulkhead and the front firewall (not directly visible) are made of AFS.

3 Secondary Treatment of Cellular Metals

Figure 3.4-5. ªEUROC 99º concept racing car: left) CAD model of entire car; right) space-frame structure with AFS parts.

ing parts. The application of AFS parts may also lead to an elimination of noise attenuation materials because of the low structure-borne sound characteristics of AFS. Another area of interest to be investigated in the future is that of exterior panel closures, e. g., doors, hoods, and decklids. This application depends on the achievement of a Class-A surface with stamped AFS panels. Taking a hood stamped out of AFS as an example, there is no longer any need for an inner panel due to the inherent stiffness of the AFS outer layers, thus reducing expenses for material, tools, and the complete assembly. In spite of higher material expenses, an AFS bonnet may (depending on the shape) be more cost-effective than a steel hood up to a production volume of 100 000 units. This is attributed to the reduction of manufacturing and tooling expenses. This means that light weight AFS constructions may be applied economically in low and middle production volumes due to the reduced investment costs compared to conventional steel components. In general applications, possible additional costs of AFS panels should be compared to the advantages that can be expected. Even if only one of the improved characteristics of AFS is required for a particular application, the associated increase of expenditure may be of secondary interest. In general, the application of AFS components will increase overall material costs, so that an enhanced performance must be achieved as justification. In the future, this situation may change as vehicle operating costs gain more significance due to the higher energy costs. As a consequence, this implies that the amount of money available for the use of light materials, which is right now about 2.5 5 Euro per kg weight reduction, will increase.

Technological Benefits Besides the advantages already known (the combination of high torsional stiffness with low weight) further properties of AFS must be taken into account as they also may have a major impact on the implementation strategy. 3.4.2.1

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Acoustic Properties Considering the customers comfort requirements, a new lightweight body material is not allowed to show inferior acoustic properties than steel. Therefore, the good acoustic properties of AFS should be emphasized. Especially cars with aluminum bodies show poor damping properties. To improve this situation, a large amount of damping material must be added, thus sacrificing the mass saving potential. A joint research by the TU Dresden and Karmann has revealed that AFS offers a significantly better acoustic behavior especially in the range 50 400 Hz. Additional insulation measures may be reduced: weight is saved. The acoustic performance of special insulation materials will of course not be attained, so that AFS cannot exclusively serve as a sound damping material. Thermal Properties Thermal conductivity is another important aspect when selecting body materials. Due to the entrained air bubbles, the heat transport capabilities of foams are low. Depending on the density, the thermal conductivity of AFS is reduced to 1/12 1/20 of the conductivity of bulk aluminum. Furthermore, AFS satisfies most of the fire protection regulations. No adhesives are contained and the AFS components maintain their shape up to the melting point of 600 hC and in some cases even above. The exceptional welding characteristics together with minimal distortion justify to characterize AFS as ªthermally very stableº. Robustness Sandwich components, as known from aerospace technology, are relatively vulnerable in impact situations. Even small damages of honeycomb panels may lead to a complete breakdown of the core panel structure. As a result of the metal link between core and panels, this does not occur in an AFS panel. Cracks may only occur in the core and their expansion is limited. A delamination of core and panels has not been detected with parts manufactured and tested to date. This is very important since structural body components are not subject to special checks during the product life cycle Other Properties Additional properties of AFS that enhance product performance are: good energy absorption, recyclability, and low manufacturing time periods for the sandwich components. The foaming process, e. g., takes only 30 45 s even for large parts. Therefore, mass production with a comparably low number of parallel production lines is possible.

Technical Limitations When selecting applications for AFS components, their formability and geometry after the foaming process must be taken into consideration. A constant component thickness may only be achieved with plane sheets. Complex formed structures will 3.4.2.2

3 Secondary Treatment of Cellular Metals

Figure 3.4 -6.

limitations of manufacturability of AFS.

have a variable thickness in different areas of the component. However, these thickness variations are predictable and may be adjusted to component loads by simulations, since the upper layers maintain their original geometry during the foaming process. The form tolerance after foaming is e1 mm. Drills and trim cuts will be performed with the help of a trimming/calibration tool, so that additional reference surfaces and flanges may be established. U-form shapes should generally be avoided, as they show an adverse relation between the side and base surfaces, which leads to differences in the thickness of the foam (Fig. 3.46). This effect is primarily due to the stiff inner layer, which should shorten up when the thickness is constant. There are limitations to the determination of the gage relation between outer layers and core due to current processing techniques. The minimum thickness of the outer layer is limited to 0.6 mm. A skin thickness less than this may cause a degradation of the alloy during foaming and is undesirable. Under optimum process conditions, the foam layer may expand up to the extent of seven times of its original thickness. The maximum achievable height ranges from 25 30 mm. Thicker foam cores should be avoided because of the different cooling rates within the foam, which may result in a non-uniform core porosity. 3.4.3

Joining Technology of AFS

In order to be able to efficiently exploit the advantages of AFS technology, it does not suffice to exchange highly stressed parts with AFS parts. AFS technology requires special construction as well as joining techniques, adjusted to the characteristics of sandwich parts. The joining of AFS parts may be attained by a variety of possible processes. The most important ones are given in Table 3.4-1.

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3.4 Sandwich Panels Table 3.4 -1.

Overview of joining techniques for AFS.

Process

Details

Laser welding

CO2 -laser, Nd:YAG

TIG welding MIG welding

by hand, partly mechanized, by robot

Pin/bolt welding

by hand, mechanized

Punch riveting

AFS/aluminum; AFS/steel

Riveting nuts/screws

M4

M8

Flow drilling

M4

M8

Riveting

blind riveting, splay riveting

Bonding

1-K and 2-K systems

Laser Welding The process of laser welding is suitable for series production. In order to weld face sheets of 1.2 mm 3 kW power are required. By bluntly welding sandwiches, only the face sheets are bonded, while the core layers remain unaffected. As shown in Fig. 3.4-7a the filigree cell structure is not damaged by the local thermal impact. In welding flat AFS sheets with linear joints, a maximum speed of 10 m/min has been achieved. If both face sheets have to be bonded, usually the part has to be turned thus decreasing the welding speed to a rate less than 5 m/min. 3.4.3.1

TIG/MIG Welding Welding of AFS parts by common welding techniques is also possible. The principle techniques worth mentioning are TIG- and MIG-welding (Fig. 3.4-7b). Both techniques are exceptionally well suitable both for joining two AFS parts and also AFS parts with aluminum parts. The advantages of these techniques include flexible application possibilities, the amount of experience in this field and the low investment costs. The high degree of stiffness of AFS sandwich parts, their low thermal conductivity and the resulting low thermal distortion rate minimize the necessary efforts for clamping and fixing the parts. As in laser welding, only the face sheets have to be welded. Welding rates for manual TIG welding reach 0.3 m/min, those for MIG welding reach 0.8 m/min. Partly mechanized welding with a linear carriage may achieve a rate up to 1.3 m/min. 3.4.3.2

3 Secondary Treatment of Cellular Metals Different welding techniques for AFS: a) laser welding, b) TIG welding, c) bolt/pin welding.

Figure 3.4 -7.

a)

b)

c)

Bolt/Pin Welding Another joining technology of considerable interest for AFS sandwiches is that of welding bolts (Fig. 3.4-7c). These bolts do not transfer high forces but are employed for fixing cable bundles and wires or as mass contacts. The welding process is completely controlled and monitored with the help of a welding head with a linear motor. This technology allows for the regulation of variations of the thickness of the sandwich. As with the other techniques, the core layer remains intact in the welding area. Even welding a bolt directly onto a flaw, e. g., a void or a large pore 3.4.3.3

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3.4 Sandwich Panels

has no impact on the quality of the bonding as the joining zone is obviously limited to the face sheet.

Punch Riveting Due to the increase of mixed constructions and the problem of thermal impact on the structure by assembling parts by welding, this joining technology has been strongly forced in the recent years. Since 1994, Punch Riveting is applied in construction of the AUDI A8 and has reached its momentary peak in the construction of the A2 with 1800 die casts per car. Figure 3.4-8a shows the joining area as well as a cut of the fusion. Studies of the settling properties of the core layer have shown another positive characteristic of AFS sandwiches. If AFS is highly com3.4.3.4

a)

b)

c) Figure 3.4-8. Different joining techniques for AFS: a) punch riveting, b) riveting nuts and screws, c) flow drilling.

3 Secondary Treatment of Cellular Metals

pressed, its tensile strength drops to a value of 50 % plastic deformation, but regains the original mechanical values of the nondistorted sandwich at maximum compression. This property is a result of the increasing mechanical clutching of the collapsed cell structures and the likewise increasing friction. The mechanical values of compression strength and shear stress do decrease in this range but they stabilize again at a low level under static as well as under dynamic load.

Riveting Nuts and Screws Another possible joining technique consists in the placing of riveting nuts and screws (Fig. 3.4-8b). The joint cannot transfer high forces. It is rather employed to fix holders and devices. The size of the nuts and screws may range from M4 to M10, depending on the thickness of the AFS parts and the face sheet. 3.4.3.5

Flow Drilling Flow Drilling (Fig. 3.4-8c) is an alternative to riveting nuts. Frictional heat is generated by a multi-polygon that is pressed onto the face sheet in axial direction at a high revolution rate/speed. The material plastifies and becomes easily formable. One will get a defined drill-hole and the material of the face sheets will flow into the core. The length of the formed hole wall will be three to five times the thickness of the face material. The minimum revolution rate for flow drilling lies at about 2400 rpm at a spindle moment of 1.5 kW. A coated thread cutter is used at a revolution rate of 500 rpm. The lifetime of the flow former and the thread cutter amounts to 10 000 drills and threads. But so far only feasibility studies have been carried out. 3.4.3.6

Riveting AFS parts may also be riveted. Especially in mixed constructions, riveting is very well suitable. It is important to choose a relatively large diameter of the rivet head since too small a diameter leads to a fastening pressure of the rivet that compresses the core. Due to the high surface pressure one will find plastic deformations on the face sheets. 3.4.3.7

Bonding AFS with face sheets of aluminum may be bonded with the same technology as conventional aluminum sheets (Fig. 3.4-9). The same parameters have to be respected as there are the creation of a defined surface, a construction adapt for bonding and especially the choice of an adequate bonding system. The strength of today's bonding systems partly exceeds the physical values of the aluminum foam cores. One of the main advantages of bonding lies in the optimum transmission of the applied forces. This technology allows the AFS parts to be excellently integrated into the surrounding structure. 3.4.3.8

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3.4 Sandwich Panels Figure 3.4 -9.

Bonding of AFS

3.4.4

Cutting of AFS

Cutting of AFS structures, the unfoamed precursor material as well as the foamed sandwich panels, can be quite a challenge, especially in the latter case. Here, conventional mechanical cutting techniques cannot be applied in a straight-forward way because of the danger of uncontrollable deformation of the material. Therefore, two alternative methods have been evaluated.

Laser Beam Cutting Laser beam cutting of the unfoamed material has been successfully evaluated [10±12]. A high precision of cutting into the desired net-shape without the need for further processing was achieved (see Section 3.1). Cutting of the foamed materials required a special adaptation of process parameters to take account of the specific nature of AFS. Both face sheets have to be cut simultaneously. Moreover, the low-density foam tends to melt more than the face sheets leading to the deposition of metal and dross at the opposite side of the sandwich panel, which lower the quality of the lower cutting edge [13]. Good results with cutting a 12 mm AFS could be obtained by adjusting the laser power to 5 kW and the cutting speed to 0.8 m/min. 3.4.4.1

Water Jet Cutting Water-jet cutting of unfoamed AFS precursor is possible without any problems. Cutting of AFS sandwiches, however, imposes the problem, that abrasive particles remain in the pores after cutting and cannot be entirely removed even by repeated swilling with water or solvents. Such contaminations are not acceptable in cases in which the sandwich panels have to be varnished as they would lead to inferior surface qualities [14]. 3.4.4.2

3 Secondary Treatment of Cellular Metals

References

1. M. F. Ashby, A. G. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal foams: a Design Guide, ButterworthHeinemann, Oxford 2000. 2. M. Maurer, E. Lugscheider, Materwiss. Werkstofftechn. 2000, 31, 523. 3. F. Heinrich, C. KoÈrner, R. F. Singer, Materwiss. Werkstofftechn. 2000, 31, 428. 4. T. HoÈpler, F. SchoÈrghuber, F. SimancõÂk, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT-Verlag, Bremen 1999, p. 79. 5. J. Baumeister, J. Banhart, M. Weber, German Patent 44 26 627, 1994. 6. J. Baumeister, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT-Verlag, Bremen 1999, p. 113. 7. J. Banhart, H. Stanzick, L. Helfen, T. Baumbach, Appl. Phys. Lett. 2001, 78, 1152. 8. J. Banhart, H. Stanzick, L. Helfen, T. Baumbach, Adv. Eng. Mater. 2001, 3, 407±411 (2001).

9. W. Seeliger, Entwicklung und Programmierung eines Materialmodells fuÈr elastoplastische MetallschaÈume, Thesis, University of Bremen, MIT-Verlag, Bremen 2000. 10. W. Seeliger, ªFertigungs- und Anwendungsstrategien fuÈr AluminiumschaumSandwich Bauteile, AFS (Aluminum Foam Sandwich)º in Proc. IIR Werkstoff-Kongress, 22 23 Jan 2001. 11. R. Braune, A. Otto, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT-Verlag, Bremen, 1999, p. 119. 12. R. Braune, A. Otto, Materwiss. Werkstofftechn. 2000, 31, 562. 13. R. Braune, C. Beichelt, in Lasertechnologien im Automobilbau, Stuttgart, 29 Feb 1 Mar 2000. 14. C. Beichelt, in MetallschaÈume Verfahren und Komponenten fu È r den Leichtbau, J. Baumeister (ed), Workshop, Bremen, 7 8 Mar 2001.

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Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

4 Characterization of Cellular Metals B. Kriszt

We are familiar with natural cellular structures such as wood and bone: these natural materials are structured hierarchically. In engineering, man-made cellular materials (porous construction materials and cellular polymers) have been used for a long time because of their remarkable thermal insulation. A new group of cellular materials has been invented more recently: the cellular metals. When we study different man-made cellular materials we soon recognize that they also show a hierarchical architecture. As in nature, every production process leads to a different cellular structure, so clearly cellular structures are determined by the process by which they are made. However, when we want to describe a cellular metal we say Alporas, Alulight, or Inco foam, and do not describe exact structural quantities. So before we can characterize cellular metals, we need to understand the significant parameters necessary to describe the architecture and the hierarchy. First, we can think of a cellular metal as a heterogeneous composite material of a metal and a gas. If only the metal matrix is observed, the microstructure consisting of grains, precipitates, dendrites, or different phases can be seen, but there is no information on the architecture of the cellular metal. This hierarchical level is often called the microstructure of the metal. The density of the cellular metal depends on the volume fraction of metal and gas. Consequently, cellular metals are characterized by their density compared to the parent metal: the relative density. Typical metal foams have relative densities of less than 0.3. Typical porous metals have relative densities greater than 0.3 but less than 1.The density of cellular metals, in absolute units or as relative density, is one of their main characteristics. From the density of a cellular metal part, we have an instrument for describing the material at the ªmacroº level. The second main characteristic is the cellular architecture. Often fluctuations in cellular architecture lead to inhomogeneity in density, so the local density distribution can describe a cellular metal more precisely. This way of describing cellular structures belongs to the ªmesoº level.

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However, the definition of macro, meso, and micro is not yet standardized: in Section 4.1 a scheme is discussed that helps to clarify the classification of the hierarchical structure. Real cellular metals do not have perfect ideal cells, but the analysis of ideal cells is nevertheless helpful for describing the architecture of cellular metals. The ideal cells model describes the whole structure in terms of at least one space-filling three-dimensional unit cell; in most cases we can think of polygonal cells. For example, honeycombs are networks of channels having hexagonal cross section; metallic foams, sponges, or lattice block material are representatives of real 3D polygonal cellular metals. Cellular structures in which adjacent cells are separated by cell walls or faces are called closed-cell foams or metals: the other group, open-cell foams or metals, are permeable. Sometimes this classification is not clear, because in some cellular metals both closed cells and open cells can be observed. To get a feeling for a 3-D structure, we conceptualize a space-filling unit cell of an ideal structure (Fig. 4-1). From a geometric point of view it is helpful to think of a cellular structure formed by a skeleton of cell edges (struts), which merge at nodes (vertices). One space-filling unit cell is the Kelvin tetradaidecahedron cell. This cell has a low surface area per unit volume. Most foams made by expanding a gas in a liquid tend to form such a cell shape. For this reason, this cell type is often chosen for modeling cellular metals [1 6]. Knowing the geometry of the unit cell allows us to calculate the relative density of the cellular metal. From the example of the Kelvin cell, we can elaborate the main structural features used for characterization. Certain parameters are needed to describe the cell shape, the cell size, the topology, the geometry of cell struts, nodes, and walls, and their relation to neighboring cells. Often it is helpful to define also parameters that describe the imperfections or the defects of a cellular material compared with the ideal unit cell (see Section 4.1). A long list of parameter can be defined, but we have to ask critically if these serve a useful purpose. If we want to understand relations between processing parameters and cell structure (Chapter 2, and Section 4.1), as well as between cell structure and the property profile (Section 4.1 and Chapter 5), we need to investigate and quantify the cells and their imperfections as precisely as possible. Another task that requires structural parameters is modeling the mechanical behavior of cellular metals (Section 4.1 and Chapter 6). Input data derived from characteristic cell features of real foams are needed for generating virtual cellular networks, such as the Voronoi network, for examples.

Figure 4-1. Space-filling ideal tetrakaidecahedral unit cell (Kelvin cell) showing cell walls, edges, and nodes.

4 Characterization of Cellular Metals

Typical metallographic methods are used to characterize features of metallic cells. Ordinary methods such as optical microscopy and quantitative image analysis give information on pore size, cell-wall thickness, orientation, and neighboring correlation (Section 4.1). Another task for characterization (which might become more important) is the inspection of the quality of cellular components: the definition of which is not yet established (Section 4.3). The basis of any specification is the apparent density. A rough estimate of density can be gained by weighing a sample of known volume. A more accurate result can be obtained using the principle of Archimedes. Unfortunately, not all components have a closed surface, so the penetration of the test liquid has to be prevented or it will invalidate the result. The local density distribution of cellular components can be determined by X-ray radiography or computed tomography (XCT) (Section 4.2). A local density can be determined to check if the distribution of the metal is homogeneous; if not there might be hard or soft regions in the component. Technical XCT scanners having a spatial resolution of up to ten microns allow us to study the cell structure and the defects in the cells. Besides XCT, other nondestructive testing methods such as ultrasonic testing, eddy current measurements, or lock-in thermography are under consideration for the inspection of density distribution and defects. From this introduction it can be concluded that structural analysis is the basis of cellular metal and foam research. We seek relationships between the structure and the processing technique, the property profile, and the description by modeling. Chapter 4 will give an overview of typical structures of metallic foams and show how structure influences the property profile (Section 4.1). In Section 4.2 an outline of XCT, a typical nondestructive testing method for cellular material, is given. Based on XCT technology, quality features can be derived, which are discussed in Section 4.3.

References

1. L. J. Gibson, M. F. Ashby, Cellular Solids: 4. N. J. Mills, A. Gilchrist, J. Appl. Mech. 2000, Structure and Properties, 2nd ed, Cambridge 122, 67. University Press, UK 1997. 5. J. L. Grenstedt, K. Tanaka, Scripta Mater. 1999, 40(1), 71. 2. M. J. Silvia, L. G. Gibson, Int. J. Mech. Sci. 1997, 39(5), 549. 6. T. Daxner, H. J. BoÈhm, F. G. Rammerstorfer, 3. W. E. Warren, A. M. Kraynik, J. Appl. Mech. R. Denzer, M. Maier, Materwiss. Werkstoff1997, 64, 787. techn. 2000, 31, 447-450.

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4.1

Characterization of Cellular and Foamed Metals

B. Kriszt, U. Martin, and U. Mosler

It is known from modeling of ideal cell structures and demonstrated by experiment, that the real cell structure of a cellular material is the key factor that determines its properties. This fact leads to the need for characterization of cellular materials. The objective of characterization is to define the relevant structural parameters and to understand their influence on the properties of the cellular material. In this section the main structural features are described and their influence on properties is shown. 4.1.1

Definition of Structural Features of a Cellular Metal and Influence on Property Profile

As can be seen in Fig. 4.1-1, we can define a list of more than 30 structural parameters for describing the geometrical structure (architecture) and the microstructure of cellular materials. As already discussed in the introduction of Chapter 4, cellular metals are heterogeneous materials, like composites, because the pores are embedded in the metal cell skeleton. The shape and arrangement of the cells is called the geometrical structure or architecture. In some cellular metals the geometrical architecture

List of parameters for describing structure of metallic foam; depending on the resolution, geometrical structure and microstructure can be defined.

Figure 4.1-1.

4 Characterization of Cellular Metals

can be observed visually, so the length scale of cell size can range from some tenths of millimeters to some centimeters. For acquiring images of the outside appearance of the geometrical structure either digital video cameras or ordinary scanners can be used. Typical magnifications that can be reached with these systems are up to tenfold. If we zoom in on the cell material, we will see another hierarchical level or substructure, the microstructure of the cellular skeleton. We can observe the structure of metallic cell material, micropores, and cracks at a resolution of microns by using light microscopy or scanning electron microscopy. If transmission electron microscopy is used, the lateral resolution is increased to nanometers and we may observe dislocation structure or small precipitates. From this, it becomes clear that cellular materials are more than heterogeneous materials: they are structured hierarchically. When describing cellular materials, one has to be aware that different structural features that can influence the properties of the cellular material can be defined for each hierarchical level. Understanding such a complex system is rather difficult. As a consequence, no general material rules based on real structures can be developed to explain the influences of structure and architecture on properties. Furthermore, no guidelines for the characterization of cellular metals have been established. In recent years structural features that influence the properties have been identified but their interactions and effects on real metal foams are not known quantitatively.

Density and Volume Fraction of Pores One of the most significant structural characteristics seems to be the density distribution. A clear relation between relative density, stiffness modulus, and compression plateau stress was derived from the scaling model of Gibson and Ashby [1]. The scaling laws were verified recently by others [2,3]. Based on the scaling laws the influence of inhomogeneous density distribution on mechanical properties is understood quite clearly (see Section 6.2). Originally the scaling law was derived from structural parameters such as length and thickness of edges of a cubic cell; these structural features were assumed to be constant and can be replaced by the relative density [1]. Astonishingly, density is not commonly determined in quantitative structural analysis [4]. The density distribution of real cellular metals is influenced by many structural features as shown in Fig. 4.1.-2. The higher the volume fraction of pores in a cellular material, the lower is the density of the material. So the volume fraction of pores seems to be a significant quantity. With the exception of CT tomography (see Sections 4.2 and 4.3), investigations of nontransparent 3D structures is restricted to analysis of cross sections. Assuming certain boundary conditions, the laws of quantitative image analysis give relations between 2D and 3D structural features [5]. Using these laws, the volume fraction of pores can be derived from the area fraction of pores. The volume fraction of pores is a global parameter and gives no information about the arrangement, size, or shape of pores. For example, two types of cellular metal can have 4.1.1.1

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132

Figure 4.1-2.

Dependence of density on structural features of pores and cell skeleton.

the same density, but one samples can have one or two big pores that represent most of the volume fraction of the gaseous phase, and the other sample (for instance made by a replication technique or investment casting) can consist of a network of nearly uniform small pores. Figure 4.1.-3 shows differences in structures of cellular material.

a)

Figure 4.1-3. a) Closed-cell foam, geometrical structure of Alulight foam produced by PCF: irregular pore size and shape can be seen.

4 Characterization of Cellular Metals Figure 4.1-3. b) Open-cell Ni: regular and uniform pore size and shape.

b)

Shape and Size of Pores Even if the pore (or cell) size is uniform and the pores are arranged regularly, this information is not sufficient to describe the cellular metal. Also, pores can take preferred orientations. Because of the structural characteristics explained before, two more sets of quantitative parameters have to be defined: one to describes the properties of each pore (object parameters) such as size, shape, or orientation and the second to characterize the topological properties of the cellular material, such as arrangement and neighborship relations. For each of these sets of features it is possible to define a certain number of structural quantities. So, for instance, the pore size can be described either by 4.1.1.2

x

x

an equivalent diameter of the pore, which is defined as the diameter of a sphere or circle having the same volume or area, or as the maximum, minimum, or average length of the pore.

The impact on properties is different; it has been shown that cell size of carbon foams has an influence on compression strength, but not on stiffness and fracture toughness [6]. Even if we assume that pore size has an impact on the mechanical behavior, no experimental work shows how large pores act in real metallic foams, so they have to be classified as a ªknock-downº factor, or defect, for mechanical properties. It has been shown that the size of the pores, combined with a certain shape, for example an elliptical shape and a certain orientation, can allow deformation bands to start [7]. In Fig. 4.1-4, orientated and elongated pores in Alulight are marked. A study of pore characteristics in Alulight foam revealed that pores in the deformation zone have significantly different orientation from pores in undamaged material [8]. Similar behavior was deduced from in-situ experiments using computed tomography [9]. Unlike structural applications, the pores size becomes an important feature if the cellular metals are used in heat exchangers or in filter systems (see Section 7.2).

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Figure 4.1-4. Inhomogeneous distribution of pores size: misoriented and large pores.

Cell Skeleton After characterizing the pore structure, it still remains to define quantities for describing the cell skeleton. As explained in the introduction of this chapter, the skeleton consists of cell nodes interconnected by cell edges. In a closed-cell structure, the cell edges are connected by cell walls that separate the cells. The volume fraction of metal in nodes, edges, and walls defines the density of the cellular material. The features that can be described are number of nodes, number of cell edges and walls per cell, length, thickness, and curvature of cell edges, angle between nodes and cell edges, and shape of cell edge, number of cell walls connected of edges and of edges connected at nodes (connectivily). A drawback of quantitative image analysis of nontransparent samples is that it is difficult to define the exact position and extent of the cell walls, edges, and nodes, as well as the range of these features. All these parameters have an influence on mechanical properties. As long as the cellular material is nearly uniform and perfect, these are the most important parameters, but in real foams parameters are necessary to characterize agglomeration of solid material. Klocker proposed the analysis of covariance function for detection of clustering [10]. In a comparison of undeformed and crushed Alporas samples, clustering of cells could be shown by a drop in covariance. Another way of characterizing clustering is the pair correlation function [16], but this method has not yet been applied for describing cell clustering in metallic foams. Defects in Cellular Metals and Foams Another important aspect of characterizing the cell material is the description of imperfections. All structural features that degrade the properties determined by the scaling law of Gibson and Ashby, are classified as ªknock-downº factors or defects. First of all there are geometrical imperfections. These are deviations from ideal polygons or irregularities in edge pattern. Models (see Chapter 6.1) revealed that imperfections or defects such as wavy distortions of cell walls, variations of cellwall thickness, or non-uniform cell shape decrease the stiffness and strength of

4 Characterization of Cellular Metals

cellular material [11 14]. Unfortunately, most metallic foams tend to show many of these defects. Defects in cell edges and walls have been identified as reducing the elastic modulus of metallic foams significantly. Two different typical defects are known: curved cell edges and corrugated cell walls and edges. Corrugated cell walls are typically found in metal foams such as Cymat (Alcan) or Hydro foams, which have rather thin cell walls compared to the cell size (Fig. 4.1-5). Curved or corrugated cell walls occur during forming or on solidification. In modeling, cell edges or walls are often described by beam or shell elements having an ideal shape and constant thickness. In real foams, the metal is thicker at cell nodes and edges because of the dynamics of metal flow during foaming. Flow of the melt also causes the rupture of cell walls. During solidification, dendritic growth at a free surface and shrinkage of the melt can induce roughening of cell walls, edges, or nodes. Figure 4.1-6 shows the surface of a solidified cell wall. The shrinkage of the melt during solidification and cooling leads to cell-wall wriggling and also cracks in cell walls. The influence of initial cracks on toughness or fatigue behavior is still under discussion. The formation of micropores is also connected to sucking of liquid into the nodes (Plateau effect). Owing to the increased amount of liquid in nodes, the solidification starts at the surface of the nodes caused by the heat flow. While the

Figure 4.1-5. Corrugated cell walls in foam produced by the melt process (Combal).

Figure 4.1-6. Defects in cell walls

(microcracks, roughness of surface).

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nodes solidify the melt is consumed and, as know from casting, small voids occur in the middle of the node. This can be observed as micropores in cell nodes or thicker cell edges.

4.1.2

Characterization Methods and Quantities of Geometric Architecture of Real Metallic Foams

Although XCT is now established for the investigation of metallic foams (see Section 4.2), the characterization of metallic foams is usually performed using quantitative 2D image analysis methods. Most papers concentrate on the characterization of cell structure derived from analysis of cross sections. For further reading on the principles of stereology the reader is referred to the basic literature of Exner [15] and Ohser [16]. In the following section the structure of cellular metals and metallic foams are described and typical structural features are discussed. Before going into detail on structural analysis, some information on the preparation techniques for metallic foams is given.

Sample Preparation The first step in preparing a metallographic specimen is to cut a sample from a foamed part. In the early days of foam research, great uncertainty led to insistence that metallic foam should only be cut using spark erosion machines in order to prevent damage to cells or cell walls. Our results have shown that using a precision saw at low cutting speed and force gives results just as good as spark erosion, but with a reduction in time and cost. In the next step, the specimens are often embedded under vacuum in epoxy, so that the pores are filled and a conventional metallographic preparation with grinding and polishing can follow. The procedure of filling epoxy in the pores has be repeated several times until all the pores are filled. This method gives good results if the microstructure of the cell-wall material is studied using light microscopy. If using scanning electron microscopy on epoxy-embedded samples the surface can become charged: a higher conductivity embedding substance, such as Cu-enriched epoxy, will help to improve the resolution and quality of the images. Another method of preparing the sample for digitizing by scanning was proposed by Kriszt et al. [17]. In this method the foamed samples are precision cut, followed by coloring the sample and smooth grinding, so that the contours of the cell structure on top of the sample regain their metallic luster. This is a practical way of analyzing the geometrical structure of big areas. After the preparation, the surface can be scanned using a high resolution mode and converted into a digital image. Figure 4.1-7 depicts prepared cross sections of Alporas foam prepared by this technique. 4.1.2.1

4 Characterization of Cellular Metals Geometrical structure of Alporas foam, sample preparation for digitizing by scanning technique.

Figure 4.1-7.

Pore Size Figures 4.1-3a, 4.1-4, 4.1-5 and 4.1-7 depict the differences in structure between metal foams produced by the powder compact technique, such as Alulight or Fraunhofer foam, and the melt process route, such as Alporas, Cymat, and Combal Foam. Alulight seems to have more irregular cell shape and size than Alporas. This is a typical feature of PCF materials. Another structural feature of metallic foams such 4.1.2.2

a)

Figure 4.1-8. Pore-size distribution of Alulight: a) equivalent diameter versus frequency of pores; b) equivalent diameter versus b) frequency of area.

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4.1 Characterization of Cellular and Foamed Metals Figure 4.1-9. Pore-size distribution of Alporas: a) equivalent diameter versus frequency of pores; b) equivalent diameter versus frequency of area.

a)

b)

as Alulight is the non-uniform distribution of solid metal in the foamed part (see Fig. 4.1-3a and 4.1-4). Zones having an enrichment of solid material are referred as hard spots in the literature [18]. Measurements of the pores size for both foam types have shown that they have the same average equivalent diameter of about 3 mm. The distribution curves of equivalent diameter versus frequency of pores of both foam types show a bimodal shape (Fig. 4.1-8a and Fig. 4.1-9a). The large fraction of small pores is caused by solidification shrinkage. Interestingly, it seems that the Alulight material always shows a broader distribution curve. Because of the high number of small pores, the cell-size distribution is dominated by the small pores. The presentation of area fraction of a pore class over equivalent diameter helps to emphasise the contribution of big pores to geometric structure (Fig. 4.1-8b and Fig. 4.1-9b). The presence of outliers can be made more visible if this method of presenting the results is used. Outliers having a pores size bigger than five times the average pore size can be detected in nearly all samples produced by PCF techniques, such as Alulight. This is not the case in metallic foams produced by the melt route.

4 Characterization of Cellular Metals

Figure 4.1-10. Density as a function of pore size for various foam types (data for FORMGRIP process from [20]).

Measurements of cell size published by Miyoshi et al. distinguish between two types of Alporas foams: one conventional type for sound absorption having a cell-size range of 1 13 mm and another type having smaller cells of 1 7 mm [19]. While Alulight and Alporas have a similar pore size, metallic foams such as Hydro or Cymat foams are known for a pore size of more than 1 cm. The main difference between these two groups of foams is that for Alulight and Alporas TiH2 particles are used as the blowing agent and in the second group gas blown directly into the melt leads to the formation of pores. As already discussed in Section 4.1.1, the density and the pores size are two quantities that are used to characterize foams. It is recognized that these quantities are interdependent, but nevertheless many users demand that density and cell size be tailored independently. Taking data from the FORMGRIP process [20], it can be shown that density is a function of pore size (Fig. 4.1-10). The same result was confirmed by KoÈrner et al., who investigated pore evolution during foaming [21]. They proposed that the mean cell size is proportional to the reciprocal value of density. This holds true if Alulight, Alporas, Hydro, or Cymat foams are examined.

Pore Shape Assuming that cells of metal foams have ideal polyhedral shapes, such as the Kelvin cell, it should be possible to find a correlation between that number of sides of each pore in the 2D cross section and 3D shape [15,16]. But Degischer et al. showed that the pores in metallic foams do not have an ideal polyhedral unit cell [18]. Hence, in 2D analysis the characterization of shape is limited to the use of shape factors for comparison of different foam types. 4.1.2.3

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From quantitative structology different methods for defining shape factors are known. Klocker defined the ratio between the largest and the smallest principle cell dimension as the shape anisotropy ratio [10]. A similar definition was used by Simone (ellipse shape ratio) [22]. Another shape factor is circularity, which is the ratio of pore area and the square of pore perimeter [23]. For all mentioned shape factors a value of 1 corresponds to a circular shape. The circularity allows one to interpret the shape of the cell; the circularity of a rectangle is 1.4 and that of a regular pentagon is 1.1. Klocker has shown that the shape anisotropy ratio of Alporas and Alulight has an average ratio of 1.5 [10]. The ellipse shape ratio of Alulight foam is Gaussian distributed, and has an average value of 0.6 [17]. In Cymat foam an ellipsoidal shape ratio of a factor of 1.8 was found [22]. Studies of evolution of pore shape during foaming revealed that foams having a low expansion rate (high density) tend to have pores with a circular shape. As the foaming process proceeds the shape of the pores becomes rectangular or ellipsoidal [23].

Pore Orientation The definition of pore orientation is only sensible if a reference system is defined. Depending on the target of the investigation, reference axes are oriented to some main directions of processing, such as the foaming direction or the feed direction of conveyor-belt systems. Another kind of reference system can be defined by the direction of loading. The only foam types in which the pores have a systematic and significant orientation in relation to processing are Hydro and Cymat [22]. Generally, Alulight and Alporas foams do not have a pronounced pore orientation [17,22]. 4.1.2.4

Thickness of Cell Edges and Walls Although the cell-wall thickness has a great influence on mechanical properties, very little information on real cell-wall thicknesses is published. This might be due to the difficulty of defining the transition from node to cell wall or edge. Hence it is difficult to measure this structural feature with quantitative image analysis. Berger showed that the distribution of cell-wall thickness has an asymmetric shape for foams produced by powder metallurgical technique [23]. The smallest cell-wall thickness that was found is about 70 mm. The maximum cell-wall thickness was about 500 mm. A cell-wall thickness of about 150 mm was the most frequent thickness. Astonishingly, the thickness of cell walls is independent of foam density. Klocker characterized the ratio of mean thickness to mean length of cell wall for Alulight and Alporas [10]. Both foam types show an extremely asymmetric distribution. The maximum frequency of about 40 % at a ratio of 0.1 in Alporas is more pronounced than the maximum frequency in Alulight with 15 % at a ratio of 0.18. 4.1.2.5.

4 Characterization of Cellular Metals

The ratio of mean thickness/length in crush-fronts revealed that in both foam types the distribution is the same. The most frequent ratio is 0.1. Mosler et al. analyzed the width of cell edges in Alulight foams [24]. The average width does not exceed 130 mm, so it can be calculated that the average length of cell edges in Alulight foams is about 750 mm.

Topological Features The most difficult task in characterizing the foam structure is the description of topological relations. If no model for the complex geometrical structure of real foam is known, our understanding of topology of cellular material based on a 2D analysis is limited. First attempts have been made by calculating tessellation for cell structures. Klocker measured the average number of neighbor cells for Alporas and Alulight [10]. The number of neighbor cells varies between 1 and 10. The average number of neighbor cells in Alporas is 4.5, in Alulight material the average number is 5 cells, slightly higher than in Alporas. In deformation bands caused by compression, the analysis of neighbor cell zones gave a smaller number [10]. Another parameter that helps to describe the topological relations is the distance to nearest neighbors. For Alulight foam Mosler et al. found a mean average distance of about 900 mm [24]. The characterization of the pattern of 2D cell arrangement can be described by tessellations. Some information on tessellations of cellular structures can be found elsewhere [10,24]. Klocker's results are optimistic about the description of Alporas foam by Voronoi tessellations, whereas the results on Alulight, because of its strong dependence of cell structure on the position in the specimen, are not so promising. Klocker suggested the Johnson Mehl tessellation as an alternative that takes into account the curvature of cell walls. In contrast to Klocker's work, the investigations of Mosler et al. confirmed that Voronoi tessellation give good agreement with the geometric structure of Alulight [24]. The explanation for the contrary results might already be given by Klocker, who assumed that inhomogeneity in the structure of Alulight causes this result. 4.1.2.6

4.1.3

Characterization of Microstructure of Massive Cell Material

Knowledge of the microstructure (grains, grain boundaries, precipitates, dislocations etc.) of metallic foams is essential, because of the effect of microstructure on mechanical properties. As has been shown, foamed samples having the same density but made of different alloys reach different plateau stresses [25]. Different hardnesses support the theory that the microstructure is responsible for different plateau strengths [26]. More ductile alloys, such as wrought aluminum alloys, show a ductile collapse of cells under compression; brittle cast alloys deform by crushing of cells. This different behavior is why the strength of a foam made of a wrought aluminum alloy in-

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creases continuously, while the second foam shows remarkable fluctuations in strength [25]. Another phenomena where influence of microstructure can be observed clearly is the increase of strength after tempering treatment of metallic foams due to precipitation hardening [26,27]. In most metal foams alloying elements or particles have to be added so that a stable liquid foam is gained (Fig. 4.1-12). These additions often modify the alloy or even change it completely. For instance, the Alporas foam consists of an unusual aluminum alloy, additions of 2 % calcium change the constitution completely. The reader is referred elsewhere for further information on microstructure of Alporas, Cymat, and Alcan foams or FORMGRIP samples [28,29]. FORMGRIP samples are stabilized by adding particles such as SiC, so they show a microstructure similar to that of particle-reinforced composites [29]. All microstructures of foamed materials are in a solidified undeformed state. like the microstructure of castings. Depending on the chemical composition, metallic dendrites, eutectic cells, precipitates, or particles are found in metal foams (Fig. 4.1-11). Even if the cell walls are thin, it can be estimated that the cooling rate is not too high, because dendrites have a size of hundreds of microns. In many cases the size of dendrites or eutectic cells is equal to the thickness of cell walls. Most of the dendrites are equiaxed or sometimes even globular (Fig. 4.1-11a) [30]. This can be explained in two ways: first the superheating of the melt during foaming is as much as in common melts, because superheating immediately leads to collapse of foam. This allows homogeneous distributed nuclei to remain in the melt, which lead to equiaxed dendrites.

Microstructure of cell walls. a) Dendritic structure of Alulight made of a wrought aluminum alloy. b) Interdendritic eutectic structure of Alulight made of cast AlSi7 alloy.

Figure 4.1-11.

4 Characterization of Cellular Metals Figure 4.1-12. Microstructure of particlestabilized metallic foam.

Figure 4.1-13.

Ti-rich particle in cell wall.

Another interesting result was found by MuÈller et al. when studying the microstructure of Fraunhofer foams made of the casting alloy AlSi7 [30]. They found some Ti-rich particles after foaming (Fig. 4.1-13). It can be assumed that these particles are residuals of the TiH2 blowing agent, which are stabilized by the formation of a diffusion barrier. Braune et al. (Section 3.1) reported that they observed refoaming in some foamed samples when the samples were heated before hot forming. Both observations indicate that due to the formation of intermetallic layers surrounding the TiH2 particle, it is likely that the dissociation decelerated. 4.1.4

Conclusions

Most of the work on structural analysis of cellular structures is concentrated on the study of cell architecture or local density, little knowledge has been gained on the special microstructure of foamed metals influencing the property profile. This development in foam research was triggered by material models of cellular structures, from which we can learn that the architecture and the density of cellular metal have a dominant impact on the behavior of metals. Most of the structural data available are measured on metallographic cross sections, scarcely any data on structure analysis is derived from 3D analysis or XCT data.

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But with the ongoing research on cellular metals the investigation of microstructure is important. Often there are typical defects, such as irregularity in cell shape, cracks in cellular structure, or micropores caused by the intrinsic properties of the massive metal. So in future, the emphasis in foam research will be put on the microstructure, because not all material properties can be explained by the architecture of the cellular metal and knowledge of microstructure is essential for understanding processing.

References

1. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, 2nd edn, Cambridge University Press, UK 1997. 2. R. Gradinger; F. G. Rammerstorfer, Acta Mater. 1999, 47, 143 148. 3. M. F. Ashby, A. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: A Design Guide, ButterworthHeinemann, Oxford 2000, p. 42. 4. F. N. Rhines, Microstructology, Riederer Verlag, Stuttgart 1986. 5. H. E. Exner, H. P. Hougardy, Einfu È hrung in die Quantitative GefuÈgeanalyse, DGM Informationgeschellschaft, Oberursel 1986. 6. R. Brezny, D. J. Green, Acta Metall. Mater. 1990, 38, 2517. 7. B. Kriszt, A. Falahati, K. Faure, H. P. Degischer, Bauteilversagen durch Mikrodefekte, DVM-Bericht 518, 1998, p. 195. 8. B. Kriszt, B. Foroughi, K. Faure, H. P. Degischer, in Metal Foams and Porous Metal Structures, J. Bahnhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 241. 9. H. Barth-Smith, A.-F. Bastawros, D. R. Mumm, A. G. Evans, D. J. Sypeck, H. N. G. Wadley, in Porous and Cellular Materials for Structural Application, D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS, Warrendale, PA 1998, p.71. 10. T. Klocker, ªImage Analysis of Metallic Foamsº, Thesis, Vienna University of Technology, Austria 1999. 11. J. L. Grenestedt, J. Mech. Phys. Solids 1998, 46, 29. 12. J. L. Grenestedt, K. Tanaka, Scripta Mater. 1999, 40, 71.

13. J. L. Grenestedt, in Porous and Cellular Materials for Structural Application, D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS, Warrendale, PA 1998, p. 3. 14. A. E. Simone, L. J. Gibson, Acta Mater. 1998, 46, 3929. 15. H. E. Exner, Int. Metall. Rev. 1972, 17, 25. 16. J. Ohser, U.Lorz, ªQuantitative GefuÈgeanalyseº in Theoretische Grundlagen und Anwendung, Freiberger Forschungshefte Reihe B, 276, Deutscher Verlag fuÈr Grundstoffindustrie, 1994. 17. B. Kriszt, A. Kottar, T. Klocker, H. Knoblich, H. P. Degischer, Fortschritte in der Metallographie, G. Petzow (ed), Prakt. Met. Sonderband, Vol. 30, DGM-Informationsgesellschaft, Frankfurt 1999, p. 385. 18. H. P. Degischer, A. Kottar, B. Foroughi, in X-Ray Tomograhy in Material Science, J. Baruchel, J.-Y. Buffiere, E. Maire, P. Merle, G. Peix (eds), Hermes, Paris 2000, p. 165. 19. T. Miyoshi, M. Itoh, A. Akiyama, K. Kitahara, in Metal Foams and Porous Metal Structures, J. Bahnhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 125. 20. V. Gergely, T. W. Clyne, in Metal Foams and Porous Metal Structures, J. Bahnhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 83. 21. C. KoÈrner, F. Berger, M. Arnold, S. Stadelmann, R. F. Singer, Mater. Sci. Technol. 2000, July-August, 781 784. 22. A. E. Simone, ªPorous Metals and Metallic Foamsº, Thesis, Massachusetts Institute of Technology, Boston, MA 1997.

4 Characterization of Cellular Metals 23. F. Berger, ªEinfluss der Prozessparameter auf die Schaumtruktur von Al-SchaÈumen auf pulvermetallurgischer Baisisº, Thesis, Lehrstuhl fuÈr Werkstoffkunde und Technologie der Metalle, UniversitaÈt Erlangen, Germany 2000. 24. U. Mosler, G. Heinzel, U. Martin, H. Oettel, Materwiss. Werkstofftechn. 2000, 31, 519 522. 25. B. Kriszt, B. Foroughi, K. Faure, H. P. Degischer, Mater. Sci. Technol. 2000, 16, 792. 26. B. Kriszt, R. Gradinger, B. Zettl, ªUntersuchung von Aluminiumschaum, im speziellen der mechanischen Eigenschaftenº in Werkstoffpru È fung, Deutscher Verband fuÈr

Materialforschung und -PruÈfung, Bad Nauheim, Germany 1998, p. 167. 27. D. Lehmhus, C. Marschner, J. Banhart, in MetallschaÈume, H. P. Degischer (ed), Wiley VCH, Weinheim 2000, p. 474 477. 28. B. Kriszt, O. Kraft, H. Clemens, Materwiss. Werkstofftechn. 2000, 31, 432. 29. Y. Sigimura, J. Meyer, M. Y. He, H. BarthSmith, J. Grenstedt, A. E. Evans, Acta Mater. 1999, 45, 5245 5259. 30. A. MuÈller, U. Mosler, Fortschritte in der Metallographie, G. Petzow (ed), Prakt. Met. Sonderband, Vol. 32, DGM-Informationsgesellschaft, Frankfurt 2001, p. 279 284.

4.2

Computed X-ray Tomography

E. Maire

X-ray tomography has recently emerged as a powerful technique capable of giving a nondestructive picture of the interior of structural materials [1,2] including cellular metals and foams [3 6]. This section gives an overview of the technique, the set-ups that can be used, and some examples of application in the field of the compression behavior of foams. In the final section, we describe how to produce finite element models from the actual 3D images of the microstructure and we show results of calculations performed with this method. 4.2.1

Principle of the Technique X-ray Radiography The X-ray radiography technique is based on the simple Beer Lambert law, which gives the ratio of N1, the number of photons transmitted after a path of length z through the thickness of a sample exhibiting a coefficient of attenuation m, over N0, the number of incident photons. If m varies along the path, the integral of m over z has to be used " Z # N1 (1) ˆ exp s m(x; y; z)dz N0 path 4.2.1.1

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4.2 Computed X-ray Tomography

a)

b)

a) Diagram of the principle of the X-ray radiography technique used in the present chapter with a diverging beam for a medium resolution. b) Diagram of the X-ray tomography technique.

Figure 4.2-1.

m depends on the composition of the local elementary volume of matter situated in x,y,z. For aluminum the photoelectric effect dominates for X-ray energies below 60 keV according to m(x; y; z) ˆ Kr

Z4 E3

(2)

where K is a constant, r and Z are the density and the atomic number of the investigated material, and E is the energy of the incident photons. Above 60 keV the Compton effect dominates, where the attenuation becomes nearly proportional to the density. This attenuation law explains the contrast observed in the X-ray radiograph of a bulky material (see Fig. 4.2-1a) because each point of a detector placed behind the sample is situated in front of a different path: if the material is heterogeneous, the integral value of m(x,y,z) varies also with x and y.

X-ray Tomography The drawback of radiography is that a large amount of information is projected on one single plane and the resulting image can be difficult to interpret if the number of microstructural features along the thickness of the sample is important. Tomography overcomes this drawback by combining the information from a large number of such radiographs, each being taken with a different orientation of the sample in front of the detector (Fig. 4.2-1b). If the angular step between each radiograph is small enough, it is possible from the complete set of radiographs to recalculate the local value of m(x,y,z) at each point of the sample. This reconstruction is performed by appropriate software based on the filtered back-projection algorithm [1]. 4.2.1.2

4 Characterization of Cellular Metals

4.2.2

Set-ups

Different set-ups can be used. They all include a source, a rotation stage on which the object is fixed, and an X-ray detector. The easiest way of getting digitized images is to use directly a two-dimensional radioscopic detector composed of a screen transforming the X-rays into visible light, which is then transferred by appropriate optic lenses to a cooled CCD camera. The common geometric constraint of the different set-ups is that the axis of rotation of the sample must be parallel to the plane of the detector and its image must be aligned with one of the columns of the CCD (preferably the central column). The crucial point in applying tomography to materials science is the achievable spatial resolution r defined as the size of the pixel of the detector in reference of the sample. Its limit value is mainly governed by the available photon flux at the level of the sample and by the set-up, as described in the next two sections. For medical tomography (XCT scanner) this limit of resolution is of the order of 300 mm. Materials scientists wishing to see and distinguish features with a size of the order of 1 10 mm had to develop appropriate tools.

Medium-Resolution Microtomography For a limit of resolution of the order of 10 mm (medium resolution), a cone beam system can be used with a classical microfocus X-ray tube as the source. Such a device has been assembled in the CNDRI laboratory at INSA Lyon. With this diverging geometry the magnification can be varied easily by changing the position of the sample in the space between the source and the detector. The limit of resolution is due to the size of the microfocus, which introduces blur in the projected image. This size has a minimum value because if the source size gets too small, the flux at the level of the sample becomes so low that the acquisition time required to record a single radiograph is too long for a realistic analysis. In such a laboratory set-up, a polychromatic source is used in order to keep the acquisition time acceptable. This may introduce artifacts due to beam-hardening and does not allow quantitative reconstruction of the absorption coefficient m. This kind of standard set-up exists now in many different academic and industrial laboratories. Some commercial and nearly portable set-ups with a good resolution (down to 6 mm) are also available. 4.2.2.1

High-Resolution Microtomography We emphasized in the previous section that the set-ups using X-ray tubes are limited because of the low flux delivered by this kind of source. The best quality images in terms of signal-to-noise ratio and spatial resolution, allowing high-resolution microtomography, are today obtained from instruments located in synchrotron radiation facilities. Such a source can be found at ESRF in Grenoble. The X-ray beam produced at this kind of third generation synchrotron facility 4.2.2.2

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4.2 Computed X-ray Tomography

is very interesting for microtomography because of the following original features [2]. x x

x

x

Very high intensity of the X-ray beam inside the cone. Nearly parallel beam: this simplifies the reconstruction of the images but shifts the resolution dependance into the detector's performance. A monochromatic beam can be used: this suppresses for example beam hardening and cupping effects and allows for a quantitative reconstruction of m. Availability of high energy photons (beyond 100 keV) that can penetrate heavy (high Z) materials.

The ID19 beam line team of ESRF has combined these specific properties with the availability of a suitable CCD-based detector exhibiting at the same time a large dynamic range (13 bits), a low noise, and a short transfer time (down to 60 ms for 1024 q 1024 pixels). This unique combination allows a resolution of the order of 1 mm to be obtained routinely today.

Resolution Required for the Study of Metallic Foams In the case of metallic foams, a medium resolution set-up is usually enough because the size of the microstructural features to image is of the order of 100 mm. The different studies presented in this book, and especially in this section, have been performed using standard laboratory set-ups but very interesting results were obtained with the high-resolution set-up in the case of the finer structures that can be found in polymer foams [7]. 4.2.2.3

Reconstruction Method Reconstruction of the images presented here is achieved using a C-language program written by the CEA-LETI (Commissariat a l'Energie Atomique, France) and based on the Feldkamp algorithm [8]. A ramp filter is selected, thus preserving the spatial resolution. A DEC 500 MHz workstation is used to reconstruct the entire volume, slice by slice. Reconstruction of a typical volume (350 q 340 q 128 voxels) takes approximately 1 hour. The final result is a 3D map of the m of elementary volumes of size r q r q r inside the sample. This map can give a certain image of the microstructure if m is transformed into a gray level. Voxels located in the aluminum will exhibit high values of m (high gray levels) whereas voxels located in the pores will exhibit low values of m (low gray levels). 4.2.2.4

4.2.3

Experimental Results Initial Cell Structure Figure 4.2-2 compares reconstructed slices (in gray level) of two different Norsk Hydro foams with different density and cell sizes. These slices are 2D images but extracted from a 3D bloc of numerical data (i. e., the reconstructed volume 4.2.3.1

4 Characterization of Cellular Metals

a)

b)

a) Slice extracted from the tomographic reconstructed volume of a sample of 6 % relative density Norsk Hydro foam. b) Slice extracted from the tomographic reconstructed volume of a sample of 11 % relative density Norsk Hydro foam. Figure 4.2-2.

of the sample). The internal structure and cell-wall arrangement is clearly imaged and the difference between the two samples is easy to visualize. The relative densities of the two materials shown in these figures are 6 and 11 %. A 3D rendering of the 6 % foam is shown in Fig. 4.2-3. This rendering is obtained by removing the pixels located in the pores, showing then only the material located in the walls of the foam. This virtual image really looks like an optical picture of foam, as can be seen in different sections of this book. From such images, 3D morphological characteristics can be measured such as the wall thickness, the wall dimensions, the cell size and so forth. These characteristics have a strong influence on the mechanical properties. Note also that these images can be used with a lower resolution to assess the density fluctuations inside the material (m is directly related to the density). It is perfectly well established that the value of the global relative density of a sample of metallic foam has a direct effect on its mechanical properties but the density fluctuations have also a strong influence and especially on the scatter of these properties. This aspect is developed in Chapter 6 of this book.

Figure 4.2-3. 3D rendered view of a 6 % relative density Norsk Hydro metallic foam.

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4.2 Computed X-ray Tomography

Evolution of the Structure During a Compression Test The deformation modes of a foam can be studied by compressing a sample and imaging by tomography its internal structure at different stages of deformation. Such a study has been performed in [4 6]. The experimental details and main results of the first study [4], performed by the author of the present chapter, are summarized below. 4.2.3.2

a)

b)

c)

d)

Figure 4.2-4. a) Two dimensional reconstructed slice showing the initial microstructure of the compressed sample. b) Sample slice as in (a) for e ˆ 0.065. c) Sample slice as in (a) for e ˆ 0.2. d) Sample slice as in (a) but e ˆ 0.6.

4 Characterization of Cellular Metals

The compression set-up used for this study was an Adamel Lomargy standard mechanical frame. The sample was placed between two plates and the force/displacement curve was recorded. The resulting s(e) conventional curve was found to be classical for this material with a yield stress of 0.7 MPa and a slight increase in the stress during the plastic collapse. We made three steps during the compression loading to allow the characterization of the internal structure by tomography. The three steps were made at increasing values of the remanant plastic true strain: 0.065, 0.2, and 0.6, measured directly from the change in dimensions of the parallelepiped after unloading. Figure 4.2-4 shows a set of 2D reconstructed slices of the same zone of the sample numerically and nondestructively extracted from the volume at the four compression stages from 0 to 0.6 of remanant true strain. These slices are parallel to the compression axis, which is vertical on the figure. One can clearly see the deformation mechanism of the studied foam in compression by comparing figures (a) (initial state) and (b) (remnant strain ˆ 0.065). The large value of the plastic strain at this stage is clearly not due to a homogeneous plastic straining of the whole sample, but to the local buckling of several walls. Between the second and the third step, we observe that the number of new buckled walls is small. The deformation process leads first to the complete closing of the collapsed cells instead of the appearance of new ones. From the observation of the entire population of buckled walls, we have observed that they are situated in a band perpendicular to the loading axis (see Fig. 4.2-4c). These 3D nondestructive observations confirm those made using other techniques [9] or with the same technique by other authors [3,5,6]. 4.2.4

Micromodeling of a Foam by Finite Elements

The internal structure of a metal foam is extremely complex: the cell size and the length of the walls are parameters that are widely spread. The nonperiodic character of the structure leads also to a very difficult calculation of the actual force applied to each wall compared to the case of honeycombs. The complexity of this entanglement suggests analyzing the distribution of the stress and deformation in each wall using an appropriate tool: finite element analysis. In the present study we have a 3D picture of the actual microstructure of the foam. In what follows, we present an easy way to use this picture to generate meshed models of the actual microstructure. These models are readable by the Abaqus commercial code, which we have used to perform calculations, firstly in 2D and then in 3D.

Direct Meshing of the Actual Microstructure As already mentioned, the result of a tomographic inspection (after reconstruction) is a 3D table of gray levels. Given the experimental resolution of the set-up used, the volume of the element is 150 mm q 150 mm q 150 mm. The method described bellow is based on a simple idea: each voxel in the 3D image can be represented by 4.2.4.1

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4.2 Computed X-ray Tomography

a cubic element in a finite element mesh. The cubic elements located in the voids are then removed from the model. Given the experimental conditions we used, we considered that the boundary between the steel plates of the compression rig and the aluminum foam was perfect. The displacement of the lower nodes were fixed in the three directions. We generated a steel plate perfectly bonded to the upper nodes and applied a displacement along the compression direction to the upper nodes of this steel plate.

Results All the calculations were performed assuming elastic behavior for the walls. 4.2.4.2

Two-dimensional (2D) The procedure described above can be very simply applied to any slice by generating only one layer of four-node 2D solid elements. We applied this technique for several slices. The elements used were plane-strain four-nodes elements (PE4 Abaqus elements). Figure 4.2-5 shows a contour plot of the s22 (i. e., the normal component in the direction of loading) component of the stress tensor in the walls calculated according to our procedure for a slice with PE elements. The higher compressive stresses are shown in black on the figure. What we want to reach with this calculation is not the absolute value of the stress but the determination of the sign of this stress so the color bar has been intentionally simplified to distinguish tension and compres-

Figure 4.2-5. Stress map (arbitrary units) calculated using the Abaqus FE code by converting the actual microstructure of a 2D slice into a mesh using the local procedure described in this chapter. The stress component shown here is the normal component.

4 Characterization of Cellular Metals

Enlargement of a region of the stress map shown in Fig. 4.2-5, which shows the bending character of the stress field when calculated in 2D.

Figure 4.2-6.

sion. Note that the values of the stresses in the walls seem to form paths of high compression loading between the top and the bottom of the section. These paths define ªpillarsº where the compression load is transferred while some other regions are much less loaded. This permits us to locate highly loaded regions in the material. If we zoom in a single wall situated in one of these pillars and oriented along the compression axis, we observe a very special stress state composed of zones in compression (black) and in tension (light gray), which indicate a high bending character of the stress (see Fig. 4.2-6) with 2D assumptions. Plane-strain elements imply that the cells that are defined in Fig. 4.2-6 are section of tubes having an infinite dimension along the third axis perpendicular to the figure. This tube shape promotes a high bending stress state within the plane of the slice only. Three-dimensional (3D) A complete 3D calculation of the entire foam with our technique would require a 1 000 000 element mesh. This amount of data is not tractable with our computer today. A region of 1003 voxels was selected from the initial raw data. In order to reduce the number of elements in the final mesh, the voxels of the region were grouped eight by eight (two by two in the three directions), which led to an increase in the actual resolution in the final mesh leading to a size of 300 mm q 300 mm q 300 mm for each element. This 503 voxels 3D block was transformed into a mesh according to the previously described procedure and the mesh was slightly compressed (0.02 % of elastic strain). The calculation took around 140 h on a standard workstation. This allowed us to analyze the stresses and strains in the walls as illus-

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trated in Fig. 4.2-7 and Fig. 4.2-8, which show a contour plot of the normal stress and of the Tresca shear stress in a layer. As for 2D simulation, the color map has been simplified to emphasize the sign of the stress rather than its absolute value. Note that Fig. 4.2-7 shows much less region loaded in tension (black) than the equivalent 2D calculation, shown for instance in Fig. 4.2-6. This indicates that when calculated in 3D, the stress state in the walls is completely different than

Figure 4.2-7. Stress map (arbitrary units) cal- applied strain was 0.02 %. The amount of tenculated using 3D elements on a representative sile stress is much lower than for the 2D calregion of the actual compressed block. The culation (compare with Fig. 4.2-6). normal stress component is shown here. The

Figure 4.2-8. A map of the value of the Tresca's shear stress calculated in the same 3D conditions as for Fig. 4.2-7.

4 Characterization of Cellular Metals

when calculated in 2D with, in particular, a much less pronounced bending character. Thus a proper calculation with this technique should be performed on a representative piece of material in 3D with a bigger computation power. 4.2.5

Conclusions

Tomography is a new powerful technique, suitable for the 3D nondestructive analysis of the mesostructure of metallic foams and its evolution under compression. We have presented illustrations which show that it is possible to use this technique to have a better determination of the microstructural features responsible for the mechanical behavior of such materials. When used at different compression stages on the same sample it also enables us to understand perfectly the deformation mechanisms of metallic foams. In the case of the Norsk Hydro foams, we have shown that deformation is due to local buckling of the edges and walls and that these events were all located in a band perpendicular to the compression axis. These images also give directly produced finite-element meshes of the actual samples. The size of these meshes can be very big and not tractable with a regular computer if the entire compression samples are meshed in 3D. Preliminary calculations were then made on entire sections in 2D, which allow us to visualize the highly loaded regions in some particular sections and the bending character of the stress state in the walls, but the local carrying function of the cell edges cannot be taken into account appropriately. A small 3D block was finally calculated and it was thus shown that the stress state in the walls has a much less pronounced bending character in the actual conditions.

References

1. J.-Y. BuffieÁre, E. Maire, P. Cloetens, G. Lormand, R. FougeÁres. Acta Mater. 1999, 47, 1613. 2. V. Kaftandjian, G. Peix, D. Babot, F. Peyrin, J. X-ray Sci. Technol. 1996, 6, 94. 3. H. Bart-Smith, A. F. Bastawros, D. R. Mumm, A. G. Evans, D. J. Sypeck, H. H. g. Wadley, Acta Mater. 1998, 46, 3582. 4. E. Maire, F. Wattebled, J. Y. Buffiere, G. Peix, in Proc. Euromat `99 Conf., Vol. 5, Munich, T. W. Clyne, F. Simancik (eds), Wiley VCH, Weinheim 1999, p. 68. 5. H. P. Degischer, A. Kottar, B. Foroughi, Ch. 12 in X-ray Tomograhy in Material Science, J. Baruchel, J.-Y. Buffiere, E. Maire, P. Merle, G. Peix (eds), Hermes, Paris 2000.

6. A. H. Benaouli, L. Froyen, M. Wevers, Ch. 10 in X-ray Tomograhy in Material Science, J. Baruchel, J.-Y. Buffiere, E. Maire, P. Merle, G. Peix (eds), Hermes, Paris 2000. 7. P. Cloetens, W. Ludwig, J. P. Guigay, J. Baruchel, M. Schlenker, D. Van Dyck, ªPhase contrast tomograhyº in X-ray Tomograhy in Material Science, J. Baruchel, J.-Y. Buffiere, E. Maire, P. Merle, G. Peix (eds), Hermes, Paris 2000, p. 115 125. 8. L. A. Feldkamp, L. C. Davis, J. W. Kress. J. Opt. Soc. Am. 1984, 1, 612. 9. A. M. Harte, N. A. Fleck, M. F. Ashby, Acta Mater. 1999, 47, 2511.

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4.3 Considerations on Quality Features

4.3

Considerations on Quality Features

H. P. Degischer and A. Kottar

The quality of a material is defined by its properties with respect to the expected performance. A general demand for engineering materials (not necessarily for objects of arts) is reproducibility in the sense that the product exhibits the same properties within specified limits delivered in different samples or batches in order to be predictable in its performance and an engineer can design a reliable component suitable for series production. Material science relates properties to microstructural features of bulk materials, for which quality criteria can be deduced defining limits for structural variations (for instance grain size) and for inhomogeneities (for instance frequency and size of inclusions). Usually the processing steps producing the microstructure are specified to guarantee the correlated properties. 4.3.1

Introduction

Cellular metals are a new class of materials on the brink to industrial application and therefore the producers have to develop specifications for their product with respect to the application aimed for. In Chapter 7 various applications are proposed, each requiring different property profiles. Applications in architecture obviously will require different quality criteria than heat exchangers or crash absorbers. A design guide [1] based on the available properties of different cellular metals and material laws has been offered to the engineers for product development. The great variety of processes and products presents a considerable challenge for the selection of the appropriate cellular material for a potential application. 4.3.2

Non-Uniformity of Cellular Metals

Regular cellular structures like those considered for modeling [2] can hardly be produced. The most regular 3D structures are achieved in lattice block material (LBM) [3], which can be simulated by a 3D periodic array of volume elements that represent the main structural features and exhibit the corresponding properties. The behavior of any macroscopic part made of LBM can be calculated (see Chapter 6) by means of known properties of the representative volume (RV), which contains just as many cells that the volume related properties do not change by adding more cells, but would change if one cell were taken off. RV is the smallest volume exhibiting the properties of the corresponding cellular structure of a given material with a certain cell architecture yielding an uniform average density. Consequently, no dimension of a component should be smaller than the RV, if the performance of the specified cellular structure were required. Any disturbance in the regularity of

4 Characterization of Cellular Metals

ideal cellular microgeometry (see Section 4.1) could be quantified microscopically to assign a material quality level. The engineers expect narrow variations and guaranteed lower limits (in some cases upper limits as well) of properties of the materials considered, which depend neither on dimension nor on shape and are valid for each segment of the component. A RV should contain all the geometrical features that determine the property profile of intrinsically heterogeneous materials like cellular metals. In the case where the geometrical features of a cellular structure scatter in a certain statistical range within the sample, the question arises, which variations (for instance in cell size or crack probability) are typical for the cell architecture and can be taken into account for the definition of a RV (examples are given in Chapter 6.1). Features not being accounted for in such a RV have to be classified as structural defects (for instance over-sized pores). Anyhow the frequency and the extent of defects and their effects on properties have to be known in order to be able to qualify a cellular material [4]. Most real cellular metals exhibit a further type of irregularity besides that of geometrical architecture: the mass may not be evenly distributed along the Plateau borders and cell walls [5], furthermore the relation between pore volume and surrounding material may vary, resulting in a non-uniform density distribution within the sample [6]. The local density distribution is greatly affected by geometrical defects as well (for instance an over-sized pore surrounded by thin cell walls causes a local density minimum). Non uniform mass distributions may occur in cellular metals in combination with variations in the cell architecture [7]. Cellular materials that are produced as shaped parts with or without skin (either by casting or by foaming) could yield properties characteristic only for the given shape fabricated by a certain process. Still, such parts should exhibit reproducible properties for series applications, not only macroscopically over the whole part, but as well locally where the load is transferred. The range of scattering of these properties will define the quality with respect to the requirements. Figure 4.3-1 shows a skeleton of a cross section of an irregular cellular structure, where no common RV smaller than the whole image could be defined. This problem exists strictly for castings in a similar way, where material properties depend on the solidification process and vary across the thickness of the part. If one puts up with the inhomogeneities of cellular metals, these have to be quantified in their range of variation and with respect to their location within the sample. An irregularly structured sponge with non-uniform density distribution can be considered as a multiphase material consisting of an arrangement of sub-domains of various cellular materials exhibiting different properties each (see Chapter 6.2). The non-uniformity can be described by different volume elements (sub-domains). Each sub-domain consists of an ensemble of cells of similar microgeometry and density at least as big as the corresponding RV. If a sub-domain is big enough, it can be subdivided into a number of equal RVs. In the cross section of the irregular cell structure in Fig. 4.3-1, some regions representing different cell structures are marked. Shape-independent quality criteria for cellular metals for engineering application can only be defined for semi-products like for instance Alporas or Cymat material delivered as blocks. Net shape cellular parts have to be considered with respect to

157

158

4.3 Considerations on Quality Features Skeleton of a cross section of an irregular cellular structure (compact powder foamed aluminum), where three regions of different cell structures are marked, each of them can be regarded as a reasonably uniform cell architecture that can define a mesoscopic sub-domain.

Figure 4.3-1.

their specific loading conditions related to the geometry and to the surface. In a first approach, the cellular metal or part is defined by its processing route, although the interaction of the different processing parameters cannot be fully correlated to the produced cellular structure yet. Each type of product may be characterized by investigating the statistics of achieved properties and the correlated structural features accessible to quality control [7]. The range of scatter of properties acceptable for the envisaged service performance has to be defined, which can be related to the scatter of structural features. Beyond specification limits, defects can be defined, which have to be weighted in their influence on the service properties. According to the actual development stage, it can be expected that some defects could be eliminated or considerably reduced by improved processing techniques. A hierarchical approach is proposed for defining quality criteria of cellular metals by addressing different description levels according to the characterization levels described in Section 4.1: macro-, meso-, and microscopic. Corresponding features are to be defined that can be quantified and validated with respect to material properties. The average density of a part or component is an example of a macroscopic level. The question is: How reproducible is the density of a given part in series production? How much variation is tolerable with regard to the scatter of related properties? Even for a given average density of a part the properties might scatter owing to the local scatter of mass densities within the part, which may vary on a mesoscopic scale. Going into further structural details on the microscopic level, the variations in shape factors, in dimensional and microstructural features of the cell walls and nodes have to be quantified statistically and assessed with respect to tolerable variations or irregularities beyond.

4 Characterization of Cellular Metals

4.3.3

Macroscopic Parameters

All those parameters are referred to as macroscopic, which can be assigned to the whole cellular part without looking into the structure in detail: the general appearance of a cellular architecture, the composition of the ingredients, and the processing method.

Type of Cellular Metal The terms for identification of cellular metals are defined in Chapter 2. The architecture of the cellular structures can be deduced qualitatively from the processing route that defines primarily the type of porosity (open or closed). The degree of open porosity can be determined by measurements of the permeability for liquids or gas. Cellular structures produced by foaming are of closed cell character in the liquid state, but, contrary to polymer foams, metal foams suffer from shrinkage porosity and hot tearing during solidification and further cooling (see Section 4.1), which make them permeable to gas and wetting low viscosity liquids. The total surface, inner and outer, could be determined by BET gas adsorption techniques. The composition of the ingredients (the metal and the foaming additives) can be quantified. Usually the ingredients are specified and not the resulting composition of the matrix metal. The relatively large surface may extract some elements from the alloy, which may change the composition of plateau borders and cell walls slightly due to eventual chemical reactions with the surrounding media (for instance surface oxides formed predominantly by one or the other constituent). The sensitivity of the properties of cellular metals on slight changes in compositions has not been identified as a major concern. In the contrary, impurities have been found to improve foamability promoting the use of secondary alloys for foam production (see Section 2.1.3). The oxide content (analogous to metal powder quality specification) could be analyzed to estimate the portion of metallic components bound by the surface. In the case of foams made from metal matrix composites (like Cymat or FORMGRIP [8]), usually the particulate content of the precursor melt is given, which might differ from the local particulate concentration within the cellular structure. The overall microstructural condition of the solid metal can be deduced roughly from the manufacturing parameters like cooling rates, heat treatment and plastic deformation. 4.3.3.1

Surface and Dimensions The surface of cellular parts has to be considered separately disregarding any additional surface treatments: either the cellular material has been machined producing free ends of the cell walls or it was foamed in a mold forming a more or less closed skin. Useful quality criteria for the surface depend on the service environment and greatly on the way the cellular part is connected to the surrounding system. 4.3.3.2

159

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4.3 Considerations on Quality Features

In Section 7.3 the problem of deforming the cell walls during mechanical cutting operations is addressed. The degree of such deformations could be of importance for following joining operations. The enlargement of outer surface in comparison with a carefully prepared cross section could be employed to quantify the smearing of cross sections of elements of the cellular structure by machining. Foamed and cast cellular metals are usually surrounded by a metal skin. The oxide content will be much higher than on interior cell surfaces, because that skin was exposed directly to the atmosphere in the liquid state and during solidification and cooling. The roughness depends greatly on the used mold and its coating and may be qualified similar to sand casting quality. Attempts to measure the thickness of the skin by eddy current tests did not succeed so far. A skin region of about 1.5 mm thickness can be deduced from Fig. 4.3-2 of an Alulight sample, where the local density is almost twice of that in the center of the plate. Still the skin cannot be regarded as solid metal, but consists of porous material. There are as well pores open to the environment in such skins, which can be detected by dye penetrant tests [6]. Although these pores may be in the range of tenths of a millimeter in diameter, they form a passage to the cells below, which might be of a few millimeters in diameter. Such open pores might adsorb humidity and thus enhance corrosion attack. These pores prohibit chemical treatments like anodizing, because the electrolyte penetrates and can hardly be removed. On the other hand, if those pores are sealed by a coating, which has to be baked, it might form blisters when the temperature rises and the internal gas pressure increases. Ambient temperature coating processes with a strong sealing effect can be applied successfully [9]. The number of surface pores per surface area and their distribution of diameters are quantifiable surface quality features. A pore density of 1-3 pores/cm2 has been measured on Alulight samples [6]. The dimensional accuracy of net shape metal foam parts depends on the thermal stability of the mold and the uniform shrinkage of the foam during solidification and cooling. The cell-size distribution, especially along the surface of the part, affects the surface roughness. Big pores (in the range of one centimeter) may cause dents due to the drastic reduction of pressure of the gas in the closed pores during cooling. The achievable tolerances for net shape metal foams may be in the range of percent, but no detailed study has been published so far.

Figure 4.3-2. Local density distribution across a 20 mm thick Alulight plate (r ˆ 0.57 g/cm3) determined by computed X-ray tomography of a resolution of I0.3 mm.

4 Characterization of Cellular Metals

Apparent Density The apparent density of a cellular metal part still is the most important selection criterion. It can be measured by the Archimedes principle provided the surface can be sealed to avoid penetration of the test liquid. Foamed net shape parts with a skin can be measured in high viscosity liquids preventing penetration into the surface pores. Generally, a measurement uncertainty of about e2 % in the apparent density of a part has to be reckoned with. The result includes the surface skin, the density and thickness of which are usually unknown. This may cause a considerable uncertainty in the apparent density of the interior structure. The apparent density of the whole sample referred to in Fig. 4.3-2 for instance, with a high density skin layer occupying about 15 % of its volume, is overestimated by about 15 % (0.57 g/cm3 for the whole sample, without skin about 0.5 g/cm3). The reproducibility of the apparent density depends on the processing technique: cellular metals produced on the basis of polymer foam space holders are highly reproducible, but powder compact foaming achieved so far only about e15 % reproducibility in the apparent density of similar samples from small series prototype production. An overall non-uniform mass distribution can be identified by determining if there is a difference in the position of the center of gravity of the shape and that of the mass. 4.3.3.3

Properties Macroscopic properties of test samples are described in Chapter 5, where they are usually related to the apparent density of the specimens. The observed scatter in mechanical properties, like the plateau stress for instance, depends very much on the uniformity of the cellular structure. In general, the properties are closely related to the quality of the cellular architecture. The scatter in the test results indicate the variations in structure of the individual test specimens. Most of the tests are executed without knowing the microgeometry of the test sample exactly, therefore there is little evidence on the correlation with structural features, especially when the tests are destructive. A systematic correlation of properties to the three-dimensional cellular architecture is highly desirable in order to give rise to process developments aiming for improvements in the reliability of the service related performance of the foams. 4.3.3.4

4.3.4

Microscopic Features

In terms of microscopic features the individual cells are to be considered: the microstructure of the metal forming the cell walls and their topological parameters described in Section 4.1.

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4.3 Considerations on Quality Features

Microstructure of the Metal The microstructural features of the metal, the cellular structure is made of, are alike any metal: grain size, dendritic sub-structure, phase distributions, segregation, precipitates and dislocation densities. These are considered in Section 4.1 in detail. Typical features for foamed metals are remnants of foaming agents, distribution of additives to increase viscosity, the consequences of the large internal surface on solidification, of grain growth with only partial impingement, and of temperature gradients during cooling depending significantly on the position in the sample. The resulting local properties of the metal are presumably not equal throughout the cellular structure. An important quality criterion is again the uniformity of the microstructure throughout the sample, although characteristic differences between Plateau borders and cell walls are inherent. Owing to the small dimensions of cell walls comparable with the grain size, the mechanical, chemical and physical properties will differ with respect to those of the polycrystalline bulk solid. Generally it has to be assumed that the material properties of the metal in bulk are not identical to those of the same material in the cell structure. In the case of molten metal casting and foaming processes, there will be a difference between faster cooled surface near regions and the slowly cooled interior for alloys sensitive to cooling rates, especially if the cellular aluminum alloys are age hardening. Some indications for PCF aluminum are given elsewhere [10,11]. 4.3.4.1

Geometrical Features The shape of cells and cell walls has been investigated so far by metallographic methods either by light microscopy or by scanning electron microscopy. Average cell-size distributions from cross sections are only representative when the pores are spherical. The presentation of pore-volume distributions is more relevant than equivalent linear pore diameter statistics. Average pore size figures are of little significance because the width of the distribution determines the properties according to the weakest link principle. The distributions may be Gaussian only for hollow sphere structures and those produced by replication techniques, where the narrow width of the distribution provides a quality measure. Generally, the shape of the pore volume distribution curves could provide a quality criterion for the cellular structure. The portion of pores bigger than the average is especially important for the properties of foamed metals. In a first approach the statistics of ªover-sizedº pores could be used as quality criterion: for instance, the volume fraction occupied by the biggest 10 % or the pores bigger than 20 % of the sample's thickness. Not only the size of the big pores is relevant, but as well their positions and the microgeometry of surrounding pores. A centrally placed big pore would not affect the stiffness of a component and the strength could be compensated by surrounding small pores (see Chapter 6.1.3). A surface near big pore could be harmful at the position of load transfer, where the local pore size distributions would be of interest. Some attempts have been made to determine the three-dimensional geometry of pores by computed X-ray microtomography [5,12]. It gives the most exact tool for 4.3.4.2

4 Characterization of Cellular Metals

the 3D description of cellular structures. The determination of the maximum and minimum pore diameters and their orientation distribution would be relevant information needed to identify an anisotropy of the architecture of the cellular structure. Examples of the potential of X-ray microtomography are shown in Fig. 4.3-3 and Fig. 4.3-4 and elaborated in [13,14] and in Section 4.2. The 2D architecture of cellular light metal can be represented similarly to metallographic cross sections but nondestructively by selecting the intensity distribution of an arbitrary plane of the 3D microtomography. The examples given in Fig. 4.3-3 and Fig. 4.3-4 have been measured at Bundesanstalt fuÈr MaterialpruÈfung, Berlin [6] and represent the mass distribution for different aluminum foams in Fig. 4.3-3 within a slice of 40 mm and an aluminum metal matrix foamed in the melt [15] in Fig. 4.3-4 (slice of 0.1 mm). The difference in the architecture (pore size and shape, frequency of irregularities) can be qualitatively observed. Cross sections of Plateau borders and cell walls are only representative if they are oriented end on. Cell walls oriented parallel to the imaged slice appear as mass concentrations like thick nodes, especially when the cell size is small like in Fig. 4.3-3a and c. The 3D architecture can be visualized by iso-surfaces like presented in Fig. 4.3-4b. It can be observed on a screen by scrolling the data set of 3D tomography slice by slice or by means of an observation point travelling through the cells by techniques of virtual reality [16]. The distribution of mass between nodes and Plateau borders in open-cell structures, and additionally in cell walls of closed cell foams can be estimated from metallographic sections or determined by computed X-ray microtomography [5,14]. The uniformity of this material distribution parameter is another quality criterion. The connectivity of pores can only be determined by computed X-ray microtomography [5]. This parameter affects the permeability, some thermophysical and acoustic properties. The shape of the struts or cell walls or edges can be compared with ideally straight members or shells. The buckling could be quantified by the relation between shortest distance between the ends and the real curved length or by the circularity in 2D and the sphericity in 3D. Most of these geometric microstructural features are described in detail in Section 4.1. The statistics of these factors and

Cross sections of mass distributions computed from X-ray microtomograms (voxel size 40 mm q 40 mm q 40 mm) of foamed aluminum: a) Alporas of r ˆ 0.45 g/cm3, b) Figure 4.3-3.

Alulight AlMgSiCu of r ˆ 0.39 g/cm3, c) Alulight AlSi10Mg r ˆ 0.37 g/cm3, d) same material as (c), but specially foamed small cell architecture r ˆ 0.56 g/cm3.

163

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4.3 Considerations on Quality Features

Figure 4.3-4. Mass distributions computed from micro X-ray tomograms of foamed AlSi9Mg/SiC/20p melt of r ˆ 0.11 g/cm3 (voxel size 0.1 mm q 0.1 mm q 0.1 mm): a) cross section showing different plateau borders and

polygonal cell walls (same magnification as Fig. 4.3-3; note that not all of them are end-on), b) 3D cell reconstruction of a cuboid volume element (22 mm q 18 mm q 16 mm) indicating curved shapes of the cell walls.

the identification of predominantly buckled orientations can be correlated to the initial deformation behavior in tension and compression [17,18] (see Chapter 6.1.3).

Microdefects Of course, pores created in cellular metals due to processing imperfections like shrinkage pores, imperfect sintering, spraying pores etc., may not to be considered as essential defects. But in general the consistence of the percolating solid should be of similar metallic properties throughout the cellular structure. Cellular structures processed in the melt or at elevated temperatures suffer thermal stresses during solidification and cooling. Hot tearing and cracking is very probable because of the multi-axial stress situations created in walls of little strength (see Section 4.1). Almost 100 % connectivity of the pores have been determined within powder compact foamed aluminum [5], although almost 40 % of the solid is located within the cell walls. Cell-wall cracks have been observed frequently in powder compact foams [19]. The material properties of the metal in the cellular structure have to be considered to be of poorer quality than those of the same metal in bulk. For those produced from the melt it is expected that the alloy exhibits the properties of a low quality casting. If the frequency of microdefects depends on the position within a sample, their effect should be considered as deviation from uniformity. 4.3.4.3

4 Characterization of Cellular Metals

4.3.5

Mesoscopic Features

The mesoscopic description of real cellular metals assumes that a sample or part can be described as an arrangement of volume elements, each representing a characteristic microgeometry. The local inhomogeneities in architecture and in mass distributions can be classified by different mean cellular structures approximating the properties of each sub-domain of the material. A mesoscopic model for uniaxial compression has been proposed [20,21], which divides the samples into layers of cellular materials with different apparent densities. Generalizing this concept, any sample or part can be divided into a 3D arrangement of sub-domains of different cellular phases of known features and properties. Thus the cellular sample is considered as a multiphase material (see Fig. 4.3-1), where a cellular phase is defined by its composition, microgeometry, and mass distribution occupying the volume of a sub-domain. The mesoscopic behavior of each sub-domain corresponds to that of the associated RV, so that each sub-domain behaves like a cellular material to which macroscopic material laws of cellular metals can be assigned. In the extreme case, where the sub-domains were smaller than RVs (i. e., most cells were essentially different from their neighbors), such a mesoscopic approximation would not make sense and complex finite element modeling of the real microstructure would be necessary as shown in Section 4.2. In the best case of samples of uniform microgeometry like Duocel, Incofoam, or those cast by replication, the mesoscopic consideration is superfluous and the macroscopic treatment would result satisfactorily. In general, the range of variations in size, volume fractions and properties of the mesoscopic sub-domains can be quantified providing a quality measure on uniformity of the considered part.

Geometry of Cellular Structure A sub-domain of a sample or part has to be big enough to behave like a cellular metal the mechanical properties of which can be approximated by continuum mechanics. It should measure about five cells in diameter, if their shape is similar to each other [22]. This criterion would require a statistically representative number of more than 100 cells per representative volume. If the shape factors of the cells varied significantly, the sub-domain should contain as many cells as necessary to represent the statistical scatter of geometrical features. In general, the processing method of cellular metals defines a certain type of cell architecture. Most foamed metals exhibit some gradation in their structure depending on the dimension of the part and/or on an anisotropy in foaming [7,23] and in solidification [1]. If the variation of the geometrical features of the cells is not statistical, but can be related to different regions of the samples, arrangements of uniform sub-domains can be defined to represent a graded structure. For instance a sub-domain of the thickness of the surface layer representing the skin as indicated in Fig. 4.3-2. Systematic variation in the cell architecture can be pro4.3.5.1

165

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4.3 Considerations on Quality Features

duced by intentionally graded or anisotropically cast cellular metals [24]. If the shape factors of the pores or the material properties are preferentially oriented, the anisotropic behavior can be assigned to the sub-domains. The cell-size distribution cannot be considered as a mesoscopic parameter. There is no directly quantitative measure of mesoscopic geometrical features. Quantified data would have to be determined microscopically by three-dimensional analysis and evaluated statistically. Anyhow the pre-dominating geometrical features can be assigned to each sub-domain.

Density Distribution If the microgeometry of the cells were uniform, except the local variations in cell size, the density distribution would become non-uniform. Powder compact foamed samples usually contain bigger cells in the center of samples of a few centimeters in thickness yielding a graded density distribution (similar to that shown in Fig. 4.3-2). Furthermore it has to be admitted that inhomogeneities in foamed metals (over-sized pores and local mass concentrations) cannot be fully controlled so far. The point is to take them into account by simulation. The non-uniformity in solid distribution of foamed metals can be characterized by inhomogeneous density distribution [6]. Regions of similar mass densities can be approximated by a mean density value [25]; thus the sample can be divided into sub-domains of different mass densities. A procedure to produce such sub-domains will be described in Chapter 4.3.7. 4.3.5.2

4.3.6

Systematics of Quality Features

The features characterizing parts or samples made of cellular metals are correlated to the structural hierarchy described above in a matrix presented in Table 4.3-1, from which quantifiable magnitudes for quality considerations are deduced. Most of the microscopical parameters are described in Section 4.1 and require considerable effort to be determined statistically, especially in 3D. The macroscopic magnitudes can be obtained from the manufacturer and can be complemented by nondestructive tests except the mechanical properties. The mechanical properties of uniform cellular metal parts can be calculated by simulating the geometrical condition with input data from test samples of equal materials. The properties of non-uniform cellular parts (either intentionally graded or inhomogeneous due to the processing conditions) can be estimated from their mesoscopic structure when the scaling laws with respect to the relevant microstructural features are known. Mesoscopic parameters can be defined on the condition that ensembles of cells exhibit similar microstructural features, which form more or less uniform sub-domains of a sample of cellular metal. An attempt is made to characterize a cellular material without determining microscopic features quantitatively. Irregularities in a certain depth from the surface can be detected by ultrasonic spectroscopy [26] as

Microscopic Magnitudes

Cell size, shape and orientation of pores and cell walls, connectivity

Dimensions of constituents of cells, irregularities

Composition, structure, thickness of outer and inner surface

Grain structure, phase distributions

Fraction of mass in cell constituents

Metal properties on microscopic scale different from bulk

Cell architecture

Dimensional accuracy

Surfaces

Metal matrix

Mass distribution

Properties

Lateral dimensions, radii at corners

Fabrication method, properties, roughness measure, surface porosity index Chemical analysis of ingredients, thermomechanical manufacturing parameters Absolute or relative mass density, difference of centers of gravity of geometry and of mass Experimental data and simulation results with scatter and validity limits

Achievable tolerances in dimensions

Surface formation and topology

Alloy composition, additives, metal condition

Average, apparent mass density; center of gravity

Service properties of component

Dependence of sub-domain arrangement on the averaging limits for microstructural features Boundary conditions for interfaces of subdomains; specific phase for outer surface region Correspondence of subdomain volumes with uniform relevant microstructure Correspondence of subdomain volumes with continuous uniform mass distributions Criteria for definition of properties of subdomains or RV, scaling laws and their accuracy

Sensitivity of subdomain volumes on averaging parameters Interface between sub-domains or sections of outer surface Similar condition (microstructure) of the solid

Similar solid distribution, uniform apparent density

Properties of an ensemble of similar cells

Statistics of dimensions of cell edges/ faces; buckling, wiggles, circularity, sphericity, cracks Definition of surface region/skin, form of constituents, chemical composition, topology

Mass distribution coefficient between faces, Plateau borders and nodes Physical and mechanical properties of solid in function of position in cell and sample

Grain size and interdendritic spacing, inclusions, precipitates in function of position in cell/sample

Processing parameters, category of architecture, permeability coefficient, surface/volume ratio

Quantifiability

Processing method, cell type, permeability

Macroscopic Magnitudes

3D data set of arrangement of sub-domains in size and shape composing the cellular component

Quantifiability

Definition of volumes of sub-domains of similar microgeometry

Mesoscopic Magnitudes

Cell volume histogram shape, shape factors and orientation distributions, connectivity parameter

Quantifiability

Matrix of features of considered quality aspects and correlated quantities within the structural hierarchy of cellular metals.

Feature

Table 4.3-1.

4 Characterization of Cellular Metals 167

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4.3 Considerations on Quality Features

long as the cell architecture is essentially uniform. In the case of regular Duocel samples relative density variations could be observed by eddy current measurements [27]. The following paragraphs describe the possibilities to determine mesoscopic parameters of non-uniform cellular metals and discuss their applicability for quality criteria that can predict, if a sample's behavior complies with the specifications of service requirements. 4.3.7

Approximation of a Cellular Structure by a Continuum

For simplicity it is assumed that the microstructure of the metal and the type of cell architecture are essentially defined by the processing method. The remaining variables are the local density distribution and the properties of the solid material, which have to be calibrated. A non-uniform object can be divided into sub-domains to which the appropriate material laws can be applied to simulate the whole part's performance. For this purpose, it is convenient to transform the cellular structure into a continuum, which behaves like a cellular architecture (crushable material). The experimental basis is provided by computed X-ray tomography [13] of the 3D metal distribution of a sample, which will be locally averaged to yield density values in each point of the sample smoothing away the originally cellular structure.

Calculation of Density Maps The density mapping method is based on determining a local density value at each point within the cellular structure by averaging the mass located in an appropriate neighborhood of the points. The cellular structure can be described ideally by a function r(r) that takes the values r(r) ˆ 0 in pores and r(r) ˆ rS in cell walls, edges, and nodes, where rS is the density of the solid material. In general a local density ra at r can be defined as Z (1) ra (r) ˆ g(r s r 0 )r(r 0 )d3 r 0 4.3.7.1

where g is a weight function that has to fulfill the normalization condition R g(u)d3u = 1. Equation (1) is also written in the form ra ˆ g*r, which denotes the convolution of the function r with g. Cellular structures can be investigated by X-ray radiography or by X-ray computed tomography as described in Section 4.2. The density distribution is represented by a voxelized data set mXCT(rijk) that can be used to calculate a density mapping as defined in Eq. (1). Due to the limited resolution of the XCT equipment mXCT(rijk) is related to the linear mass attenuation m(r) of the object by Z mXCT (rijk ) ˆ PSF(rijk s r 0 )m(r 0 )d3 r 0 ˆ PSF  m (2)

4 Characterization of Cellular Metals

where the point spread function PSF describes the ªblurringº of the object function m(r) [28]. For example, the micro XCT slices in Fig. 4.3-5a and Fig. 4.3-5d are a very good representation of the real foam (i. e., the PSF is a sharp peak), whereas the corresponding slices obtained by medical XCT (Fig. 4.3-5b and Fig. 4.3-5e) are of significantly lower resolution (the PSF is relatively broad). Since the metallic foams investigated herein consist of a single alloy, m(r) is proportional to r(r) and analogously to Eq.(2), rXCT ˆ PSF*r can be defined. Averaging these rXCT values with the weight function w yields raaccording Eq.(1) Z X X w(rijk s rlmn )rXCT (rlmn ˆ w(rijk s rlmn ) PSF(rlmn s r 0 )r(r 0 )d3 r 0 ˆ l;m;n

ˆ

l;m;n

Z X

Z w(rijk s rlmn )PSF(rlmn s r 0 )r(r 0 )d3 r 0 ˆ

g(r 0 srijk )r(r 0 )d3 r 0 ˆ ra (rijk )

(3)

l;m;n

It should be noted that rXCT is already a function of the form of Eq. (1), i. e., rXCT can be understood as a density mapping performed by the tomograph itself and a

Figure 4.3-5. Comparison of a micro XCT with pictures obtained from a human tomograph and calculated density distributions for Alulight Si12Mg of r ˆ 0.5 g/cm3: a) high-resolution micro XCT for a slice thickness of 40 mm (40 mm q 40 mm q 40 mm voxel), b) human XCT of a 1 mm slice (0.6 mm q 0.6 mm q 1 mm voxel),

c) calculated density map using averaging volumes of 6.8 mm q 6.8 mm q 6.8 mm. Alporas of r ˆ 0.45 g/cm3 d) micro XCT slice of 40 mm, e) human XCT of a 3 mm slice (0.9 mm q 0.9 mm q 3 mm voxel), f) density map calculated using the same averaging volume as in (c).

169

170

4.3 Considerations on Quality Features Illustration of the principle of 3D density mapping based on density values for each XCT voxel: the density in the center of the averaging cuboid given by l q n q m voxels is the mean average density of that averaging volume.

Figure 4.3-6.

second mathematical averaging process reveals the final mapping ra (see Fig. 4.35c and Fig. 4.3-5f). The density mappings in this section are calculated by arithmetic mean values of the voxels rXCT(rijk) over a cuboid (see Fig. 4.3-6) ra (rijk ) ˆ

1X rXCT (rlmn ) N l;m;n

(4)

where l, m, n run over the voxel indices of the selected cuboidal surrounding of the location rijk and N is the number of voxels, i. e., the weight function in Eq. (3) is w ˆ 1/N within the cuboid and w ˆ 0 otherwise. Figure 4.3-7 shows a one-dimensional model r(x) of a cellular metal with walls of the solid density rS and embedded empty pores. Convolution of r(x) with the PSF results in the depicted rXCT(xi) values and further averaging over intervals [xi 34, xi ‡ 34] with N ˆ 69 yields the mean local density function ra(xi). As long as the averaging volume of the density mapping is bigger than the resolution of the tomography, the resulting density map is almost independent of the XCT resolution [29]. Using averaging cuboids approximately as big as the cells suppresses microstructural details, but allows to determine local differences in

Figure 4.3-7. One-dimensional model of the density mapping procedure: the real mass distribution r(x) is imaged by the XCT data rXCT(xi) of the voxels, which are resulting from the convolution of r(x) with the PSF; applying

Eq.(4) for each voxel with an averaging interval of xi e 34 voxels yields the smoothed density values ra(xi). rm is the average density; the variations e Dr correspond to e rm/3.

4 Characterization of Cellular Metals

Figure 4.3-8. Example of the effect of the size of the averaging volume on the presentation of density variations in a AlMgSiCu/Al2O3/20p melt foamed sample of r ˆ 0.25 g/cm3 [15]: 1st column, microscopic XCT images (0.1 mm q 0.1 mm q 0.1 mm voxel) of parallel planes

10 mm apart; 2nd to 5th column, calculated density distributions of the same planes for averaging volumes of 4 mm q 4 mm q 4 mm, 6 mm q 6 mm q 6 mm, 9.5 mm q 9.5 mm q 9.5 mm, and 15 mm q 15 mm q 15 mm.

the material distribution in the cells on a mesoscopic scale. Reasonable averaging volumes should contain at least essential portions of at least one cell so that there results no point of zero density. Appropriate averaging volumes for Alporas measure 4 mm q 4 mm q 4 mm, whereas about 6 mm q 6 mm q 6 mm has been shown to be suitable for all Alulight foams. Figure 4.3-8 shows an example of AlMgSiCu/Al2O3/20p foamed in the melt for different averaging volumes. It contains a considerable fraction of pores bigger than 6 mm [15]. The intensity variations due to the cell walls disappear from 9.5 mm q 9.5 mm q 9.5 mm averaging volume upwards, which is an appropriate mesoscopic scale still representing the scatter in density within the foam. Even the averaging volume as big as 15 mm q 15 mm q 15 mm shows some non-uniformity of the sample. Figure 4.3-9 shows examples of 3D density distributions of Alporas and Alulight samples for the same averaging volume. The cellular structure disappears, but the non-uniformity of the mesoscopic mass distribution is clearly visible. The local

171

4.3 Considerations on Quality Features

172

a)

b) Figure 4.3-9. Illustration of the 3D local density distribution obtained from 4 mm q 4 mm q 4 mm averaging volumes for a series of six layers at distances of 3.7 mm of the same samples as in Fig. 4.3-5: a) Alporas of

r ˆ 0.45 g/cm3; b) Alulight AlSi12Mg of r ˆ 0.5 g/cm3; the gray value represents the indicated deviation from the apparent density rm (white ˆ high density).

mass densities for the considered averaging volume size vary in these examples between 40 % and 160 % of the apparent density of the Alporas sample, but between 0 and more than twice of rm of the Alulight sample. The gray scale presentation in Fig. 4.3-9 divides the samples into density classes of 0.1 rm. It is clear from the density distribution of the Alulight sample, that no uniform material behavior can be expected. Representation of Non-Uniformity of Densities Histograms of density distributions can be calculated for specified averaging volumes, which are at least as big as the majority of the cells. Alporas shows the narrowest scatter of local density in Fig. 4.3-10. Both types of Alulight have their maximum frequency below the average density caused by the extended tail in the higher density range. Isolated high density regions may not affect the mechanical properties significantly according to the weakest link principle, but would represent a surplus of material. The shape of density histograms seems to be characteristic for the processing method of a cellular metal [15]. Density maps can be used to quantify local density variations. The line of average density rm and arbitrary limits of density variations of eDr are indicated in the linear model in Fig. 4.3-7. An allowable density variation can be defined and the volume fraction of material with mass densities below or above the lower and upper limit, can be calculated. The 3D arrangement of volumes of extreme density values can be presented by iso-surfaces of densities smaller or bigger than a given limit as shown in Fig. 4.3-11. The local position, orientation and connectivity of such hard and soft sections may be important as well for the performance of a 4.3.7.2

4 Characterization of Cellular Metals Figure 4.3-10. Histograms of density distributions of different metal foams with similar apparent density of r ˆ 0.4 g/cm3, showing the mesoscopic differences for averaging volumes of 6 mm q 6 mm q 6 mm.

Figure 4.3-11. Presentation of hard and soft regions within an Alulight AlSi12Mg sample (a ˆ b ˆ 22 mm, c ˆ 30 mm) of apparent rm ˆ 0.5 g/cm3 by iso-surfaces computed from den-

sity maps with averaging volumes of 6 mm q 6 mm q 6 mm: a) iso-surface of hard sub-domains with r i 1.33 rm; b) iso-surface of soft sub-domains with r I 0.67 rm.

part [30]. If there were cells bigger than the chosen averaging volume, so that points result in the sample where no contrast is found within the surrounding cuboid, the density mapping would contain co-ordinates of zero density. The approximate size, volume fraction, and position of pores bigger than the averaging volume can be determined by means of the calculated 3D density map. An example for an Alulight specimen with over-sized pores is shown elsewhere [6]. X-ray radiography can be applied to flat samples. The intensity of the transmitted columns contains the density integrated over the thickness of the sample yielding the contrast of pixels in the projected plane. This can be transformed into 2D density maps by applying the analogous procedure of averaging over m q n pixels in the image plane. Examples given elsewhere [6] illustrate an improved detectability of inhomogeneities (like ensembles of big pores, drainage effects, or dense skins)

173

174

4.3 Considerations on Quality Features

by planar density mapping. Of course, radiography does not provide any information on density variations in the direction of the thickness. A compromise between 3D tomography and radiography is provided by X-ray laminography [31], where the density distribution of parallel layers of a sample can be determined with moderate resolution.

Mesoscopic Basis for Material Modeling The earlier developed approach to approximate a non-uniform cellular structure by an arrangement of sub-domains, which themselves are uniform, can be realized on the basis of density maps. These density maps are a three-dimensional distribution of density values ra(xi, yj, zk) defined for every voxel (xi, yj, zk) of the XCT data source. The determined total range of mass densities can be divided into classes of density ranges. The ensemble of voxels whose density values lie within one density range form a sub domain. The average of the density values within the subdomains is used as their assigned density value. The widths of density classes have to be big enough, so that the resulting sub-domains comply with the requirement of representing a cellular material, i. e., at least as big as the RV. The cellular sample can be presented by a 3D, space filling arrangement of N sub-domains defined by N different values of mass densities. The gray scale contour map in Fig. 4.3-9 can be interpreted as presentation of sub-domains of the samples in steps of 0.1 rm. The corresponding material modeling and the deduced simulation of properties of non-uniform cellular metals is described in Section 6.2. 4.3.7.3

4.3.8

Proposal of Quality Criteria

The main concern is reproducibility of properties of interchangeable products (aiming for series production) comprising the dimensions of the part and its service relevant performance. The usual quality assurance refers to the processing, which defines the material and the architecture of the cellular structure. The product itself can be submitted to quality control regarding the dimensions, the apparent density and the surface topology. The general structure, properties and service performance can be made plausible by results obtained from corresponding test samples. An overview of these macroscopic quality features is given in Table 4.32. The specifications for each of them are not yet established. Unfortunately the accomplishment of the macroscopic quality criteria is not sufficient for a defined performance of cellular metals with non-uniform cell structures. A mesoscopic analysis of quality criteria is proposed according to Table 4.3-3. The mesoscopic quality testing is based on non destructive testing. Computed Xray tomography is most powerful tool, the resolution of which is sufficient in the range below the average cell size. Modern human X-ray tomographs are appropriate for light metals. The derived density maps calculated using an appropriate averaging volume for the investigated type of cell architecture provides the 3D data base for quantitative analysis of the uniformity of density distributions: density his-

Quality goals

Reproducible and similar throughout the sample

Tolerances of outer dimensions achieved

Reproducible surface features

Defined chemical composition

Reproducible density

Properties unambiguously related to structural quality

Cell architecture

Dimensional accuracy

Surfaces

Metal matrix

Mass distribution

Properties

Property values within specifications

Apparent mass density within specifications

Uniform solid properties

Properties, roughness, open porosity

Specified variations in lengths and radii

Reproducible processing parameters

Quality criteria

Scatter beyond specifications

Scatter in average mass density; asymmetry of mass distribution

Scatter in chemical analysis of different positions

Dents and blisters Surface porosity index

Dimensions beyond tolerances

Unsatisfactorily controlled parameters

Defect evidence

Representative tests, Correlation to structure, Service performance

Density measurements, Determination of centers of gravity of shape and mass

Chemical analysis of ingredients and product

Roughness measurement, Dye penetrant tests, Chemical analysis, hardness

Contour measurements

Process records, assessment of relevant parameter variations

Quality testing

Matrix of features of parts made of cellular metals and correlated macroscopic quality criteria proposing their verification.

Features

Table 4.3-2.

4 Characterization of Cellular Metals 175

Quality goals

Reproducible space filling sub-domain arrangement

Sub-domain volumes contain statistically representative number of cells

Outer surface boundary conditions according to loading, independent of interface boundaries

Properties insensitive to microstructural variations within averaging limits

Properties of sub-domains represented by the local average mass density of the corresponding volume

Appropriate scaling laws and constitutive equations known

Cell architecture

Dimensional accuracy

Surfaces

Metal matrix

Mass distribution

Properties

Definition of critical property relevant irregularities Definition of critical dimensions, connectivity and positions

Establishing confidentiality limits for different types of materials

Determination of location of soft and hard regions

Calibration by experimental tests

Testing stiffness in different directions, comparison with computer simulations (e DE(x,y,z) for small strains)

Definition of critical Dr Shape, connectivity and size of extreme densities (iso-surfaces) Check of gradients in main directions

Estimated differences of solid properties compared with bulk (calibration of input properties)

Comparison of modeling with deformation experiments recorded by XCT or digital video images

Load transfer area smaller than interacting subdomain Limited correspondence of loading, sub-domains, FE-mesh

Free surface except area of load actuation Spatial displacement of sub-domain interfaces

Experience from microstructural examinations of same type of cellular metal

Averaging volume bigger than dominant cell sizes, smaller than 1/3 of sample's minimum thickness; Sensibility tests for variations of averaging volume size

Averaging volume size too big in relation to sample size, large sub-domains of only few not representative over-sized cells

Convergence criterion for size of averaging volume deduced from width of density histogram

Quality testing Histogram of mass density distribution from XCT; Difference of rm and histogram's maximum; Volume fraction of r I rm Dr and of r i rm ‡ Dr

Defect evidence Histogram shape, Volume fractions below and above certain limits

Master curves of local density distributions

Quality criteria

Matrix of features of cellular metals and correlated mesoscopic quality criteria proposing their verification.

Feature

Table 4.3-3.

176

4.3 Considerations on Quality Features

4 Characterization of Cellular Metals

togram, the volume fractions of the sample with densities outside a certain specification and the local position of those extremely soft or hard regions. Even the existence of over-sized pores can be indicated. The following uniformity criteria are proposed for the example of Alulight foams: x

x

x

the local density variations should be within e30 % around the mean apparent density; regions of smaller mass densities than the specified range (including zero for over-sized pores) should in any direction not be bigger than 1/3 of the thickness of the sample; the sample's regions with mass densities beyond the specified limits should not be connected in any preferential orientation causing anisotropy, and should occupy less than 5 vol.-%.

A stiffness test in different directions is proposed as an experimental check of the mechanical behavior of a part in order to reveal any significant irregularity and macroscopic anisotropy. The absolute stiffness values can be compared with simulations of the elastic performance of that part (see Section 6.2). Up to now there is little experience on the applicability of any quality criterion for cellular metals and specifications will have to be developed on the basis of the experience that will be gained from the first series products.

Acknowledgements

The authors are grateful to Leichtmetall Kompetenzzentrum Ranshofen, Austria, Slovak Academy of Science, Bratislava, Slovakia, and Shinko Wire, Japan for the provision of test samples. The X-ray tomograms have been recorded at Bundesanstalt fuÈr MaterialpruÈfung, Berlin and the Division of Osteoradiology, University of Vienna.

References Schwartz, D. S. Smith, A. G. Evans, H. N. G. 1. M. F. Ashby, A. G. Evans, N. A. Fleck, L. J. Wadley (eds), MRS Symp. Proc. Vol. 521, Gibson, J. W. Hutchinson, H. N. G. Wadley, MRS, Warrendale, PA 1998, p. 109 117. Metal Foams: A Design Guide, Butterworth4. J. L. Greensted, in Porous and Cellular Heinemann, Oxford 2000. Materials for Structural Application, D. S. 2. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, 2nd edn, Cambridge Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS Symp. Proc. Vol. 521, University Press, UK 1997. MRS, Warrendale, PA 1998, p. 3 13. 3. M. L. Renauld, A. P. Giamei, M. S. Thompson, J. Priluck; in Porous and Cellular 5. A. Elmoutaouokkail, L. Salvo, E. Maire, G. Peix, in Proc. Cellular Metals and Metal Materials for Structural Application, D. S.

177

178

4.3 Considerations on Quality Features Foaming Technology (MetFoam 2001), J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT, Bremen 2001, p. 245±250. 6. H. P. Degischer, A. Kottar, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 213 220. 7. F. Simancik, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 235 240. 8. V. Gergely, T. W. Clyne, Adv. Eng. Mater. 2000, 4, 175 178. 9. Th. Schambron, R. Gramlinger, R. Kretz, in Proc. Cellular Metals and Metal Foaming Technology (MetFoam 2001), J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT, Bremen 2001, p. 461±466. 10. H. P. Degischer, U. Galovsky, R. Gradinger, R. Kretz, F. Simancik, in Proc. MetallschaÈume, J. Banhart (ed.), MIT, Bremen 1997, p. 79 90. 11. D. Lehmhus, C. Marschner, J. Banhart, Materwiss. Werkstofftechn. 2000, 31, 474 476. 12. B. Illerhaus, J. Goebbels, Materwiss. Werkstofftechn. 2000, 31, 527 528. 13. J. Baruchel, J.-Y. Buffiere, E. Maire, P. Merle, G. Peix (eds), X-Ray Tomograhy in Material Science, Hermes, Paris 2000. 14. H. Bart-Smith, A. F. Bastawros, D. R. Mumm, A. G. Evans, D. J. Sypeck, H. N. G. Wadley, in Porous and Cellular Materials for Structural Application, D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS Symp. Proc. Vol. 521, MRS, Warrendale, PA 1998, p. 71 81 15. D. Leitlmeier, H. Flankl, in Proc. Cellular Metals and Metal Foaming Technology (MetFoam 2001), J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT, Bremen 2001, p. 171±174. 16. A. H. KoÈnig, H. Doleisch, A. Kottar, B. Kriszt, E. GroÈller, in Data Visualisation 2000, Springer, Vienna 2000, p. 279. 17. W. Sanders, L. J. Gibson, in Porous and Cellular Materials for Structural Application,

D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS Symp. Proc. Vol. 521, MRS, Warrendale, PA 1998, p. 53 57. 18. A. F. Bastawros, A. G. Evans, Adv. Eng. Mater. 2000, 4, 210 214. 19. B. Zettl, S. Stanzl-Tschegg, Materwiss. Werkstofftechn. 2000, 31, 484 487. 20. S. Huschka, S. Hicken, F. J. Arendts, in Proc. MetallschaÈume, J. Banhart (ed.), MIT, Bremen 1997, p. 189 197. 21. R. Gradinger, F. G. Rammerstorfer, Acta Mater. 1999, 47, 143 148. 22. E. W. Andrews, P. R. Oneck, L. J. Gibson, Int. J. Mech. Sci. 2001, 43, 681 699. 23. J. Banhart, J. Baumeister, Metallurgy 1997, 51, 19. 24. V. I. Shapovalov, in Porous and Cellular Materials for Structural Application, D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS Symp. Proc. Vol. 521, MRS, Warrendale, PA 1998, p. 281 290. 25. B. Kriszt, B. Foroughi, K. Faure, H. P. Degischer, Mater. Sci. Technol. 2000, 16, 792 796. 26. A. Wanner, B. Kriszt, Materwiss. Werkstofftechn. 2000, 31, 481 483. 27. K. P. Dharmasena, H. N. G. Wadley, in Porous and Cellular Materials for Structural Application, D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS Symp. Proc. Vol. 521, MRS, Warrendale, PA 1998, p. 171 176. 28. W. A. Kalender, Computed Tomography, Publicis MCD, Munich 2000. 29. A. Kottar, H. P. Degischer, B. Kriszt, Materwiss. Werkstofftechn. 2000, 31, 465 469. 30. H. P. Degischer, B. Kriszt, B. Foroughi, A. Kottar, in Metal Matrix Composites and Metallic Foams, Euromat 1999, Vol. 5, T. W. Clyne, F. Simancik (eds), Wiley-VCH, Weinheim 2000, p. 74 82. 31. S. F. Buchelle, H. Ellinger, Rev. Prog. Quant. Nondestructive Evaluation, 1989, 8A, 449.

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

5 Material Properties R. Pippan

Foaming dramatically extends the range of properties of metals, as demonstrated in Table 5-1 for some commercially available metal foams. These physical, mechanical, and thermal properties are usually measured by the same methods as those used for dense solids. We designate the properties of the cell-wall material with the subscript ªsº and the properties of the cellular structure without the subscript ªsº (e. g., rs is the density of the solid cell-wall material and r is the density of the foam). It is clear that not all properties will change in the same way. There are properties that do not change, for example: x x x

crystal structure, thermal expansion coefficient, and melting temperature (solidus liquidus range).

Other physical properties, such as the heat capacity, are typically linear functions of the density. More exactly it is the sum of the heat capacity of each phase multiplied by its weight fraction. Even in low density metallic foams the weight fraction of gas is small, so that the specific heat of the cellular structure is essentially equal to that of the parent metal. Finally, there are many properties that depend on the density (or porosity) not only linearly, but also on the geometrical structure or the microarchitecture of the cellular structure: the stiffness, the mechanical strength, the thermal and electrical conductivity as well as acoustic properties, for example. It is the aim of this chapter to give a short overview of the most important properties for the application of cellular metals. A much more general and detailed treatment can be found in the book on cellular solids by Gibson and Ashby [1]. The increasing interest in the properties of metal foams is clearly visible from the increasing number of recent publications in leading materials journals [2 13], proceedings [14 18], and the data supplied by different research groups.

179

180

5 Material Properties Table 5-1.

Ranges for properties of commercial metallic foams [6].

Property, symbol [units]

Cymat

Alulight

Alporas

ERG

Inco

Material

Al SiC

Al

Al

Al

Ni

Relative density, r/r0

0.02 0.2

0.1 0.35

0.08 0.1

0.05 0.1

0.03 0.04

Structure

Closed cell

Closed cell

Closed cell

Open cell

Open cell

Young's modulus, E [GPa]

0.02 2.0

1.7 12

0.4 1.0

0.06 0.3

0.4 1.0

Poisson's ratio, n

0.31 0.34

0.31 .34

0.31 0.34

0.31 0.34

0.31 0.34

Compressive strength, s pl [MPa]

0.04 7.0

1.9 14.0

1.3 1.7

0.9 3.0

0.6 1.1

Tensile elastic limit, s y [MPa]

0.04 7.0

2.0 20

1.6 1.8

0.9 2.7

0.6 1.1

Tensile strength, s UTS [MPa]

0.05 8.5

2.2 30

1.6 1.9

1.9 3.5

1.0 2.4

Endurance limit, s ce [MPa]

0.02 3.6

0.95 13

0.9 1.0

0.45 1.5

0.3 0.6

Densification strain, eD

0.6 0.9

0.4 0.8

0.7 0.82

0.8 0.9

0.9 0.94

Tensile ductility, eUTS

0.01 0.02

0.002 0.04

0.01 0.06

0.1 0.2

0.03 0.1

Fracture toughness, KcIC [MPa.m1/2]

0.03 0.5

0.3 1.6

0.1 0.9

0.1 0.2

0.6 1.0

Thermal conductivity, l [W/mpK]

0.3 10

3.0 35

3.5 4.5

6.0 11

0.2 0.3

Resistivity, R [10 8Vpm]

90 3000

20 200

210 250

180 450

300 500

The parameters that influence the structure-sensitive properties of cellular metals are (ordered by their importance): intrinsic properties (properties of cell wall material), relative density, type of cellular structure (open or closed cells), in a closed-cell foam, the fraction of the solid contained in the cell nodes, edges or the cell faces, irregularity or gradients in mass distribution, the cell size and size distribution (including exceptional sizes), shape of the cells and the anisotropy of cells (including exceptional shapes), connectivity of cell edges, and defects, by which we mean buckled or broken cell walls.

x x x x

x x x x x

5 Material Properties

Some scaling relations have been developed for idealized structures [2], between the properties of the solid, the density, and the type of cellular structure: a few of them are listed here. These relations clearly point out that the most important structural characteristic of a cellular material is the relative density r/rs. The importance of other structural parameters can be easily seen in the density dependence of the thermal and electrical conductivity. The thermal conductivity of metal foam is mainly dominated by the conductivity through the solid. The contribution of the gas, radiation across the pores, and convection within the cell play a minor role. Therefore, the thermal and the electrical conductivity should behave in the same manner. The conductivity of the cellular metal should be equal to the conductivity of the dense solid times its volume fraction (r/rs) multiplied by an efficiency factor, which is given by the geometry and takes into account the tortuous path of the heat flow. If we assume that a variation of the relative density is caused by a proportional change of the thickness of the cell wall and struts, or an increase of the size of the cells maintaining the cell wall thickness the efficiency factor should be constant. For Al foams it was shown that a variation of the efficiency factor can be expressed also in a power law of the relative density, it is about proportional (r/rs)0.5, hence the conductivity is about proportional (r/rs)1.5. In contrast to thermal and electrical properties, the influence of the density and the architecture of the cellular metal on the mechanical properties is much stronger and more complex. For load bearing structures, packaging, and crash elements their importance is evident, however, for functional applications, for example, heatexchange systems, damping, and filtering the structural stability is also essential. In general, one can distinguish between elastomeric, elastoplastic, and brittle foams (this is not a classification of the solid material, it describes the behavior of the cellular structure). In compression, these three types of foam show a similar behavior [2] but for different reasons. Metallic foams, having a relative densities of r/rsI0.2, exhibit after an elastic loading a more or less clear plateau regime, leading into a final regime of steeply rising stress. The differences are visible in the mechanism of deformation or by unloading of the compressed cell structure: in elastomeric foams the collapse is by elastic buckling of the cell walls and is more or less recoverable; in plastic foams it is the formation of plastic hinges; and in brittle foams it is the brittle fracture of the cell wall (crush) that causes the plateau region: the last two are not recoverable. Cellular metals are usually ductile. Figure 5-1 compares schematically the stress strain curve of a cellular and a solid metal in tension and compression. The foam shows a linear elastic regime, which is not so clearly established as in a solid; followed by a ªhardeningº, which is not only hardening as in a solid, it is induced by a redistribution of deformed regions; in compression one reaches then a plateau regime and a final densification; in tension the maximum stress is reached at relative small strains, typically 1 4 %, which is much smaller than in a solid metal. The characteristic values are the Young's modulus E (strictly the stiffness of the cellular structure), the elastic limit s y (which may be slightly different in tension and compression), the tensile strength, s UTS, the plateau stress

181

182

5 Material Properties

in compression s pl (where the subscript ªplº means plastic), the densification strain, the ultimate tensile strain, and the fracture strain ef. The shape of the stress strain curve in Fig. 5-1 is typical of cellular metals. The characteristic parameters for a certain relative density depends on the type of foam, open- or closedcell, the anisotropy, and other architectural parameters. The standard scaling relation [1], however, only takes into account the properties of the solid metal, the relative density, and the type of foam. Such simplified scaling relations exist also for creep [1], fatigue [19], and fatigue crack propagation properties, but they are based only on a limited number of experimental evidence. Compression behavior has been relatively extensively investigated [14 18], whereas studies of the behavior under tensile and shear loading are rather limited, the latter is especially important for the design of sandwich panels. A further important difference between a solid metal and a metal foam becomes visible under multiaxial loading. For example, the yield behavior in a solid metal is not affected by the hydrostatic component of the stress tensor that is different in cellular metals [1]. In the following, the different properties and some specific problems with measuring these properties of cellular metals are discussed. Finally it should be emphasized that, for the application of a foam, not only one property has to be considered. For example, in the automotive industry the stiffness, crush behavior, the energy absorbing, acoustic damping, as well as the cheap production of a complex shape are important. In such multidimensional requirements metal foams can be the best solution. It is furthermore important to note that redesign (foam specific) of the component is usually necessary. For example, the simple filling of a given shell structure with a foam does not necessarily improve the property of a component.

Figure 5-1.

Schematic comparison of the stress strain behavior of a metal and a metal foam.

5 Material Properties

References

1. L. J. Gibson, M. F. Ashby, Cellular Solids, Cambridge University Press, UK 1997. 2. W. E. Warren, A. M. Kraynik, J. Appl. Mech. 1988, 55, 341 346. 3. T. G. Nieh, K. Higashi, J. Wadsworth, Mater. Sci. Eng. A 1999, 283, 105 110. 4. J. Grenestedt, K. Tanaka, Scripta Mater. 1999, 40, 71 77. 5. J. Grenestedt, F. Bassinet, Int. J. Mech. Sci. 2000, 42, 1327 1338. 6. A.-F. Bastawros, H. Bart-Smith, A. G. Evans, J. Mech. Phys. Solids 2000, 48, 301 322. 7. H. Bart-Smith, A.-F. Bastawros, D. R. Mumm, A. G. Evans, D. J. Sypeck, H. N. G. Wadley, Acta Mater. 1998, 46, 3583 3592. 8. J. Banhart, J. Baumeister, J. Mater. Sci. 1998, 33, 1431 1442. 9. Y. Yamada et al., Mater. Sci. Eng. A 2000, 277, 213 217. 10. K. A. Dannemann, J. Lankford Jr., Mater. Sci. Eng. A 2000, 293, 157 164. 11. A. Paul, U. Ramamurty, Mater. Sci. Eng. A 2000, 281, 1 7. 12. M. MuÈnch, M. Schlimmer, Mater. Sci. Eng. Tech. 2000, 6, 544 546. 13. O. B. Olurin, N. A. Fleck, M. F. Ashby, Mater. Sci. Eng. A 2000, 291, 136 146.

14. J. Banhart (ed.), MetallschaÈume, MIT Verlag, Bremen, Germany: The proceedings of a conference held in Bremen in March 1997 (in German). 15. J. Banhart, M. F. Ashby, N. A. Fleck (eds.), Metal Foams and Foam Metal Structures, Proc. Int. Conf. Metfoam `99, 14 16 June 1999, MIT Verlag, Bremen 1999. 16. A. G. Evans (ed.), Ultralight Metal Structure, Division of Applied Sciences, Harvard University, Cambridge, MA, USA: the annual report on the MURI programme sponsored by the Defense Advanced Research Projects Agency and Office of Naval Research, 1998. 17. D. S. Schwartz, D. S. Shih, A. G. Evans, H. N. G. Wadley (eds.), Porous and Cellular Materials for Structural Application, MRS Proceedings Vol. 521, MRS, Warrendale, PA, USA, 1998. 18. H. P. Degischer (ed.), MetallschaÈume, Proceedings of the DGM Symposium ªMetallschaÈumeº, 28 29 February 2000, Vienna, Austria, MATWER 31, 6, Wiley-VCH, Weinheim 2000 (in German). 19. B. Zettl, H. Mayer, S. E. Stanzl-Tschegg, H. P. Degischer, Mater. Sci. Eng. A 2000, 292, 1 7.

5.1

Mechanical Properties and Determination

C. Motz, R. Pippan, and B. Kriszt

5.1.1

Young's Modulus

One of the most important properties of structural materials is the linear elastic behavior, which is described by a set of moduli. For isotropic materials two moduli are needed: the Young's modulus, E, and the shear modulus, G, to characterize the linear elastic response. Some foams are not isotropic owing to the manufacturing processes and therefore more than two moduli are necessary to describe the linear elastic behavior.

183

184

5.1 Mechanical Properties and Determination

In the isotropic case, which will be accounted for in this section owing to simplification and because many closed-cell metal foams are more, or less isotropic, the following well known relations between Young's modulus E, shear modulus G, bulk modulus K, and elastic Poisson's ratio n exist G ˆ

E E , K ˆ 2(1 S v) 3(1 s 2v)

(1)

In the situation of cellular material, or foams it is in general not appropriate to use the term ªmodulusº, because a foam is a structure (like a framework) and one should use ªstiffnessº instead. However, it is now usual to consider that new class of materials as a continuum, hence common material properties are used to characterize them. But it is important to note that the Young's modulus of a cellular structure is not a material constant and depends therefore mainly on the architecture of the cellular metal.

Influence of the Foam Structure There is an essential difference between open-cell and closed-cell structures. Opencell foams are represented by a network of connected struts. The main deformation mechanism is bending of the cell edges and, at higher relative foam densities, rr i 0.1 [1], additional extension and compression of the edges. In closed-cell foams the cell walls between the cell edges stiffen the structure. Besides bending, extension and compression of the cell edges and the membrane stresses in the cell walls also play a major role on the deformation mechanisms. Owing to the higher constraints, arising form the existence of cell walls, in closed-cell structures the Young's modulus is theoretically higher by several magnitudes compared with open-cell structures of the same relative density. Imperfections in the structure, like corrugations and curvature of cell walls and cell edges [2] have also a significant influence on the stiffness. There can be a large impact on the Young's modulus of a foam if these imperfections reach a larger extent. Other structural parameters, like cell size, cell shape, and their variations have a minor influence on the Young's modulus [3]. Since the structural parameters are not easily controllable during the manufacturing process, finite element studies of the dependence of the elastic stiffness in foams with respect to different parameters have been performed [4,5], which support these experimental observations. 5.1.1.1

5 Material Properties

Influence of the Foam Density The relative foam density rr has the largest influence on all mechanical parameters. For lower density foams (rr I 0.2) Gibson and Ashby [2] have applied a simple bending strut model to a cubic foam structure and found the following relation between Young's modulus and density 5.1.1.2

E z Es

r rs

E z F2 Es

!2 (open-cell)

r rs

(2)

!2 S(1 s F)

r (closed-cell) rs

The subscript ªsº indicates the properties of the solid from which the cell walls and cell edges are made. F is the fraction of solid that is contained in the cell edges for closed-cell foams. Although these equations are based on a simple model of a cubic foam structure, which considerably deviates from a real foam, there is a fair agreement with experimental results (Fig. 5.1-1). The equations are valid as long as the main deformation mechanism is bending of cell edges. For higher-density foams extension and compression of cell edges becomes more important and therefore a deviation from these relations should be observed.

Figure 5.1-1. Dependence of the Young's modulus on the relative foam density for different types of closed-cell (closed symbols) and open-cell (open symbols) aluminum foams [6].

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5.1 Mechanical Properties and Determination

Influence of Deformation Deformation changes the structure of a foam by bending, buckling, stretching, and cracking of the cell edges and cell walls. Therefore, the Young's modulus will change with strain. In general, there is only a very small linear elastic part in the stress strain curve of a ductile foam, which makes the measurement of the initial Young's modulus difficult. For that reason many authors measure an unloading modulus at a certain strain and use this one as Young's modulus, E. It is important at which strain the modulus is measured because it changes with increasing deformation. Figure 5.1-2 shows the stress strain curves in compression and tension and the unloading compliance of an Alporas foam (rr ˆ 0.1). It is evident that the Young's modulus with increasing strain |e| decreases much faster in compression than in tension. This is induced by the fact that buckling cell edges and cell walls reduce the stiffness much stronger whereas stretching will increase the stiffness before the initial cracking of cell walls during tension loading. Ultrasonic test methods apply a very small deformation on the foam and permits the measurement of the Young's modulus during deformation experiments. The obtained Young's moduli are significantly higher than those measured in standard compression or tension tests [7]. Figure 5.1-3 shows the dependence of the Young's modulus on the deformation obtained with a ultrasonic test method. For structural applications usually an ªinitialº Young's modulus is needed. Since the determination of the initial Young's modulus is difficult, it is suggested to use the unloading modulus E0.2 at 0.2 % total strain in compression, or tension, which seems to be a good compromise between measurability and the effect of plastic deformation. 5.1.1.3

Figure 5.1-2. Stress strain response with measured unloading moduli indicated for a closed-cell aluminum foam (Alporas, rr ˆ 0.1).

5 Material Properties Figure 5.1-3. Dependence of the Young's modulus (stiffness) on the deformation at which the modulus is measured [7]. The change of density is used as measure at the deformation in compression.

5.1.2

Compression Behavior

In compression, cellular metals show a unique stress strain response with a plateau region in which the stress is nearly constant over a wide range of strain (Fig. 5.1-4). This behavior makes cellular metals interesting for energy absorbing applications where at a relatively low constant stress a large amount of deformation can be absorbed. More about energy absorbing and crush behavior can be found in Section 5.1.3. Depending on the material from which the foam is made, different deformation mechanisms (elastomeric, brittle, and ductile behavior) can be observed. Metallic foams usually show a considerable ductile behavior. Many investigations have been performed on compression behavior and energy absorbing performance of metal foams in recent years. The behavior is similar to many polymer foams. Thus the basic deformation mechanisms and the stress strain response are well known. Compression loading at small strains of ductile foams yields to bending and extension/compression of cell edges and cell walls. If the stresses in the edges and walls exceed the yield stress s y,s of the solid, the onset of plastification is reached and the deformation is no longer reversible. Caused by the inhomogeneous structure of real cellular metals the stress concentrations exceed the yield stress in some elements at relatively low strains, which leads to an early ªplastificationº of the foam. Therefore the linear elastic part of the stress strain curve of a ductile foam is in general hard developed. Increasing the load on the foam causes to buckling of cell edges and walls in weaker regions of the foam. A deformation band perpendicular to the loading direction develops, in which plastic collapse of the cells takes place. This is accompanied by the beginning of the plateau region in the stress strain curve. With increasing strain, additional deformation bands are formed until most of the cells have collapsed and the

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5.1 Mechanical Properties and Determination

Stress strain response in compression for a ductile aluminum foam and a brittle alumina foam [11].

Figure 5.1-4.

densification region is reached [8,9]. Depending on the cellular structure and the properties of the solid, the plateau region of the stress strain curve may not be flat, but a slight slope, or waviness of the curve can occur. Two extreme cases are depicted in Fig. 5.1-4, the behavior of a ductile aluminum foam and a brittle alumina foam, showing a smooth and a jagged plateau, respectively. For the estimation of the plateau stress s pl depending on the foam density r and the yield stress s y,s of the solid, Gibson and Ashby used a simple cubic-cell model for the foam. The plateau stress is reached, when the moment exerted to the cell edges exceeds their fully plastic moment s pl z 0:3 s y; s s pl z 0:3 s y; s

r rs F

!3=2 (open-cell)

r rs

(3)

!3=2 S0:4(1 s F)

r (closed-cell) rs

Figure 5.1-5 shows the stress strain curves in compression of Alulight aluminum foams with different densities. The increase of the plateau stress with increasing density is clearly obvious. Different methods exist for the measurement of the plateau stress depending on the course of the stress strain curve. If there is a stress peak at the beginning of the plateau, this peak or a clear flat section stress will be taken as plateau stress [10]. In

5 Material Properties

Figure 5.1-5.

compression.

Stress strain curves of aluminum foams (Alulight) with different densities in

the absence of a stress peak the plateau region will be extrapolated to lower strains and the intersection with the initial elastic line, or the ordinate (Rpe) delivers the plateau stress [10,27]. The plateau stress plays an important role to characterize the energy absorbing behavior and is a good material property for the compression performance of a foam. However, for structural design with foams the plateau stress may not be applicable, because of the relatively high deformation and damage of the foam that is accompanied with this stress level. The determination of a yield stress s y is problematic owing to the usually poorly developed linear elastic regime of the stress strain curve. To compromise, an offset yield stress, like s 0.2, or Rp02 should be used, depending on the mechanical response of the cellular metal. For the experimental determination of a stress strain curve, standard equipment for compression tests can be used. If the measurement of the Young's modulus E and the 0.2 % offset yield stress s 0.2 is needed, the displacement should be measured directly at the specimen with a clip gauge, or a videoextensiometer. To avoid errors arising from inhomogeneous deformation of the foam the displacement should be measured at more than one position on the specimen. The specimen size must exceed the average cell size by 7 to 10 times in each principal direction to reduce the influence of the inhomogeneous cell structure.

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5.1 Mechanical Properties and Determination

5.1.3

Energy-Absorbing and Impact Behavior

Good energy absorbers should support large strains at a relatively low constant stress level. Owing to their compression behavior, cellular metals (especially foams) and also some polymer foams, are especially suited for energy absorbing applications. The advantages of metal foams for these applications are their relatively low density, adjustable plateau stress level, good temperature resistance and non-flammability. Thus their application fields are the transport and packaging industries.

Energy Absorbing Capability Cellular metals have a good energy absorbing capacity with a good energy absorbing efficiency because of the extensive plateau regime. In the event of an impact, the forces are controlled by the stress level at which the kinetic energy is absorbed. To avoid damage of a package, or injury to a person, the impact forces must not exceed a certain value. Therefore, not only is the energy absorbing capacity important, but also the stress strain response of the material plays a major role (Fig. 5.1-6). 5.1.3.1

Figure 5.1-6. Comparison of stress strain re- the same for both. The peak stress of the absponse of two different energy absorbers. The sorber that has no plateau region is higher and amount of absorbed energy per volume in a this will enhance the impact forces. certain strain interval is indicated as EV and is

5 Material Properties

Figure 5.1-7. The energy absorbing efficiency, h, is the ratio between absorbed energy of the material EV and the absorbed energy of an ideal plastic material EV,ideal in a certain strain range.

The absorbed energy per unit volume EV in a certain strain interval [e1, e2] is equal to the area below the stress strain curve and can be expressed as Z e2 s(e)de EV ˆ (4) e1

The efficiency of energy absorption, h, is the ratio between the absorbed energy of the real material and the absorbed energy of an ideal absorber that is an ideal plastic material R e2 s(e)de (5) h ˆ e1 s 0 (e2 s e1 ) Most cellular metals have a nearly flat plateau region and therefore a high energyabsorbing efficiency depending on the used strain interval, and in general, a good absorbing capacity (Fig. 5.1-7).

Impact Behavior For the application of cellular metals as crash absorbers in transport systems not only is the energy absorbing capacity but also the impact behavior important. At high deformation rates, which may occur in crash situations, the mechanical properties of the foam may change. There are two points that must be taken into consideration: the inertial mass of the cell edges and walls and the gas pres5.1.3.2

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5.1 Mechanical Properties and Determination

sure and gas flow inside the cells of a closed-cell foam. Both effects can increase the flow stress and therefore also the plateau stress of the foam with increasing strain rate [12]. In open-cell structures no significant increase of flow stress is observed at higher strain rates, which suggests that the inertial masses of the structural elements have no contribution to the flow stress [12]. In closed-cell foams the situation is different, because some of the metal foams show a strain-rate dependence. Real closed-cell metal foams are, in general, not completely closed-cell structures because they frequently contain some initial defects in the cell walls arising from the manufacturing process. Additional defects are generated during the deformation process when cell walls rupture. The gas flow between the cells through these defects is strain rate dependent. Thus the gas pressure inside the cells increases during high-speed deformation and contributes to the flow stress [13]. Owing to the strain localization in deformation bands, the local strain rate is much higher than the measured global one, which will increase the strain rate effect. As a result, the plateau stress and the energy absorbing capacity of closed cell metals foams ise [12,13]. Investigations on aluminum foams show an increase in the plateau stress of 20 90 % when the strain rate increases from 10 3 to 103 s 1 (Fig. 5.1-8). The strain rate effect is mainly controlled by the cell morphology and the alloy from which the foam is made.

Figure 5.1-8.

Strain-rate dependence of the plastic strength of two types of aluminum foams [12].

5 Material Properties

5.1.4

Tension Behavior

Improvements in the manufacturing processes of metal foams have increased their quality and opened new applications as a real structural material. Therefore mechanical properties, like tension and fracture behavior need to be known in addition to compression and energy absorbing performance. The failure mechanisms and the stress strain response deviate from those observed in compression.

General Tensile Behavior The initial deformation mode is very similar to compression and consists of bending of cell edges in open-cell foams and additional extension and compression of cell walls in closed-cell foams. In the post-yield stage, however, the deformation mechanism differs significantly from compression. In compression, plastic, or brittle collapse of cells occurs within deformation bands perpendicular to the loading axis. Owing to the dominance of tensile stresses in the cell edges and cell walls in tension, buckling of these elements is improbable. Finite element simulations show that such plastic instabilities may only occur at very large strains [14], whereas the strain to fracture of real ductile metal foams is of the order of a few percent. The deformation is concentrated in weak regions of the cellular metal. No deformation bands are formed except during the final failure. The final failure mechanism depends on the ductility of the material from which the foam is made. Brittle ceramic foams usually show microcracking of highly stressed cell walls and edges before final failure. If these defects exceed a critical size, a main crack propagates through the foam and catastrophic failure occurs. The critical fracture strength s cr of the foam can be obtained by applying linear elastic fracture mechanics [2] 5.1.4.1

p s cr z C l=a s fs; s

r rs

!3=2 (open-cell)

(6)

where C is a constant, l is the cell size, a is the critical initial defect size, and s fs,s is the fracture strength of the solid. For closed-cell metals the situation is more complicated. In ductile cellular metals (such as aluminum foams) cracking of cell walls and cell edges can also be observed before a main crack starts to propagate. With increasing deformation, a fracture-process zone starts to develop within which the whole deformation is concentrated. In closed-cell metals, several cell walls rupture inside this fracture-process zone. Further deformation leads to development and propagation of a main crack along the weakest path in the cellular structure. Only the strongest cell edges remain intact and hold the two foam parts together. This process is accompanied by a decrease in flow stress, which is evident in the stress strain curve depicted in Fig. 5.1-10. Figure 5.1-9 shows the corresponding

193

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5.1 Mechanical Properties and Determination

deformation process and the failure mechanism of a ductile closed-cell aluminum foam. The estimation of the peak stress, s UTS, or the fracture strain for ductile cellular metals is complicated, because a relation for the ductile fracture of the cell edges and cell walls must be established and incorporated into the geometrical models. The experiments show that s UTS is usually compatible with the plateau stress in compression.

Failure mechanism in aluminum foam in tension. Crack initiation in some weak cell walls and subsequent development of a fracture-process zone (stress strain curve in Fig. 5.1-10).

Figure 5.1-9.

Figure 5.1-10. Stress strain response in tension of aluminum foam with some unloading moduli indicated (Alporas, 3r ˆ 0.18).

5 Material Properties

The Influence of Notches Common metals reveal a different behavior in tension if notches are present. Brittle materials show a lower average net section stress at fracture with notched specimens compared with unnotched ones. Owing to the stress concentration at the notch root, the fracture strength of a brittle material is reached at a lower average stress and the specimen fractures. Ductile materials behave differently and show a higher average net section stress at fracture if notches are present. At the notch root the deformation is constrained, which results in a higher stress triaxiality and therefore in a higher flow stress. In the case of metal foams, the situation is more difficult because the plastic deformation do not take place at constant volume, which results in a plastic Poisson's ratio npl smaller than 0.5. Therefore, the transverse strains, and consequently also the constraints at the notch root, are smaller than in common metals. Under compressive loads the plastic Poisson's ratio is near zero in the plateau region and the foam should show a notch-insensitive behavior. Whereas in tension (and also in compression at strains smaller than the onset of the plateau region) the plastic Poisson's ratio is similar to the elastic one. The elastic Poisson's ratio n depends on the cellular structure and for most commercially available closed-cell foams (Alulight and Alporas) n is in the range 0.30 0.40 [15]. Thus, these foams should show a notch sensitivity in tension. This is supported by finite element simulations [16], which indicate that a notch sensitivity should be observed, if the plastic Poisson's ratio is greater than 0.3. In Fig. 5.1-11 the stress strain curves of notched foam specimens with different notch depth ratios are presented. An increase in the net section stresses and a decrease in the strains to fracture can be observed with increasing notch depth. 5.1.4.2

Figure 5.1-11. Influence of the notch depth ratio, a/W, on the stress strain response of a ductile aluminum foam in tension.

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5.1 Mechanical Properties and Determination

Foam-Specific Test Problems in Tension For the testing procedure standard methods for tension tests can be used. Owing to the relatively low fracture strains of most cellular metals in tension, the displacement should be measured with a clip-gauge attached directly to the specimen and not with the cross-head displacement of the testing machine. The specimen size should exceed 7 to 10 times the average cell size in all principle directions to obtain reliable results. The specimen should be mounted carefully into the testing machine to avoid damage to the foam. A good method is to glue the foam specimen to two metal plates that are then mounted into the test machine. Important mechanical properties that can be obtained from tension tests are Young's modulus, the peak stress, s UTS, the yield stress s 0.2, the strain at maximum stress eUTS and the elastic and plastic Poisson's ratios n and npl. The strain to total fracture does not represent a material property but one of the individual specimen. Therefore eUTS is recommended, where considerable degradation starts progressing usually rapidly. 5.1.4.3

5.1.5

Torsion Behavior

In torsion the cell edges are subjected to bending and the cell walls to a combination of bending and shearing. The shear behavior is important for the development of material laws and also for the application in sandwich structures, where core shear may occur in particular load situations. Alternative methods for testing the shear strength are, for example, the double-lap shear test or the ASTM C-273

Stress strain response of aluminum foam in torsion with no axial stress (black line) and with tensile axial stress (gray line) [17].

Figure 5.1-12.

5 Material Properties

test method. Most foams exhibit significantly larger deformation up to failure in free torsion compared with tension tests. A typical example is depicted in Fig. 5.1-12. If the specimen ends are axially fixed during the torsion test, additional tensile stresses are built up in the sample and the strain to fracture is reduced to the level typical observed in tension tests. Important properties are the shear modulus G, the shear strength g t and the shear strain to fracture g t. By applying tensile or compressive loads on the specimen during torsion tests a variety of stress states in the sample can be achieved and the failure mechanisms can be studied. 5.1.6

Fracture Behavior

Fracture behavior and fracture toughness values may play a major role for the application of cellular metals foams in load-bearing structural components. The fracture of brittle foams, where linear elastic fracture mechanic (LEFM) can be applied, were discussed briefly in the section on tensile behavior. The situation in closed-cell ductile metal foams is more complicated, where LEFM usually can not be applied, which is considered in this section.

Crack Initiation and Crack Propagation Owing to the inhomogeneous structure of most metal foams, it is expected that localization effects may appear during fracture tests. Figure 5.1-13 shows a sequence of micrographs of a region in front of the notch root at different load steps for a ductile aluminum foam. Crack initiation and crack propagation are clearly visible. Loading a notched or pre-cracked specimen results in plastic yielding in the vicinity of the crack tip [18]. The deformation is localized to the thinnest regions of the cell walls surrounding the crack tip. With further loading, the strain to fracture is reached in some cell walls and microcracks appear in the vicinity of the crack tip. Cell walls that are few cell sizes away from the crack tip can be plastically deformed too, whereas other regions remain nearly undeformed. A so-called fracture-process zone (FPZ) with an extent of several cell sizes develops, which contains localized deformation and microcracking. The definition of a plastic zone in cellular metals is complicated, because at higher loads localized yielding can occur over the whole ligament length. With increasing load a main crack is initiated at the notch root, or at the pre-crack by a coalescence of microcracks, and starts to propagate through the cell structure. The crack follows the weakest path through the structure and builds thereby secondary cracks and crack bridges. Crack bridging length and microcracking should depend on the cell structure and the solid of which the foam is made. 5.1.6.1

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5.1 Mechanical Properties and Determination

Figure 5.1-13. Diagram of the load displacement curve and the corresponding SEM images to demonstrate crack initiation and crack propagation in a ductile aluminum foam acquired from insitu fracture tests.

Fracture Toughness For ductile cellular metal foams, linear elastic fracture mechanics is usually not applicable, because they show an extensive plastic regime and the specimen sizes are limited by the manufacturing processes. Therefore elastoplastic fracture mechanic tests, like J-integral tests, or COD (crack opening displacement) tests, must be used to determine the fracture toughness of metal foams. Common standards, like ASTM E813 for J-integral tests, are optimized for ductile solids and can only be used in a limited manner for foams. Size restrictions for the specimen geometry 5.1.6.2

5 Material Properties

to obtain valid fracture toughness values should be thought about because, for example, the required specimen size also depends on the cell size, l, of the foam. For the determination of J Da curves according to ASTM E813 or ASTM E1152, the following parameters must be measured: the force F, the load-line displacement vLLD, and the crack extension Da. Figure 5.1-14 shows a load versus loadline displacement curve obtained in a fracture mechanics test and the crack extension as a function of the load-line displacement of a ductile aluminum foam. The calculated J Da curve is plotted in Fig. 5.1-15. The ASTM standard provides that the initial J-value, J0.2, is obtained by the intersection of the blunting line at 0.2 mm crack extension with the straight line achieved from a linear regression of the J Da curve in the Da interval 0.15 1.5 mm. A crack extension of 0.2 mm is rather low for metal foams, because it is one magnitude smaller than the usual cell size (the characteristic microstructural length) and can be caused by other effects (microcracking, localized yielding) rather than crack extension, depending on the measurement method used. Fleck and Ashby [19] introduced a steady-state J-value, JSS, which is measured as the plateau J in the J Da curve. They assumed that this JSS is a measure of the fracture toughness for cracks, where the bridging zone is fully developed. However, not all cellular metals show a typical plateau region in the J Da curve and the plateau is reached at rather high crack extensions. The standardization of the evaluation of initial, or steady state fracture toughness values from J Da curves is a problem that has not yet been solved satisfactorily. Gibson and Ashby [6] established the following relation between the fracture toughness and the foam density for ductile metal foams

Figure 5.1-14. Load and crack extension versus load-line displacement curve for a ductile metal foam (Alporas, rr ˆ 0.1).

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5.1 Mechanical Properties and Determination

J-integral versus crack extension plot with fracture toughness values JSS and J0.2 indicated (J-values obtained from Fig. 5.1-14). Figure 5.1-15.

JIC z Cs y; s l


r rs

!3=2 (7)

This equation correlates the fracture toughness with the cell size (compare with Eq. 8, it is assumed that COD ˆ l), which is demonstrated only for a limited number of foams and densities. Other fracture toughness values, like KIC, or CODC, can be derived from this equation using the well-known fracture mechanics relations. An alternative method for the determination of the fracture toughness of a ductile material is the measurement of the critical crack opening displacement (COD). Although this is a direct method, it is rarely used owing to the difficulties in experimental determination. Schwalbe [20] suggested to measure the COD 5 mm away from the crack tip, COD5, which can be more easily performed. We have adapted this technique to foams. Figure 5.1-16 shows COD5 Da and CTOD Da curves of a ductile aluminum foam (CTOD ˆ crack tip opening displacement). The advantage of this method is the similarity of the COD Da curves for different foams and the easier evaluation of critical fracture toughness values. The relation between COD and the J-integral is given by the following equation J ˆ k s  COD

(8)

where s * is the mean value between yield stress s y and ultimate tensile stress s UTS and k is 1 for plain stress state and 1,3...2,6 for plain strain state for common metals. In the case of metal foams the value of k for the (macro) plain strain state depends on the Poisson's ratio of the foam in the plastic regime. It is im-

5 Material Properties

Crack opening displacement (COD) in terms of COD5 and crack tip opening displacement CTOD versus crack extension curves for the same foam as shown in Fig. 5.1-14 and Fig. 5.1-15. The CTOD value is Figure 5.1-16.

measured behind the crack tip and reaches a constant value after a certain crack extension, whereas COD5 is measured at a fixed position 5 mm behind the initial crack tip.

portant to note that we have to distinguish the macro- and micro- stress states (the stress state in the cell wall). Since npl is much smaller than in solid metals, k should be only somewhat larger than 1.

Foam-Specific Test Problems Fracture mechanics tests are usually performed with compact tension specimens. The criteria for the load and load-line displacement measurements are given in the corresponding ASTM standards. The determination of the crack extension Da in cellular metals is more complicated owing to their inhomogeneous structure. Experimental tests show that potential drop techniques and compliance methods give reasonable results for Da. The specimen size is not only limited by fracture mechanics constraints, but also by the cell size of the structure. The specimen ligament and initial crack length should not be smaller than ten times the average cell size and the thickness should be larger than five times the average cell size to obtain specimen size independent results. It should be noted that at this time there are no standards for determining critical fracture toughness values for metal foams. 5.1.6.3

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5.1 Mechanical Properties and Determination

References

1. W. E. Warren, A. M. Kraynik, J. Appl. Mech. 1988, 55, 341 346. 2. L. J. Gibson, M. F. Ashby, Cellular Solids, Cambridge University Press, Cambridge 1997. 3. T. G. Nieh, K. Higashi, J. Wadsworth, Mater. Sci. Eng. A 1999, 283, 105 110. 4. J. Grenestedt, K. Tanaka, Scripta Mater. 1999, 40, 71 77. 5. J. Grenestedt, F. Bassinet, Int. J. Mech. Sci. 2000, 42, 1327 1338. 6. M. F. Ashby, A. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: A Design Guide, ButterworthHeinemann, Oxford 2000. 7. A. Wanner, B. Kriszt, Mater. Sci. Eng. Tech. 2000, 6, 481 483. 8. A.-F. Bastawros, H. Bart-Smith, A. G. Evans, J. Mech. Phys. Solids 2000, 48, 301 322. 9. H. Bart-Smith, A.-F. Bastawros, D. R. Mumm, A. G. Evans, D. J. Sypeck, H. N. G. Wadley, Acta Mater. 1998, 46, 3583 3592. 10. J. Banhart, J. Baumeister, J. Mater. Sci. 1998, 33, 1431 1442. 11. Y. Yamada et al., Mater. Sci. Eng. A 2000, 277, 213 217.

12. K. A. Dannemann, J. Lankford Jr., Mater. Sci. Eng. A 2000, 293, 157 164. 13. A. Paul, U. Ramamurty, Mater. Sci. Eng. A 2000, 281, 1 7. 14. A. Ableidinger, ªMicro-macromechanical Investigations of the Strength and Structure Behaviour of Metallic Foamsº, Thesis, Vienna University of Technology, Austria 2000. 15. C. Motz, R. Pippan, ªDeformation Behavior of Aluminum Foams in Tensionº, Acta Mater 2001, 49, 2463±2470. 16. P. R. Onck, ªApplication of a continuum constitutive model to metallic foam DENspecimens in compression,º International Journal of Mechanical Sciences 2001, 43, 2947±2959. 17. M. MuÈnch, M. Schlimmer, Mater. Sci. Eng. Tech. 2000, 6, 544 546. 18. C. Motz, R. Pippan, in Proc. ECF-13 Conf., 6 9 Sept 2000, San SebastiaÂn, Spain, CDROM, 2000. 19. O. B. Olurin, N. A. Fleck, M. F. Ashby, Mater. Sci. Eng. A 2000, 291, 136 146. 20. K. H. Schwalbe, A. Cornec, Fatigue Eng. Mater. 1991, 14, 405 412.

5 Material Properties

5.2

Fatigue Properties and Endurance Limit of Aluminum Foams

B. Zettl, H. Mayer, and S. Stanzl-Tschegg

Fatigue properties of aluminum foams are of great interest, if foamed structures are subjected to repeated mechanical straining or vibrations. Endurance experiments have been performed under cyclic compression [1 6], cyclic tension [1,2,5,6], and under fully reversed loading condition [7,8]. These experiments show that the foam structure rapidly looses strength after a certain number of load cycles depending on the stress amplitude and the mean stress. Cyclic compression loading leads to the formation of deformation bands, whereas fatigue failure of foams under cyclic tension stresses is caused by the initiation and growth of fatigue cracks [2 5]. Under fully reversed loading conditions [7,8] fatigue cracks cause rupture of specimens, similar to the damage mechanism under cyclic tension stress [8]. Fatigue investigations of metallic foams described in the literature concentrate on the regime of numbers of cycles to failure below approx. 106 to 107. In practical application, however, foamed components may be exposed to greater numbers of load cycles. Automotive components, for example, may be subjected to more than 108 cycles during lifetime, and the high cycle fatigue properties and the determination of an eventual fatigue limit is necessary therefore for a comprehensive description of the cyclic properties of foams. Although most authors assume an endurance limit at 107 cycles, an experimental verification is only found in one report [7] where several specimens have been tested to 109 cycles or more. In this work, fatigue data available in the literature will be summarized and the high cycle fatigue properties of three aluminum foams will be evaluated. 5.2.1

Literature Survey of Endurance Data

Results of endurance tests of several aluminum foams are available in literature. Fatigue data determined by different authors have been analyzed to evaluate the influence of material properties and loading conditions on the fatigue behavior of aluminum foams. Published original data have been obtained from articles and conference proceedings. Endurance data represent numbers of cycles to failure for a certain foamed material (foam type and material density) at a certain cyclic stress and load ratio. However, the authors have used different ways to define the magnitude of cyclic loading and the load-ratio R: some authors have used |s max| / |s min| as a definition of the load-ratio [1,2,4 6], whereas others have used |s min| / |s max| [3]. In the present report, as well as elsewhere [7,8] the load ratio R is defined in accordance to the major part of the fatigue literature: R ˆ s min/s max [9], where positive values represent tension stresses and negative values represent compression stresses. Conse-

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5.2 Fatigue Properties and Endurance Limit of Aluminum Foams

quently, the load ratio R is 1 for fully reversed loading, 0 J R I 1 for cyclic tension loading and 1 J R J T for cyclic compression loading. The amplitude of a stress cycle Ds/2 ˆ (s max s min)/2 is used to describe the cyclic stress range. A summary of S N curves described in the literature is shown in Fig. 5.2-1. The S N data are approximated by power-law curve-fits with a 50 % survival probability. Nn

Ds ˆ C 2

(1)

The values of the exponent, n, and the coefficient, C, (in MPa) have been evaluated and are shown in Table 5.2-1. Different symbols and lines refer to different materials and loading conditions (cyclic compression, cyclic tension, or fully reversed loading). Fatigue properties of the different aluminum foams show significant variations. The cyclic stress amplitudes that lead to mean lifetimes of 105 cycles, for

Figure 5.2-1. S N curves of aluminum foams. Hydro. Loading condition: continuous Literature references and material properties line ˆ cyclic compression, broken line ˆ cyclic are shown in Table 5.2-1. Materials: x Alcan, tension, gray line ˆ fully reversed cycling. y Duocel, k Alporas, b IFAM, v Alulight,

Alcan

Duocel

Alporas

Alporas

Alporas

Alporas

Alporas

Alulight

IFAM

Alulight

Alcan

Duocel

Alporas

Alporas

Alporas

Alporas

Alulight

Hydro Al

IFAM

Alulight

#2

#3

#4

#5

#6

#7

#8

#9

#10

#1 1

#12

#13

#14

#15

#16

#17

#18

#19

#20

Foam

[11]

[8]

[8]

[5]

[6]

[2]

[6]

[6]

[2]

[1]

[5]

[3]

[5]

[6]

[2]

[6]

[6]

[4]

[2]

[1]

Ref.

0.56

0.40

0.29

0.86

0.30

0.30

0.25

0.25

0.19

0.15

0.50

0.63

0.45

0.30

0.30

0.25

0.22

0.22

0.19

0.15

Density [g/cm3]

7.0

4.4

3.5

17.0

2.25

1.9

1.75

1.47

0.53

0.25

19.5

8.8

6.3

2.34

1.9

1.71

1.37

1.4

0.53

0.25

Plateau stress [MPa]

rever.

rever.

rever.

tension

tension

tension

tension

tension

tension

tension

compr.

compr.

compr.

compr.

compr.

compr.

compr.

compr.

compr.

compr.

Loading condition

1

1

1

0.1

0

0.1

0

0

0.1

0.1

10

10

10

T

10

T

T

10

10

10

Load ratio

51

19

19

14

26

5

33

30

4

8

7

13

7

30

8

28

30

5

7

7

Tested specimens

6.988

15.691

5.296

13.645

2.254

1.355

1.467

1.068

0.554

0.131

12.514

6.232

3.393

1.759

1.332

1.028

0.710

0.626

0.546

0.133

Coefficients C [MPa] n

0.110

0.189

0.111

0.090

0.093

0.068

0.080

0.072

0.081

0.108

0.031

0.074

0.038

0.053

0.063

0.038

0.028

0.037

0.079

0.064

List of references for S N curves shown in Fig. 5.2-1. Coefficients C and n refer to a power-law approximation of data (Eq. 1) [1 6,8,11].

#1

Table 5.2-1.

5 Material Properties 205

206

5.2 Fatigue Properties and Endurance Limit of Aluminum Foams

example, may vary by a factor of 200, depending on the investigated foam and the load ratio. The main reasons for the large variations of the fatigue properties of aluminum foams are their different mass densities and structures. Literature data show a significant trend, that fatigue properties of foams increase with increasing plateau stress. As an example, the stress amplitude for 50 % survival probability of 105 cycles and of 107 cycles, respectively, are shown in Fig. 5.2-2. Irrespective of foam type and loading condition (cyclic tension, cyclic compression, or fully reversed), the fatigue strength increases with the plateau stress. The linear relation shown in Fig. 5.2-2 indicates, that the stress amplitude for mean lifetimes of 105 cycles is approximately 0.35 of the plateau stress, and Ds/2s pl ˆ 0.27 leads to mean lifetimes of approximately 107 cycles. This means that the fatigue lifetime of an aluminum foam is mainly determined by the cyclic stress amplitude, Ds/2 with respect to the plateau stress, s pl, and Ds/2s pl is an appropriate measure of the magnitude of cyclic loading. To compare different aluminum foams it is reasonable to normalize the cyclic properties with respect to the plateau stress s pl. Eq. (1) may be rewritten as follows Nn

Ds C ˆ 2s pl s pl

(2)

In Fig. 5.2-3, literature data obtained under cyclic compression, under cyclic tension, and under fully reversed loading conditions are summarized. Additionally, mean S N curves for these three loading conditions are shown. The algebraic expression of the mean curves of the literature data is

Figure 5.2-2. Stress amplitudes at 105 cycles to failure (full symbols, solid line) and 107 cycles to failure (open symbols, dashed line) for: x compressive, k tensional, v reversed loading. Data obtained from Fig. 5.2-1.

5 Material Properties

N nmean

Ds C ˆ ˆ C0 2s pl s pl

(3)

The values of the exponent, nmean, and the coefficient, C0, of the mean curves are shown in Table 5.2-2. The largest absolute value of the exponent nmean is found for fully reversed loading and the smallest for cyclic compression loading. Using the relative stress amplitude, Ds/2s pl to describe the magnitude of loading, Duocel foam shows good fatigue properties under cyclic compression Table 5.2-2.

Coefficients for mean curves (Eq. 3) under different loading conditions. Coefficient C0

Exponent nmean

Cyclic compression loading

0.628

0.0491

Cyclic tension loading

0.800

0.0825

Fully reversed loading

1.738

0.1351

a)

b)

Normalized load amplitudes versus number of cycles to failures for: a) cyclic compression, b) cyclic tension, c) fully reversed loading.

Figure 5.2-3.

c)

207

208

5.2 Fatigue Properties and Endurance Limit of Aluminum Foams

(Fig. 5.2-3a: #2) and cyclic tension (Fig. 5.2-3b: #12). Duocel foam was the only open-cell foam where fatigue data were found in the literature. Similar relative fatigue strength is visible for Alporas foam (Fig. 5.2-3a: #3 #7, Fig. 5.2-3b: #13 #16), Alulight foam (Fig. 5.2-3a: #8,#10, Fig. 5.2-3b: #17, Fig. 5.2-3c: #20) and IFAM foam (Fig. 5.2-3a: #9, Fig. 5.2-3c: #19). Hydro aluminum foam has been tested under fully reversed loading conditions only (Fig. 5.2-3c: #18) and shows the highest relative strength at R ˆ 1. Alcan foam, which is the material with the lowest density, shows the lowest relative fatigue strength under cyclic compression and cyclic tension (Fig. 5.2-3a: #1, Fig. 5.2-3b: #11). 5.2.2

High Cycle Fatigue Properties and Endurance Limit

To evaluate the high cycle fatigue properties and to determine an eventual fatigue limit for aluminum foams, specimens have to be tested up to very high numbers of cycles. These investigations are time consuming using conventional fatigue testing equipment working at low frequencies, since several specimens have to be tested to obtain statistically relevant data of this rather inhomogeneous material. Therefore, the ultrasonic fatigue testing method has been used in this study to investigate the high cycle regime in an efficient and time saving manner.

Material and Procedure The aluminum foams used in the present investigation are produced from powder metallurgical prepared precursor material with entrapped titanium hydride as foaming agent. The chemical composition of the investigated foams is Al 0.6 wt.-% Mg 0.3 wt.-% Si (named AlMg0.6Si0.3), Al 1 wt.-% Mg 0.6 wt.-% Si (AlMg1Si0.6), and Al 12 wt.-% Si (AlSi12). The commercial name of the materials is Alulight. The material was produced as rods of 160 mm length and of 17 mm diameter; material density is 0.56 g/cm3. The specimens were 60 mm long and all materials have been tested as fabricated. Additionally, a series of AlMg1Si0.6 foam specimens were artificially aged before testing (T5, age hardening at 160 hC for 14 h). Using the ultrasonic fatigue testing method, specimens are subjected to a fully reversed tension compression resonance loading at a frequency of approximately 20 kHz. The cyclic loading was controlled with an electromagnetic displacement gauge, which measured the vibration amplitude at one end of the specimen. The maximum of the cyclic strain amplitude at the half-length of the specimen was measured with strain gauges on the surface of the rod. To obtain an average value of the cyclic strain amplitude, strain gauges with a gauge length larger than the median cell size were used (measuring area 6 mm q 6 mm). Along the circumference of a specimen the strain amplitudes measured with strain gauges coincided within 5 10 %. Experiments were performed in pulsed form (pulse length: 1000 cycles) and were interrupted by periodic pauses of adequate length to cool the specimen. A fan was used additionally. The specimen tempera5.2.2.1

5 Material Properties

tures were 20 25 hC during the experiments. Details of the ultrasonic equipment are described elsewhere [9].

Results Results of endurance tests with AlMg1Si0.6 foam are shown in Fig. 5.2-4a. Numbers of cycles to failure are related to the experimentally determined cyclic strain amplitude, De/2. Assuming a mean Young's modulus of 3.9 GPa, the stress amplitude, Ds/2 can be calculated from the measured cyclic strain as shown in Fig. 5.2-4a (right ordinate). Specimens that did not fail within 109 cycles (runouts) are marked with an arrow. Fatigue data are subjected to pronounced scatter, which is typical for inhomogeneous materials. The solid line indicates a mean fracture probability of 50 % assuming power-law dependence between stress amplitudes and cycles to failure. The S N measurements of AlMg1Si0.6 foam indicate a well-defined fatigue limit: Specimens either fail before about 107 cycles are reached or they survive 109 cycles or more. The median endurance limit (failure probability of 50 %) is in5.2.2.2

a)

b)

c)

d)

Results of endurance fatigue tests under fully reversed tension compression cycling: a) AlMg1Si0.6 foam, b) AlMg1Si0.6/T5 foam, c) AlMg0.6Si0.3 foam, d) AlSi12 foam. Figure 5.2-4.

209

210

5.2 Fatigue Properties and Endurance Limit of Aluminum Foams

dicated with a line parallel to the abscissa in Fig. 5.2-4a at a stress amplitude of 1.3 MPa, which is approximately 23 % of the plateau stress. However, specimens may fail at significantly lower cyclic stresses due to the statistical distribution of defects and areas of stress concentrations. The highest stress amplitude, where no specimen failed within 109 cycles, is 1 MPa. Endurance tests on AlMg1Si0.6 T5 foam are summarized in Fig. 5.2-4b. The heat treatment leads to longer mean lifetimes at all stress levels in comparison with the not heat treated material. Additionally, the endurance limit increased. The maximum stress amplitude, where no specimen failed, is 1.2 MPa, and the median fatigue strength at 109 cycles is 1.4 MPa (approximately 20 % of the plateau stress). The results of endurance tests with AlMg0.6Si0.3 and AlSi12 foams are shown in Fig. 5.2-4c and d, respectively. At a stress amplitude of 1 MPa, one (of five tested) AlMg0.6Si0.3 foam specimens failed. The fatigue limit for 50 % survival is 1.1 MPa (approximately 22 % of the plateau stress). The median fatigue strength at 109 cycles of AlSi12 foam is 1.3 MPa (approximately 19 % of the plateau stress). Fatigue data of AlSi12 foam are subjected to the most pronounced scatter among the investigated Alulight foams. At stress amplitudes of 1.2 MPa three specimens did not fail within 109 cycles, whereas one specimen failed at 1 MPa. 5.2.3

Mechanism of Crack Initiation

The initiation of fatigue cracks leads to an increase of specimen compliance and thus to a decrease of resonance frequency of the ultrasonic vibration. This allows to determine eventual crack initiation during fatigue cycling. After starting a fatigue experiment, the resonance frequency decreases until about 60 80 % of the lifetime is reached. If fatigue cycling is stopped then and specimens are cut into pieces, studies with a scanning electron microscope (SEM) show fatigue damage at several locations in the interior of the foam. Cracks initiate and grow from already existing material defects, like holes, precracks, and tied up areas with reduced cell wall thickness that were introduced during foaming (Fig. 5.2-5a) or cooling of the material (Fig. 5.2-5b). No significant further variation of resonance frequency is found after approximately 107 cycles, if a specimen is cycled at the endurance limit. This indicates that the process of fatigue damage is stopped, and cracks cannot grow until final failure. Cracks remain arrested in the interior of cell walls (Fig. 5.2-6a and b) and are trapped when the crack tip reaches cell nodes. The largest cracks in cell walls of specimens, which did not fail until 109 cycles, were about 3 mm long. If specimens are cycled above the fatigue limit, a main crack is formed in the inner section of the specimen during the remaining 20 40 % of the lifetime (Fig. 5.2-6c). Microscopical surface investigations of several specimens showed no evidence of fatigue cracks at the skin surface until about 80 % of the lifetimes have been reached. This means, that fatigue cracks preferentially initiate in the interior of a foamed rod.

5 Material Properties

Figure 5.2-5.

cooling.

Cell-wall defects in AlMg1Si0.6 foam introduced: a) during foaming, b) during

SEM studies at higher magnification show, that the fatigue fracture surface is relatively smooth and transcrystalline. The general fracture appearance is ductile, and striations are visible in some areas. Figure 5.2-7 shows both, a fatigue fracture surface in a cell wall (Fig. 5.2-7a and b) and a fracture surface that has been formed by static rupture of the specimen after fatigue testing (Fig. 5.2-7c). Fatigue cracks show clear differences compared with cracks formed by static loading or during cooling of the melt due to the far lower plastic deformation of the material around the crack path. Fatigue crack paths preferentially follow areas where the cell wall is thin. In Fig. 5.2-7, the thicknesses of cracked cell walls are approximately 30 60 mm, whereas the most frequent wall thickness obtained by image-analysis is 250 500 mm [10]. SEM studies of the fracture surface do not show deformation bands or plastic buckling as it could be found for uniaxial compression or for cyclic compression fatigue loading. The role of cell nodes, where fatigue cracks may be trapped, helps to understand the influence of different foam structures on the fatigue properties. Duocel is an

211

212

5.2 Fatigue Properties and Endurance Limit of Aluminum Foams

Typical fatigue cracks: a) fatigue crack inside a cell wall, length about 300 mm, b) crack starting from a cell-wall defect, length about 150 mm, c) fatigue crack causing rupture of a specimen.

Figure 5.2-6.

5 Material Properties

Figure 5.2-7. Fracture surfaces of AlMg1Si0.6 T5 (Ds/2 ˆ 1.96 MPa, number of cycles to failure 8.3 q 104): a) fatigue fracture surface, b) striations indicating crack growth direction, c) fracture surface formed by static rupture.

213

214

5.2 Fatigue Properties and Endurance Limit of Aluminum Foams

open-cell foam with r ˆ 0.15 g/cm3 and consists of cell nodes only and approximately the same amount of material is distributed to nodes and cell walls inside Alcan foam (r ˆ 0.19 g/cm3). Fatigue cracks initiated in Alcan foam may find lower growth resistance since cell nodes contain less material compared with Duocel foam. This may be one reason, why Duocel foam (Fig. 5.2-3b, #11) shows far better cyclic tension properties than Alcan foam (Fig. 5.2-3b, #12). 5.2.4

Summary

A survey of literature data (20 S N curves determined with six different aluminum foams under cyclic compression, cyclic tension, and fully reversed loading) shows that the fatigue strength is related to the plateau stress, s pl. x

x

The stress amplitude, Ds/2 for mean lifetimes of 105 cycles (107 cycles) is approximately 35 % (27 %) of the plateau stress. Numbers of cycles to failure and relative stress amplitudes, Ds/2s pl may be correlated by a power law function. The largest gradient is found for fully reversed loading and the smallest for cyclic compression loading.

To investigate the high cycle fatigue properties of aluminum foams, three Alulight foams have been investigated at numbers of cycles between 104 and 109. Cylindrical rods with a continuous surface layer and a closed cell structure were tested. The foam density is 0.56 g/cm3. x

x

x

The investigated Alulight foams show a fatigue limit, and cycles to failure above 107 are rare. The median endurance limits, Ds/2 are 1.1 1.4 MPa, which is 19 23 % of the plateau stress. Fatigue damage under fully reversed tension-compression loading is governed by the formation of cracks. Preferential areas for crack initiation are initial defects like precracks or holes in the interior sections of cell walls. No strain localization or formation of deformation bands (as reported for cyclic compression tests) is found. Fatigue cracks preferentially grow in the inner sections of cell walls where wall thickness is small. Below the endurance limit eventual cracks are trapped at the nodes of cells.

Acknowledgements The authors acknowledge financial support by the ªFonds zur FoÈrderung der wissenschaftlichen Forschung (FWF)º, Vienna, (project no. P13230PHY) and the LKRCenter of Competence on Light Metals, Ranshofen, Austria, for the grant through the K-plus project and for supplying the Alulight foams.

5 Material Properties

References

1. O. B. Olurin, N. A. Fleck, M. F. Ashby, in Proc. Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 365 371. 2. A. M. Harte, N. A. Fleck, M. F. Ashby, Acta Mater. 1999, 47, 2511 24. 3. J. Banhart, W. Brinkers, J. Mater. Sci. Lett. 1999, 18, 617 19. 4. Y. Sugimura, A. Rabiei, A. G. Evans, A. M. Harte, N. A. Fleck, Mater. Sci. Eng. 1999, A269, 38 48. 5. K. Y. G. McCullough, N. A. Fleck, M. F. Ashby, Fatigue Fract. Eng. Mater. Struct. 2000, 23, 199 208. 6. T. BoÈllinghaus, H. v. Hagen, W. Bleck, in Proc. DGM Symp. MetallschaÈume,

H. P. Degischer (ed), Vienna, Austria, WileyVCH, Weinheim 2000, p. 488 492. 7. B. Zettl, H. Mayer, S. E. Stanzl-Tschegg, H. P. Degischer, Mater. Sci. Eng. 2000, A292, 1 7. 8. O. Schultz, A. des Ligneris, O. Haider, P. Starke, Adv. Eng. Mater. 2000, 2, 215 18. 9. S. Suresh, Fatigue of Materials, 2nd ed, Cambridge University Press, Cambridge 1998. 10. H. P. Degischer, B. Kriszt, Structural Investigations of Al-Foam using Quantitative Image Analysis (Project-Report), Institute for Material Science, University of Technology, Vienna 1997.

5.3

Electrical, Thermal, and Acoustic Properties of Cellular Metals

F. Simancik and J. Kovacik

It is evident that the presence of gas bubbles will significantly affect also electrical, thermal, and acoustic properties of cellular solids. In the case of polymer foams these properties play an important role: thermal insulation and noise attenuation are beside packaging the main fields of application for this kind of materials. However, only a little attention is paid to the mentioned properties when cellular metals are considered, although the multifunctionality is often the prerequisite for their successful application. The aim of this chapter is therefore to reveal and critically discuss the potential of cellular metals in this field with respect to published models and rarely reported experimental data. For better understanding of considered properties, the basic physical background will be also briefly introduced. 5.3.1

Electrical Properties

Cellular metals are in distinction to polymer and most ceramic matrices electrically conductive. This simple fact changes the typical applications drastically: ceramic and polymeric foams can be used for insulation or for structural enclosures that

215

216

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

must transmit microwaves, while the metallic counterparts are good for the opposite purpose. The electrical conductivity of foamed metals, although considerably reduced by the porosity, is still sufficient enough to provide good electrical grounding, low voltage contacts, or capability to absorb electromagnetic waves. In the case of metallic sponges with open cell structure, the conductivity allows to distribute the electric potential on large accessible area, which makes them attractive for battery electrodes. Cellular nickel is extensively used in this application [1]. It is generally accepted, that cellular material inherits electrical characteristics of the solid of which it is made. The electrical conductivity s of material is defined according to Ohm's law sˆ

l I
S U

(1)

where U is a potential drop along the distance l when current I is applied. As can be seen conductivity depends strongly on the cross-sectional area S of the sample. In a case of cellular metals only a small portion of cross section is electrically conductive. These are the cell walls with roughly the conductivity of the base alloy. The main part of the cross section is created by pores, which are usually filled with dielectric air. The cell walls form a complex 3D network of electric conductors of varying cross section, whereas cell walls oriented normally to the potential gradient do not contribute to conduction because of no potential difference. Moreover, the cells are mostly continuously covered with electrically nonconductive metal oxides. The cellular structure provides therefore much lower electrical conductivity than bulk material. To calculate the electrical conductivity according to Eq. (1) the effective length l of the cell walls conducting along the potential difference and in the cross-sectional area S effectively contributing to conduction has to be known. Unfortunately, it is extremely difficult to determine it in real samples, although for example computed tomography offers this possibility. More reasonable and cheaper is to consider the sample as a black box of given outer geometry with macroscopically homogeneous and continuos distribution of a material within the box and to investigate the so called effective electrical conductivity. It is evident that the dependence of effective cross-sectional area on relative density of the structure is non linear. One of the first models of this dependence was introduced by Ashby et al. for the case of open-cell sponge [2]. The structure was idealized with narrow struts of given length and thickness. The struts were arranged in a perfect cubic lattice, with nodes linked by struts. Only struts oriented parallel to potential gradient contributed to conduction. For higher relative density they added also the contribution of the nodes and obtained the following relation s r ˆ f s0 r0

! S(1 s f)

r r0

!3=2 (2)

5 Material Properties

where s and r are the effective property and density of the foam respectively, while s 0 and r0 are the corresponding properties of the cell-wall material. The first term of this equation describes the contribution of struts and the second one that of nodes. Therefore, a structural parameter f was introduced, which characterizes how the material is distributed between cell nodes and struts. However, in real sponges the ratio between volume of cell nodes and cell struts is not constant and varies also with the density. Thus f in Eq. (2) must be obtained experimentally for each material and is valid only for certain density interval. Another approach for modeling of the relationship between relative density and selected physical property uses the principles of percolation theory [3 6] and covers the whole density range. In this case the cellular metal is considered as an ªinfiniteº cluster of randomly distributed gas pores in the metallic matrix. According to percolation theory the effective property near the connectivity threshold (in this case set to zero) behaves like a power-law function of a relative density !t s r ˆ z (3) s0 r0 where s and r are the effective property and density of the foam respectively, while s 0 and r0 are the corresponding properties of the cell-wall material. Constant t (often called as a critical exponent) can be theoretically predicted for the specific property. The theoretically estimated value for electrical conductivity in 3D is t ˆ 2.00 [7]. The constant z ought to be 1, because for bulk material r ˆ r0 and the effective property s ˆ s 0. Also this approach has some difficulties: It does not take into account defects such as cracks in pore walls, which influence the conductivity but not the relative density. Moreover, the theoretical predictions of critical exponents in 3D are still under development and optimization, especially when finite size clusters or anisotropic orientations are considered. Only little data for electrical conductivity of cellular metals have been reported [8 12] up to now (see also Table 5.3-1). Therefore, a serious verification of recent theoretical models is very difficult, if possible at all. f ˆ 0.33 and f ˆ 0.05 were obtained for ERG open-cell sponge and for Alulight closed-cell foam, respectively, applying Eq. (2) to fit the reported data [2]. The considerable difference in a, confirms an assumption that a is strongly material and structure dependent and for each case has to be obtained experimentally. The power law seems to be a good characterization of the relationship between experimental data of electrical conductivity and density measured on Alulight samples [3 5] (see Fig. 5.3-1 and Table 5.3-2). The characteristic exponents obtained experimentally have been found slightly lower than the critical exponent value theoretically predicted by the percolation theory. It can be explained by the fact that in distinction to the theory, where an infinite cluster is taken into account, the real experimental samples have always a finite size and in the referred case possess a surface skin. The volume fraction of the surface skin increases with decreasing

217

218

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals Overview of the electrical and thermal conductivity of cellular aluminum with various density from suppliers data sheets [8 12] measured at room temperature.

Table 5.3-1.

Suppliers

Density [kg.m 3]

Thermal conductivity [W/mK]

Electrical conductivity [m/Vmm2]

Alporas [10]

570

±

9.9

400

±

5.0

300

±

3.8

200

±

2.6

94

±

1.0

500

13

3.1

400

10

2.6

300

8.9

1.9

540

0.91

±

410

0.7

±

270

0.4

±

160

0.36

±

68

0.28

±

330

±

2.1

250

±

1.6

200

±

1.2

140

±

0.9

300

2.1

0.50

250

2.1

0.36

150

1.5

0.27

Alulight [9]

Cymat [11]

ERG [8]

Norsk Hydro [12]

size of the sample. The high portion of surface skin can diminish the effect of the porosity on the reduction of electrical conductivity of the foam. If the surface skin is removed from the sample the reduction of the conductivity due to increasing porosity is enhanced and characteristic exponent becomes higher. The similar effect can be observed when the sample size increases. It implies that the conductivity of the foam is not only a function of the porosity, but it is strongly affected also by the shape and size of the foamed part.

5 Material Properties Table 5.3-2. The obtained fitting parameters for the dependence of normalized electrical conductivity on the relative density for Alulight Al 99.7. x 2 is a minimization function [7].

z

t

x2

s/0 (mix.) [4]

0.999 e 0.009

1.55 e 0.02

7.31 qx 10

5

s/s0 (Al 99.7) [4]

0.979 e 0.025

1.75 e 0.06

6.54 qx 10

4

Although the behavior can be qualitatively understood by noting that with decreasing density the cross section available for conduction decreases and the tortuosity of the current path increases, a quantitative theory is still lacking [13]. Good electrical conductivity of cellular metals minimizes the penetration of electromagnetic waves into the structure, especially in the case of closed-cell foam parts covered by a surface skin. This fact can be successfully utilized for the protection of electronic devices or humans from the effect of electromagnetic noise. The ability for electromagnetic wave shielding can be defined by shield effectiveness depending on the wave frequency and the material thickness. The main advantage of metallic foam is a possibility to achieve a thickness required for low magnetic permeability at lower weight than in the case of bulk metals. The experimental measurements on closed cell Alulight and Si-steel sheet of the same weight are illustrated in Fig. 5.3-2 and Fig. 5.3-3 [9]. The shielding effectivity of the foam is even slightly better than that of a bulk aluminum plate of the same thickness, additionally the foam weight was approximately five times lower in this case (see Fig. 5.3-2). Cellular aluminum foam exhibits much better magnetic field

Figure 5.3-1. The power-law dependence of normalized electrical conductivity on the relative density for Alulight Al 99.7 foam (cylindrical samples with surface skin, s 0 ˆ 37.6 q 106 S m 1, r0 ˆ 2700 kg m 3) [4], for the fit parameter see Table 5.3-2.

219

220

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

Figure 5.3-2. Magnetic field shielding effectiveness as a function of frequency for cellular aluminum (Alulight) and Si-steel samples of the same weight and a massive Al sheet of the same thickness (t ˆ 8.5 mm) as the aluminum foam. Sample size 140 q 140 q t, density of foam 500 kg m 3 (KEC-method) [9].

Electric field shielding effectiveness as a function of frequency for cellular aluminum (Alulight) and Si-steel samples of the same weight. Sample size 140 q 140 q t, the density of foam 500 kg m 3 with t ˆ 8.5 mm (KEC-method) [9].

Figure 5.3-3.

shielding properties than Si-steel sheet of the same weight. The electrical shielding effectivity of Alulight is comparable with the properties of Si steel (see Fig. 5.3-3) up to 10 MHz. For higher frequencies the aluminum foam is superior. Similar results have been reported for Alporas foam [10]

5 Material Properties

5.3.2

Thermal Properties

The main thermal properties of practical importance with respect to cellular metals are the melting point, specific heat, coefficient of thermal expansion, thermal conductivity, thermal diffusivity, emissivity of the surface, fire and thermal shock resistance. Some of these properties are almost the same as for bulk materials, other ones depend strongly on the porous structure. Melting point of cellular metals is practically the same as for an alloy from which it is made. However, the surface is often covered by a continuous oxide layer, the melting point of which is usually considerably higher: for example in the case of cellular aluminum. The surface area covered with oxide layer increases with increasing porosity and decreasing pore size. When the oxide layer is sufficiently thick it can support the porous structure even above the melting point of the alloy, provided that no significant external force is applied on the structure. If the structure is heated in air or oxidizing atmosphere at the temperature close to melting point for sufficiently long time, the thickness of oxide layer increases and material becomes more stable. After a threshold thickness depending on the mechanical stability of the sample, the metallic cell walls oxidize completely by subsequent heating converting the cellular metal into a ceramic foam. This behavior is utilized for instance for the preparation of ceramic sponges from open-cell metallic precursors like Duocell sponges [14]. The energy needed to increase the temperature of cellular structure by a unit temperature is almost the same as required for cell-wall materials when the unit mass is considered. The slight difference can be accounted to the presence of thin surface oxides and the contained air. However, the specific heat per unit volume Cv of a cellular structures is of cause significantly lower. It makes them attractive for applications where low thermal capacity is required, for example for rapid heating and cooling systems. The coefficient of thermal expansion a of cellular metals is also almost the same as for the cell-wall material, while the thermal conductivity l is much lower. Higher thermally induced distortion has to be expected that increases with raising a/l ratio. To avoid it, the temperature differences in the cellular structure on heating or cooling should be minimized. On the another hand if the temperature shock resistance is considered, the situation is not so unambiguous. When a sudden temperature difference occurs between outer surface and inner material regions the thermal expansion causes thermally induced strains, the related elastic stress depend on the modulus of elasticity of the material. The stresses depend on the product a E and as the modulus of elasticity of cellular metal decreases with decreasing relative density the same temperature difference induces smaller thermal stresses the higher the porosity of the cellular structure, assuming the coefficients of thermal expansion is constant. However, with decreasing density also the collapse or tensile stress of the material decreases. If this stress scales with relative density at smaller exponent than the modulus of elasticity does, the temperature shock resistance of the foam will improve.

221

222

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

If not, the foam may yield or even break earlier than bulk material. In distinction to bulk materials, cellular metals are able to withstand much higher compressive strains without fracture because of the existence of a plateau stress. Therefore their temperature shock resistance is usually considered to be higher than that of bulk metals. It should be noted, that the same sudden change of ambient temperature causes higher temperature difference within a foam than within solid metal because of significantly smaller thermal conductivity of the cellular metal. It is evident that the thermal conductivity, l, of cellular metal will be significantly lower than the corresponding conductivity of bulk material. In comparison with electrical conductivity this property is more complex. Apparent thermal conductivity of porous structure has four contributions [13]: besides the thermal conductivity of the solid cell walls also the conductivity of enclosed gas, convection and radiation effects should be taken into account l ˆ lS S lG S lc S lr

(4)

where indexes S, G, c, and r denote the contribution to thermal conductivity of the solid cell wall material, the gas within pores, convection within the cells, and radiation through the cell walls. The thermal conduction is additionally affected by the presence of low conductive metal oxides on the surface of pore walls and cracks. However, in a case of cellular metals only the first term in Eq. (4) is important, the last three are practically negligible of moderate temperature levels. The contribution of conduction through gas lG is very low in comparison with the conduction through metal, because of low thermal conductivity of gas (thermal conductivity of air is 0.025 W m 1 K 1). Convection within the cells is important only when the Grashof number (the ratio between force driving convection and opposing viscous force) is greater than about 1000 [13]. This value is achieved with air filled pores at room temperature, when the pore diameter exceeds 10 mm. However, the pore size in real metallic foams usually is smaller, so the convection should be negligible in this case. Radiation through the cell walls is not possible in a case of optically nontransparent metals. Radiation within the cells can be ignored as well, when the conduction of the cell-wall material is greater than 20 W m 1 K 1 [15]. The contribution of the metal to the thermal conductivity of cellular structure (ls) depends on relative density r/r0 and similarly as for electrical conductivity it can be expressed by power law [3 6] !t r lS ˆ l0 (5) r0 where l0 denotes the thermal conductivity of solid metal. Constant t is the critical exponent for thermal conductivity and according to percolation theory its theoretically predicted value in 3D is t ˆ 2.0 [7]. The characteristic exponents obtained experimentally are listed in Table 5.3-3. The power-law dependence is illustrated in Fig. 5.3-4.

5 Material Properties Table 5.3-3. The obtained fitting parameters for the dependence of normalized thermal conductivity on the relative density for Alulight foam at various temperature. x 2 is a minimization function.

z

t

x2

l/l0 (20 hC) [5]

1.000 e 0.006

1.60 e 0.03

2.97 qx 10

5

l/l0 (100 hC) [5]

1.000 e 0.008

1.55 e 0.03

5.66 qx 10

5

l/l0 (300 hC) [5]

1.000 e 0.010

1.48 e 0.04

9.10 qx 10

5

l/l0 (400 hC) [5]

1.000 e 0.005

1.51 e 0.03

4.00 qx 10

5

As the thermal conductivity of bulk metals increases with increasing temperature, the same behavior is expected also in a case of cellular metals, in accordance with Eq. (5). Experimental values determined for Alulight foams made from various aluminum alloys at higher temperatures are shown in Fig. 5.3-5. As expected, with increasing temperature the effective thermal conductivity of foam increases. However, a little drop of this property has been observed at temperatures above 300 hC. This small reduction may be caused by heat losses due to increasing radiation effects, but more probably by extensive oxidation of the foam surface at higher temperatures. The alloys (such as AlSi12), which are less sensitive to oxidation, exhibit also less reduction of the effective thermal conductivity at higher temperatures.

Figure 5.3-4. The power-law dependence of normalized thermal conductivity on the relative density for Alulight foam at 20 hC. The corresponding fit parameters are given in Table 5.3-3 (cylindrical samples with surface skin, l0 ˆ 232 W m 1 K 1, r0 ˆ 2700 kg m 3) [3].

223

224

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

Thermal conductivity of Alulight foams made of various alloys as a function of testing temperature and density r: y, Al 99.6 base alloy, r ˆ 320 kg m 3 (ls ˆ 230 W m 1 K 1); Y, AlMgSi0.6 base alloy, r ˆ 420 kg m 3 Figure 5.3-5.

(lsˆ 200 W m 1 K 1); v, AlMgSi0.6 base alloy, r ˆ 500 kg m 3, V, AlSi12 base alloy, r ˆ 440 kg m 3 (ls ˆ 120 W m 1 K 1), x, AlSi12 base alloy, r ˆ 330 kg m 3

Thermal diffusivity a governs heat flow through a material before a steady state flow by thermal conduction is achieved. It is defined as a ratio l/Cv between thermal conductivity l and volumetric specific heat Cv. Foams have usually higher thermal diffusivity than bulk cell-wall materials and thus they achieve a steady state heat flow earlier. This property makes the cellular metals attractive for use as heat exchangers. The emissivity of the foam surface is almost always higher than that one of the metal from which it is made of. As the actual surface area of the foam is also much larger at equal outer dimensions the foam will emit or absorb more thermal radiation than bulk material. This property in combination with small specific heat per unit volume can be utilized in applications where rapid heating or cooling by radiation is required. Although polymer and ceramic foams are used more for thermal insulation than for any other purpose, application of cellular metals in this field is unlike because their thermal conductivity l is about two orders of magnitude higher than polymers (see Table 5.3-1). However, higher thermal conductivity and diffusivity of cellular metals can be successfully utilized in heat exchangers or heat sinks for power electronics, air-cooled condenser towers and regenerators. This application is restricted only to open cell structures enabling flow of cooling gas or fluid without significant pressure drop. The main design principles for heat exchangers made from cellular metals are [2]: high conductivity of metal (preferably Cu, Al), turbulent flow of fluid to enhance local heat transfer; and minimized low-pressure drop between fluid inlet and outlet. For any system there is a trade-off between heat flux and pressure drop. Optimum can be achieved with cell sizes in the mesorange and with relative densities of order r ˆ 0.2. [16]

5 Material Properties

Relatively small thermal conductivity, noncombustibility and low weight make the metallic foams attractive also for application as fire resistant panels. Thermal fire resistance of a structural component can be defined as the time to failure by excessive heat transmission. In case of panels it can be defined as a time at which the temperature of the unexposed surface of the panel reaches a critical value TC, for example the melting temperature. The thermal fire resistance strongly increases with increasing Biot number calculated for the panel [15] Bi ˆ hL=l

(6)

where h is heat transfer coefficient, L is the thickness, and l is the thermal conductivity of the panel. For given Biot number the fire resistance is infinite if the impose fire temperature is smaller than a threshold value TF TF ˆ TC S Bi(TC s T0 )

(7)

where TC and T0 are critical and initial temperatures of the panel, respectively. The Biot number for a panel made of metallic foam is always higher than that one for a corresponding metal sheet of the same weight. For example, it takes 8 min to heat up the opposite side of a Cymat sheet (density 160 kg m 3, geometry 24 cm q 30 cm q 5.5 cm) from room temperature up to 500 hC using oxy/acetylene torch (theoretical temperature 3100 hC) rotating at 15 cm distance from the foam front side. The burn-through time for corresponding aluminium sheet of the same weight (density 2700 kg m 3, geometry 24 cm q 30 cm q 0.34 cm) is only 23 s [11]. This illustrates the opportunities of metallic foams for this application. 5.3.3

Acoustic Properties

Sound is a form of the energy transmitted by the wave of collisions of molecules or atoms one against the next, and so on. It is important to note that there is no transfer of matter in this case. The speed of longitudinal elastic vibrations c in a given media is usually proportional to the ratio of the square root of the media modulus of elasticity E to media density r ratio s E ct (8) r For this reason the sound travels at velocity of about 5000 m/s in solid steel or aluminum, and only 343 m/s in air at the sea level. The wave velocity of sound is related to the wavelength l and frequency f of sound wave by c ˆ lf. The normal human ear responds to the frequencies from about 20 Hz up to 20 kHz, which corresponds to wavelengths of 17 m to 17 mm. For the noise control and reduction it is often enough to reduce sound pressure mainly in the range of 500 4000 Hz. The amplitude of sound wave determines the loudness of sound. The amplitude of sound pressure is measured in Pascals (Pa), but it is more convenient to use the logarithmic scale in decibels (dB) [2].

225

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

In general, the three basic cases can be distinguished with respect to noise attenuation materials: x

x

x

materials for sound insulation: they keep airborne sound out of the protected space, materials for sound absorption: they reduce or fully absorb the sound intensity within the room where the sound is generated, materials for damping: they reduce the amplitude of the structure acoustic response and hence the sound intensity born by the structure.

In the following the physical principles that determine the potential use of cellular metals for sound management purposes will be briefly reviewed considering all three mentioned cases. Guidelines for material selection and procedures ensuring successful practical applications will be suggested.

Materials for Sound Insulation The performance of sound insulation material is described in terms of sound reduction index, which is proportional to the reciprocal value of the sound transmission coefficient in logarithmic scale. Sound transmission coefficient for a panel is given by the ratio of the transmitted to incident sound intensity. The sound reduction index depends on the frequency and, of course, on the material and geometry of the structure. For a given material the sound reduction index is controlled by various mechanisms, which become important in the specific frequency range. The general form of the transmission loss curve is shown in Fig. 5.3-6 [17]. Coincidence controlled

Mass controlled

Resonance controlled

Stiffness controlled

5.3.3.1

Sound reduction index [dB]

226

aw

sl

f

no

s ma

io ns

te

Ex

Coincidence dip

Effect of damping Critical Frequency Hz frequency Principal dependence of sound reduction index of a panel as a function of frequency for given material and structure geometry [17].

Figure 5.3-6.

5 Material Properties

At very low frequencies the sound reduction is controlled by the stiffness of the panel. In this case the application of cellular metals can be very attractive because of their excellent stiffness to weight ratio (see parameter E/r3 in Table 5.3-4). At somewhat higher frequencies the sound transmission is determined by the natural resonance of the panel depending on the used material, panel size, and mounting conditions. Also in this frequency range the cellular metals can be useful, because of their better damping properties in comparison with bulk metals (see also later in this Section). Moreover, they can shift the first resonant frequency towards higher values and thus extend the stiffness controlled frequency range (see Table 5.3-4). This can be important when the panels of smaller size are used. However, for typical sound insulation, the most important is the frequency range, where the sound reduction is controlled by mass of the panel according to (9)

TL0 ˆ 20log10 (mf † s 43

where TL0 in dB is the sound reduction index for normal incidence, m is the superficial density in kg m 2 of the soft impervious panel and f is the frequency in Hz. This is known as Mass Law [17]: the sound transmission loss increases with increasing mass of the panel. Therefore, the application of cellular metals for sound insulation in this frequency range is highly disadvantageous.

Table 5.3-4. Design parameters for the materials suitable for sound insulation. Thickness h, 1st resonant frequency f1 of fully clamped plate and critical frequency fc are calculated for the square plate of given weight (10 kg) and area of 1 m q 1 m. Parameter E/33 demonstrates the bending stiffness at minimum weight of the panel. AlSi12 aluminum foam of density 500 kg m 3 and modulus of elasticity 5 GPa was introduced for comparison.

Material

Lead

E [GPa]

E/r3 [m8.s 2.kg 2]

h [mm]

11.2

0.01

0.89

204

8.1

0.4

1.2

Reinforced concrete

23

2.3

1.9

Glass

38

2.5

Aluminium

69

2.7

Aluminium foam

5

0.5

Plywood

4.2

0.58

Plasterboard

1.5

0.75

Steel

14.3

r [g.cm 3]

f1 [Hz]

f1* [Hz]

60000

7

11

9770

43

4.4

24

4400

95

2.4

4.0

27

3900

108

3.5

3.7

32

3220

130

40

20.0

110

960

434

22

17.2

81

2241

323

13.3

33

3200

131

3.6

1.8

fc [Hz]

* 1st resonant frequency calculated for the panel size of 0.5 m q 0.5 m q h m in order to demonstrate the size effect

227

228

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

At an even higher frequency a phenomenon of coincidence between bending waves within the panel and the incident sound wave can occur accompanied with a slight reduction of the sound insulation performance. Therefore this frequency should be designed as high as possible. The lowest critical frequency fc for the coincidence is given by r c2 r (10) fc ˆ 1:8h E where c is the velocity of sound in air, h is the thickness, E is the modulus of elasticity, and r is the density of panel material. The use of cellular metals usually lowers the coincidence frequency and thus it cannot be recommended also in this case (see Table 5.3-4).

Sound Absorbing Materials There are various ways how the sound absorption takes place: by viscous losses as the sound pressure pumps air in and out of the absorber's cavities, by direct mechanical damping in the absorber itself, by thermoelastic damping. The ability of material to absorb a sound is characterized by sound absorption coefficient, a. The sound absorption coefficient is the ratio of the unreflected sound intensity at the surface to the incident sound intensity. Full sound absorption means that incident sound wave is neither reflected nor transmitted and its energy is absorbed within the absorbing material. The sound absorption coefficient varies with frequency and angle of incidence of sound wave and for any given material is a function of material thickness, density, and flow resistance of the structure (depends on fiber or pore size) [17]. The absorption coefficient for normally incident sound waves of small samples (diameter up to 100 mm) can be easily measured using an impedance tube. If the sound absorption for all angles of incidence is required to be known, the measurement in a reverberation room is usually applied. Much larger samples (often up to 10 m2) are needed in this case. Although the theoretical maximum value of a is unity, the latter method can result in data slightly in excess of 1.00 because of edge effects. The sound wave particle velocity immediately adjacent to a rigid wall is zero, and therefore the absorber will be most effective, if it is situated in a distance of a quarter wavelength from the surface. This leads to a great thickness of absorber if the absorption at low frequencies is required. For sound absorption purposes highly permeable materials such as open-cell polymer foams and glass or mineral wool fibers are generally used. Flammability and evolution of toxic gases when subjected to excessive heat is the main disadvantage of polymer foams. On the other hand fibrous materials are very sensitive to erosion by shedding or fraying especially under the effects of air flow or vibration. Both type of absorbers usually require various facing materials in order to improve durability or to protect the absorber from contamination. The facing materials are often also aesthetic (various surface finishing and colors) with added advantages of thermal insulation, fire safety, humidity and oil resistance. 5.3.3.2

5 Material Properties

Beside bulk absorbers two types of resonant absorbers are in general use, especially for sound absorption at lower frequencies. The panel absorber is a resonant system formed by the mass spring combination of the facing panel and the stiffness of enclosed air. The resonant frequency of panel absorber at which the maximum absorption is reached is given by 600 f ˆ p md

(11)

where m is the superficial density of the panel in kg m 2 and d is the depth of air gap in cm. The Helmholtz resonator or cavity resonator is essentially a vessel in which the mass of air in the neck is driven in and out in resonance upon the stiffness of enclosed air volume. The resonant frequency is given by r S (12) f ˆ 55 LV where S is the cross-sectional area of the neck, L is the length of the neck, and V is the enclosed volume of air. The perforated panel often used for protection of porous absorbers can provide an additional resonance effect, similarly, as it is in a case of Helmholtz resonator. Such semiresonant performance is found when the percentage of open area of front panel is below 20 30 %. Above this value, the system behaves primarily as a simple porous absorber [17]. The faced material itself can be constructed more sophisticated containing a plenty of small Helmholtz resonators (see Fig. 5.3-7). The frequency at which the maximum sound absorption is reached can be tuned by cavity geometry. Such combination usually shifts the maximum absorption performance towards low frequencies, preferably in the range 100 1000 Hz.

Figure 5.3-7. Typical construction of sound absorber: thick glass fiber absorber (1), thin protective and damping foil (2), facing wood panel with resonator cavity (3), and outer design (4) [18].

229

230

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

Accordingly, the main parameter for good sound absorption is the permeability of the absorber. Therefore, cellular metals can be used for this purpose only if they meet this fundamental requirement. The closed-cell metallic foams are too stiff to convert sound energy into heat by vibration of their cell walls. According to Eq. (11), they cannot be effectively applied for panel resonators because of their very low weight. Unfortunately, the experimental measurements performed in impedance tube on various types of cellular metals [19,20] are in a good coincidence with these discouraging expectations (see Fig. 5.3-8). The best sound absorbing performance was obtained using Access-sponge metals having open-cell structure and thus very low flow resistance [21]. Such structure absorbs the sound energy mainly by viscous losses as the sound pressure wave pumps air in and out of the interconnected pores. Alporas closed cell foam (made by melt-route process) [22] is manufactured in large blocks from which the absorbers are machined. Machining results in rough open-pore surface that slightly improves the sound absorption. Alulight closed-cell aluminum foam [9] is prepared in net shape and therefore is covered with a surface skin. This relatively flat and pore free skin reduces the sound absorption performance almost to zero: the sound is entirely reflected.

Figure 5.3-8. Sound absorption coefficient of various types of cellular aluminum foams in comparison with fiberglass sound absorbing material (directly on rigid background).

Sample

Access sponge

Alporas

Alulight

Fiberglass

Thickness [mm]

20

10

9

48

Density [kg m 3]

1060

270

580

40

5 Material Properties

Access material has a good potential to be applied for sound absorption purposes after optimization of the structure. In a case demonstrated in Fig. 5.3-8 the flow resistance was too low to provide sufficient viscous losses. However, the manufacturing process allows to adjust the optimum pore size or even to obtain gradient pore structure in relatively easy and inexpensive way [21]. Figure 5.3-9 demonstrates the effect of the reduction of open area at the surface on the sound absorption performance of this material. Although the sound absorption performance of cellular metals is not very impressive, it can be significantly improved by optimal opening of close cell structure. In this case the foams can serve as multiple cavity resonator (see Eq. 12) with much longer ªneckº than in the case of bulk materials of the same weight. The variability of the pore size will provide a wider frequency range of good sound absorption than typical resonators. Various methods, such as cutting of surface skin, sand blasting, compressing, rolling, and drilling of holes were examined to open the foam structure [19,20]. It was shown that sound absorption of as received Alporas aluminum foam can be significantly improved by partial compression, rolling, or hole drilling. However, the combination of these method offers only a little additional benefits [19]. Similar results were obtained for Alulight foams covered with surface skin (see Fig. 5.3-10). The significant improvement of the sound absorption was reached already after opening of only 1.4 % of the surface area by drilling of holes. The opening of the surface area can be more economically realized by simple punching of the foam surface without the need to make the throughgoing holes (Fig. 5.3-11).

Figure 5.3-9. Sound absorption coefficient of Access aluminum sponge without and with perforated facing Al sheet (air gap of 48 mm behind the absorber, Access sponge: density 1180 kg m 3, thickness 20 mm; facing Al sheet: thickness 1 mm, 61 holes diameter 2 mm).

231

232

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

Figure 5.3-10. Sound absorption coefficient as a function of opened surface area for Alulight foam (8.9 mm thick AlSi12 foam, density 580 kg m 3, holes drilled through the sample, 20 mm air gap between sample and rigid wall).

Surface opening

0.07 %

0.19 %

0.61 %

1.40 %

2.49 %

Number of holes

7

19

61

61

61

Diameter of holes [mm]

1

1

1

1.5

2

As expected [23], the increasing thickness of absorber shifts the maximum of the sound absorption coefficient towards lower frequencies (see Fig. 5.3-12), while the shape of the curves remains almost unchanged provided, that the density and pore size do not depend on thickness. At constant sample thickness, the foams with low density were found to be better sound absorbers than the foams with high densities in the frequency range of 200 1700 Hz [19], however the obtained results are affected by an increasing pore size with decreasing density. Another experimental measurement [24] indicates that there exists an optimal pore size for a sound absorption with respect to sample thickness at constant density. This experimental finding agrees with theoretical calculations made by Wang and Lu [25] for 2D cellular solids of Voronoi structure: the sound absorption performance will be improved with increasing pore size for sample, which is infinitely thick. It implies that the sound absorption coefficient is a complex function of foam thickness, density, and pore size. It is not always feasible to increase the thickness of absorber, because of the weight limitations. The use of a thinner section of absorber spaced by an air gap gives very similar results to a thick section (see Fig. 5.3-13), however at significantly lower weight. Therefore, the frequency range of maximum sound absorption

5 Material Properties

Figure 5.3-11. Sound absorption coefficient as a function of opened surface area for Alulight foam (AlSi12 foam 15 mm thick, density 380 kg m 3, diameter of holes 1 mm, holes were punched into the depth of 8 mm, directly on rigid background).

Figure 5.3-12. Sound absorption coefficient as a function of absorber thickness (Access AlSi sponge, average pore size 4 5 mm, density 1000 kg m 3, directly on rigid background).

233

234

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

Figure 5.3-13. Comparison of sound absorpis thicker foam at zero distance from rigid wall tion for two designs of sound absorbing panels (Access AlSi sponge, density 1000 kg m 3, average pore size 4 5 mm). at two constant thicknesses: 1st type is the foam at given distance from rigid wall, 2nd type

can be tailored by creating an optimum air gap between the absorber and rigid wall [19,20,24] without need to increase weight. The sound absorption can also be enhanced for wider frequency range by the combination of several foam plates with an air gap between them [20]. Although the cellular metals cannot provide a high level of sound absorption itself, they can be attractively used as a facing materials, especially in combination with fibrous absorbers, provided, that the structure is sufficiently opened. The frequency corresponding to the maximal sound absorption can be tuned by the thickness of foam panel or by changing of pore size. The sound absorbing performance is then comparable with typical solutions using facing wood panels (see Fig. 5.3-14). The cellular metals offer additionally very high stiffness at low weight, are selfsupporting and stable at elevated temperature, does not release toxic gases when subjected to excessive heat, possess high durability under the effects of air flow or vibration, exhibit sufficient fire resistance and can be recycled. Moreover, as a relatively new material with impressive surface design, it can be very attractive for architects and designers of building interiors (see Table 5.3-5). The potential applications are expected in sterile (antiseptic, dust free) environment, in the structures where nonflammability is important (airplanes, hotels, commercial, and industrial buildings) or in interiors under difficult conditions (elevated temperature, moisture, dust, flowing gas, and vibrations).

5 Material Properties

Figure 5.3-14. Sound absorption coefficient of fiber glass itself and faced with AlSi12 Alulight (thickness 13.2 mm, density 330 kg m 3, diameter of holes 2 mm) with Helmholtz resonators inside (cavity diameter 6.5 mm, length 8 mm). For comparison the sound absorption characteristic of facing sheet of Topperfo acoustic panels TP 16/16/12-2 [18] is presented.

Table 5.3-5.

Surfaces of cellular aluminum for improved sound absorption.

Sample

Access

Alporas

Alulight

Thickness [mm]

25

10

8.9

Density [kg.m 3]

1060

480

450

Weight [g]

208

38

31

Surface

Cut

Cut

Foamed skin

Opening

As-received

Compressed

Drilled holes

Structure

235

236

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

The cellular Alporas already has been applied commercially in sound-absorbing linings on the underside of highway bridge, and in sound-absorbing wall panels at the entrance of tunnels in Japan [22].

Structural Damping If the structure is subjected to external excitations by sound waves or by mechanical vibrations, the sound can be transmitted or even born by the structure itself. This is most important in the cases, when the structure oscillates at its resonant or eigen frequencies. The amplitude of the structure acoustic response and hence the sound radiation can be dramatically reduced by increasing the damping of the structure. Structural damping is owing of internal friction in a material by conversion of the vibrational energy into heat and subsequent dissipation of heat into the surrounding area. The high level of damping in the structure can be realized either by utilization of high damping materials or by friction between sliding surfaces of closely attached structural components interface damping. The rate of vibrational dissipation or the damping in the structure can be characterized by the loss factor h. The measurement of the loss factor is normally carried out by one of two basic methods [26]: The ªfrequency responseº method is used when the damping is high (h j 10 3). The loss factor can be calculated from the bandwidth Df at the amplitude drop of 3 dB points and resonant frequency fn according to 5.3.3.3

h ˆ Df =fn

(13)

The second ªdecay-rateº method is used for materials with lower damping. The loss factor is calculated from the vibration amplitude decay D in dB s 1 at resonant frequency after instant stopping of exciting force, according to h ˆ 0:0366 D=fn

(14)

The typical structural materials with high strength (for example steel, cast iron, aluminum alloys) have unfortunately very little damping. On the another hand, the high damping materials, such as lead, rubber, or soft plastic, have little strength and cannot be regarded as structural materials [17]. The cellular metals exhibit at least one order of magnitude higher values of the loss factor h [20]. The dissipation of the vibrations mainly results from the friction between the attaching surfaces of the cracks appearing in the structure and partially due to the vibration of the thin pore walls. Thus, the damping can be enhanced by the reduction of the cell-wall thickness or/and by introducing of imperfections into the structure. Higher loss factor values are therefore obtained with for example foams made of casting aluminum alloys, which can be prepared with very thin cell walls and contain a lot of cracks. If the nonsoluble ceramic particles, for example SiC, Al2O3, or graphite are additionally introduced into the structure of metallic cell walls, the damping will be further improved. New sliding surfaces born in the cell walls in this way are responsible for this behavior (see

5 Material Properties

Figure 5.3-15. Effect of addition of nonsoluble particles on the damping properties of aluminum foams and steel tubes filled with them (30 mm diameter q 300 mm, foam density 600 kg m 3).

Fig. 5.3-15). Nevertheless, the loss factor of typical cellular metals is still too low compared with standard damping materials having h in the range 0.01 0.1. Recently, there is some effort to apply the cellular metals as stiffeners or cores in metallic hollow parts, castings, or sandwiches. Beside the stiffening and the increased capability to absorb impact energy, also the reduction of noise and vibrations is expected (see Fig. 5.3-16) [27]. In this case the structural damping is significantly affected by the quality of contact between cellular metal and bulk metallic shell. If the attached surfaces can slide on each other under pressure an additional interface damping will be obtained. The damping effect is produced by dry friction, which can provide very effective attenuation of excessive vibrations.

Figure 5.3-16. Frequency spectra of reciprocal mass for a hollow profile and a profile foamed with various types of Alulight foams (steel tube 22 mm diameter q 245 mm filled with 18 mm diameter q 245 mm foams of density 700 kg m 3).

237

238

5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

Thus, though disappointing, in a case of a very good (usually metallurgical) bonding, which is a precondition for good mechanical properties, the good damping cannot be expected. On the other hand, the best damping will be obtained without bonding or using ªslidingº contact provided by an elastic adhesive (see Fig. 5.3-17). The high values of loss factor can indicate the absence of bonding or even insufficient filling of the cavity (see Fig. 5.3-18) with cellular metal. This effect can be utilized for the nondestructive testing of the quality of foamed profiles for various industrial applications.

Vibrational damping in complex epoxy (foam density approximately 700 kg m 3). aluminum casting and its variations due to the For comparison the damping solution with presence of Alulight foam insert injected or bitumen layer (3 mm thick) is also plotted. fastened with either elastic adhesive or cured

Figure 5.3-17.

Figure 5.3-18. Effect of the foaming on the values of resonant frequency and damping characteristics of hollow steel profile.

5 Material Properties

Figure 5.3-19. Dependence of the first resonant frequency on the apparent density of Alulight foams: longitudinal vibrations of AlSi12 foam 25 mm diameter q 300 mm (left axis) transverse vibrations of Al 99.7 foam 140 mm q 140 mm q 8.5 mm (right axis).

Figure 5.3-20. Property gain obtained by use of material was used (weight 390 kg, self deflecaluminium foam for stiffening of hollow mation 4 mm, first resonant frequency 240 Hz, chine table (800 mm q 720 mm q 250 mm) damping at first resonant frequency 0.15 %) [28]. As a reference the table made of bulk

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5.3 Electrical, Thermal, and Acoustic Properties of Cellular Metals

Beside mentioned approaches there is also a possibility to avoid the effect of resonant vibrations by stiffening of the structure. The stiffening arrangements do not damp the resonances, they merely shift them towards higher frequencies. If the resonances can be shifted to frequencies that will not be excited during normal operation of the equipment this solution to the problem of reducing vibrations may be very efficient. The resonant frequencies generally depend on the modulus of elasticity E and the density r of the material of which the component is made and, of course, on its geometry. For example, the first resonant frequency f1 of longitudinal vibration of cantilever is s 3:52 EI (15) f1 ˆ 2p rSL4 where I is area moment of inertia of beam cross section S and L is the length of the beam. To shift a frequency either the geometry or material ought to be altered. The changes of the part's geometry are often not possible. The altering of the material may not be always successful at least in the case of metallic parts, because E/r ratio of many metals is almost the same. Here the cellular structure can be very attractive, while both the modulus of elasticity as well as the density can be varied without changing the outer dimensions of the component (see Fig. 5.3-19). This feature can be very effectively utilized for shifting the resonant frequencies in hollow machine components by filling them with cellular metals. Figure 5.3-20 shows the effect of the utilization of aluminum foam as a filler in hollow machine table. Beside stiffening and improving of the damping a significant shift of the first resonant frequency towards higher values has been achieved [28].

References

1. J. Babjak, V. A. Ettel, V. Passerin, US Patent 4 957 543, 1990. 2. M. F. Ashby, A. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: A Design Guide, ButterworthHeinemann, Oxford 2000. 3. J. Kovacik, F. Simancik, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 303. 4. J. Kovacik, F. Simancik, Scripta Mater. 1998, 39, 239. 5. J. Kovacik et al., in Proc. Int. Conf. Effect of Non-Standard External Factors on Physical

Properties of Solids, Military Academy Liptovsky Mikulas, 1996, p. 57. 6. J. Kovacik, Acta Mater. 1998, 46, 5413. 7. D. Stauffer, A. Aharony, Introduction to Percolation Theory, 2nd edn, Taylor & Francis, London 1992. 8. ERG, Data Sheets, ERG Materials and Aerospace Corp., Oakland, USA 1996. 9. Mepura, Data Sheets, Mepura GmbH., Ranshofen, Austria 1995. 10. Alporas, Data Sheets, Shinko Wire Company Ltd., Nakahama, Japan 1994. 11. Cymat, Data Sheets, Cymat Aluminium Corporation, Mississauga, Canada, 1996.

5 Material Properties 12. Norsk Hydro, Data Sheets, Hydro Aluminium Ltd., Sunndalsora, Norway, 1995. 13. L. J. Gibson, M. F. Ashby, Cellular Solids, Pergamon Press, Oxford, 1988. 14. E. S. Park, S. D. Poste, US Patent 4 808 558, 1989. 15. T. J. Lu, C. Chen, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 391. 16. A. G. Evans, J. W. Hutchinson, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 45. 17. P. D. Wheeler, in Industrial and Machinery Noise Control Practice, Institute of Sound & Vibration Research, University of Southampton, UK 1978, p. 11.1. 18. n'H Akustik ‡ Design AG, Data Sheet, Lungen, Switzerland, 1999. 19. T. J. Lu, A. Hess, M. F. Ashby, J. Appl. Phys. 1999, 85, 7528. 20. J. Kovacik, P. Tobolka, F. Simancik, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 405.

21. F. Grote, P. Busse, Giesserai 1999, 10, 75 78. 22. T. Miyoshi, M. Itoh, S. Akiyama, A. Kitahara, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 125. 23. H. Utsumo, T. Tanaka, T. Fujikawa, J. Acoust. Soc. Am. 1989, 86, 637. 24. F. Chen, D. P. He, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 163. 25. X. Wang, T. J. Lu, J. Acoust. Soc. Am. 1999, 106, 1. 26. Bruel & Kjaer, Mechanical Vibration and Shock Measurements, K. Larsen & Son, Soborg, Denmark 1980. 27. F. Simancik, F. Schoerghuber, in Porous and Cellular Materials for Structural Application, D. S. Schwartz, D. S. Smith, A. G. Evans, H. N. G. Wadley (eds), MRS Symp. Proc. Vol. 521, MRS, Warrendale, PA 1998, p. 151. 28. R. Neugebauer, Th. Hipke, in MetallschaÈume, H. P. Degischer (ed), Wiley VCH, Weinheim 2000, p. 515.

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Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

6 Modeling and Simulation F. G. Rammerstorfer, T. Daxner, and H. J. BoÈhm

The modeling and simulation of cellular metals is a field of research that has attracted considerable interest from researchers, research groups, foam manufacturers, and industrial end-users. Two major directions of research can be distinguished: the design of metallic foams on the one hand and the design of components made of cellular metals on the other. Modeling and Simulation for Material Design From the point of view of the manufacturers, the design of mechanically efficient metallic foams is the paramount aspect of foam modeling and simulation, the aim being the development of ªoptimumº cellular metals. The most important design variables are the production technologies and the choice of the metal making up the solid phase of the foam. Besides the apparent density and the properties of the metal, the mechanical behavior of metallic foams is determined by the geometrical arrangement of voids and solid regions in the material, which will be referred to here as the microgeometry. Consequently, a considerable number of studies have aimed at exploring the connections between the microgeometry and the mechanical properties of cellular materials and thus belong to a research field known as micromechanics of materials. At the length scale of the voids, the deformation of cellular materials tends to be dominated by local mechanisms that must be accounted for in any modeling effort. Because detailed descriptions of the microgeometries of large structures or components made of foam are far in excess of present capabilities, the most fruitful approaches for simulating the thermomechanical behavior of metallic foams have aimed at studying representative regions of appropriate model materials in detail. Most commonly, actual foams are approximated by periodic microgeometries that can be described via unit cells subjected to appropriate boundary conditions. Alternatively, a geometrically detailed microregion may be embedded in a larger region for which a much simpler description is employed, leading to embedded cell models. A discussion of such micromechanical approaches is presented in Section 6.1.2. Microgeometrical models covering a wide range of complexity can be studied with the above methods to give predictions for the overall mechanical behavior

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of metallic foams and link it to specific local deformation processes. In addition, microscale geometrical imperfections can be introduced in a controlled way and assessed for their influence on the macromechanical material response, making it possible to isolate the influence of individual parameters. It has been found difficult, however, to make fully quantitative predictions on the basis of micromechanical simulations, the main reason being the high geometrical complexity of actual foams and the dearth of reliable data on the in-situ material behavior of the metallic phase. Nevertheless, micromechanical approaches have provided important instruments for gaining a better understanding of the thermomechanical behavior of metallic foams, see Section 6.1.3. If the mean cell size or the effective density of the foam exhibit spatial variations or gradients over a sample or component, additional information can be obtained by explicitly considering length scales that lie between the micro- and macroscales. Such mesomechanical studies are described in Sections 6.1.4 and 6.2. Modeling and Simulation for Component Design Designers of components made of metallic foams are interested in easy-to-use methods of describing the constitutive behavior of these materials, for example in the form of constitutive material laws for use with general purpose finite element codes. For such purposes it is neither possible nor desirable to account for details of the foams' microgeometry at each position in the component. Instead, the material behavior of the foam is described in terms of a (fictitious) equivalent homogeneous material. Such constitutive models may be derived from micromechanical studies by homogenization, or they may take the form of phenomenological macroscopic descriptions that employ material parameters, which have to be obtained from experiments. Because metallic foams typically show a limited elastic range, such constitutive models have to be nonlinear for general application. For some purposes full constitutive descriptions are not required and material characterization can provide the necessary information. This can take the form of experimentally based relations, for example in the form of stress strain relations parameterized by the effective density of the foam. Alternatively, micromechanical reasoning may be used to derive generic mathematical relationships, which can then be fitted to experimental results and provide physically based regression formulae. Knowledge of the effective elastic stiffness on the continuum level is sufficient for linear stress analysis, where the foam is treated as a homogeneous, linear elastic solid. Depending on the complexity of the problem, such structural analyses can either be performed analytically or numerically, for example by using the finite element method. If only the macroscopic stresses within the component are of interest, the knowledge of the homogenized material properties (in this case the tensor of elasticity) will be sufficient. These macroscopic stresses have to be assessed with respect to failure of the structure by yielding, fracture, or buckling, so that additional information in the form of macroscopic strength data is required. More sophisticated structural analysis must take into account the nonlinear behavior of metallic foams; this is an absolute necessity when large strains are pres-

6 Modeling and Simulation

ent, for example in crushing or crash situations. Here, incremental macroscopic material laws, that is, relationships between increments in stresses and strains, must be available to allow the use of typical numerical analysis tools. Several constitutive material laws describing the overall behavior of cellular metals have been proposed and applied in the simulation of components consisting of or containing metallic foams. Obviously, the selection of a particular material law is governed by the required material parameters and by the effort necessary for calibrating them by experiments or via micromechanical studies. Because they are based on the use of an equivalent homogeneous continuum, macroscopic material laws should only be used for studying components or samples that are considerably larger (and thicker) than the typical cell size of the foam. Macroscopic material laws for foams are the focus of Section 6.1.5, where the advantageous use of metallic foams in energy absorbing structures and modeling strategies for assessing crashworthiness are discussed. Because metallic foams show some potential for controlled spatial variation of their effective density and, as a consequence, of their mechanical properties, they offer the possibility of designing functionally graded cellular materials. Some considerations pointing in this direction can be found in Section 6.1.6. Considering all the facts mentioned above, the structural analysis of components made of or employing metallic foams is likely to become a standard procedure in finite element simulations. As new production technologies and new practical applications emerge, the micro- and macromechanics of metallic foams continue to be promising fields for future research.

6.1

Modeling of Cellular Metals

T. Daxner, H. J. BoÈhm, M. Seitzberger, and F. G. Rammerstorfer

In the course of the last decade the modeling and simulation of cellular materials have gained in importance. Well-established representatives of this group, such as honeycombs or polymer foams, as well as recently developed materials, such as metallic foams, have been the subjects of various studies. Cellular materials, which consist of a solid skeleton in the form of struts and/or cell walls and a high volume fraction of voids, are highly inhomogeneous. This heterogeneity leads to thermomechanical responses that are markedly different from those of bulk solids and it gives rise to material properties that have made cellular materials attractive for many engineering applications. It also presents an obvious target for modeling studies aimed at gaining an improved understanding of the mechanical behavior of cellular materials and structures made of them.

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6.1.1

Motivation

Metallic foams, which are the subjects of the present discussion, have entered the stage of practical application, their most important mechanical properties being excellent energy absorption capacity as well as high specific strength and stiffness. Studying their mechanical behavior has attracted considerable research interest, both from the theoretical and the applications points of view. Simulations of the mechanical responses of cellular metals may be carried out at different length scales. In micromechanical approaches the inhomogeneous structure of these materials is accounted for at the level of individual cells, cell walls, struts, and vertices either via statistical arguments or by discrete geometrical models. The corresponding length scale, which is of the order of the size of individual cells, is called the microscale in the following. Studies at this level provide information on the local deformation and load-transfer behavior that can then be correlated to the mechanical behavior of the material at the structural level. A good understanding of the mechanics of cellular metals on the microscale is especially important for identifying advantageous microgeometrical parameters for materials design and development. Microscopic models for metallic foams are the focus of Section 6.1.2. For studying samples and components that are, say, two or three orders of magnitude larger than the size of an individual cell, only the overall thermomechanical behavior is of interest and local details of the metallic foam do not have to be accounted for explicitly. In other words, at the macroscale the foam is treated as a homogeneous continuum rather than an inhomogeneous medium. Modeling approaches appropriate for describing metallic foams at the macroscopic level, which are often rather application specific, will be discussed in Section 6.1.5. In addition, questions involving the spatial variations or gradients of cell sizes and shapes within a given sample or structure may be studied at length scales that are intermediate between microscale and macroscale. Some simple models involving such a mesoscale will be presented in Section 6.1.4, while Section 6.2 is largely devoted to mesoscopic approaches. In the following some important aspects of the present state of the modeling and simulation of metallic cellular materials are discussed. It should be noted, however, that no attempt is made to give a full overview of this research topic. For comprehensive information on the behavior of cellular materials and of its modeling the reader is referred to the books by Gibson and Ashby [1,2] and to an overview by Weaire and Fortes [3]. A recent review of the mechanical behavior of metallic foams was given by Gibson [4].

6 Modeling and Simulation

6.1.2

Micromechanical Modeling of Cellular Materials: Basics

From the point of view of micromechanical modeling, cellular metals fall into three groups: honeycombs, which can be studied by 2D models, open-cell foams, the solid scaffold of which is dominated by beam-like members, and closed-cell foams, in which membrane- or shell-like cell walls are present. All of these materials typically show a limited elastic range and their mechanical behavior tends to be dominated by local deformation mechanisms such as bending, buckling, plastic yielding, and fracture of cell walls and struts. These deformation mechanisms, in turn, are highly sensitive to details of the microgeometry, which, in practice, may be quite regular for some honeycombs, but tends to be complex and highly non-uniform in the case of metallic foams. The mean field and Hashin±Shtrikman-type methods that play an important role in continuum micromechanics of composites and materials with small volume fractions of pores [5], have seen only limited use for cellular materials. Hashin± Shtrikman upper bounds for the elastic moduli can be evaluated for macroscopically isotropic cellular materials by prescribing vanishing stiffness for the void phase (the lower bounds, however, vanish trivially). Typically, the elastic moduli of metallic foams lie considerably below these upper bounds, but for honeycombs it was possible to identify microgeometries that realize the upper bounds [6]. As a consequence, most micromechanical studies of cellular materials in general and of metallic foams in particular have been based on discrete microgeometrical models. Owing to the high geometrical complexity and irregularity of actual metallic foams such model microgeometries tend to be highly idealized. One common modeling strategy is based on studying periodic ªmodel foamsº, the thermomechanical behavior of which is fully described by appropriate unit cells. Alternatively, cells or geometrical units may be studied in isolation without requiring them to be space filling. A third type of approach employs a geometrically fully resolved microregion (ªcoreº) that is embedded in a much larger region in which the microgeometry is not resolved and smeared-out material behavior is used (ªembedded cell modelsº). Discrete microgeometrical modeling approaches facilitate the controlled variation of selected geometrical parameters in order to assess their effect on the mechanical response. These modeling strategies, which have well-established equivalents in continuum micromechanics of composite materials, allow studying both the local deformation mechanisms and the corresponding overall behavior, which can be obtained by homogenization.

Analytical and Numerical Models When a sufficiently high degree of abstraction is introduced into discrete microgeometry models of cellular materials, the mathematical description of the micromechanical system becomes accessible to analytical methods and closed-form solutions can be obtained. A by now classical example of such an approach is the work of Gibson and Ashby [1], who based their models on single cells that do not give 6.1.2.1

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rise to space-filling periodic arrangements and developed a large body of results on the elastic deformation, elastic buckling, plastic collapse, brittle fracture, viscoelastic deformation, creep, and creep buckling of honeycombs, open-cell, and closed-cell foams [7,8]. Developments of this class of models have included, among others, large deformation analyses of the buckling collapse of honeycombs [9] and studies on the power-law creep of honeycombs [10]. Analytical formulae for the elastic behavior of a number of perfectly regular periodic cellular geometries were given by Grenestedt [11], and scaling relations for arrangements of this type were published by Christensen [12]. Tetrakaidecahedral cells were used in a series of papers by Zhu et al. to describe the elastic behavior [13] and the finite deformation compressive response of periodic open-cell [14] and closed-cell [15] foams, numerical methods being used to resolve the resulting equations in some cases. In addition to studying perfectly regular cellular microgeometries, imperfections of the cells, such as waviness of cell walls and struts, can be accounted for [16,17]. Analytical methods may also be applied to predict the plastic collapse of cellular structures as proposed by Santosa and Wierzbicki [18] who presented a kinematic model for the crushing of a column of truncated cubes. Generally, analytical descriptions can only be used for relatively simple generic microgeometries. More complex geometrical arrangements typically have to be analyzed via numerical engineering methods, the finite element (FE) method having become the most popular tool for this purpose. In some FE based studies of honeycombs it was possible to simulate actual experimental setups [19]. In most cases, however, unit cells were employed, which, in combination with appropriate periodic boundary conditions, are capable of resolving any periodic deformation mode and deformation mechanism of the corresponding infinite cellular arrangement. Some care, however, is required in the selection of a cell for a given analysis. In order to provide reliable results the unit cell ideally should be a proper representative volume element, the geometry of which contains the full statistical information on the material's microgeometry [20]. For modeling the inelastic behavior of cellular materials, the unit cell must be designed to allow for very large local deformations, and self-contact between the cell walls has to be provided for if the behavior in the densification range is to be explored. Furthermore, the choice of the unit-cell geometry is often influenced by the necessity of allowing for realistic deformation and buckling patterns, which in most cases precludes the use of symmetry boundary conditions. In all cases, of course, there is a requirement to keep the complexity of the unit cell, and thus the computational costs, within acceptable bounds. When using unit-cell descriptions it is important to keep in mind that the resulting models are periodic in all respects. As an example, inhomogeneous densification of cellular materials as predicted by unit-cell models will always take place in periodic patterns, the period of which is strongly influenced by the choice of the size of the unit cell. Single crack tips (as opposed to periodic patterns of cracks) cannot be handled by periodic microgeometries, and free surfaces are restricted to layer-like geometries in which at least one direction is nonperiodic. For these types of problem, embedded cell approaches are the methods of choice.

6 Modeling and Simulation

Classification of Microgeometries This section represents an attempt at systematically classifying the most important types of cellular microgeometries that have been or may be used for unit cells or in the core regions of embedded cell models. The main classification criteria are the dimensionality (2D versus 3D) and the microscale morphology (regular periodic, perturbed periodic, random, and ªreal structureº arrangements) of the geometrical models. 2D discrete microgeometry models are directly applicable to investigating the mechanical behavior of honeycombs. Owing to their relative simplicity they have also been used as tools for studying metallic foams in a qualitative way (in the following planar models are generally referred to as ªhoneycombsº). The ªbaselineº regular morphology are periodic hexagonal honeycombs, which show in-plane elastic isotropy and, in the context of 2D liquid foams, may be viewed as surfaces of minimal surface energy. Because hexagonal honeycombs (albeit of reduced symmetry) are applied routinely as sandwich cores, cellular metals of this type have been closely studied both experimentally and analytically [21]. Alternative regular microgeometries for 2D cellular materials were also discussed in the literature [11,12]. In contrast to the regular microgeometry of idealized models, real cellular metals are subject to morphological defects that tend to lead to softer and weaker mechanical responses. Periodic 2D models have been an important means for studying the influence of imperfections such as curved or corrugated cell walls [16,17,22], perturbed cell shapes [23], and non-uniform material distribution between cell walls and cell vertices (Plateau borders) [24] as sketched in Fig. 6.1-1. Within such honeycomb models local defects can be introduced into cell walls [17,25,26], individual cell walls can be eliminated [26,27], vertices and the adjoining cell walls can be removed to leave large voids in the honeycomb structure [26,28], and cells or groups of cells can be filled with solid material to assess the influence of nodal inclusions [26], Fig. 6.1-2. In addition, periodic arrangements of large and small cells [29] may be used to study influences of relative cell sizes. Random honeycomb arrangements can be generated on the basis of Voronoi tesselations [17,25,27,30], which may be interpreted in terms of geometries that emerge when the fronts of bubbles growing with the same linear rate from ran6.1.2.2

Figure 6.1-1. Schematic representation of imperfections at the level of individual cell walls: left) Plateau borders, center) corrugated cell walls, right) curved cell walls.

Schematic representation of a honeycomb containing imperfections in the form of a large hole, cells filled with material, fractured cell walls, and geometrical perturbations (from left to right).

Figure 6.1-2.

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domly distributed nuclei meet. A different type of random microgeometry are Johnson±Mehl cells [31], a tessellation that corresponds to cases where new cell nuclei are added while others are in the process of growing. Finally, 2D microgeometries may be based on micrographical sections of metallic foams [32]. Such ªreal structureº unit cells typically require some manipulation in the boundary regions in order to achieve periodicity. Planar models obviously can emulate the behavior of 3D microgeometries only to a limited extent (note, for example, that in the 2D case there are no equivalents of open-cell and closed-cell topologies). Accordingly, there has been growing research interest in 3D models of cellular materials despite their high demands on computational resources. In the case of open-cell foams, beam theory or beam finite elements provide comparatively inexpensive solutions for describing the mechanical behavior of the solid skeleton. Micromechanical studies of closed-cell foams, however, require an appropriate modeling of the cell faces and, consequently, shell theories must be invoked or shell elements must be used, which increase the complexity of the simulations. Perfectly regular 3D periodic microgeometries can be generated from space filling regular polyhedra, leading to models based on cubes, rhombic dodecahedra and regular tetrakaidecahedra (or Kelvin structures). None of these arrangements is elastically isotropic, but tetrakaidecahedral geometries have the advantage of giving face and edge counts per cell that are similar to the average values found in actual polyhedral foams [33]. Accordingly, tetrakaidecahedral microgeometries have been widely used for studying open-cell [34,35] and closed-cell [15,32] foams, see Fig. 6.1-3. Somewhat more complex microgeometries were also proposed in the form of regular arrangements of two populations of polyhedral voids of different size [18]. Most 3D studies of the effects of imperfect periodic cellular arrangements have been based on closed-cell tetrakaidecahedral microgeometries subjected to various kinds of perturbations. Unit-cell models of varying levels of complexity were used to study the effects of plateau borders [24], of curved or corrugated cell walls [16,22], of perturbed cell shapes [23,32], and of cell walls that have randomly assigned thicknesses [36].

Figure 6.1-3. Regular tetrakaidecahedral model for a closed-cell foam [32].

6 Modeling and Simulation

In analogy to 2D models, Voronoi diagrams may be used to generate irregular 3D microgeometries for open-cell [37,38] and closed-cell foams [23,39,40]. Because they typically require large numbers of shell elements, investigations of this type tend to be computationally expensive. 3D real structure models of cellular materials can be generated on the basis of microtomographical data, each voxel being typically mapped to a finite element. Analyses of this kind were pioneered by groups studying the mechanical behavior of cancellous bone [41,42], which may be viewed as an open-cell foam, and were recently also reported for closed-cell metallic foams [43]. This modeling strategy typically gives rise to ragged surfaces of the solid skeleton of cellular materials, which may lead to difficulties in analyses involving large deformations and large strains.

Information Obtainable from Micromechanics Before presenting specific results from micromechanical simulations in Section 6.1.3, a short discussion is given concerning the information on the mechanical behavior of cellular metals that can be obtained from micromechanical studies. The most basic aspect of the mechanical material characteristics of inhomogeneous materials is their linear elastic behavior, which can be described in terms of an overall elasticity tensor or appropriate effective moduli. Linear analysis requires comparably little effort and, therefore, the linear elastic properties of a wide range of cellular microgeometries are well researched. Cellular metals typically have small elastic ranges, beyond which nonlinear behavior sets in owing to yielding, loss of stability or fracture at the microscale. In contrast to bulk metals, the elastic range of metallic foams is also limited under purely hydrostatic loading. Micromechanical analyses of such behavior may be carried out in terms of material characterization by simulating, for example, uniaxial or multiaxial tests to obtain homogenized stress versus strain curves. In terms of the overall behavior the onset of nonlinear responses can generally be described via appropriate surfaces in stress space, of which the classical von Mises yield surface for plastic yielding of bulk metals is a well-known example. Analogous surfaces for cellular metals can be obtained from micromechanical analyses by monitoring the material response while following loading paths that are radial in macroscopic stress space. Deviations from linear overall behavior are mainly due to local yielding (typically at the transitions between cell walls and cell edges) or to local elastic buckling of the cell walls or struts. The onset of nonlinear behavior is, in fact, caused by yielding in the majority of cases, and microscale buckling plays an appreciable role only for highly regular microgeometries, for which the above surfaces may be viewed as ªgeneralized yield surfacesº. If only the onset of plastic yielding is considered in this context the superposition of elastic solutions is possible, and only one simulation per dimension of the macroscopic stress space is required for determining the overall yield surface of macroscopically isotropic materials. 6.1.2.3

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The above concept can also be used to follow the evolution of the yield surface as a given macroscopic loading path is traced. To do this, the loads are applied incrementally and complete unloading is carried out after each step followed by the evaluation of a new yield surface. This may again be done by superimposing elastic solutions. It should be noted, however, that the application of linear superposition analyses for such purposes is limited to the small deformation regime. In cellular metals geometrical nonlinearities (caused, for instance, by marked bending of cell walls) may give rise to noticeably nonlinear overall responses even before yielding sets in. As a foam is subjected to increasing compressive stresses a load will be reached at which the first collapse of a cell occurs. In metallic foams the initial collapse of a cell under these conditions tends to be followed by the growth of the collapsed region, which typically takes place at stress levels that show only limited variation, giving rise to a so-called plateau region in the overall stress versus strain behavior. When a considerable percentage of cells have been ªconsumedº the foam densifies, the plateau region ends, and a much stiffer response sets in. The accumulation of considerable compressive strains at nearly constant stresses is of particular interest for cellular metals that are to be employed for impact energy absorption. Collapse stresses under uniaxial loading have been studied for many cellular morphologies and for various imperfections. For general load cases the initial collapse stress states form an envelope surrounding the initial yield surface, which may be called a collapse surface. For the point-wise evaluation of collapse surfaces fully nonlinear analyses along individual load paths are required. Relatively little work has been reported on the modeling of fracture of metallic foams, which is the dominant failure mechanism under macroscopic tensile loading. Embedded cell models provide a flexible approach for studying cracks in idealized cellular metals, see Section 6.1.3.8. 6.1.3

Selected Results of Micromechanical Simulations

In this section, a number of selected results on the mechanical behavior of metallic foams obtained by micromechanical modeling and simulation are discussed, which cover a wide field of subjects, from the influence of microgeometrical imperfections to the evaluation of collapse surfaces in macroscopic stress space.

Influence of Material Distribution in the Cell Walls The production of metallic foams typically involves the solidification of a molten precursor material into an appropriate shape. In the liquid state a redistribution of material driven by surface tension results in the formation of concave transition regions between the cell walls, which are known as Plateau borders and give rise to non-uniform cell wall thicknesses, see Fig. 6.1-4. This phenomenon may influence the mechanical behavior of the foam on both the micro- and the macroscales and has, accordingly, been the subject of considerable research interest. 6.1.3.1

6 Modeling and Simulation Figure 6.1-4. Section through aluminum foam produced by the powder metallurgical route (courtesy Institute of Materials Science and Testing, Vienna University of Technology).

Simone and Gibson [24] developed unit cells for hexagonal honeycombs and tetrakaidecahedral foams in which Plateau borders were modeled by appropriate curved and parallel regions. Their results indicate that the distribution of material in the cell walls has little influence on the Young's modulus and only a moderate effect on the uniaxial yield strength of closed-cell metallic foams. A different approach was followed by Chen et al. [17], who studied honeycombs with wall thicknesses that increase linearly from the middle of the walls to the vertices. This simplifies the mathematics of the problem sufficiently for analytical solutions for the overall yield surfaces of the models to be obtained. Investigations of the deformation patterns of honeycombs in the large strain regime, which determine the materials' energy absorption capacity, can also be carried out with unit-cell models. In such simulations the initiation of densification can be identified from the occurrence of self-contact of the surfaces of the collapsed voids, the modeling of which requires special provisions in terms of the unit-cell geometries. Unit cells with all boundaries running within the cell walls have been found to answer well, see Fig. 6.1-5, which shows symmetric and periodic deformation modes before the onset of densification. The main advantage of unit cells of the above type is that all free surfaces of the voids face inwards, which allows a straightforward use of contact algorithms. Obviously, such models can also be adapted for studying the dependence of the deformation patterns on prescribed distributions of mass between cell walls and vertices. Drainage of the material into Plateau borders reduces the cell wall thickness, which is the governing parameter for the strength and the stiffness of the arrange-

Predicted deformation modes of hexagonal honeycombs with Plateau borders: left) symmetric, right) periodic.

Figure 6.1-5.

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ment. This is especially important in the case of foams of very low density, in which the cell wall thicknesses approach zero. At higher densities, however, the redistribution of material towards the cell vertices and, therefore, into regions subjected to higher bending moments can be beneficial for the overall properties of foams [17,24]. As more material is accumulated in the vertices, the plastic hinges under bending tend to form closer to the mid-region of the cell edges, so that the size of the nearly rigid regions around the vertex is increased. Although such a zone can rotate during compression it still takes up more space if the distance between the hinges and the vertex centers is increased. Together with changes in the folding kinematics this causes the cell walls to contact each other at lower strains than is the case for microgeometries with less pronounced plateau borders. This effect dominates the energy absorption potential as shown in Fig. 6.1-6, Fig. 6.1-7, and Fig. 6.1-8. Even in cases where the collapse and pre-contact loads are increased by the material redistribution, the decrease of the usable deformation length reduces the amount of energy that can be dissipated by plastic deformation before the densification regime is reached. Microscale fluctuations of the material distribution in cellular materials may, on the one hand, be due to thickness variations within individual cell walls as discussed above in connection with Plateau borders or, on the other hand, be caused by the individual cell walls in a microgeometry having different thicknesses. The latter problem was addressed by Grenestedt and Bassinet [36], who developed a 3D tetrakaidecahedral model of a closed-cell foam that contains a total of 112

Figure 6.1-6. Predicted nominal strain at first cell wall contact as a function of the material distribution between walls and cell vertices (Plateau borders) for three different apparent densities.

6 Modeling and Simulation

Predicted normalized collapse stress as a function of the material distribution between cell walls and cell vertices (Plateau borders) for three different apparent densities.

Figure 6.1-7.

Figure 6.1-8. Predicted normalized absorbed energy (up to first cell wall contact) as a function of the material distribution between cell walls and cell vertices (Plateau borders) for three different apparent densities.

cell walls, the thicknesses of which could be assigned individually. The results show that the stiffness of regular closed-cell arrangements is rather insensitive to the presence of cell walls of different thickness. This was explained by noting that such microgeometries deform primarily by cell wall stretching, which is less sensitive to wall thickness effects than bending modes induced, for example, by corrugated cell walls.

Influence of Wavy and Curved Cell Walls In addition to inhomogeneous thickness distributions, the geometries of cell walls may also be perturbed by deviations from simple linear (honeycombs) or planar (3D foams) connections between the vertices. Such simple strut or wall geometries, in fact, are good approximations for low-density organic foams. In metallic 6.1.3.2

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foams, however, curved and corrugated (ªwavyº) cell walls typically are present, see Fig. 6.1-4. Grenestedt [16] studied the influence of wavy imperfections of the walls on the elastic stiffness of cellular solids and found that the bulk modulus decreases by some 50 % when corrugations with an amplitude of twice the thickness of the cell walls are present. Simone and Gibson [22] documented the detrimental effect of curved and corrugated cell walls on the stiffness and strength of regular honeycombs and perfectly tetrakaidecahedral unit-cell models. The Young's modulus was shown to be more adversely affected by these imperfections than the collapse stress. Chen et al. [17] gave analytical expressions for the yield surface of regular honeycombs with wavy cell walls. They found that corrugations significantly reduce the hydrostatic yield strength of honeycombs, whereas the deviatoric yield stress is hardly affected. Evidently, cell-wall bending is activated in addition to membrane deformations under overall hydrostatic loading.

a)

b)

c)

d)

Figure 6.1-9. Predicted yield surfaces for regular and irregular honeycombs with different types and degrees of imperfections [29]. Dashed and dash-dotted lines denote elastic buckling stress states.

6 Modeling and Simulation

The influence of corrugated and curved cell walls on the onset of nonlinear behavior was studied by Daxner et al. [29] by evaluating initial yield surfaces. Figure 6.1-9 shows such curves that represent overall stress states that give rise to the local onset of yielding or to local elastic buckling in regular and perturbed honeycombs that have curved and wavy cell walls of varying curvature. In perfect regular honeycombs in-plane hydrostatic compression leads to pure membrane stresses in the cell walls, which give rise to an elongated overall initial yield surface in the s x s y stress plane. For low-density, perfect honeycombs, this yield surface is truncated by the failure surface for elastic cell wall buckling, see Fig. 6.1-9a, which shows a kink owing to a change of the buckling mode. This type of behavior is maintained in the presence of small corrugations, but when the amplitudes of wiggles exceed about 5 % of the wall thickness yielding alone determines the onset of nonlinearity. The influence of wiggles and curved cell walls on the yield surfaces of honeycomb microgeometries that are irregular from the outset is much less pronounced, see Fig. 6-1.9b±d. Perturbing the geometry by randomly displacing cell vertices causes the yield surface to shrink even more than the presence of severe wiggles, see Section 6.1.3.3. Corrugated or curved cell walls generally have little effect on the uniaxial yield strength, but severe wiggles can reduce the in-plane hydrostatic yield stress by some 35 %. Curved cell walls typically give rise to similar effects as wiggles, see Fig. 6.1-9c, but cell walls incorporating only slight curvature can lead to minor increases of the in-plane hydrostatic yield stress.

Influence of Irregular Vertex Positions Generic models for cellular materials are commonly based on regular periodic microgeometries, the simplest 2D geometry being hexagonal honeycombs. A comparison between such a honeycomb structure and a cross section of an actual metallic foam as shown in Fig. 6.1-4 makes clear that the latter is far from being a regular structure. A standard assumption in modeling efforts is that different types of geometrical imperfections may be studied in isolation. Following this strategy, the present section concentrates on the effects of overall cell geometry while neglecting the cell wall imperfections discussed above. It can be shown that the elastic stiffness of a honeycomb model is not very sensitive to irregularities and perturbations of the vertex positions. In fact, upon comparing the elastic stiffnesses of hexagonal and Voronoi honeycombs Silva et al. [30] reported that the overall elastic moduli are some 5±10 % higher in the latter case. Zhu et al. [44] defined a measure for the irregularity of Voronoi honeycombs which they correlated to the predicted elastic properties. They found the effective Young's and shear moduli of periodic Voronoi honeycombs to increase with growing irregularity, whereas the effective bulk modulus decreases. They applied the same methodology to 3D open-cell foams and obtained analogous results [38]. Grenestedt and Tanaka [23] examined the elastic behavior of 3D closed-cell Voronoi unit cells, finding a decrease in the bulk modulus of 5±10 % compared to regular tetrakaidecahedra. 6.1.3.3

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The uniaxial yield stress of honeycomb models can be reduced by some 40 % by perturbing the positions of the cell vertices, see Fig. 6.1-9. Silva and Gibson [27] reported a similar decrease in the yield strength of Voronoi honeycombs compared to hexagonal honeycombs, but a less pronounced reduction for the uniaxial yield stress was obtained by Chen et al. [17], who attribute this difference to the use of periodic rather than mixed boundary conditions for their unit cells. In addition to Voronoi honeycombs, they studied configurations obtained from hexagonal arrangements by randomly shifting the vertices and obtained results on the uniaxial compressive yield stress that are in good agreement with Fig. 6.1-9. Both planar Voronoi microgeometries and perturbed hexagonal arrangements give rise to reduced yield stresses under in-plane hydrostatic loading as compared to regular honeycombs because the deformation mode tends to be cell wall bending rather than membrane compression [17]. As mentioned above, randomly shifting the vertex positions of regular honeycombs typically leads to more pronounced reductions of the overall yield limits than does the introduction of corrugations of the cell walls. In addition, the collapse stress, which is closely related to the macroscopic plateau stress, is decreased. Again, the most affected loading condition is in-plane hydrostatic loading. Loss of stability due to elastic buckling plays a significant role only in extreme cases of near-perfect microgeometries and very thin cell walls. For microgeometries with significant irregularities of the vertex positions elastic buckling would require uniaxial applied stresses that are about one magnitude higher than the predicted yield stress. Clearly, irregular microgeometries are required for obtaining realistic results from simulations of the mechanical behavior of metallic foams. This is especially true when multiaxial loads or deformations are to be studied. In the presence of irregular vertex positions other imperfections such as cell wall corrugations typically are relegated to secondary roles.

Microgeometries Containing Cells of Different Sizes In metallic foams the sizes of the cells are typically far from uniform, see Fig. 6.1-4, and often regions containing small cells as well as clusters of very large cells can be identified. In order to gain some understanding of the interaction between larger and smaller cells, simulations of 2D geometries consisting of generic periodic arrangements of cells of two different sizes, see Fig. 6.1-10, were performed [29]. They comprise a regular hexagonal honeycomb (HC), serving as reference configuration, as well as clusters of small cells surrounded by large cells (SBS) and isolated large cells surrounded by small cells (BSB). The main focus was on large strain deformation owing to its importance in energy absorption by cellular metals. When observing stress strain relationships predicted for uniaxial compression, two qualitatively different deformation and collapse mechanisms become apparent. If shear localization occurs, the microgeometry can deform at nearly constant applied stress through cell wall bending, and, after collapse of the shear bands, by sliding within the collapsed layer, giving rise to comparably smooth stress strain 6.1.3.4

6 Modeling and Simulation

Honeycomb geometries for studying the interaction of cells of different sizes [29]: Regular hexagonal arrangement (HC, left), a cluster of small cells surrounded by big cells (SBS, center), and big cells surrounded by small cells (BSB, right).

Figure 6.1-10.

curves. If, in contrast, cell wall buckling and extensive layer-wise collapse perpendicular to the loading direction are the dominant mechanisms, the stress strain relationship shows marked oscillations on account of the sequential collapse of ªcell rowsº that are incapable of accommodating subsequent deformation by sliding. Figure 6.1-11 shows deformation modes of the above types for the case of an imperfect hexagonal honeycomb, with the corresponding stress versus strain curves being given in Fig. 6.1-12. In addition to these general observations on collapse modes some specific rules for the interaction of small and big cells can be identified. Comparing the deformation patterns developed by arrangements SBS and BSB, see Fig. 6.1-13, one can observe that in the latter the clusters of small cells do not contribute very much to the overall deformation and may become obstacles in the densification regime. The framework of small cells surrounding the large ones in model SBS, however, provides more uniform stiffness and deforms more evenly. In general, clusters of small cells tend to be detrimental to the deformation and energy absorption potential of cellular metals as they typically deform less than their bigger neighbors, the longer struts of which confer lower bending stiffness and strength.

Undeformed and deformed configurations (as predicted by unit cells with periodic boundary conditions) of an imperfect hexagonal honeycomb subjected to uniaxial

Figure 6.1-11.

loads applied in the horizontal and vertical directions. Note the occurrence of shear localization (left) and layer-wise collapse (right), respectively.

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Predicted overall stress strain relationships of an imperfect hexagonal honeycomb [29] corresponding to the deformation modes shown in Fig. 6.1-11.

Figure 6.1-12.

Deformed configurations predicted for imperfect models describing small cells surrounding big cells (BSB, left) and big cells surrounding small cells (SBS, right) based on the configurations presented in Fig. 6.1-10.

Figure 6.1-13.

These observations lead to the conclusion that whenever smooth stress versus strain relationships are desired, the cell size distribution should be as uniform as possible and the cells should be small compared to the sample or structure to either prevent localization or to limit its detrimental effects.

Influence of Holes and Solid-Filled Cells A further group of imperfections of cellular geometries may be generated by eliminating some vertices as well as the cell walls connected to them, which leads to holes that are larger than typical cell sizes, or by filling selected cells with solid material, see Fig. 6.1-2. 6.1.3.5

6 Modeling and Simulation

Experiments by Prakash et al. [28] have shown that the filling of some cells leads to local strengthening of honeycombs, increases the elastic modulus and the degree of strain hardening, but reduces the densification strain. The opposite effect is caused by removing individual cells or whole cell clusters as demonstrated by Guo and Gibson [45] in a FE study on intact and damaged honeycombs. They reported on correlations between the undamaged cross-sectional area perpendicular to the loading direction and the elastic buckling load as well as the plastic collapse strength. The interaction between separate defects of this type was found to have a range of about ten cell diameters. Chen et al. [26] investigated the influence of solid inclusions as well as holes on the stiffness and on the uniaxial and in-plane hydrostatic yield strengths of perfect honeycombs and of 2D arrangements in which some 5 % of the cell walls were randomly fractured. Solid inclusions were shown to lead to minor increases of the elastic stiffness and to have a negligible effect on the uniaxial and in-plane hydrostatic yield strength of both the otherwise perfect and the fractured honeycombs. Because the solid inclusions introduce additional mass, however, the specific properties were negatively affected. Large holes were found to induce cell wall bending in otherwise perfect honeycombs, leading to significant reductions in the bulk modulus and the hydrostatic yield strength. For prefractured honeycombs the decrease in overall stiffness due to holes could be estimated from the reduced overall relative density of the honeycomb.

Influence of Fractured or Removed Cell Walls Cell walls that are damaged by fracture or that are bodily removed may weaken cellular materials to a considerable extent. Having introduced such defects into regular hexagonal and Voronoi honeycombs, Silva and Gibson [27] reported that the reduction of overall mechanical properties due to the removal of cell walls tends to be 2 3 times greater than that caused by an equivalent (in terms of density) uniform reduction of the cell wall thickness. A typical Voronoi honeycomb was predicted to be, on average, 30 35 % weaker than a periodic hexagonal honeycomb of the same density. The same degree of weakening can be obtained by removing 5 % of the cell walls. Experiments on honeycombs [28] showed that removal of cell walls triggers localized deformation because the weakened cells collapse first. Whether or not cells with defects interact to form a common deformation band depends on their distance and their position relative to the symmetry axes and the loading direction. Albuquerque et al. [46] performed similar experiments on Kevlar honeycombs. In addition to confirming the results of Silva and Gibson [27] and Prakash et al. [28] they found that the compressive behavior is hardly affected by having the defects uniformly dispersed or concentrated in a region, provided the concentration of defects is low. Upon removing 10 % of the cell walls in Voronoi honeycomb models, Silva and Gibson [27] obtained a reduction of the compressive strength by some 40 % and found that mechanical stiffness and strength tend to zero when 35 % of the cell 6.1.3.6

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walls are removed. To study fatigue accumulation in cancellous bone Schaffner et al. [25] removed struts in an open-cell model once the lengths of fatigue microcracks in them (assumed to grow according to a Paris law) exceeded a user-specified limit. They found that Voronoi honeycombs are more sensitive to fatigue damage than are regular hexagonal geometries. After comparing several types of morphological imperfections in honeycombs Chen et al. [17] identified the removal of cell walls as the most critical of them in terms of reduction of the yield strength.

Yield and Collapse Surfaces In Section 6.1.2 the evaluation of yield surfaces, ªgeneralized yield surfacesº and collapse surfaces from unit-cell analyses was discussed. For a given cellular metal, the availability of such data allows multiaxial stress states to be assessed for the onset of nonlinear behavior and for the commencement of cell collapse, which defines the start of the plateau region in the overall stress versus strain behavior. Initial yield surfaces for hexagonal honeycombs with corrugated or curved cell walls were mentioned in Section 6.1.3.2. Here, some aspects of yield and collapse surfaces will be discussed for more realistic microgeometries. To study the behavior of irregular honeycombs, a unit cell was generated on the basis of a 6.1.3.7

Unit cell for a periodic ªreal structureº honeycomb model [32] adapted from a micrograph [16]. Note the wide range of cell sizes, cell shapes, and cell wall imperfections.

Figure 6.1-14.

6 Modeling and Simulation

section through a sample of closed-cell aluminum foam given by Grenestedt [16], suitable adaptations being introduced to support periodic boundary conditions, see Fig. 6.1-14. The predicted collapse surfaces typically surround the initial yield surfaces, and for irregular honeycombs the shapes of the two surfaces tend to be somewhat similar, see Fig. 6.1-15. It may be noted that for uniaxial overall stress states, where the dominant local deformation mechanism is bending, the collapse stress exceeds the initial yield stress by a factor of about 2.4, which is far in excess of the value of 1.5 given by simplified beam analysis (assuming ideally plastic beams of rectangular cross section and neglecting stress redistribution). The collapse surface presented in Fig. 6.1-15 is not given for all possible loading paths, only the purely compressive regime (3rd quadrant) and those parts of the shear regimes (2nd and 4th quadrants), for which the larger principal stress is compressive, being covered. These restrictions were necessary because the predicted stress versus strain responses do not allow the extraction of plateau stresses once the tensile principal stresses exceed the compressive ones. To obtain peak stresses and a plateau region from such tension dominated loading paths additional failure criteria, for instance cell wall fracture, would have to be introduced. By definition an initial yield surface allows the presence of plastic yielding to be assessed on the basis of linear analysis. This obviously is an important step in the development of a macroscopic elastoplastic constitutive model. It is not, however, sufficient for carrying out nonlinear studies such as crushing or crash analyses, for which detailed information on the evolution of the yield surface under loading as provided by a hardening law is indispensable and strain rate effects may have to be accounted for. One of the hardening laws used in connection with metal foams is

Figure 6.1-15. Overall yield and collapse surfaces [32] predicted for the real structure honeycomb model presented in Fig. 6.1-14. The collapse surface is not evaluated for load cases for which a distinct maximum could not be found in the overall stress versus strain relationship.

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isotropic hardening [47]. It assumes that the origin and the shape of the yield surface stay the same, but its size increases driven by the accumulated volumetric plastic strains. In the Crushable Foam model [48] mixed hardening is assumed, where the yield surface keeps the same shape with increasing size (isotropic hardening), but shifts its origin (kinematic hardening) so that the hydrostatic tensile yield stress remains constant. Micromechanical analyses based on the real structure geometry shown in Fig. 6.1-14 paint a somewhat more complex picture. Figure 6.1-16 displays predictions for the evolution of the overall yield surface corresponding to progressive uniaxial compressive loading in the x-direction. At several points during the loading sequence the analysis was interrupted, the model was unloaded and then subjected to linear superposition analyses to estimate the onset of nonlinear behavior. This way the yield surface corresponding to the actual state of hardening can be generated. The initial hardening behavior was predicted to be essentially kinematic, the yield surface being shifted in the direction of the applied stress without major changes in shape or size. At elevated compressive stresses, however, the evolving yield surface changes its shape and contracts as well. Because Fig. 6.1-16 is based on the superposition of solutions from linear analyses that cannot account for the geometrical nonlinearities, which may be expected to play an increasing role as compressive collapse is approached, its reliability in the latter regime is not fully clear. Accordingly, the results can be interpreted as clearly favoring kine-

Evolution of the overall yield surface under uniaxial compressive loading in x-direction predicted for the real structure honeycomb model presented in Fig. 6.1-14.

Figure 6.1-16.

6 Modeling and Simulation

matic hardening models for low inelastic strains and hinting at possible changes in the hardening behavior in the high strain regime. As mentioned before, planar models are directly applicable to honeycombs, but are not necessarily directly transferable to real foams, which require 3D simulations for quantitative predictions. Denzer developed 3D closed-cell microgeometries [32] based on a body-centered cubic arrangement of tetrakaidecahedral cells, using symmetry boundary conditions to limit the computational costs. Initial overall yield surfaces under compressive loading were evaluated for configurations with perfect cell geometry as well as for models with statistically perturbed vertex positions, see Fig. 6.1-3 and Fig. 6.1-17. The general shapes of these yield surfaces in principal stress space are ellipsoid-like and their major axes are aligned with the hydrostatic axis, see Fig. 6.1-18. This can be explained by the stress states induced in the cell walls, which are mainly membrane-like for hydrostatic loads (even though regular tetrakaidecahedra are not elastically isotropic) whereas uniaxial loads tend to give rise to bending close to the vertices. These effects are less pronounced for the imperfect models, where the ªaspect ratioº of the yield surface tends to be lower. This behavior is qualitatively similar to predictions obtained from honeycomb models, but the yield surfaces for the perfect tetrakaidecahedra are less elongated along the hydrostatic axis, see Fig. 6.1-9. By projecting selected points of the yield surface shown in Fig. 6.1-18 (left) onto the equivalent stress versus mean stress plane a standard representation is obtained, see Fig. 6.1-19, that can be readily compared with other results. The projected points can be seen to be scattered around an ellipse the major axis of which coincides with the mean stress axis, the hydrostatic yield stress being about 2.5

Figure 6.1-17. Irregular tetrakaidecahedral model for a closed-cell foam [32]. As can be seen from the planar section, perturbations were introduced only in the core of the model to allow for the use of symmetry boundary conditions.

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Yield surfaces predicted for regular (Fig. 6.1-3) and irregular (Fig. 6.1-17) tetrakaidecahedral closed-cell foams [32].

Figure 6.1-18.

Projection of the yield surface shown in Fig. 6.1-18 (left) onto the von Mises equivalent stress versus mean stress surface.

Figure 6.1-19.

times larger than the uniaxial yield stress. It may be noted that many material laws for foams use yield surfaces that give rise to ellipses when projected to the equivalent stress versus mean stress plane, among them the model of Deshpande and Fleck [47].

Fracture Simulations for Metallic Foams Unit-cell based micromechanical methods give rise to periodic deformation, stress and strain fields and, as a consequence, periodic patterns of damage and cracks. Although this may be acceptable for distributed damage, a useful alternative for 6.1.3.8

6 Modeling and Simulation

studying small samples consists in employing microgeometries that essentially model the whole specimen. For example, Schaffner et al. [25] used a Voronoi honeycomb to study fatigue damage of cancellous bone. Crack tips in discrete cellular microstructures were studied by Gibson and Ashby [1], who gave expressions for the fracture toughness of brittle honeycombs by considering failure of the first unbroken cell wall in the path of an advancing crack in simple planar and 3D models. An approach in which hexagonal honeycombs are homogenized as a micropolar elastic material, for which the asymptotic crack tip fields are computed and then used to estimate the displacements and rotations of the cell walls surrounding the crack tip, was developed by Chen et al. [49]. Probably the most flexible approach available at present for studying crack tips in cellular materials, however, is the use of embedding techniques. Such a strategy was followed by Ableidinger [35] for studying the influence of a number of microgeometrical and material parameters on the macroscopic fracture mechanical behavior of a compact tension (CT) specimen made of an open-cell aluminum foam subjected to monotonic loading [50]. The region surrounding the crack tip was modeled with a fully resolved, but highly generic, 3D tetrakaidecahedral open-cell microgeometry discretized with beam elements. This kernel was embedded into the remainder of the CT specimen, see Fig. 6.1-20 (left), which was treated as a homogeneous structure with an effective material behavior obtained from unit-cell analyses of the same tetrakaidecahedral microgeometry. In the out-of-plane direction the core consisted of a single layer of tetrakaidecahedra, the embedding region having the same thickness, and symmetry boundary conditions were applied at the top and bottom planes, so that the model actually corresponds to an inner layer (plane strain conditions) of the specimen. Tensile loads were applied at the positions of the loading fixtures of the CT specimen, so that the crack proceeded in fracture mode I on the macroscale. Crack propagation at the micro level as resolved in the kernel region was assumed to be caused by sequential ductile failure of the most highly loaded struts, see Fig. 6.1-20 (right). From the predicted force versus displacement diagrams of the CT specimens, see Fig. 6.1-21, effective KI versus Da (crack resistance) curves as shown in Fig. 6.1-22

Embedded cell model of an open-cell foam using a tetrakaidecahedral core and a homogenized outer region (left) and detail of the core around the crack tip (right), from [35]. Note that symmetry with respect to the crack plane is assumed.

Figure 6.1-20.

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Figure 6.1-21. Macroscopic force versus displacement curves of CT specimens made of open-cell aluminum foams predicted by embedded cell models, see Fig. 6.1-20, for different effective densities and different aluminum alloys [35].

Figure 6.1-22. Macroscopic crack resistance curves of CT specimens made of open-cell aluminum foams predicted by embedded cell models, see Fig. 6.1-20, for different effective densities and different aluminum alloys [35].

were obtained. For this purpose, the macroscopic stress intensity factor KI was evaluated at each maximum of the force versus displacement curves according to standard expressions for CT specimens, the crack length increments Da being dictated by the selected microgeometry. Both Fig. 6.1-21 and Fig. 6.1-22 show results for three values of the apparent density of the foam and for two aluminum alloys differing in ductility.

6 Modeling and Simulation

Within such a modeling approach parameters such as the mass density of the foam (which determines the void volume fraction), the size of the cells (which influences the fracture behavior in terms of an internal length scale), the yield strength, and the strain to fracture of the bulk material (which govern the ductile damage and failure of the struts) can be varied easily in order to study their respective influences on the fracture behavior of open-cell metallic foams. 6.1.4

Modeling of Mesoscopic Density Inhomogeneities

Foams are not only heterogeneous in terms of consisting of solid regions and voids, but in many cases also show an inhomogeneous distribution of their apparent density, mean cell size and other geometrical parameters. These variations correspond to length scales larger than that of the voids (the microscale) and smaller than that of the sample or component (the macroscale) and are, accordingly, termed mesoscopic inhomogeneities in the following. Fig. 6.1-23 (left) shows such density variations in a cross section of a foam sample. Shim et al. [51] introduced uniaxial lumped mass±spring mesoscopic models for the simulation of the dynamic uniaxial crushing of foam samples with uniform apparent density. Systems of elastic-plastic springs were employed by Gradinger and Rammerstorfer [52] for studying the compressive force displacement behavior of crush specimens with deterministically distributed meso-inhomogeneities. These two approaches were combined by Daxner et al. [53] to assess the influence of inhomogeneous density distributions on the impact response of foam plates with generic variations in their apparent density, the interaction of density inhomogene-

Figure 6.1-23. Micrographical cross-section of an aluminum foam with three regions of differing apparent density (left) and sketch of the corresponding mesoscopic simulation model (right) [53].

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ities in directions normal to the orientation of the load being also accounted for, see Fig. 6.1-23 (right). The influence of mesoscale inhomogeneities in the apparent density is of particular interest when the metal foam is applied as protective padding. Strong mesoinhomogeneities reduce the energy absorption efficiency, because they lead to strain localization resulting in a decrease of the initial plateau stress and a less pronounced plateau region [52,53], as can be seen in Fig. 6.1-24. This holds true for density variations occurring in the loading direction and perpendicularly to it [53]. Accordingly, for such applications it is desirable to tune foam production technologies for achieving uniform density distributions. When a metallic foam is treated as a homogenized material, inertia effects [54] lead to wave propagation phenomena that are controlled by the interaction of foam density, layer thickness, impact energy and impact velocity [53]. At moderate impact speeds those inertia effects give rise to an impact resistance that only slightly exceeds the static yield strength, see Fig. 6.1-25. Nevertheless, the dynamic effects of wave reflection and superposition are noticeable under these conditions, as is evident in Fig. 6.1-26, where the stacking order of foam layers with different density is shown to significantly influence the time history of impact stresses. The results obtained with simulations that treat cellular metals as homogenized materials, however, will have to be compared to dynamic tests to assure that no artificial inertia effects are introduced by the homogenization approach. Possibly, the mass density used for the homogenized material may have to be adjusted to closely fit the experimental results for dynamic events.

Figure 6.1-24. Stress strain diagrams prea meso-homogeneous plate, the open circles dicted for foam plates that consist of layers of denote a two-layer structure and all other cases different density while maintaining the same are three-layered arrangements [53]. overall density. The solid line corresponds to

6 Modeling and Simulation

Figure 6.1-25. Predicted influence of impact velocity and foam density on the initial stress response s dyn normalized by the static collapse stress s 0,stat [53].

Figure 6.1-26. Predicted contact stress between an impacting mass and a foam cube composed of two equally thick layers of different densities [53]. The two possible stacking orders of the layers were simulated.

Mesoscopic mass±spring models as described above are restricted to specific load cases and, in general, cannot handle arbitrary multiaxial loading paths. More generalized mesoscopic simulations can be carried out by using the FE method with standard volume elements, see Section 6.2.

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6.1.5

Macroscopic Modeling and Simulation

From the perspective of modeling samples and structural components made of cellular metals, discretization down to the level of individual cells is not only infeasible with current computer and software technology, but also appears to be impracticable with regard to the required modeling effort. As a consequence, macroscopic constitutive descriptions of metallic foams have been developed. The main condition for their use is that the overall dimensions of the sample or structure must be significantly larger than the dimensions of single foam cells. Structural analysis of cellular metals in the elastic range is relatively straightforward in that only the homogenized elasticity tensor must be known. For isotropic metallic foams, accordingly, two elastic moduli have to be calibrated; more material parameters are required for foams of lower symmetry. Experiments, however, have shown that metallic foams may not display a distinct elastic regime under compressive loading, but rather begin to deform irreversibly at stresses that are low compared to their collapse or plateau stress. Thus, it is not fully clear to what extent cellular metals can be treated as linear elastic materials in structural analyses. Practically relevant constitutive models for metallic foams, accordingly, must be capable of accounting for nonlinear macroscopic material responses. If, for example, the FE method is to be used in the engineering analysis of components made of cellular metals, constitutive descriptions are required at the integration point level, which may have to be coded specifically [55]. Macroscopic yield surfaces appropriate for metallic foams typically can be represented by ellipses in the mean-effective stress plane. The yield surface proposed by Deshpande and Fleck [47] is symmetrical with respect to compressive and tensile stress states. Furthermore, it evolves by uniform scaling in all directions (isotropic hardening) and uses an associated flow rule, which implies that the plastic Poisson ratio is generally not equal to zero. In contrast, the Crushable Foam material model [48] is characterized by a constant tensile hydrostatic yield stress, which causes the origin of the yield surface to move along the hydrostatic axis as the yield surface expands during hardening. The non-associated flow rule governing this material model is formulated to always prevent a plastic Poisson effect. The accumulated plastic volumetric strain is the internal variable driving the hardening process. For additional macroscopic constitutive models proposed for metallic foams see [56 58]. For the above material models additional parameters determining the shape of the yield surface and the hardening behavior must be provided by the user, requiring information on the mechanical behavior of the material under multiaxial loading conditions. Since multiaxial experimental data [47,59] is scarce, the user very often must rely on appropriate assumptions, which can be derived either from microstructural FE simulations or via parameter identification techniques (that is, by minimizing the discrepancy between simulations and experimental results). Fortunately, applications that are dominated by hydrostatic loading conditions are rare. To illustrate this point, in the next section a case study will be pre-

6 Modeling and Simulation

sented in which the uniaxial compressive stress strain relationship is the most important material characteristic: the impact of a large sphere on an aluminum foam pad.

Low Energy Impact on Thin Metallic Foam Paddings At present paddings made of organic foams, which exhibit relatively low strength, are widely used for impact protection. In some situations, however, the available design space is too small to allow an organic foam layer of a depth sufficient for providing adequate energy absorption. Metallic foams are candidate materials for use in such cases due to their higher collapse strength. In the literature impact studies may be found in which the performance of foam specific material laws is compared to experimental data [60]. Such investigations provide results in terms of overall quantities such as contact forces or accelerations. The following discussion refers to simulations of a large rigid sphere impacting a layer of aluminum foam simulated by the FE code ABAQUS/Explicit (Hibbitt, Karlsson & Sorensen, Pawtucket, RI, 1998) and using the Crushable Foam model [48]. Figure 6.1-27 shows an acceleration history predicted for this setup; the severity of the impact studied can be judged by the impression left in the foam pad by the sphere, see Fig. 6.1-28. If the predicted evolution of the stress states in selected material points of the foam target is followed during the impact event, this data can be used to assess which level of complexity of the flow rule and the hardening law is required for performing satisfactory simulations. Essentially, radial paths in stress space indicate that simple isotropic constitutive laws suffice for describing the local material state, whereas distinct changes in the direction of the stress paths signal that phenomena such as anisotropic hardening will have to be considered. Soften6.1.5.1

Figure 6.1-27.

Predicted acceleration versus time history of a typical impact event.

273

274

6.1 Modeling of Cellular Metals

Figure 6.1-28. Schematic view of an impact event (left) and predicted deformed configuration after the impact (right).

ing due to fracture of cell walls may also occur when stress states enter tensile regimes. The evolution of local stress states can be visualized in the mean versus equivalent stress diagram used commonly for describing pressure dependent material laws. Figure 6.1-29 shows such stress paths for three different material points. These stress paths lie mostly between the axis of uniaxial compression (inclination 3:1) and the vertical axis that represents pure shear, indicating that these two types of loading will dominate the local deformation of the foam. The `Axis, top' line in Fig. 6.1-29 is associated with a point under the center of the impact mass. It is surrounded by an ellipse, which is the projection of the Crushable Foam yield surface corresponding to the highest value of the hardening parameter, namely the accumulated volumetric plastic strain. Uniaxial stress states can be seen to prevail in the impact event considered here, indicating that the simulation should not be very sensitive to changes in the hydrostatic parameters of the material. This is comforting, since only limited information is available on the behavior of foams under hydrostatic pressure. Furthermore, the principal stress axes maintain roughly the same orientation throughout the impact event, so that the selected hardening model does not play a major role. These findings narrow down the requirements on improved material laws for crash simulations involving a comparatively thin padding and a large impactor.

6 Modeling and Simulation

Evolution of Some Local Stress States During Impact

111111111111 000000000000 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 000000000000 111111111111 00 11 000000000000 111111111111 00 11 000000000000 111111111111 00 11

2.5

Effective Stress [MPa]

2.0

Initial yield surface Axis, bottom Axis, top Top, Border Uniaxial Compression Hardened yield surface

1.5

1.0

0.5

0.0 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Negative Mean Stress; Pressure [MPa] Figure 6.1-29. Stress states of selected material points visualized as paths in the von Mises equivalent versus mean stress plane during a typical impact event.

Crushing of Foam-Filled Crash Elements The energy absorption characteristics of tubular metal structures during axial crushing may be improved by filling them with appropriate lightweight materials such as honeycombs or foams. The main mechanisms providing improvements (compared to an empty tube) are the compression of the filler material itself and the activation of interaction effects between filler and tube. These interactions lead to higher energy dissipation of the tubular members owing to changed buckling modes and also increase the energy dissipation of the filler material owing to multiaxial compression. Experiments in which aluminum foams were applied as filler material reveal that particularly efficient crush elements may be designed this way [61 63]. Concerning the numerical analysis of such energy absorption structures the FE method may be applied, see [61,64] and Fig. 6.1-30. For preliminary design and for parameter studies, however, simplified methods, which only consider the essential variables, can also be utilized. Experiments show that the collapse process of thinwalled structures is, in general, accompanied by the development of localized plastic mechanisms, that is, the formation of a more or less complicated pattern of folds and wrinkles. Based on these observations simplified kinematic mechanisms were proposed to predict the crushing response of thin-walled members of simple geometry under different loading conditions, see Fig. 6.1-31. Such models typically lead to small computer codes or even to closed-form solutions and, therefore, can be used efficiently in the preliminary design of energy absorbing systems [65 68]. Using simple design formulae it is also possible to apply advanced optimization strategies for predefining mass efficient foam-filled crash elements [68,69]. 6.1.5.2

275

6.1 Modeling of Cellular Metals 100 FE analysis / filled FE analysis / empty 3 No. 1396 / 0.52 g/cm No. 1404 / empty

80

Load [kN]

276

60

40

20

0

0

20

40 60 Displacement [mm]

80

100

FE models of the crushing of filled and empty square tubes: Comparison of computed and measured load±compression curves [61] (left) and stages of compressive axial deformation (right).

Figure 6.1-30.

Folding mechanisms for empty prismatic profile (left) and simplified deformation kinematics of foam core (right).

Figure 6.1-31.

6.1.6

Design Optimization for Cellular Metals

With growing knowledge about the mechanical performance of cellular metals, and in particular of metallic foams, methods for the design of foam components for applications such as packaging, energy absorption and sandwich structures have evolved significantly [1,7,54]. The ability of cellular metals to compete with other materials can be underlined by emphasizing their multifunctionality [70]. Furthermore, it was shown that in certain structures, such as cylindrical sandwich shells, metal foam cores are more weight efficient than other stiffening concepts [71]. In studies dealing with the design and optimization of metal foam components usually a foam of uniform density has been assumed.

6 Modeling and Simulation

Metallic foams show some potential for being produced with controlled spatial variations of their density, introducing inhomogeneities on a mesoscale as defined in Section 6.1.4. In the case of foams produced via powder metallurgical routes the foaming process, and, as a consequence, the final density distribution may be controlled by suitable choices of the distribution of the blowing agent and of process parameters such as temperature and pressure. This suggests employing such foams as graded materials in space filling lightweight structures designed in analogy to cancellous bone, a natural functionally graded cellular material that displays increased density in regions of high loading, see Fig. 6.1-32. Reiter et al. [72,73] presented algorithms for the optimization of composite materials that are based on procedures for simulating the natural adaptation of bone to applied loads. Daxner et al. [74] implemented the algorithm of Reiter [73] for a self-adapting material, providing options for converging towards a uniform distribution of the local strain energy density or towards the satisfaction of a local yield criterion by iteratively adapting the local density. The former choice gives rise to configurations of increased stiffness and the latter to density distributions in which the material shows uniform safety against plastic failure. It was shown that strength optimization with material parameters that are typical for metallic foams leads to continuous solutions showing density gradients, see Fig. 6.1-33, which may indeed be realizable by suitable processing technologies. Attempts to optimize the specific stiffness of foam structures resulted in the formation of discrete structures such as frameworks of struts. This indicates that cellular metals may not be ideal for stiffness-optimized structures, at least in the presence of concentrated loads. For sandwich beams with foam cores as studied by Vonach et al. [75] smooth mesoscopic density distributions were also obtained for stiffness optimized configurations under distributed loads. 6.1.7

Outlook

A number of different strategies for modeling the mechanical behavior of cellular metals were presented. Their present use in studying these materials and their contributions to improving the understanding of metallic foams were discussed. The future of micromechanical modeling can be expected to bring an increased interest in modeling 3D cellular arrangements and in transferring methods that have become successful in the analysis of planar morphologies into the 3D domain. This process is facilitated by the steadily increasing capabilities of computer hardware and software. Therefore, the advent of micromechanical models that better capture the behavior of 3D microgeometries (especially for closed-cell foams) may be forecast. Larger and more sophisticated 3D micromechanical models will provide more precise information on the behavior of cellular metals under multiaxial loading states. This, together with additional information from corresponding multiaxial experiments, can be expected to lead to new insight into phenomena related to the macromechanics of cellular models and may give rise to the development of more refined constitutive theories.

277

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6.1 Modeling of Cellular Metals Figure 6.1-32.

human femur.

Section through a typical

Strength optimized symmetric beam with fixed supports under a central load. Highly stressed regions such as the supports and the lower and upper regions in the middle of the beam accumulate the highest local foam density [74]

Figure 6.1-33.

In view of the engineering potential of cellular metals and of the research challenges they pose, it appears safe to say that studies of these materials on all length scales discussed above will remain a fertile field of study for many years to come. Acknowledgements

Many of the results presented in this contribution were obtained in connection with the Brite/EURAM project `EAMLIFe' (BE96-3605). We gratefully acknowledge the funding of this project by the Commission of the European Union. We also would like to thank the Institut fuÈr Verbundwerkstoffe (IVW) in Kaiserslautern, Germany, in particular Mr. Ralf Denzer, for the excellent collaboration, which included the presentation of a joint paper [32] at the `Symposium MetallschaÈume' in Vienna, February 2000, excerpts of which were used here. Last but not least, we want to thank the Institute of Materials Science and Testing of Vienna University of Technology for providing information and participating in many valuable discussions.

6 Modeling and Simulation

References

1. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, Pergamon Press, Oxford, 1988. 2. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, 2nd edn, Cambridge University Press, UK 1997. 3. D. Weaire, M. A. Fortes, Adv. Phys. 1994, 43, 685±738. 4. L. J. Gibson, Ann. Rev. Mater. Sci. 2000, 30, 191 227. 5. P. Ponte Castan Ä eda, P. Suquet, in Advances in Applied Mechanics 34, E. van der Giessen, T. Y. Wu (eds), Academic Press, New York 1998, p. 171 302. 6. S. Torquato, L. V. Gibiansky, M. J. Silva, L. J. Gibson, Int. J. Mech. Sci. 1998, 40, 71 82. 7. L. J. Gibson, Mater. Sci. Engng. 1989, A110, 1 36. 8. M. F. Ashby, C. J. Seymour, D. Cebon, in Proc. MetallschaÈume, J. Banhart (ed.), MIT Verlag, Bremen 1997, p. 199 216. 9. J. Zhang, M. F. Ashby, Int. J. Mech. Sci. 1992, 34, 491 509. 10. E. W. Andrews, L. J. Gibson, M. F. Ashby, Acta Mater. 1999, 47, 2853 2863. 11. J. L. Grenestedt, Int. J. Sol. Struct. 1999, 36, 1471 1501. 12. R. M. Christensen, Int. J. Sol. Struct. 2000, 37, 93 104. 13. H. X. Zhu, J. F. Knott, N. J. Mills, J. Mech. Phys. Sol. 1997, 45, 319 343. 14. H. X. Zhu, N. J. Mills, J. F. Knott, J. Mech. Phys. Sol. 1997, 45, 1875 1904. 15. N. J. Mills, H. X. Zhu, J. Mech. Phys. Sol. 1999, 47, 669 695. 16. J. L. Grenestedt, J. Mech. Phys. Sol. 1998, 46, 29 50. 17. C. Chen, T. J. Lu, N. A. Fleck, J. Mech. Phys. Sol. 1999, 47, 2235 2272. 18. S. P. Santosa, T. Wierzbicki, J. Mech. Phys. Sol. 1998, 46, 645 669. 19. S. D. Papka, S. Kyriakides, J. Mech. Phys. Sol. 1994, 42, 1499 1532. 20. Z. Hashin, J. Appl. Mech. 1983, 50, 481 505. 21. S. D. Papka, S. Kyriakides, Acta Mater. 1998, 46, 2765 2776. 22. A. E. Simone, L. J. Gibson, Acta Mater. 1998, 46, 3929 3935.

23. J. L. Grenestedt, K. Tanaka, Scr. Mater. 1999, 40, 71 77. 24. A. E. Simone, L. J. Gibson, Acta Mater. 1998, 46, 2139 2150. 25. G. Schaffner, X. D. E. Guo, M. J. Silva, L. J. Gibson, Int. J. Mech. Sci. 2000, 42, 645 656. 26. C. Chen, T. J. Lu, N. A. Fleck, Int. J. Mech. Sci. 2001, 43, 487 504. 27. M. J. Silva, L. J. Gibson, Int. J. Mech. Sci. 1997, 39, 549 563. 28. O. Prakash, P. Bichebois, Y. BreÂchet, F. Louchet, J. D. Embury, Phil. Mag. 1996, A73, 739 751. 29. T. Daxner, H. J. BoÈhm, F. G. Rammerstorfer, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 283 288. 30. M. J. Silva, S. C. Hayes, L. J. Gibson, Int. J. Mech. Sci. 1995, 37, 1161 1177. 31. T. J. Lu, C. Chen, Acta Mater. 1999, 47, 1469 1485. 32. T. Daxner, R. Denzer, H. J. BoÈhm, F. G. Rammerstorfer, M. Maier, Mater.-wiss. Werkstofftechn. 2000, 31, 447 450. 33. R. E. Williams, Science 1968, 161, 276 277. 34. W. E. Warren, A. M. Kraynik, J. Appl. Mech. 1997, 64, 787 794. 35. A. Ableidinger, ªSome Aspects of the Fracture Behavior of Metal Foamsº, Diploma Thesis, Vienna University of Technology, Vienna 2000. 36. J. L. Grenestedt, F. Bassinet, Int. J. Mech. Sci. 2000, 42, 1327 1338. 37. V. Shulmeister, M. W. D. Van der Burg, E. Van der Giessen, R. Marissen, Mech. Mater. 1998, 30, 125 140. 38. H. X. Zhu, J. R. Hobdell, A. H. Windle, Acta Mater. 2000, 48, 4893 4900. 39. A. M. Kraynik, M. K. Nielsen, D. A. Reinelt, W. E. Warren, in Foams and Emulsions, J. F. Sadoc, N. Rivier (eds), Kluwer, Dordrecht 1999. 40. R. Denzer, M. Maier, in Proc. ECCM 99, Munich 1999. 41. S. J. Hollister, J. M. Brennan, N. Kikuchi, J. Biomech. 1994, 27, 433 444. 42. R. MuÈller, P. RuÈegsegger, J. Med. Engng. Phys. 1995, 17, 126 133.

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6.1 Modeling of Cellular Metals 43. E. Maire, F. Wattebled, J. Y. BuffieÁre, G. Peix, in Metal Matrix Composites and Metallic Foams, T. W. Clyne, F. Simancik (eds), WileyVCH, Weinheim 2000, p. 68 73. 44. H. X. Zhu, J. R. Hobdell, A. H. Windle, J. Mech. Phys. Sol. 2001, 49, 857 870. 45. X. E. Guo, L. J. Gibson, Int. J. Mech. Sci. 1999, 41, 85 105. 46. J. M. Albuquerque, M. FaÂtima Vaz, M. A. Fortes, Scr. Mater. 1999, 41, 167 174. 47. V. S. Deshpande, N. A. Fleck, J. Mech. Phys. Sol. 2000, 48, 1253 1283. 48. ABAQUS Theory Manual Version 5.8 (section 4.4.6), Hibbitt, Karlsson & Sorensen, Inc., Pawtucket 1998. 49. J. Y. Chen, Y. Huang, M. Ortiz, J. Mech. Phys. Sol. 1998, 46, 789 828. 50. F. G. Rammerstorfer, H. J. BoÈhm, in Computational Mechanics for the Twenty-First Century, B. H. V. Topping (ed), Saxe-Coburg Publications, Edinburgh 2000, p. 145 164. 51. V. P. W. Shim, B. Y. Tay, W. J. Stronge, J. Engng. Mater. Technol. 1990, 112, 398 405. 52. R. Gradinger, F. G. Rammerstorfer, Acta Mater. 1999, 47, 143 148. 53. T. Daxner, H. J. BoÈhm, F. G. Rammerstorfer, Comput. Mater. Sci. 1999, 16, 61 69. 54. M. F. Ashby, A. G. Evans, J. W. Hutchinson, N. A. Fleck, Metal Foams: A Design Guide. Technical Report CUED/C-MICROMECH/ TR.3, Dept. of Engineering, Cambridge University, Cambridge 1998. 55. C. Chen, Manual for a UMAT User Subroutine. Technical Report CUED/C- MICROMECH/TR.4, Dept. of Engineering, Cambridge University, Cambridge 1998. 56. H. L. Schreyer, Q. H. Zuo, A. K. Maji, J. Engng. Mech. 1994, 120, 1913 1930. 57. W. Ehlers, A. Droste, Techn. Mech. 1999, 19, 341 350. 58. R. E. Miller, Int. J. Mech. Sci. 2000, 42, 729 754. 59. G. Gioux, T. M. McCormack, L. J. Gibson, Int. J. Mech. Sci. 2000, 42, 1097 1117.

60. J. Schluppkotten, R. Paûmann, C. Cheng, M. Maier, in ABAQUS Anwendertreffen 1999, ABACOM, Aachen 1999. 61. M. Seitzberger, F. G. Rammerstorfer, H. P. Degischer, R. Gradinger, Acta Mech. 1997, 125, 93 105. 62. A. G. Hanssen, M. Langseth, O. S. Hopperstad, Int. J. Mech. Sci. 1999, 41, 967 993. 63. M. Seitzberger, F. G. Rammerstorfer, R. Gradinger, H. P. Degischer, M. Blaimschein, C. Walch, Int. J. Sol. Struct. 2000, 37, 4125 4147. 64. S. Santosa, T. Wierzbicki, Comput. Struct. 1998, 68, 343 367. 65. W. Abramowicz, T. Wierzbicki, Int. J. Mech. Sci. 1988, 30, 263 271. 66. S. Santosa, T. Wierzbicki, Int. J. Mech. Sci. 1999, 41, 995 1019. 67. M. Seitzberger, S. Willminger, in Proc. ICRASH 2000, E. C. Chirwa, D. Otte (eds), Bolton Institute, Bolton 2000, p. 458 469, 68. Crash Cad. Impact Design, Europe, Inc., Michalowice, Poland. 69. A. G. Hanssen, M. Langseth, O. S. Hopperstad, Int. J. Mech. Sci. 2001, 43, 153 176. 70. A. G. Evans, J. W. Hutchinson, M. F. Ashby, Prog. Mater. Sci. 1999, 43, 171 221. 71. J. W. Hutchinson, M. Y. He, Int. J. Sol. Struct. 2000, 37, 6777 6794. 72. T. Reiter, F. G. Rammerstorfer, in Optimal Design with Advanced Materials, P. Pedersen (ed), Elsevier, Amsterdam 1993, p. 25 36. 73. T. J. Reiter, Functional Adaptation of Bone and Application in Optimal Structural Design. VDI Fortschrittsberichte, Reihe 17, Nr. 145, VDI Verlag, DuÈsseldorf 1996. 74. T. Daxner, H. J. BoÈhm, F. G. Rammerstorfer, Mater. Sci. Technol. 2000, 16, 935 939. 75. W. K. Vonach, T. Daxner, F. G. Rammerstorfer, in Sandwich Construction 5, H. R. Meyer-Piening, D. Zenkert (eds), EMAS, Solihull 2000, p. 291 300.

6 Modeling and Simulation

6.2

Mesomodel of Real Cellular Structures

B. Foroughi, B. Kriszt, and H. P. Degischer

6.2.1

Introduction

Cellular metals are a class of material that offers special properties as described in Chapter 5. Their successful introduction into industrial application requires the development of design methods that predict the responses of these materials to external loads. The discrete mass distribution of cellular metals causes discontinuities in their local properties. To determine the response of a highly porous solid to external loading, such a cellular structure can be modeled as a network of curved beams (open-cell foam) or shells (closed-cell foam). This model can be analyzed using available numerical solutions such as finite elements or boundary elements methods. The 3D cellular structure of a real, foamed metal (see Chapter 4) is too complex to be easily handled with such a model due to excessive calculation time. Another method is to approximate the cellular structure by a continuum model. Such a homogenization method was used by some of the theoretical studies [1]. In this approach the cellular structure is homogenized over the whole sample or component, a scale much larger than the typical microstructure. Theoretical studies [1] suggest that the mechanical properties of an ideally homogeneous foam are scaled by rn. In these relations that are also called ªscaling lawsº the r is the relative density of the foam and n is a constant that depends on the mechanism governing the deformation of the cell walls. For example, the elastic modulus of an open-cell foam with low relative density ( r J 0.1) is governed by bending of struts and scales with r2. At higher relative densities (0.1 J r J 0.3) the effect of shear and axial deformation of struts shall be considered [2]. Correction of the scaling law shows that the influence of these effects on the final response of an open-cell foam in the elastic regime is small. Prediction of such scaling laws and their correction at medium densities are compared in Fig. 6.2-1. In closed-cell foams, bending of struts is accompanied by stretching of the cell faces, which is described by an additional linear term. The equation for the theoretical elastic modulus of a closed-cell foam is expressed as [1] E=Es ˆ C1 (f r)2 S C2 (1 s f) r

(1)

where Es is the elastic modulus of the solid material of struts and cell faces. f is the volume fraction of solid contained in the cell edges, the remaining fraction (1 f) is in the cell faces. The uniaxial compression (plateau) strength, s, of low-density opencell foams is scaled with r3/2. At higher relative densities the influence of the thickness of the struts and the size of the corner becomes considerable [2].

281

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6.2 Mesomodel of Real Cellular Structures

As shown in Fig. 6.2-1b the correction of the scaling law at medium densities has a significant effect on the prediction of the value of plateau strength. The theoretical value of plateau strength is modified for a closed-cell foam with the stretching effect of cell faces as r)3=2 S C4 (1 s f) r s=s ys ˆ C3 (f

(2)

where s ys is the yield stress of solid material and C1, ... C4 are constants depending on the cell geometry [1]. These equations describe the behavior of a material that is assumed to be continuous and homogeneous. In this study, our interest lies in local variations of density and other dependent fields over scales not very much larger than the typical microscale. This may be accomplished with the help of a mesoscale window (averaging volume), which becomes the classical representative volume element (RVE) in the infinite medium. Mechanical properties at such a mesoscale can not be uniquely approximated. But they depend on the essential or natural boundary conditions of the averaging volume, which bounds the material response from above and below [3]. This bound will be tighter with increasing size of mesoscale or, in other words, with decreasing effect of boundary conditions on the response of the averaging volume. In the mesoscale, the relative density can be defined as a function of a local point X in an undeformed stress-free reference configuration, r ˆ r(X). This allows us to define an inhomogeneous mass distribution in the foamed samples. Studies on the effects of inhomogeneous or gradient distributions of mass on the behavior of metallic foams are limited. Beals and Thomson reported that density gradients have a significant effect on compression properties of Alcan aluminum foams [4]. Huschka et al. modeled foam materials with a stacking of layers of different densities [5]. Gradinger and Rammerstorfer developed a 1D model to analyze the effect of density gradient in loading direction [6]. The effect of 1D inhomogeneities on the stress strain response and on the crush energy absorption of aluminum foams has been studied. Daxner et al. improved this method to a 2D model [7]. In this model, the material is re-

Figure 6.2-1.

strength.

Correction of scaling laws at medium densities: a) elastic modulus; b) plateau

6 Modeling and Simulation

0.05

σ /σ ys

0.04

0.03

Alulight cast Alulight wrought alloy Alporas

Scaling law (Correc.) φ = 0.96

Scaling law (Correc.) φ = 0.9

0.02

Scaling law φ =1

0.01

0 0.08

0.1

0.12

0.14

0.16

0.18

0.2

Figure 6.2-2. Comparison of measured and predicted plateau strength of Alporas and Alulight samples. The plateau strengths have been normalized by the yield stress of the cell wall.

presented as an array of point masses connected by nonlinear springs and rigid cross-bridges. X-ray computed tomography (XCT) revealed the 3D inhomogeneous mass distribution in metallic foams [8,9]. The influence of the inhomogeneities on the deformation and the elastic and plastic behavior of metallic foams was also studied as a mesoscopical imperfection [10 12]. The manufacturing process of foamed metals has a major effect on the architecture of the cellular structure exhibiting inhomogeneous pore distribution, cell nodes, and walls. The plateau strength of two types of aluminum foam samples measured in uniaxial compression tests were compared with the predictions of scaling laws (Eq. 2) in Fig. 6.2-2. Two different routes are used to produce the Alporas [13] and Alulight [14] foams, respectively. The homogenized scaling laws can clearly predict the experimental results for Alporas material better than those of Alulight samples. This phenomenon can be explained by the distribution of mass in the cellular structure: the Alporas material is quite uniform while the Alulight material shows high variation in the local density [9]. A continuum model is implemented using the finite element (FE) method to simulate the effect of local mass distribution on the overall behavior of cellular samples. Three constitutive laws are used for modeling the plastic deformation of elements: classical J2 plasticity, the crushable foam model, the simplified self-similar model. It is shown that the inhomogeneous density distribution leads to plastic strain localization. The simulated plastic strain localization is compared with the real observations and the influence of inhomogeneity on calculated elastic modulus and plateau strength are studied.

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6.2 Mesomodel of Real Cellular Structures

6.2.2

3D Mesomodel

The density mapping method was used to approximate the cellular structure by a continuous, 3D density distribution at the mesolevel. The density recorded by XCT is homogenized over an averaging volume. The dimension of the averaging volume specifies the size of mesoscale where the cellular structure is assumed to be homogeneous. Overlapping of averaging volumes allows to increase the resolution of continuous density distribution up to the resolution of used XCT data. Details of the density mapping method have been explained in Chapter 4.3 and previously [8,10]. The influence of an averaging volume size (AVS) on the result of the developed mesomodel will be discussed in Section 6.2.4. The obtained inhomogeneous continuum body is then implemented by FE analysis. The mean density of each element is obtained by averaging the values of density mapping for all XCT voxels within the FE. Figure 6.2.-3. shows 2D XCT pixels overlapping with a triangular FE. The next step is to describe the inhomogeneous body as a multiple sub-domain problem. The material properties (elastic modulus and Poisson's ratio in the elastic regime and plateau strength in the plastic regime) depend on the local relative density of each element. In a general case, each element will have a mechanical behavior that is different from the behavior of neighboring elements. This high variation in the material properties can complicate the analysis of the model. To overcome this difficulty the relative density variation, [ rmin, rmax], is divided into N intervals. All elements, in which the relative densities lie in the interval i ( rFE [ ri, ri ‡ 1]) form a sub-domain Vi (i ˆ 1,2,....,N). Therefore the material consists of N sub-domains each of which is assumed to be homogeneous and isotropic. Their mechanical properties depend on the average value of the relative densities of the elements lying within the sub-domain. Although the mechanical properties in each sub-domain are assumed to be constant, they show discontinuities across any interface between sub-domains. The interfacial conditions can lead to deviation from uniaxiality of the loading condition in the sub-domains even in the case of uniaxial compression of samples. Because of this, the general form of constitutive laws is used for the description of elastic and plastic behavior of the sub-domains.

Overlapping the XCT pixels with a finite element.

Figure 6.2-3.

6 Modeling and Simulation

Elastic Regime The generalized Hooke's law is used to calculate the linear elastic strain tensor in the form 6.2.2.1

eei ˆ Sij s j

i, j ˆ 1, 2, . . . 6

(3)

where eie, s j are the elastic strain and stress tensor, respectively, and Sij is the compliance matrix. This matrix is characterized by a set of moduli. Two independent moduli describe an isotropic and homogeneous material. The Young's modulus and the Poisson's ratio are used for this purpose. The Young's modulus of each sub-domain is derived from the scaling law (Eq. 1) with the assumption that the material behaves like a closed-cell foam. The volume fraction, f, should be obtained by fitting the experimental results. The Poisson's ratio is assumed to be 0.35 in the elastic regime. There is no experimental evidence for this parameter but the computational modeling of a regular cellular structure (Kelvin cells) suggests 0.35 as a reliable value [15].

Plastic Regime The linear elasticity is limited by the yield criterion. Plastic yielding is the most usual mechanism for ªfailureº of ductile metals. This mechanism can be described by rate-dependent incremental plasticity theory. According to this theory, the elastic theory breaks down as a certain function of stress reaches a certain value. It is known as a yield surface within which the material is elastic and on which the plastic flow may take place. Various models have been developed to describe the shape of a yield surface for a homogeneous cellular material [16 18]. The present investigation focuses on three models: classical J2 plasticity [19], the crushable foam model [20], and the simplified self-similar model [16]. 6.2.2.2

Classical J2 Plasticity The classical J2 plasticity is the simplest and most common model to predict the plastic deformation in dense metals. The yield surface in this model is expressed as f ˆ se s Y ˆ 0

(4)

where Y is the yield strength of the material under uniaxial load and s e is the von Mises effective stress defined by r 3 sij sij se ˆ (5) 2 sij is the deviatoric stress tensor. This yield surface is independent of the mean stress. Such a material can not fail due to hydrostatic load and is plastically incompressible (epvol) when an associate flow rule is assumed [19]. Because of plastic compressibility of cellular structure, the J2 plasticity is used to estimate the mechanical behavior of foams at small global strain values and to determine the position where local deformation begins to form a band. Strictly, J2 plasticity is not valid for

285

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6.2 Mesomodel of Real Cellular Structures

description of plastic deformation of foams under multiaxial loads, but in uniaxial compression of an inhomogeneous material when the effects of interfacial conditions are small, this model can provide reasonable results. The model is calibrated against the response of material to the uniaxial loading. We assume, here, that each sub-domain behaves in a linearly elastic and perfectly plastic manner. The scaling law (Eq. 2) with the correction for medium densities is used to predict the plateau stress in each sub-domain. The volume fraction, f, is considered to be the same as for the prediction of elastic moduli. Crushable Foam Model ABAQUS [20] has also offered a model for simulation of plastic deformation of cellular structure. There are two advantages of this model in comparison with the J2 plasticity: the ability to model volumetrically plastic deformation, and the different responses of the material in tension and compression. Note that in tension, cell walls break and as a result the tension-bearing capacity of cellular structure is considerably smaller than its compressive strength. This effect has been considered in this model. The yield surface is defined, here, in the term of the invariant stresses with an elliptical dependence of deviatoric stress on pressure (mean) stress. " f ˆ

pt s pc Sp 2

!2 S

t M

!2 #1=2 s

pt S pc ˆ 0 2

(6a)

where " 1 1 s t ˆ se 1 S 2 K

1 1s K

!

r se

!3 # (6b)

where pc and pt are the strength of material in hydrostatic compression and tension, respectively. M is the slope of critical state line that depends on pt and on the initial yield strength under uniaxial load, Y, as well as under initial hydrostatic compression strength, pc0. K is a material parameter that defines the shape of yield surface in the deviatoric plane (Fig. 6.2-4a), and r is the third deviatoric invariant of sij. The yield surface is depicted in Fig. 6.2-4b. Non-associated flow is assumed for this constitutive model. The flow potential, g, is defined in term of hydrostatic and deviatoric effective stress, and chosen in this model as r 9 2 p S s 2e g ˆ (7) 2 This potential gives the zero plastic Poisson's ratio. This means that loading in any direction causes insignificant deformation in the other directions perpendicular to the loading. Experiments don't always confirm this property for foamed metals, specially those that have high relative densities [16]. This is a limit of the crushable foam model to describe the plastic deformation of foamed metals. Another restriction is the calibration of the model with the experimental results.

6 Modeling and Simulation S1

K=1.0

t

hardened surface

K=0.8 pt S3

plane.

pc|0

pc p

original surface

(b)

(a) Figure 6.2-4.

softened surface

S2

Crushable foam model: a) effect of material parameter K; b) yield surface in t p

Here, the hardening/softening response is controlled by the value of the hydrostatic compression strength pc. In other words, compaction or dilation of the material, which is modeled by variation of the yield surface's shape as shown in Fig. 6.2-4b, is calibrated with the response of the material in a hydrostatic compression test. It is assumed that pt remains fixed throughout any plastic deformation. Generally, we define the pressure pc versus total plastic volume strain epl vol as follows. a) plateau regime pl

pc ˆ k1 evol S pc0

pl

(8a)

pl

(8b)

evol J eD

b) densification regime pl

pc ˆ k2 eaevol

eD J evol

k1, k2, and a are material parameters that depend only on relative density. They must be evaluated by fitting the p e curves obtained by hydrostatic compression tests. Parameter eD (densification strain) is adjusted to satisfy the continuity of the function pc(epl vol) in the passage from zone (a) to zone (b). Simplified Self-Similar Model The model was developed by Deshpande and Fleck [16] assuming the hardening response is given directly by uniaxial compression responses. Hence the model can exactly predict the compression response of a homogeneous material that is loaded uniaxially. Multiaxial loading causes disagreement of the model predictions with experimental results. In uniaxial loading of an inhomogeneous material, the interface forces cause a multiaxial loading condition in the sub-domains. This can also lead to deviation of material behavior from the prediction of the model. This deviation depends on the order of inhomogeneity (difference between lowest and highest density) as well as the shape of sub-domains in the foamed sample. This constitutive law is employed for modeling the uniaxial compression (including plateau and densification regimes) of real foamed samples as an inhomogeneous material. For this

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6.2 Mesomodel of Real Cellular Structures

purpose, the hardening responses of each sub-domain to uniaxial loading should be specified until full densification. This means that the stress strain response of homogeneous cellular structures should be available for the whole density range as a function of relative density. In this study, we introduce a material model for this purpose, the aim of which is to specify the ªCauchy stress true plastic strainº of an isotropic homogeneous metallic foam. The model assumes that the hardening response of an ideally homogeneous cellular structure in the plateau regime is only governed by work hardening of cell wall material. However this hardening effect is small, consequently a homogeneous foam shows no hardening response in the plateau regime. In the densification regime, the opposing walls of cells crush together and the cell wall material itself is compressed. When this happens the stress strain curve rises rapidly. This hardening response should be approximated using experimental data, since there is no physical model for this regime. Accordingly, the material model is defined as a) plateau regime s true ˆ s

pl

etrue J eD true

(9a)

b) densification regime pl

s true ˆ cedetrue

pl

eD true J etrue

(9b)

where s is the compression strength of homogeneous material that is determined using scaling laws (Eq. 2). The material parameter d and densification strain, eDtrue, are obtained by fitting the experimental data. Finally, the parameter c is determined so that the curve remains continuous in the transition from plateau to densification regime D

c ˆ s es detrue

(10)

6.2.3

Modeling of Uniaxial Compression

Uniaxial compression tests are simulated with respect to the presented model. The compression samples are rectangular prisms with dimensions of 20 q 20 q 40 mm3. ABAQUS/Standard is employed for computation of the field variable (displacement, strain, and stress). 3D solid (continuum) elements with eight nodes of type C3D8 are used to model the sub-domains. The nodes of this element have three translational DOFs (degrees of freedom) but no rotational DOFs. The boundary conditions are chosen so that they represent the conditions of uniaxial compression tests. For this purpose, one clamping surface (bottom face) is assumed to be fully fixed within the clamping plane, so all nodes are fixed in this plane (x-, y-, z- translational displacements are assumed to be zero). Note that because of the friction effect, in practice, the lateral displacement of a sample on the clamping surface is also negligible. Nodes in the other clamping surface (top face) are fixed in the lateral directions (x and y) whereas the displacement in the axial direction (z) is given as loading.

6 Modeling and Simulation

Deformation Band The compression experiments indicate that the inhomogeneous density distribution leads to localization of deformation and the formation of deformation band(s) [11,12]. Figure 6.2-5 depicts the lateral surfaces of an Alulight sample recorded by a digital camera at 0 and 4 % nominal strain. The sample has an average density of 350 kg/m3. The deformed cells are marked by arrows. It can be seen that the deformed cells form a band in the sample. The edge length of the averaging volume chosen to homogenize the density surrounding a XCT voxel was 6.4 mm (11 pixel). The edge length of elements is chosen to be three times the size of the CT pixel in each slice. 6.2.3.1

Figure 6.2-5. Surface images of an Alulight cast alloy sample of r ˆ 0.13: a) cellular structure before deformation; b) cellular structure after deformation, 4 % nominal stain, deformed

cells are marked with white arrows; c) calculated local plastic strains in loading direction using presented model at 4 % nominal strain, yielding the first deformation band.

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6.2 Mesomodel of Real Cellular Structures

Figure 6.2-6. Results of deformation modeling using the crushable foam model for densification of first deformation band and forming the second band.

6 Modeling and Simulation

Figure 6.2-7. Simulation of large deformation of an Alulight sample using the simplified selfsimilar model.

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6.2 Mesomodel of Real Cellular Structures

To compute the effect of inhomogeneity the investigated sample was divided into nine sub-domains. The densities of the sub-domains were 220, 240, 260, 280, 330, 400, 500, 620, and 720 kg/m3. The calculated plastic strains in the loading direction happening at a nominal strain of 4 % are depicted in the Fig. 6.2-5c. Very good agreement is seen between the position of the observed and the computed deformation band. Densification of this band and forming the second deformation band was modeled using the crushable foam model as shown in Fig. 6.2-6. Large deformation of another Alulight specimen was simulated using the simplified self-similar model as shown in Fig. 6.2-7. It should be noted that field parameters (such as stress, strain, and displacement) are computed for a continuum. They are average values and must not be considered as microscopical field parameters related to deformation of the cell walls.

Mechanical Properties Figure 6.2-8 shows the predicted stress strain curve of a typical Alporas specimen. The simplified self-similar model described above was used to model the hardening response during uniaxial loading. Although no strain hardening was assumed for sub-domains in the plateau regime, the response of the whole specimens shows hardening, which follows the measured response accurately. This phenomenon can be described by large deformation of a sub-domain or of some elements in a sub-domain, which can cause local densification. Rapidly increasing stress in densification regime for these elements can lead to slow hardening of the whole specimen in the plateau regime. With an increasing number of elements that are densified the slope of stress strain curve increases quickly. The material parameters in the Eq. 9 are obtained by fitting the measured data and are considered in this simulation as follows [21]: 6.2.3.2

Figure 6.2-8. Comparison of the measured stress strain curve of a typical Alporas sample with the prediction of the mesomodel.

6 Modeling and Simulation

 s ˆ 0:507r1:56, d ˆ 2:0, eD true ˆ 1:0 s 2:13 r

(11)

The effect of inhomogeneous mass distribution on the mechanical properties can also be calculated using the developed mesomodel. For example, the Young's moduli and compressive strengths of various Alulight samples have been predicted. As described in Section 6.2.2, the mechanical properties of each sub-domain were obtained from Eq. 1 and Eq. 2 assuming f ˆ 0.94 [22]. Computed and measured values as well as the prediction of scaling laws are depicted in Fig. 6.2-9. Comparison of computed values with measured ones suggests the effect of inhomogeneity. It

0.08 0.07

E/Es

0.06 0.05 0.04 0.03 Exp. mesomodel Phi=1 Phi=0.9 Phi=0.94

0.02 0.01

(a)

0 0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.06

0.05

σp /σ ys

0.04

0.03

0.02 Exp. mesomodel Phi=1 Phi=0.94 Phi=0.94 (correc.)

0.01

(b) 0 0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

Figure 6.2-9. Comparison of measured values with predication of the mesomodel based on the simplified self-similar model: a) elastic modulus; b) plateau strength.

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6.2 Mesomodel of Real Cellular Structures

can be seen that this effect on elastic modulus is small, while the plateau strength can be significantly affected from inhomogeneous mass distribution. However, the overall response of foamed samples depends on the size and shape of soft (sub-domains with low densities) and hard (sub-domains with high densities) regions. The plateau strength will be decreased specially when a soft region is oriented perpendicular to the external compressive load [10,12]. 6.2.4

Discussion

The transformation of a discretely heterogeneous structure to an approximated continuum was one of the major challenges in this study. The discrete XCT data (microscopical density field) have been averaged over a certain volume. However, the overall response of samples is affected by the size of the AVS, which should contain a cellular structure that behaves like a ªfoamº. Figure 6.2-10a shows the calculated plateau strength of an Alulight sample versus the size of the averaging volume. The sample had an average density 419 kg/m3 and the measured plateau strength was 3.0 MPa, which is about 12 % below the predicted value of scaling laws applied to the average density. It is seen that the difference between measured and calculated values (mesomodel) is decreasing with increasing AVS (Fig. 6.2-10a). The relative error is less than 12 % for an averaging volume equal 33 pixel (19.5 mm) at 0.2 % nominal strain and less than 5 % at 4 % nominal strain (see Fig. 6.2-10). Andrews et al. [23] reported that the compressive strength of closed-cell samples reaches the plateau values if the ratio of sample size to cell size is greater than five. The average cell size of investigated Alulight samples was measured around 3 4 mm. Therefore it can be assumed that at an average volume size of about 19 mm, the effect of boundary conditions on response of the averaging volume is negligible and the homogenization requirement is fulfilled. If AVS ˆ 11 pixels (6.4 mm) the calculated stress at 0.2 % stain is 20 % below the measured plateau stress, at 4 % the difference is reduced to 8 %. The comparison of predicted strength depends on the strain at which the plateau strength is taken. The effect of AVS on the stress strain curve is relevant at the beginning of loading as shown in Fig. 6.2-10b, revealing a higher resolution of the strengthening of the cellular structure in the beginning of compression. Anyhow the first loading to plateau stress could not be simulated. Figure 6.2-11 demonstrates the difference in the resolution of the density mapping on increasing the AVS. But it is remarkable that the inhomogeneity is still very clearly imaged at an AVS of 19.5 mm (33 pixel) edge lengths. However, averaging over very large volumes leads to elimination of inhomogeneity effects. Three constitutive laws have been used to model the plastic deformation of subdomains. Because of incompressibility of J2 plasticity model it is only suitable to predict the position of the first deformation. The applicability of the crushable foam model to cellular metals should be demonstrated with more accuracy. In addition, this model must be calibrated with the results of hydrostatic compression tests. Therefore to simulate the hardening response of an inhomogeneous cellular sample with crushable foam model, the stress strain curves under hydrostatic

6 Modeling and Simulation

compression as a function of density is needed. The tests should be performed until full densification to allow the fitting of material parameters for this model, which was presented in Eq. 8. Insufficient material data lead to divergence of the method and stopping the FE analysis. The simplified self-similar model [17] assumes that the hardening is given directly by the response of a homogeneous cellular metal under uniaxial compression. Eq. 9 can model the response of Alporas material accurately. More experiments are necessary to calibrate the material parameters in these equations for Alulight specimens specially in the densification regime.

3.5

3

Stress [MPa]

2.5

2

1.5

1 Exp. AVS=11 pixel AVS=23 pixel ADS=33 pixel

0.5

(b)

0 0

1

2

3

4

5

6

Nominal strain [%] Effect of averaging volume size (AVS): a) on the computed plateau strength; b) on the predicted stress strain response.

Figure 6.2-10.

295

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6.2 Mesomodel of Real Cellular Structures

Figure 6.2-11. Influence of averaging volume size (AVS) on the density distribution derived from XCT data (0.588 mm/pixel).

6 Modeling and Simulation

6.2.5

Conclusions

A mesomodel has been developed to explain the localized deformation behavior and to calculate the mechanical properties on the basis of the mass distribution of the cellular metals measured by CT data. Density mapping method is employed to approximate the mesoscopical continuous distribution of density in investigated samples. The model confirms the correlation between the inhomogeneous density distribution and the localization of plastic strains yielding deformation bands. The position of forming and propagation of the deformation band is predicted accurately. The influence of inhomogeneity on the elastic modulus (the stiffness of the cellular structure) and yield strength of metallic foams can be demonstrated. The influence on the elastic modulus is small while the plateau strength can be affected significantly. The discrepancy between the calculated and the measured plateau strength is caused by the uncertainties for the parameters used for the scaling laws for Alulight and effects due to the assumption of isotropy.

References 1. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, 2nd edn, Cambridge University Press, UK 1997, Chapter 5. 2. L. J. Gibson, M. F. Ashby, Proc. R. Soc. Lond. 1982, A382, 43 59 3. M. Ostoja-starzewski, Int. J. Sol. Struct. 1998, 35, 2429 2455. 4. J. T. Beals, M. S. Thomson, J. Mater. Sci. 1997, 32, 3595 3600. 5. S. Huschka, S. Hicken, F. J. Arendts, in Proc. MetallschaÈume, J. Banhart (ed.), MIT, Bremen 1997, p. 189±197. 6. R. Gradinger, F. G. Rammerstorfer, Acta Mater. 1999, 47, 143 148. 7. T. Daxner, H. J. BoÈhm, F. G. Rammerstorfer, Comput. Mater. Sci. 1999, 16, 61 91. 8. H. P. Degischer, A. Kottar, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 213 220. 9. A. Kottar, H. P. Degischer, B. Kriszt, Materwiss. Werkstofftechn. 2000, 6, 465 469. 10. B. Kriszt, B. Foroughi, K. Faure, H. P. Degischer, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 241 246. 11. B. Kriszt, B. Foroughi, A. Kottar, H. P. Degischer, Proc. Euromat 99, Vol. 5, WileyVCH, Weinheim, 2000, p. 4 82.

12. B. Kriszt, B. Foroughi, K. Faure, H. P. Degischer, Mater. Sci. Technol. 2000, 16, 792 796. 13. T. Miyoshi, M. Itoh, S. Akiyama, A. Kitahara, Adv. Eng. Mater. 2000, 2, 179 183. 14. J. Banhart, J. Baumeister, J. Mater. Sci. 1998, 33, 1431 1440. 15. A. Ableidinger, Thesis, University of Vienna, 2000. 16. V. S. Deshpande, N. A. Fleck, J. Mech. Phys. Solids 2000, 48, 1253 1283. 17. R. E. Miller, Int. J. Mech. Sci. 2000, 42, 729 754. 18. W. Ehlers, H. MuÈllerschoÈn, O. Klar, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 255 262. 19. J. Lubliner, Plasticity Theory, Macmillan, New York 1990. 20. HKS ABAQUS/Standard user manual, Version 5.8, Hibbit Karlsson & Sorensen Inc., Nantucket, RI 1998. 21. B. Foroughi, Thesis Vienna, University of Technology, Austria 2001. 22. K. Y. G. McCullough, N. A. Fleck, M. F. Ashby, Acta Mater. 1999, 47, 2323 2330. 23. E. W. Andrews, P. R. Oneck, L. J. Gibson, Int. J. Mech. Sci. 2001, 43, 701 713.

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Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

7 Service Properties and Exploitability 7.1

The Range of Applications of Structural Foams Based on Cellular Metals and Alternative Polymer Solutions

C. Haberling

Lightweight construction is gaining importance in automobile technology. Alongside improvements in wind resistance and tribology, weight reduction measures are of primary importance. This is necessary because for each particular automobile class there are increasing customer demands for safety, comfort, performance, and available internal space. Using conventional methods of construction to provide these customer-oriented features leads to a considerable increase in weight, giving rise to strong pressures to reverse the weight gain. It is therefore regarded as an imperative development objective to achieve a reduction in weight relative to axle loads. 7.1.1

Introduction

Apart from using single materials in lightweight construction, increasing use is made of mixed construction methods and various forms of composite materials to achieve weight reduction. However, since these materials frequently incur higher costs, it is of primary importance to ensure that they play a multifunctional role [1]. This also applies to structural foams in the form of cellular metals based on aluminum or alternative systems based on expanding plastics, such as epoxy or polyurethane resin foams. These are required to take over functions such as energy absorption, stiffness, thrust-field reinforcement, and sound absorption in different methods of construction [2].

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7.1 The Range of Applications of Structural Foams Based on Cellular Metals

Plate structures: p  3 E Z flexual stiffness r (plate) Rp0,2 Z tensile strength r p E Z bending stiffness r (bar)

Hollow structures: q 3 Rp0,22 Z bending strength r (bar) Rp0,2 r

Figure 7.1-1.

forcements.

Z tensile strength

Typical loading of car body structure (Audi A8): strategy for structural foam rein-

7.1.2

Potential Areas of Use

The areas where these kinds of material are of potential use can be derived at an early stage in design using a finite element (FE) analysis of typical stresses in a car body. The result makes it possible to evaluate which structural components in the body structure can play a multifunctional role and what measures can be adopted to achieve the desired result cost-effectively, taking into account space availability and the factors inherent in lightweight construction. As illustrated in the car body of the Audi A8 (Fig. 7.1-1), there are many areas in the bodywork where structural foams can be used. They are particularly suitable for hollow structures where space is too restricted for other more cost-effective measures. Particular areas where the multifunctional applications profile can be exploited to beneficial effect are the side-members, the boundaries of the floor of the passenger compartment, and in the region of the sills and pillars. 7.1.3

Material Properties

The application profile of a structural foam can be derived from the density of the material, its compressive strength, and its elastic modulus. These are illustrated (Fig. 7.1-2) for a single construction method. It is quite possible to adapt the behavior of the material specifically to the local stress relationships within the structure of the vehicle owing to the wide range of material densities, types of material, and

7 Service Properties and Exploitability

Figure 7.1-2.

Mechanical properties of structural foams.

heat treatment methods that are available. Typically, metallic foams have a higher elastic modulus, whereas epoxy foams exhibit a greater compressive strength at similar densities for temperatures up to 80 hC. 7.1.4

Main Component Configurations

Using lightweight construction criteria [3], it is possible to use these material characteristics to assess which type of material is most suited for what kind of stress conditions (Fig. 7.1-1). Compared with compact materials, however, the efficiency of foam materials in single construction methods where the available building space is not an issue is somewhat limited. It is only where a differential method of construction is used with compact materials and in limited spaces, which is the predominant case encountered in automobile construction, where the effectiveness of these types of foam materials comes into its own. Even greater advantages are gained when they are used in conjunction with compact materials. In the first place, all foam materials exhibit an extremely variable behavior under tensile and compressive loads. While the compressive range is characterized by a broad, uniform, and even deformation behavior (plateau) under constant load, under tension, structural foams inherently become brittle and fail at very low loads (Fig. 7.1-3). In addition, inhomogeneous regions are formed in the material that do not particularly affect the overall behavior under compressive stress (reaching the ultimate strength either later or at a lower level) under purely axial loads, but may cause buckling or failure of the foam structure if there is an uneven distribution across

301

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7.1 The Range of Applications of Structural Foams Based on Cellular Metals

Figure 7.1-3.

Deformation behavior of cellular metals under compressive and tensile stresses.

Figure 7.1-4.

Buckling due to non-uniform loads on cellular metals: testing and FE simulation.

the stressed cross section, and thus lead to a premature total failure (Fig. 7.1-4). This would represent a risk particularly in the case of the complex stress patterns in a car body that can certainly be avoided by using a carrier structure. The foam materials on the market today that are used for structural stiffening are ideally used inside hollow components or inside a sandwich composite structure (Fig. 7.1-5). The function of these carrier materials is to avoid high local tensile stresses in the foam and to apply the forces acting externally into the core of the foam, directing them during deformation. It is of primary importance, particularly in circumstances where energy absorption is required, to obtain the correct geometric balance in the carrier/foam system. A completely foamed tubular structure that is subject to bending can serve as an example. While the empty tube de-

7 Service Properties and Exploitability

forms considerably under a low load, when it is filled completely with foam, its flexural resistance is increased considerably, but, at the same time, it will fail earlier with smaller deformations. This can be attributed to excessive local stresses in the outer tube structure that is overloaded owing to the restricted plastic deformation locally, causing brittle fracture. It is more advisable to provide a partially foam-filled structure where material is saved in the region of the neutral axis or inside the less active tensile zones in the case of structural foams. In this way, weight can be

Figure 7.1-5.

Use of cellular metals in combination with compact materials.

Figure 7.1-6.

Foam-filled tubes: variation of foam geometries in impact bending tests.

303

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7.1 The Range of Applications of Structural Foams Based on Cellular Metals

reduced while, at the same time, increasing energy absorption significantly (Fig. 7.1-6). 7.1.5

Application and Attachment Techniques

In general, there are many ways of applying and attaching structural foams. The effectiveness depends essentially on the attachment of the foam materials to the surrounding or adjacent components. This is particularly important in structures that derive their properties from a composite sandwich structure. Frequently, however, these requirements conflict with production-related conditions such as manufacturing tolerances. Several additional factors affect the stiffening of hollow bodywork structures in car construction. In one such instance, it must be ensured that the process liquids in the paint shop flow through the hollow cross sections of the bodywork, so that, in general, this objective is defeated if larger hollow sections are completely filled with foam. To prevent corrosion zones, narrow gaps must be avoided between foam elements and the basic structure, particularly where mixed construction methods are used, such as the employment of aluminum foams in a steel body. Also, incomplete contact must be avoided for acoustic reasons. The contact must be such that either it is so intimate that contact is permanently assured over the entire surface, or both parts must be protected separately against corrosion before assembly, for example by painting. However, this solution generally incurs considerable extra costs. In the case of cellular metals, both cementing and casting are feasible means of bonding surfaces. Local joining can be done using thermal and mechanical bonding processes.

Casting The casting of aluminum foams using sand and permanent molds can be regarded as state of the art. Cast-in molding in pressure die-casting is possible using diecasting machines controlled in real-time to avoid pressures in the molten metal becoming too high. Most die-cast parts used in car construction have a typical wall thickness of less than 5 mm. In order to deal with all aspects of lightweight construction in this range of applications, it is necessary to explore at what maximum pressures and casting speeds aluminum foam inserts of minimum density can be cast-in with the thinnest possible casting skin while avoiding both foam infiltration and incomplete filling of the mold (Fig. 7.1-7). This is particularly important for components with large hollow sections (such as swivel bearings) that are normally produced by gravity molding with a lost-sand core (see Section 3.3). Apart from casting, gluing is a process that can be used to join together the surfaces of foam parts. In car production it is especially important to achieve a sufficient adherence and durability against corrosion and aging. Expanding adhesives can be used to compensate for even greater manufacturing tolerances, so that, for instance, it is possible to insert a foam part in an extruded section (Fig. 7.1-7) (see Section 3.2). 7.1.5.1

7 Service Properties and Exploitability

Figure 7.1-7.

Attachment techniques: casting and gluing.

Thermal Joining Processes To produce a high quality joint, the thermal joining process is restricted to applications involving identical materials (see Section 3.2). Aluminum foams can be incorporated in the structure using soldering or welding methods. While soldering produces a joint across the entire surface, welding will result in a localized joint only. Laser-beam welding in particular (Fig. 7.1-8) places high demands on the toler7.1.5.2

Figure 7.1-8.

Attachment techniques: welding.

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7.1 The Range of Applications of Structural Foams Based on Cellular Metals

ances of the parts being joined. Other welding methods require appropriate preparation of the carrier system, such as localized perforations, since the depth of the weld is shallow. Welding with and without filler materials has been checked in numerous ways. When employed in fabricating car bodies, there still remain questions regarding the corrosion behavior in narrow gaps along the weld seam. Furthermore, the positions of the seams must be adjusted to match the stress profile of the component. This is necessary to ensure the maximum effectiveness of the foam inlay, and, at the same time, to minimize as much as possible the weakness of the surrounding sheet metal along the seam, since typically in aluminum welds the zone around the weld is subject to softening.

Mechanical Joining Processes It is not possible to achieve a joint over a large surface between the foam part and the structure using a mechanical joining process (see Section 3.2). However, these types of joining methods can compensate for broad tolerances and, if appropriate corrosion protection measures are taken, mixed construction methods can be adopted. Screw connections and riveting can be considered as well as localized crimping of the component where it is more practical when access is possible from one side only. These local joining methods are of particular benefit for preassembly of components in combination with other joining techniques. 7.1.5.3

Three-dimensional sandwich A further solution is offered by the use of a prefabricated three dimensional sandwich structure. The most notable example of this type of construction is the aluminum sandwich foam (AFS) sheet [4], in which the joint between the foam core and the outer plate is produced in a roll-bonding cladding process before foaming in situ (see Section 3.4). Since the foaming process does not take place until after the conversion process at temperatures over 500 hC, 3D sandwich contours can also be fabricated using this material. These sandwich structures are either screwed or welded to a surrounding aluminum structure using the cover plates. 7.1.5.4

Alternative Cellular Materials Based on Polymers Thermally-activated foaming is also a feature of alternative materials based on plastics. The activation temperature is lower, however, falling in the range 150 190 hC and can be incorporated into car production without incurring added expense in the paint process. Furthermore, when foamed, the plastics adhere across the full face of the surrounding outer structure, ensuring a complete joint over the whole surface even with broader tolerance bands without requiring supplementary joining measures while, at the same time, avoiding corrosion-prone gaps. 7.1.5.5

7 Service Properties and Exploitability

Figure 7.1-9.

Test piece for stiffness and impact testing.

7.1.6

Effectiveness

Physical characteristics can be checked using simple test pieces for bending, impact, torsional, and axial stresses that mirror the geometry of how hollow structures are used in a vehicle. In doing so, the assumption is made that the outer dimensions of the construction space that is being optimized are not allowed to change since an increase in the cross section of the carrier profile generally represents the most effective lightweight construction solution. This practical necessity occurs frequently in vehicle production owing to space restrictions. The test piece selected was a closed spot-welded hat section made from DC-04 sheet steel, filled with U- and O-shaped foam pads with a density r ˆ 0.55 g/cm3 made from aluminum or epoxy foam. The properties evaluated were stiffness under bending, or flexural strength, impact strength behavior, torsional stiffness, and torsional strength. This was compared with a section of the same weight with thickened walls (Fig. 7.1-9).

Bending and Torsional Stress Regarding the flexural strength of the initial section with a 0.9 mm wall thickness, although increasing the wall thickness results in an increase in the bending moment under elastic conditions, when the additional weight is taken into account, this adjustment has a negative effect on the lightweight construction factor s b,elast./m for the sections being studied. Tests on a hat section starting with a wall thickness of 0.85 mm and a 4 mm thick U-section structural epoxy foam reinforcement result, in contrast, related to the weight used, to a 95 % improvement in the flexural strength compared with an unreinforced section (Fig. 7.1-10). A U-section reinforcement is not recommended for increasing the torsional stiffness, since, in this case, the unreinforced wall fails under similar loads to those applied to unreinforced sections. On the other hand, torsional stiffness can be in7.1.6.1

307

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7.1 The Range of Applications of Structural Foams Based on Cellular Metals

Figure 7.1-10.

Bending and torsion testing of foam-reinforced test specimen.

creased by using an O-shaped structural foam insert [5]. Nevertheless, the effectiveness is considerably less than when a bending stress is applied. Removing the effect of weight (t max,elast/m), reinforcement using 4 mm thick epoxy foam produces a 20 % improvement compared with an initial section without the insert. Using an 8 mm thick aluminum foam pad (this reflects the minimum wall thickness currently possible under production conditions when producing more complex parts) results in a torsional stiffness that is scarcely any different than if one used a 4 mm thick epoxy foam of the same density, with adhesion across the complete surface. This is despite the higher elastic modulus and the greater wall thickness, and it occurs because the surfaces for gluing the upper and lower sides are reduced for technical reasons. In this case, therefore, owing to the total additional weight, the aluminum foam does not offer an advantage for lightweight construction. This applies also to unreinforced sections with increased wall thicknesses used for this application, where the increased weight make them unsuitable for lightweight construction since, again, they offer no advantages.

Impact Stresses The obvious advantage offered by a structural foam insert in relation to impact strength is the strengthening and energy absorption that it confers on a hollow structure even where there are large dynamic bending deformations. The behavior can be modeled with great precision in an FE simulation. Calculations and tests on a hat section show that, at an impact speed of 3 m/sec using a mass of 600 kg on a section reinforced with a U-shaped structural foam insert joined to the surface of 7.1.6.2

7 Service Properties and Exploitability

Figure 7.1-11.

Loading of empty and foam-reinforced test pieces in an impact bending test.

the external plate, the failure load and the energy absorption are more than doubled compared with an unreinforced hollow section of the same weight and with thickened walls. This applies also to epoxy foam variants and for aluminum foam elements glued on all sides. If the same aluminum foam element is glued only locally, however, such as along the cover plate, the stiffening effect is reduced considerably (Fig. 7.1-11). If the energy absorption is spread through the body of the composite component, the same pattern emerges. However, it is also evident that the effectiveness in relation to the mass used falls off again when the foam thicknesses are too high.

Axial Load Tests have been carried out on different sections in many different ways to study their effectiveness under axial loads with and without foaming in place. The buckling associated with folding that is usually used for this type of loading applied to hollow structural parts can also be used in cases where structural foams provide stiffening and can bring about significant improvements in its efficiency [6]. A decisive element in this is a reduction of the force levels as the folding is taking place. Nevertheless this improvement is largely offset in many instances when one takes the added weight into account [7]. Furthermore, the effectiveness of the empty structure can be improved significantly by making certain changes in shape or by using alternative composite fiber structures (carbon/aramid fibers in an epoxy matrix) (Fig. 7.1-12) with little increase in weight [2]. 7.1.6.3

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7.1 The Range of Applications of Structural Foams Based on Cellular Metals

Figure 7.1-12.

Different construction methods of axial load tubes.

Acoustics Acoustic effectiveness has been tested on different models (see also Section 3.4.3.1). Large AFS panels display good absorption qualities below 500 Hz [4]. Other compact foam parts also provide good absorption characteristics but only within a limited frequency range. Tests performed on foam-filled engine supports (Fig. 7.1-13) 7.1.6.4

A: diecast engine support

B: aluminium foam-insert

20 mm n m C: combination of A and B

Figure 7.1-13.

D: alternative solution

Aluminum-foam filled engine support for acoustic means and alternative solution.

7 Service Properties and Exploitability

revealed high acoustic effectiveness, but were considerably heavier than alternative solutions using organic materials since the minimum thickness of the foam was 8 mm. At present, therefore, the acoustic efficiency provided by closed pore cellular metals when used in car construction can only be regarded as an added benefit when taken in the context of a multifunctional role. 7.1.7

Outlook

Costs for lightweigt construction $/kg

It is important to make a clear distinction between different modes of transport when describing the cost/benefit relationship of these types of materials. Whereas structural foams in car construction represent quite a high-cost solution combined with a high degree of effectiveness (Fig. 7.1-14), in the case of aviation the evaluation turns out to be the other way round. In this case, owing to the completely different circumstances, the foam offers good value for the cost, but its efficiency is somewhat modest compared with other materials used [8]. Up to now, despite the numerous possible applications in automobile technology, aluminum-based cellular metals have not yet been used in series production. This is understandable to the extent that most vehicle bodies are based on ferrous materials, so that, owing to the problems of joining, tolerances, and corrosion associated with currently available methods, an aluminum foam core cannot be incorporated within cost budgets. The only applications where they could be used at present are in those places in vehicles that are less prone to corrosion, or inside aluminum bodies or aluminum structures. For components that are subject to higher thermal stresses, such as heat-shield panels, metal foam is unsuitable for weight reasons today owing to its minimum wall thickness of over 8 mm when formed into complex shapes in production. Regarding its acoustic efficiency, it competes with organic insulating materials that are very effective at low costs. , ls ria s al e e ti at m ss en on Cellular w roce iffer ucti metals and e n p d str structural w d n ne - an f co foams o o on d M t ho Mixed e m materials

lighter materials Starting point

Structural modification I=bh /12 W=bh /6

weight reduction, meeting requirements Figure 7.1-14.

Foam usage as function of cost and weight-saving for car bodies.

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7.1 The Range of Applications of Structural Foams Based on Cellular Metals

On the other hand, structural foams based on plastics are now found in numerous applications in car manufacture and are used in the structural regions illustrated in (Fig. 7.1-1). Large-scale use of these materials is, however, prevented in the current cost situation, although many of the additional costs associated with metallic foams, such as extra joining operations and corrosion protection do not apply in the case of these materials. It is possible to use them when the space available excludes any other solutions, or where immediate additional stiffening measures need to be taken, or when, as in the new Audi A4, additional costs or variants can be avoided in another place. AFS sandwich panels in prototypes have shown that there is a potential for using them also [7]. Even for this material, however, series production has raised new questions about joining in mixed construction methods. Furthermore, vehicle design must be adapted to the AFS sandwich in order to extract the maximum efficiency from this material. First and foremost, the quality of the material has to be improved before cellular metals can be used more in vehicle technology. It is already possible, however, to use them inside sandwich structures or in conjunction with carrier materials. Development effort is important to produce an efficient cost-effective joining method, as well as investigations on corrosion protection for using them inside steel structures that are subject to corrosive conditions. Furthermore it is essential to reduce further the present minimum wall thicknesses and the manufacturing costs in order to be able to compete with comparable polymer-based materials and other approaches.

References

1. H. G. Haldenwanger, ªKonzeptioneller Leichtbau mit neuen Werkstoffen: Verfahren, ein Zielkonflikt bei der Verifizierung der Entwicklungsprozeûkette im Karosseriebauº, in Proc. Aachener Kolloquium, Fahrzeug und Motortechnik, RWTH Aachen, IKA, VKA, 4 6 Oct 1999. 2. H. G. Haldenwanger et al., ªLeichtbau mit alternativen Werkstoffen und Verfahrenº Ingenieur-Werkstoffe 1999, 8(1). 3. B. LuÈdge, ªFunktionaler RohkarosserieLeichtbauº, in Proc. Aachener Kolloquium, Fahrzeug und Motortechnik, RWTH Aachen, IKA, VKA, 4 6 Oct 1999. 4. H. W. Seelinger, ªApplication Strategies for Aluminum-Foam-Sandwich Parts (AFS)º in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999.

5. T. Wierzbicki et al., ªCrush Behaviour of Box Columns filled with Honeycombs or foamsº Proc. Fraunhofer USA Metal Foam Symp. 7 8 Oct 1997, Stanton, DW, MIT Publishing, 1997. 6. H. P. Degischer et al., ªOn the Non-Destructive Testing of Metal Foamsº in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999. 7. Ch. Haberling et al., ªAluminum foams for energy absorbing structures under axial loadingº Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999. 8. O. Schultz, R. Schindler, ªAluminiumschaum: Dynamische Festigkeit und Anwendung im Hubschrauberº, Materwiss. Werkstofftechn. 2000, 6, 511 514.

7 Service Properties and Exploitability

7.2

Functional Applications

J. Banhart

Cellular metallic materials are finding an increasing range of applications. Whether a suitable porous metal or metal foam can be found to solve a given problem depends on many factors, summarized here by the following keywords. x

x x

x

Morphology: type of porosity needed (open versus closed), amount of porosity needed, size of porosity desired, total internal surface area of cellular material required. Metallurgy: metal, alloy, or microstructural state required. Processing: possibilities for carrying out secondary operations on the foam or cellular solid, such as shaping, cutting, joining, coating. Economy: cost issues, suitability for large-volume production.

7.2.1

General Considerations

The first point is, in particular, crucial for any evaluation of applications for cellular metallic materials. Many applications require that a medium, either liquid or gaseous, be able to pass through the cellular material. There may be a need for various degrees of ªopennessº, ranging from ªvery openº for high rate fluid flow to ªcompletely closedº for load-bearing structural applications, and appropriate materials satisfying these conditions have to be found. Figure 7.2-1 shows which types of porosity the various application fields require. Normally, a difference is made between whether an application is ªfunctionalº or ªstructuralº, but there is considerable overlap between these two notions. The question of from which metals or alloys a given type of cellular structure can be manufactured is also important. Structural load-bearing parts have to be light because otherwise they would be made from conventional massive metals or alloys. Therefore, aluminum, magnesium, or titanium cellular or porous metals are preferred for such applications. For medical applications, titanium may be preferred because of its compatibility with tissue. Stainless steel or titanium is required for applications in which aggressive media are involved or high temperatures occur. Finally, processing and cost issues have to be considered. The technology must be available to bring the selected cellular metal into the required shape and to incorporate it into the machine or vehicle where it has its function. A technology for making cellular metal will be futile if the required component cannot be manufactured at a reasonable price. In the following sections, applications for cellular metals are discussed that are predominantly ªfunctionalº in the sense discussed. Traditional powder metallurgy

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structural

load-bearing components bio-medical implants

energy absorbers

catalyst supports

kind of application

silencers sound absorbers filters

bearings

heat exchangers

functional open

partially open

closed

type of porosity

Applications of cellular metals grouped according to the degree of open porosity needed and whether the application is functional or structural.

Figure 7.2-1.

(PM) has created porous sintered metals for a wide range of applications [1 3]. It is therefore not surprising to find very similar applications for the cellular metals described in the present text, provided they have a certain degree of open porosity. 7.2.2

Biomedical Implants

Biomedical applications often have both a structural and a functional aspect, and are therefore very challenging. Titanium or cobalt chromium alloys are used for prostheses or dental implants because of their biocompatibility. To ensure ingrowth of tissue, one usually produces a porous layer of the same or another biocompatible material on the prosthesis by thermal spraying or other methods [4]. Alternatively, one could use porous titanium or titanium foam for such applications and tailor the density distribution to meet the required strength and moduli of such components. There is no unanimity about how implants should be designed to ensure maximum durability and functionality. According to one opinion, the modulus of, say, dental implants should match the modulus of the jaw bone. Knowing the relationship between modulus and density of metallic foams, one could easily

7 Service Properties and Exploitability

manufacture implants with an appropriately adapted modulus, ensure biocompatibility, and stimulate bone ingrowth into the (open) porosity [5]. Strength and design criteria have to be met as well. Magnesium foams could be used as biodegradable implants that serve as a load-bearing structure as long as the bone still grows but are gradually absorbed by the body in a later stage of recoalescence [4]. 7.2.3

Filtration and Separation

There are two types of filters: filters holding back and separating solid particles or fibers dispersed in a liquid (suspensions) or filters holding back solid or liquid particles dispersed in a gas (smoke or fog). Examples of the first type are filters for cleaning recycled polymer melts, for removing yeast from beer, or for contaminated oil. The second type includes filtration of diesel fumes or water removal in air lines. Important filter properties are fine filtration capacity, good particle retention, cleanability, mechanical properties, corrosion resistance, and cost. Some of the cellular metals described in this text possess a combination of properties not covered by the traditional PM materials and might therefore be considered as complementary to these, such as the materials described in Sections 2.1.2, 2.3 and 2.4. 7.2.4

Heat Exchangers and Cooling Machines

Highly conductive foams based on copper or aluminum can be used as heat exchangers [6]. In this case open-cell structures are needed such as those described in Sections 2.3 and 2.4. Heat can be removed from or added to gases or liquids by letting them flow through the foam and cooling or heating the foam at the same time. Owing to the open porosity, pressure drops can be minimized (see Fig. 7.2-2). An example of such an application is a compact heat sink for cooling, for example, in microelectronic devices with a high power dissipation density such as computer chips or power electronic components. Nowadays, fin-pin arrays are the standard solution in such cases. Metal foams or ordered cellular metals of the type shown Fig. 7.2-3 can perform better if they are selected so that thermal conductivity is kept as high as possible with their flow resistance maintained low. These two requirements are contradictory. Therefore, an optimization problem has to be solved [7,9,10]. The variables are the dimensions of the individual struts and their spacing in the example given. A denser arrangement of metal naturally gives rise to a better heat conduction but also increases pressure drop. The optimum determined is represented by a certain area in the plane of the diagram spanned by the heat dissipation and the pressure drop, both expressed as dimensionless quantities, in Fig. 7.2-3. Another application field for open-cellular materials is transpiration cooling. The high surface area, low flow resistivity, and good thermal conductivity of some of the materials used make them promising candidates for such purposes.

315

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Figure 7.2-2. Pressure drop in partially open-porous cellular solids of the type shown in the middle of Fig. 7.2-1 [8].

Figure 7.2-3. A diagram of an open-cell metal used as a heat dissipation medium for cooling high-power electronic components. Also shown is the tradeoff between pressure drop and heat flux, with the preferred material domain indicated [7].

7 Service Properties and Exploitability

7.2.5

Supports for Catalysts

The effectiveness of catalysis critically depends on a high interfacial surface area between the catalyst and the gases or liquids to be reacted. Therefore, the catalyst is either processed into a highly porous structure or, if this is not possible, applied to another porous system such as a porous ceramic material. Cellular metals could replace such ceramics even if they cannot compete with them on surface area because they exhibit other useful properties such as high ductility and thermal conductivity. One application concept includes the preparation of a thin sheet of corrosion-resistant metal foam, filling this foam with a slurry containing the catalytic substance, by rolling for example, and finally curing at elevated temperatures [11]. The resulting catalyst has good mechanical integrity: even after many temperature cycles the catalyst is not separated from the metal foam support. One application for such catalysts is for removing nitrogen oxides NOx from the exhaust fumes of power plants. 7.2.6

Storage and Transfer of Liquids

One of the oldest applications of porous PM materials is as self-lubricating bearings in which oil is stored in the interstices between particles and is allowed to flow slowly out, thus replacing the used oil. Of course, some of the cellular materials described in this book could fulfil the same function but with the advantage of having a higher storage volume than traditional PM parts. The application is not limited to oil: water can be kept and slowly released for automatic humidity control. Perfume can be stored and allowed to evaporate slowly. Porous rolls can hold and distribute water or adhesives to surfaces. Transport of the liquid can be driven by capillary action alone or by excess pressure in the roll. Finally, very open metallic structures can be used to store fluids at a constant and uniform temperature, for example, in cryogenic conditions. Moreover, the foam can reduce undesired movements of the liquid in partially filled tanks (ªanti-sloshingº) [10,12]. 7.2.7

Fluid Flow Control

Porous materials can be used for controlling the flow of liquids and gases [1]. It is known that PM flow restrictors are more reliable and accurate than conventional micrometering valves. Because so many degrees of ªopennessº of cellular metals are available, one could find tailored solutions for even more applications by appropriately selecting a cellular metal. Metal foams have already been used as flow straighteners in wind tunnels [12] or flow distributors in valves [13].

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7.2 Functional Applications Different types of silencers (approximate diameter of components is 10 cm).

Figure 7.2-4.

7.2.8

Silencers

Components for damping sound, pressure pulses, or mechanical vibrations are also common in industrial PM applications [1]. Materials with a certain degree of open porosity can be tailored to damp some frequencies selectively while they pass others. Sudden pressure changes occurring in compressors or pneumatic devices, for example, can be damped with porous sintered elements. Materials such as the investment cast foams described in Section 2.3 or the foams made by deposition (Section 2.4) could replace such traditional elements for reasons of cost and effectivity [13]. Figure 7.2-4 shows some silencers. The maximum diameter of the components shown is about 10 cm. 7.2.9

Spargers

Some applications require that a gas be introduced into a liquid homogeneously and at a constant rate. An example of such an application is the carbonation of beverages. This operation requires a porous part that creates sufficiently small gas bubbles and satisfies criteria such as corrosion, heat, or shock resistance. Porous metals can be a superior solution compared to other materials such as porous ceramics. 7.2.10

Battery Electrodes

Lead foams could serve as supports for the active material in lead acid batteries in replacement of conventional lead gratings, thus allowing for constructing very light electrodes [14]. The electrochemically active mass, a paste containing very fine lead oxide powders, could be filled into the open voids of a lead foam where it would contact the electrolyte (sulfuric acid). The lead foam acts as a highly conductive lattice leading to a low internal resistance of the battery. The nickel

7 Service Properties and Exploitability

foams described in Section 2.4 are already used as electrodes in pasted rechargeable NiCd or NiMeH batteries where weight savings and a higher energy density can be achieved [15 17]. Porous PM materials with their extremely high surface area are being used in fuel cells [1,15]. 7.2.11

Electrochemical Applications

Nickel foams can be used as electrode material in electrochemical reactors. In filter-press electrodes, for example, a stack of isolated metal plates is used. The plates are separated by a turbulence-promoting plastic mesh and insulating membranes. If these meshes are replaced by sheets of cellular nickel with open channels (with each sheet attached to one of these plates), one increases the electrode surface while maintaining the turbulence promotion [18]. The reactors can be built more compactly this way. Nickel foams can also be used to improve electrocatalytic processes such as the electrooxidation of benzyl alcohol assisted by NiOOH, which is electrogenerated on nickel anodes. Packed beds of nickel foams were shown to improve the performance of such reactors [19]. 7.2.12

Flame Arresters

Cellular metals with high thermal conductivities of the cell-wall material can be used to stop flame propagation in combustible gases. Open-cell foams of the type described in Section 2.4 have been shown to be capable of arresting flames even when they were travelling at velocities up to 550 m/s. In practice, long runs of pipes transporting combustible gases are protected close to possible sources of ignition so that, if ignition does occur, the flame cannot accelerate to high velocities [13]. 7.2.13

Water Purification

Cellular metallic materials could be used to reduce the concentration of undesired ions dissolved in water. In this application the contaminated water flows through a highly porous cellular metal with an open structure. The ions react with the matrix metal of the cellular structure in a redox reaction. An electroless reduction of Cr(VI) ions by cast aluminum foams has been investigated [20] 7.2.14

Acoustic Control

A sound-wave control device can be obtained if one creates a lens- or prism-shaped part from a rigid open-cell material, such as a metal foam. The sound waves will then be guided and redirected by this acoustic device [21]. Moreover, closed-cell

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7.3 Machinery Applications

foams have been studied for their suitability as impedance adapters for ultrasound sources. Noise reduction functions are described in Section 5.3.

References

1. M. Eisenmann, in Metal Powder Technologies and Applications, ASM Handbook Vol. 7, ASM International, Materials Park, OH 1998, p. 1031 1042. 2. P. Neumann, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 167 170. 3. W. R. Johnson, M. Shenuski, Machine Design 1987, Jan, 89 91. 4. W. U. Bende, Guo Fuhe, Advances in Powder Metallurgy and Particulate Materials, Vol. 6, J. M. Capus, R. M. German (eds), Metal Powder Industries Federation, Princeton, NJ 1992, p. 145. 5. K. R. Wheeler, M. T. Karagianes, K. R. Sump, in Titanium Alloys in Surgical Implants, H. A. Luckey, F. Kubli (eds), ASTM, Philadelphia 1983, p. 241 254. 6. W. Frischmann, European Patent Application EP 0 666 129, 1995. 7. A. G. Evans, J. W. Hutchinson, M. F. Ashby, Prog. Mater. Sci. 1998, 43, 171 221. 8. J. Banhart, Aluminium 1999, 75, 1094 1099. 9. T. J. Lu, H. A. Stone, M. F. Ashby, Acta. Mater. 1998, 46, 3619 3635. 10. M. F. Ashby, A. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley,

Metal Foams: A Design Guide, ButterworthHeinemann, Oxford 2000. 11. H. Swars, German Patent Application 36 19 360, 1987. 12. ERG Inc., Oakland, USA, Product information of ªDuocelº 1996, and http://www.ergaerospace.com 13. SEAC International BV, Krimpen, Netherlands, Product data sheet of ªRecematº 1998, and http://www.seac.nl 14. J. Banhart, German Patent Application 100 15 409, 2000. 15. Inco Ltd., Canada, Product data sheet of ªIncofoamº 1998 and http://www.inco.com 16. V. Ettel, in Proc. NiCad `98, Prague 21 22 Sept 1998. 17. I. Matsumoto, T. Iwaki, N. Yanagihara, US Patent 4 251 603, 1981. 18. A. Montillet, J. Comiti, J. Legrand, J. Appl. Electrochem. 1993, 23, 1045 1050. 19. P. Cognet, J. Berlan, G. Lacoste, P.-L. Fabre, J.-M. Jud, J. Appl. Electrochem. 1996, 26, 631 637. 20. J. G. Ibanez, A. Fresan, A. Fregoso, K. Rajeshwar, S. Basak, Proc. Electrochem. Soc. 1995, 12, 102 108. 21. K. Iida, K. Mizuno, K. Kondo, US Patent 4 726 444, 1988.

7.3

Machinery Applications

Th. Hipke and R. Neugebauer

Cellular metals have existed as particularly innovative new materials for several years [1 3]. Since the development of foaming technology, a number of prototypes for use in the car and machine tool industries have been demonstrated [4 6]. This Section describes possible applications of foamed metals in mechanical engineering.

7 Service Properties and Exploitability

7.3.1

Parameters

For applications in mechanical engineering, design engineers need the necessary information to enable them to dimension cellular components. These design parameters are required for composites such as sandwich panels, foamed profiles, or special combinations of foamed and solid materials, as well as for components completely made of foamed metal. We describe two examples in which powdercompacted foamed aluminum was used.

Thermal Behavior To evaluate the thermal characteristics of metal foams, the response of sandwich sheets with a foamed aluminum core to thermal impacts was investigated. The sheets (400 mm q 300 mm) were clamped on one side and warmed by a heating mat placed on the top cover plate. The room temperature was kept constant at 20 hC by a thermal cell. The sheet temperature was recorded by two probes, one attached to each of the bottom and top plates. The thermal expansion was recorded by path sensors and was transformed into the resulting linear expansion coefficient. The expansion coefficients of foamed sheets covered with aluminum range from 0.020 to 0.024 mm/K mm. These values are slightly higher than those of the AlSi12 alloy (0.0199 to 0.0206 mm/K mm) that had been foamed. The face plate expansion coefficient is 0.0235 mm/K mm, so the cover plates dominantly influence the total expansion. The lower expansion coefficient of steel (0.012 mm/K mm) also diminishes the resulting strain on the sandwich sheet (see Fig. 7.3-1). The expansion coefficients of the plates covered by steel sheet range from 0.0105 to 0.014 mm/K mm. 7.3.1.1

Coefficient of thermal expansion [µm/(K*mm)]

0,030 0,025

x-direction z-direction

0,020 0,015 0,010 0,005 0,000 Alu 1 mm

Alu 2 mm

Steel 1 mm

Steel 2 mm

Expansion coefficients as a function of cover plate material and plate thickness for a two-face sandwich (density 0.65 g/cm3; sandwich 25 mm).

Figure 7.3-1.

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7.3 Machinery Applications

Pull-Out Strength of Detachable Joints Foamed parts have to be joined to other components and assemblies. One essential fastening is the screwed joint. A study carried out at the Fraunhofer Institute for Machine Tools and Forming Technology (IWU Chemnitz) determined the tensile load limits of such a joint. The failure behavior depends on the type of joint. For adhesive joints, there is a huge growth in force. The slope of the curve reflects the elasticity of all the integrated components such as the tensile testing machine, the tongs, the connection element, and the foam strip. For high-density foams, the joint pulls out after the adhesive bond has failed, but for lower-density foams the foam structure gives way. For screwed elements, the force-path progression includes a wide range of plastic deformation before the maximal force is achieved. These connections also pull out in several steps, each interrupted by the interlocking of cell walls. It was shown that in some cases very high forces can be transmitted. The foams vary widely in their ability to transmit large forces at a screwed joint. Figure 7.3-2 shows that screwed joints have a smaller load carrying capacity than glued and fastened joints. At a metal foam density of 0.7 g/cm3, which is relatively low, the pores are quiet big and with partially open cell walls, so that the adhesive fills the entire environment of the joint. Thus, an entirely new material is created locally, which has a large surface area so the applied force can be well distributed. The advantages of the adhesively bonded joints are not apparent at higher foam densities. With high-density foam the adhesive cannot flow through the material into the pore structure because the cell structure collapsed on drilling. In this foam the screwed fastenings intersect enough material to make a loadable thread 7.3.1.2

Sheet metal screw, screwed Wood screw, screwed Recoil, screwed Hexagon screw, screwed Hexagon screw, glued Hexagonal nut, glued Knurled nut, glued Sonic Lok 862, glued Sonic Lok 860, glued Sonic Lok 853, glued Sonic Lok 855, glued Ensat 302, glued

Figure 7.3-2.

0.7 g/cm3).

Maximal forces for different connecting elements (diameter M6, Al foam density

7 Service Properties and Exploitability

shape. The joint length with the screws was always 20 mm, but the nuts and inserts had a joint length that ranges between 6 and 20 mm. 7.3.2

Examples of Application Foamed Steel Pipes To make stiff, light structures hollow profiles of various shapes and dimensions are often used. To make such hollow sections very stiff, very large cross sections are required, but then the walls tend to oscillate. Filling hollow sections, or pipes, with metal foam is one possible way of influencing frequency and damping vibrations. The following pipe profiles were used, being rectangular steel pipes of various cross sections and lengths, with different wall thicknesses: Height q Width q Wall thickness 160 q 80 q 4 mm length: 2000 mm 160 q 80 q 3 mm length: 1000 mm 160 q 80 q 4 mm length: 1000 mm 160 q 80 q 5 mm length: 1000 mm 120 q 60 q 4 mm length: 1000 mm 80 q 40 q 4 mm length: 1000 mm The purpose of these investigations was to find out about damping as a result of foaming of pipe profiles with aluminum. The influence of the foams on the frequency spectrum can also be clarified. The investigation was performed to find out how far the natural frequencies are shifted by foaming, and to determine the dominant frequency and the sequence of the natural frequencies. For the design engineer, it is important to know whether the first natural frequency causes a locally limited transverse vibration or a bending vibration of the entire structure. Reference values were determined by finite element (FE) analysis and measured on the hollow profiles. To minimize the influence of the fixture, at the nodal points (the Bessel points), the pipes were laid on two thin wires (see Fig. 7.3-3). This installation is more advantageous than a one-end fixture. Vibrations were excited by hitting the pipe on a free end using an impulse hammer. The attenuation of the freely damped vibration was recorded by an accelera7.3.2.1

Figure 7.3-3.

Sketch of the beam for vibration studies.

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7.3 Machinery Applications

tion sensor. From this curve, we obtain the logarithmic damping decrement and consequently damping, D ! ^1 1 X (1) D ˆ ln ^z 2p(z s 1) X Natural Frequencies and Characteristic Types The simulation runs showed that the frequency spectrum depends on all three pipe geometry variables: cross section, length, and wall thickness. Consequently, the first natural frequency of long pipes is not necessarily lower than for shorter pipes. Assuming identical cross sections, pipes with thin walls are characterized by lower natural frequencies (see Table 7.3-1). The first natural frequencies are mostly bending vibrations in the x direction, which is the direction of minimum area moment of inertia. In two pipes, the first frequency is a local vibration of the pipe wall. This only occurs if the wall is very thin or if the wall-thickness to cross-section ratio is small. Such wall vibrations are almost excluded by the metal foam, since the transverse motions are hardly hindered. For that reason, these frequencies are shifted towards higher values (Table 7.3-2). For bending vibrations, frequency can only be improved if the stiffness grows more than the weight due to foam filling, but this cannot be achieved for thick-walled pipes. As shown, the first bending frequency for the hollow pipe appears as the 5th frequency only. For the foam-filled pipe, wall vibration can totally be avoided and only appears in conjunction with bending vibrations of the entire pipe at higher frequencies. The frequencies determined experimentally were in good agreement with the simulation values, which is crucial for damping measurement. If the measured

Table 7.3-1 Natural frequencies of hollow profiles and foam-filled profiles. Vibration type: W ˆ local oscillation of pipe walls; X ˆ oscillation in x direction (direction of minimum area moment of inertia).

Pipe type Cross-section [mm]

Length [mm]

Hollow profile First natural frequency [Hz]

Characteristic type

Foam filled First natural frequenzy [Hz]

Characteristic type

160 q 80 q 4

2000

151.3

X

134.4

X

160 q 80 q 3

1000

324.9

W

493.4

X

160 q 80 q 4

1000

432.7

W

506.3

X

160 q 80 q 5

1000

531.2

X

513.8

X

120 q 60 q 4

1000

430.4

X

397.1

X

80 q 40 q 4

1000

290.8

X

271.9

X

7 Service Properties and Exploitability Frequencies and characteristic types in comparison: pipe 160 q 80 q 3, length 1000, foam-filled/hollow.

Table 7.3-2.

Frequency no.

Hollow profile

Foam filled

Frequency [Hz]

Characteristic type

Frequency [Hz]

Characteristic type

1

325.0

Walls oscillate

493.4

First bending in x

2

369.6

Walls oscillate

805.7

First bending in y

3

459.2

Walls oscillate

1135.0

First torsion

4

476.6

Walls oscillate

1222.5

Second bending in x

5

479.0

First bending in x

1879.5

Second bending in y

6

530.8

Walls oscillate

2102.5

Second bending in x whereby the walls are slightly buckled

damping values are to be integrated into the simulation runs, it is of particular importance that the calculated and the measured values coincide. This is the only way making sure that the measured damping values can be used for the calculation of component dimensions Damping of Structure Damping was determined at the same time as the frequency was measured. Contrarily to expectations, the location of the supports did not influence the frequency and the damping parameters. This is because, in a dynamic understanding, the ropes used are soft. So the ropes would only influence a much lower frequency range than that investigated here. Having kept all the other conditions constant, even the scanning rate was without any obvious influence: when comparing scanning procedures at 2.5 and 1.25 kHz, the difference between both damping values was merely 0.46 %. The evaluation showed that the damping factor was slightly higher for the first vibrations than for more attenuated vibrations. In one experiment, damping between peak 200 and 700 was D ˆ 0.66 q 10 5, and between 1000 and 1500, it was D ˆ 0.64 q 10 5. This effect is caused by the higher damping influence of the surrounding air for high amplitudes. To minimize this influence of about 3 %, the evaluation range was selected as widely as possible. In the follow-up investigation of pipes, the damping values shown in Fig. 7.3-4 were determined for the corresponding frequencies. In the investigation, the dependency of damping on the pipe cross sections or the wall thickness could not be recognized. Instead the damping values are related to the natural frequency. It makes sense to compare the damping of equal pipe frequencies before and after foaming.

325

326

7.3 Machinery Applications

Growth of damping [%]

800 700 Tube 1

600

Tube 2

500 400 300 200 100 0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Test no. Figure 7.3-4.

Damping growth of the individual pipes (at 300 % change in mechanics assumed).

The increase in damping by foaming varied: the mean change ranged from 133 to 645 %, or 799 % for actual, rather than mean, values. Figure 7.3-4 shows that the majority of measured values are located below 300 % (see line); few values lie above, but these are notable. We suppose that the damping mechanisms that acted in both types of pipes (above and below the 300 % line) are different. For the types below the line, material damping is the active mechanism, assuming that the foamed cores and the steel pipes do not move relative to each other, thereby excluding any frictional or joint damping. These conditions are obtained for an optimal foaming procedure with clean steel pipes, so a direct metal connection between the steel pipe and the foam core is brought about, without any gap that would permit a relative motion. If the steel pipes are slightly rusty, then metal-to-metal contact between the pipe and the foam core may be incomplete, and some frictional damping may then occur. Frictional damping depends on many factors such as pressure, surface roughness, the medium in the gap, and others. In pipes lying above the 300 % limit, a combination of material and frictional vibration can be assumed. We cut sample sections from the foamed pipes, which confirmed that in some there was good metal-to-metal contact and in others there was a visible gap between the foam and the pipe wall. It is too simple to classify the foamed pipes into ªgoodº and ªpoorº categories, but the following statements can be postulated. x

x

For foam-filled pipes in which the foam adheres to the inner steel wall in an optimum manner, damping is increased by up to 300 % in comparison with hollow pipes. Damping beyond this limit suggests that the foam has not been completely bonded. This phenomenon could be used as the basis of a nondestructive quality inspection of the foaming process.

7 Service Properties and Exploitability

Comparing the measured damping values with those taken from literature, we note that a damping for steel of D ˆ 3.7 q 10 4 [7] is in the range of our steel pipes. The values for metal foam range from D ˆ 9 q 10 4 to 2.1 q 10 3 and are clearly higher than those of steel. Taking both materials together, a higher total damping should be provided. However, a direct comparison is not possible, since damping does not only depend on the material and load, but also the shape of the specimen [8]. For that reason, the damping measured on a workpiece is sometimes defined as the workpiece vibration instead of the material vibration.

Machine Table On the occasion of the CPK `98 conference, the first functioning assembly filled with metal foam was demonstrated. The part size was 800 mm q 720 mm q 250 mm, so it can be justifiably called an assembly relevant for practice. A conventional machine table (Fig. 7.3-5) on the linear motor test bench of the IWU in Chemnitz was replaced a steel framework filled with aluminum foam, optimized by FE analysis. The static and dynamic properties of the conventional assembly, the steel framework, and the foam-filled framework were measured (Fig. 7.3-6). The main goal was to reduce weight whilst maintaining stiffness and strength. The weight of the foamed structure was 72 % of the conventional table (Fig. 7.3-7), but deflection only decreased by 19 %. These results were obtained by increasing the table thickness and having a higher area moment of inertia. The static behavior of the foamed table is much better than the hollow steel frame, because of the improved stiffness and hence minimal deflection (Fig. 7.3-8). 7.3.2.2

Original design of machining table made of steel.

Figure 7.3-5.

Design of hollow steel profile to be filled with Al-foam (800 mm q 720 mm q 250 mm).

Figure 7.3-6.

327

7.3 Machinery Applications 500

Figure 7.3-7.

Comparison of weights.

Figure 7.3-8.

Comparison of maximum

Figure 7.3-9.

Frequencies of the first charac-

Mass [kg]

400 Solid table

300

Stell frame 200

Foamed table

100 0

Deflection [µm]

25 20 15

Solid table Steel frame

10

Foamed table

5

deflection.

Natural frequency [Hz]

0 600 500 400

Solid table

300

Steel frame

200

Foamed table

100

teristic type.

0

Very good results were obtained for dynamic parameters: the first natural frequency was increased by 80 % (Fig. 7.3-9), which is mostly due to wall vibrations being almost eliminated by the foam. Such vibrations can only be detected at very high frequencies. The damping was multiply increased for the foamed version: for the first natural bending frequency, a 10 times improvement was achieved (Fig. 7.3-10). Increased damping arises from the material damping of the metal foam and from the properties of the adhesive that bonds the steel and the foamed parts. This result is of special interest for applying the technique in mechanical engineering. In present machine tools, assemblies move with enormous accelerations. To meet the increased demands for manufacturing accuracy, surface quality, and tool life, the vibrations resulting from deceleration, acceleration, and the manufacturing process, have to be damped in an efficient manner. 2 Damping [%]

328

1,5 Solid table 1 0,5 0

Steel frame Foamed table

Figure 7.3-10.

frequency.

Damping of the first natural

7 Service Properties and Exploitability

Cross-Slide As a second example, the cross-slide of a high-speed milling machine constructed from steel and foamed aluminum is shown after fabrication (Fig. 7.3-11). The cross-slide represents the connecting element between the z slide spindle and the machine bed. Obvious improvements compared with conventional castings can be anticipated from simulations (Fig. 7.3-12). Thus, weight is reduced by 46 %. The deformation deteriorated by 12 %. This worsening could be fully compensated by increasing the wall thickness. Even then, an evident mass reduction would remain. Nevertheless, the first natural frequency is increasing by 35 % in any case, which means a clear enhancement in the field of mechanical engineering. Apart from this, the position of the natural frequencies can be selected by varying the foam density. 7.3.2.3

Figure 7.3-11.

Cross-slide of a high-speed milling machine.

140

Change [%]

120 100 80 60 40 20

112

135

54

0 Mass Figure 7.3-12.

Total deformation

1. natural frequency

Comparison of variants: original design (light) and foamed construction (dark).

329

330

7.4 Prototypes by Powder Compact Foaming

7.3.3

Conclusions

Metal foams are characterized by very useful physical and mechanical characteristics. Examples from mechanical engineering show some beneficial properties of hollow components and sandwiches when filled the metal foam material and how to make use of them in innovative products.

References

1. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, Pergamon Press, Oxford 1997. 2. J. Baumeister, ªÛberblick: Verfahren zur Herstellung von MetallschaÈumenº in Proc. MetallschaÈume, J. Banhart (ed.), MIT, Bremen 1997, p. 3. 3. Alulight ein neuer Werkstoff aus Aluminiumschaum, Mepura Prospectus, Metallpulvergesellschaft mbH, Ranshofen, Austria 1995. 4. T. Hipke, ªMaschinentisch in Leichtbauweiseº in Jahresbericht des Fraunhofer-Institutes fuÈr Werkzeugmaschinen und Umformtechnik 1998, 1998, p. 56.

5. H.-W. Seeliger, ªApplication strategies for aluminium-foam-sandwich parts (AFS)º in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 29 6. R. Neugebauer, C. Harzbecker, T. Hipke, ªLeichtbaustrukturen im Werkzeugmaschinenbauº in Proc. Werkzeugmaschinenkolloquium 2000, Bern, CH 21 Nov 2000. 7. M. Weck, Werkzeugmaschinen und Fertigungssysteme, Vol. 2, Konstruktion und Berechnung, 4th edn, VDI, DuÈsseldorf 1991, p. 3 8. F. Holzweiûig, H. Dresig, Lehrbuch der Maschinendynamik, 3rd edn, Fachbuchverlag, Leipzig-KoÈln, 1992, p. 52, p. 286.

7.4

Prototypes by Powder Compact Foaming

R. Kretz

When metallic foams were revived by new manufacturing technologies such as powder metallurgy, investment casting, and other processes in the early nineties, the new material was introduced to the industry and to potential customers in a very enthusiastic manner and with great advertising expense. Information was widely spread by companies and institutes who worked on the development of metallic foams. Metallic foams became highlights at industrial fairs and at many conferences researchers, designers, and materials engineers discussed the structures and the properties of cellular metals that are relevant to industrial application. The foam developers missed no chance to present their work and to introduce their new product,

7 Service Properties and Exploitability

although the first material samples were only demonstrators: they were small, had very irregular pore sizes and pore distributions, and a high degree of scattering in their properties. They were all ªhand madeº and their producers were very proud of their creations from porous metals. With the growing knowledge and experience, manufacturing methods were further improved and very soon the presented foams were of a respectable quality with a certain reproducibility. Whenever people held the new material in their hands, they were impressed and almost everybody had a new idea concerning an application of metal foams. 7.4.1

Introduction

But very soon the discussion came round to real parts or components and then the foam manufacturers had to think about manufacturing net-shape parts, considering particular problems of geometry or function. Since real net-shape parts are not flat plates, cubes, or cylinders, new manufacturing methods using mold and furnace technologies had to be introduced. The manufacturing of the powder metallurgical (PM) precursor material as well as the foaming technique for the compacted powder are called the powder compact foaming technique (PCF), which is practiced by IFAM, Bremen, Germany, Leichtmetallkompetenzzentrum, Ranshofen (LKR), Austria, and the Slovak Academy of Science (SAS), Bratislava, Slova-

Figure 7.4 -1. Crucible melting furnaces.

331

332

7.4 Prototypes by Powder Compact Foaming

Figure 7.4 -2.

Simple foam parts.

kia. The manufacturing of prototypes for component testing or demonstration is described in the following pages by examples from a bilateral research project at LKR. Step-by-step prototype manufacturing methods were developed, starting with the foaming of parts in crucible melting furnaces (Fig. 7.4-1) and the use of steel molds. The geometry of the first aluminum-foam parts was rather simple, as shown in Fig. 7.4-2. 7.4.2

Methods, Machines, and Molds

From the very beginning the application of the PCF route for making net-shape parts was the goal. This method, using compacted aluminum powder and titanium hydride as a foaming agent, is described by several authors [1,2].

7 Service Properties and Exploitability

Manufacturing Methods for Precursor Material The first step in the PM process is to make foamable precursor material from aluminum powder. Small amounts of aluminum powder (50 kg) were mixed by mechanical stirring, then poured into aluminum liners, then closed and extruded by a conventional aluminum extrusion machine. This method was easily performed using existing facilities and an extrusion plant at AMAG in Ranshofen. However, the bulky liner material in some cases caused insufficient foaming. An alternative route for producing precursor material for PCF is the Conform process (Section 2.1.1.1) [3]. Small amounts of precursor material made in this way were supplied by Holton Ltd. and trials showed that the Conform route could be a suitable manufacturing method for strip like dimensions of precursor material. Generally, the small batches of manufactured aluminum-foam prototype parts made in this stage of development led to a large scatter in the foam properties. The reproducibility of the whole process and the properties of the components were relatively poor. This was due to the handwork involved in producing the parts, which typically resulted in varying process parameters. However, samples with uniform pore sizes and good pore distribution could be achieved. These undesired property variation could only prevented by a ªseries production likeº manufacturing route of the precursor material. With growing demand for precursor material and with an increasing volume of foamed prototypes the process flow and the quality of the prototypes could be improved by an approach to series production conditions. The batch sizes reached 1000 kg and more. Industrial partners, such as Metallwerk Plansee, Tyrol and Peak, Germany carried out the cold isostatic pressing (CIP) process, and three staff members performed the prototype manufacturing. Although this process led to good results, the economic disadvantages were the high transportation costs and varying process parameters caused at different process steps in different companies. A further improvement in process flow was achieved following the installation of a CIP machine, so that all steps from the powder production to the production of extrusion billets were achieved within one company. From this day on the powder was mixed with the foaming agent in an industrial scale impulse mixer and compacted in a special CIP. Then it was transferred to an aluminum extrusion machine to produce the precursor material by this ªconventionalº extrusion route. The process steps as it is currently performed in PCF are: 7.4.2.1

x x x x x x

x

manufacturing of Al powder (alloyed or unalloyed) and grain size classification, mixing Al powder with foaming agent (TiH2), CIP of the mixture to form foamable extrusion billets, heating and extrusion of the billets to form precursor material, filling the precursor in steel or cast-iron molds, foaming in a suitable foaming furnace (heating rate, temperature above solidus), and cooling and removal of the foamed parts from the mold.

333

334

7.4 Prototypes by Powder Compact Foaming

Foaming Process For successful manufacturing of aluminum-foam parts in the PCF, it is necessary to observe furnace temperature, heating rate, temperature distribution within the mold, foaming time, and cooling conditions that have to be kept in certain ranges to achieve aluminum-foam components of high quality. These parameters are not the same for all types of component; they depend on their geometry and dimensions (wall thickness), on the alloy, and also on the properties and design of the mold. In prototype manufacturing it is not possible to modify the whole equipment or to change the layout of machines whenever a new component with a new geometry has to be foamed. Compromises concerning the furnace used and the process parameters must be made to enable the best possible technical and economic manufacturing conditions to be achieved. Nevertheless, it is possible to make parts in a wide range of different geometries with the use of adequate equipment. From the beginning of aluminum-foam development, prototype manufacturing was the main goal. This policy led to a large number of prototype projects producing components with very different geometries and applications. The development of the foaming process, applied to a particular component, was carried out along with component testing to verify material properties. In series production it would be necessary to adapt the furnace and the mold to the product to achieve the optimized foaming parameters as well as the most economic production conditions for the particular product. The number of parts that has to be produced is also an important process parameter to be considered in the design of an aluminum-foam production machine and the necessary additional equipment. 7.4.2.2

Foaming Furnaces One of the most important pieces of equipment in the aluminum-foam manufacturing route is the foaming furnace. The foaming parameters have to be kept in their optimized range, the precursor material in the mold has to be heated to the foaming temperature in the foreseen time, and the temperature distribution within the mold must be kept within small tolerances to avoid irregular foaming within the mold. The heat transfer from the furnace to the mold with the precursor material can occur by three different mechanisms: conduction, convection, and radiation. For the development of prototype manufacturing methods various furnaces working with these three physical principles were tested. Basic calculations concerning heat capacity and heat transfer were carried out before testing the different furnace systems. The heating rate in the foamable precursor material is the key parameter, influenced by the foam part dimensions and foaming mold properties. Considering the described intentions, the very first trials to make simple foam parts were performed by immersion of the mold into an aluminum melt. To achieve a high heating rate by intensive heat transfer by conduction, the molds containing the precursor material were submerged into liquid aluminum that was kept in a conventional holding furnace. The conductive heat transfer was 7.4.2.3

7 Service Properties and Exploitability

very high and a uniform temperature distribution could be achieved. This method worked quite well and the aluminum-foam samples yielded good properties, but chemical attack of the molds by the Al melt caused short lifetimes of the molds and the mold attachments. Furthermore, the handling of the molds in liquid aluminum is dangerous and problematic. High-convection furnaces (air-circulating furnaces) are used in industry for rapid heating processes. A ventilator in the furnace effects very high heat transfer from the heat source to the mold. The rapid heat transfer, caused by high flow velocity, causes high heating rates, but the gas flow is influenced by the geometry of the mold and that leads to uneven temperature distribution within the mold. This effect can be avoided by the installation of baffle plates, which must be adapted for every new mold that is used in the furnace. Therefore air-circulating furnaces can be employed in series production, where high numbers of aluminum-foam parts have to be made with the same mold geometry, but they are not suitable for prototype manufacturing, where flexible and universal furnace systems are required. For prototype manufacturing it is essential to cover a wide range of different components. For this purpose a special chamber furnace with adequate heating capacity had to be developed. One example of a foaming furnace especially built for foaming of big components, is the 100 kW Nabertherm Chamber furnace at LKR,

Figure 7.4 -3.

Nabertherm aluminum-foam chamber furnace.

335

336

7.4 Prototypes by Powder Compact Foaming

having internal dimensions 900 mm q 900 mm q 1800 mm and a modified control unit to keep the required temperature distribution tolerances within the chamber. This furnace is shown in Fig. 7.4-3.

Foaming Molds In the PCF process the mold giving the aluminum-foam part its shape contains the foamable precursor material during the heating cycle. The thermal energy that is necessary to start the foaming of the precursor material has to be transmitted through the mold. Consequently the thermal conductivity of the mold should be as high as possible and the thermal capacity of the mold as low as possible. On the other hand the molds must be stable enough to keep the required dimensional tolerances of the net-shape foam part. The first molds for the PCF process were made from common steel sheets. The very first aluminum-foam parts were very simple, regular shaped pieces such as small plates, cubes, or cylinders and the development was focussed mainly on the foaming behavior of the precursor material and the production of test samples. But when customers required 3D net-shape prototypes, the mold became an important part of the prototype development. The experience of foundry die makers was combined with the experience in foaming precursor material. Conventional casting dies are very heavy and bulky. A lot of energy is wasted on heating the whole die during the foaming process. The precursor material would not be heated fast enough to achieve sound foam components. An economic route is to use cast iron, which allows casting of thin walled foaming dies, using wood or plastic patterns as well as the lost foam casting process. Depending on the molding sand used, the surface in the die may require machining. 7.4.2.4

Table 7.4 -1.

Comparison of various mold materials.

Mould material

Advantages

Disadvantages

Steel 5 10 mm thick

‡ easy machining ‡ low material costs ‡ heat conductivity

mold lifetime distortion

Cast iron

‡ heat conductivity ‡ free-form shapes

high material costs high production costs mold lifetime

High-temperature tool steel

‡ mould lifetime ‡ low distortion

high material costs

Copper

‡‡ heat conductivity

high material costs chemical reactions

Ceramics

‡ shapeability ‡ free-form shapes ‡ no distortion

heat conductivity mold lifetime

7 Service Properties and Exploitability

This method was used for foaming car structural parts, the largest prototypes so far manufactured in net shape. Besides structural steel and cast iron, high-temperature tool steel, copper, and ceramics were also used as mold materials in a large number of prototype development projects. Table 7.4-1 shows an overview of different mold materials and their properties. To avoid sticking of the aluminum-foam product in the molds, the cavity of the die was coated with common facing materials. 7.4.3

Prototypes and their Applications

It is a long way from the first idea to the first prototype, and it is even further from the prototype to a series product. Some of the product ideas had to be rejected because the aluminum-foam properties were over-estimated. The outstanding me-

Figure 7.4-4.

Aluminum-foam prototypes.

337

338

7.4 Prototypes by Powder Compact Foaming

chanical properties of closed-cell metal foams are their energy absorbing potential and specific stiffness. Figure 7.4-4 shows a couple of aluminum-foam samples made for testing mechanical and technological properties of the material. The feasible applications are spread in a wide range of various industrial fields. The automotive and transportation industries are interested in metallic foams as well as mechanical engineering, architecture, and building construction companies.

Automotive Applications Owing to their particular properties, metal foams are considered to be an appropriate material for impact-energy absorbing components. Depending on foam type (PCF or melt-based foam), alloy, and density, the energy absorbing behavior can be influenced within a certain range. This property makes metal foams a candidate 7.4.3.1

Figure 7.4 -5.

types.

Figure 7.4 -6.

A-column absorbing element.

Energy-absorbing proto-

7 Service Properties and Exploitability

material for crash-relevant components in cars as well as in trucks, trains, and tramways. Specific stiffness is also an important property in automotive applications. The energy-absorbing behavior is described in many papers and presentations [4 6]. Manufacturing of aluminum-foam prototypes at LKR included a couple of crashrelevant components that were tested either as specimens or as real components. The crash elements can be made of aluminum foam only, or in combination with other materials such as steel tubing or aluminum castings. Figure 7.4-5 shows a steel tube specimen [7] after performing a compression test to investigate its energy-absorbing behavior. A component testing project was carried out with the Austrian car manufacturer Steyr Daimler Puch [8]. After the original absorbing element in the A-column was replaced by an aluminum-foam absorbing element, the A-column cover was mounted and head impact tests were performed. Figure 7.4-6 shows the A-column absorbing component.

Figure 7.4 -7.

parts.

Structural

339

340

7.4 Prototypes by Powder Compact Foaming

Figure 7.4 -8.

Aluminum-foam front panel

High specific structural parts such as intermediate panels or front panels are feasible applications. Figure 7.4-7 shows a couple of structural part prototypes including an intermediate panel [9] that was made for DaimlerChrysler in 1995. The largest aluminum-foam prototype part made by LKR was a front panel that was foamed by order of Opel in 1999. The dimensions of this panel, shown in Fig. 7.4-8, are about 140 cm q 50 cm; it is a net-shape foamed in a cast-iron mold [10].

Construction and Architecture In constructional and architectural applications, aluminum foams can be applied as panels for fireproof doors and walls, light and stiff covers of installations, technical equipment, and other attachments. Architects seem to approve of the appearance of the as-cast aluminum-foam skin. Plate prototype manufacturing is very different from the production of complex shaped aluminum-foam parts. In most cases, it is difficult to fulfill the required thickness tolerances of the plates. Special furnace designs and mold materials have been developed at SAS. For all outdoor applications they must be protected against moisture penetration and corrosion, which can easily be achieved using common surface treatment processes such as painting or powder coating. Figure 7.4-9 shows surface-treated aluminumfoam plates. 7.4.3.2

Other Technical Applications Two additional groups of feasible systems have a good chance of realization in the future: aluminum sandwich sheets, consisting of aluminum-foam plates, covered with high strength aluminum face sheets, and aluminum-foam cores in aluminum or magnesium castings. 7.4.3.3

7 Service Properties and Exploitability

Figure 7.4 -9.

Surface treated foam plates.

Up until now sandwich sheets have had to be made in two process steps. A foam plate is made and the face sheets are applied by adhesives. Manufacturing of sandwich parts and foam filled aluminum profiles by forming the foam between two aluminum sheets is reported in Section 3.3. Aluminum-foam filled steel profiles can also be used as energy absorbing components in cars, trucks, trains, and other vehicles. Manufacturing of these profiles is relatively easy because the steel profile can be used as a foaming mold. In Fig. 7.4-10 a couple of foam-filled profiles and sandwich specimens are shown. Aluminum or magnesium castings with permanent aluminum-foam cores should meet the requirements of improved energy absorbing potential, higher stiffness than hollow castings and good vibration damping behavior. The use of foam cores can also improve the manufacturing process in a number of ways: no sand cores have to be removed from the casting, complicated quasi-hollow shapes can be cast, and improved solidification conditions can be achieved. Target applications for castings with foam cores, as shown in Fig. 7.4-11, are suspension and struc-

341

342

7.4 Prototypes by Powder Compact Foaming

Figure 7.4 -10. Foam-filled profiles and sandwich parts.

Table 7.4 -2.

Feasible aluminum-foam applications.

Aluminum foam prototype part

Application field/Customer

Focus/property

Plates

construction, architecture furniture industry street furniture

weight, design

Cylinders, cubes

car component suppliers

impact energy absorption

Tube

physical research (DESY)

physical properties: conductivity, permeability

Foam cores, cubes, ring

foundries, cores in castings

casting conditions, damping behavior, weight, energy absorption,

7 Service Properties and Exploitability Table 7.4-2.

Continues

Aluminum foam prototype part

Application field/Customer

Focus/property

Compact structural parts

automotive industry, electrical appliance camera casings

stiffness, damping, weight

Structural parts

intermediate panels, automotive structures (DaimlerChrysler, Opel)

Stiffness, damping behavior

Structural parts

automotive structures sunroofs

Stiffness, weight

Structural parts

ships, boats, yachts

weight

Sandwich structures

transportation, rail vehicles

stiffness

Compact structural parts

weapons, stock

weight

Foam-filled profiles

engine mount (CRFiat) structural car components, rail vehicles, aircraft, windmills,

crash behavior

Foam-filled profiles

machine tool (IWU) robot brackets building industry

damping properties

Compact structural parts

objects of art, design

optical appearance

3-dimensional parts

sculptures, art

optical appearance

tural parts with improved energy absorbing properties, and wheels. Also mechanical engineering components with good damping behavior and good castability [11]. In addition to the applications already described a large variety of other potential technical applications of aluminum foam have been discussed. Table 7.4-2 contains an overview of feasible aluminum-foam applications.

Improbable Applications As mentioned earlier, many of the possible applications of aluminum foams were discussed with researchers and designers who had to solve very specific technical problems, by use of suitable materials. People were fascinated by metal foams and sometimes they over-estimated their potential. For instance, aluminum foam was thought to provide the highest strength combined with lowest weight, which is not the case. Table 7.4-3 shows a couple of improbable applications and ideas, which could not be considered as applications for metal foams. 7.4.3.4

343

344

7.4 Prototypes by Powder Compact Foaming

Figure 7.4 -11. Aluminum-foam cores for castings.

A very important task of foam developers and foam manufacturers must therefore be to give their customers and potential material users up-to-date and accurate information about the material properties and convenient applications, but also its limits. Otherwise they run the risk of losing interest in this material altogether.

Table 7.4 -3. Improbable applications.

Aluminum foam prototype part

Application/Customer

Focus

Plates

bulletproof jackets, plates

safety, military

Plates

skateboard, snowboards

weight

Plates

milk tanks

weight

7 Service Properties and Exploitability Table 7.4-3. Continues

Aluminum foam prototype part

Application/Customer

Focus

Compact structural parts

gear box

weight

Structural parts

musical instruments

acoustic properties

Plates, cubes

speakers and headphones

acoustic damping

Gas-permeable plates

plastic industry molds

weight

Gas-permeable cylinders

filters and catalysts exhaust system

porosity, weight

Gas-permeable cylinders

heat exchangers

porosity

Foam cylinders

latent heat accumulator

heat capacity

Foam cylinders, spheres

floats

density

Foam-filled cylinders

drums, rollers

textile machines paper industry

Buttons

clothes

design

Precursor nails

construction fastening device

joining by foaming precursor nails

References

1. H. P. Degischer, U. Galovsky, R. Gradinger, R. Kretz, F. Simancik, in Proc. MetallschaÈume, J. Banhart (ed.), MIT, Bremen 1997, p. 79. 2. H. Cohrt, F. BaumgaÈrtner, D. Brungs, H. Gers, in Proc. MetallschaÈume, J. Banhart (ed.), MIT, Bremen 1997, p. 15. 3. H. P. Degischer, H. WoÈrz, DE Patent 4206303 1992. 4. H. P. Degischer, U. Galovsky, R. Gradinger, R. Kretz, F. Simancik, in Proc. MetallschaÈume, J. Banhart (ed.), MIT, Bremen 1997, p. 79 5. L. Lorenzi, M. Parisi, M. Valente, A. Zanoni, in Metal Matrix Composites and Metallic Foams, Proc. Euromat, Vol. 5, T. W. Clyne, F. Simancik (eds), Wiley-VCH, Weinheim 1999, p. 96. 6. J. Siebels, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 13.

7. R. Gradinger, M. Seitzberger, H. P. Degischer, M. Blaimschein, Ch. Walch, Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 313. 8. B. GoÈtzinger, R. Kretz, in Vom Werkstoff zum Bauteilsystem, Proc. LKR, H. Kaufmann, P. J. Uggowitzer (eds), ISBN 3-902092-009, 1999, p. 185. 9. R. Kretz, E. Hombergsmeier, K. Eipper, in Metal Foams and Porous Metal Structures, J. Banhart, M. F. Ashby, N. A. Fleck (eds), MIT Verlag, Bremen 1999, p. 23. 10. R. Kretz, E. Wolfsgruber, in MetallschaÈume, H. P. Degischer (ed), Wiley VCH, Weinheim 2000, p. 400. 11. R. Kretz, H. Kaufmann, in Metal Matrix Composites and Metallic Foams, Proc. Euromat, Vol. 5, T. W. Clyne, F. Simancik (eds), WileyVCH, Weinheim 1999, p. 63.

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7.5 Applying the Investment Methodology for Materials (IMM) to Aluminum Foams

7.5

Applying the Investment Methodology for Materials (IMM) to Aluminum Foams

E. M. A. Maine and M. F. Ashby

Innovations in material development are high-risk investments [1], characterized both by long gestation periods between invention and widespread market adoption [2], and by uncertainty of ultimate success. For these and other reasons, they have generally been driven by large enterprises [3] and national governments. An investment methodology for new materials (IMM) has been developed [2,4] that could both reduce risk and shorten gestation time. IMM provides a structured, informed procedure for assessing the attractiveness of investing in the industrial scale-up of the production of a new material. This section presents the results of an IMM analysis on the viability of aluminum foams. 7.5.1

Introduction: The Investment Methodology for Materials (IMM)

IMM consists of three linked segments: viability analysis, market assessment, and value capture (Fig. 7.5-1). A material is viable in an application if the balance between its technical and economic attributes is favorable. Assessing viability involves technical modeling of the application, cost modeling of manufacturing, input from the market assessment, and value analysis. Market assessment deploys techniques for identifying promising market applications and for forecasting future production volumes. Likelihood of value capture is assessed through an

The investment methodology for materials (IMM).

Figure 7.5-1.

7 Service Properties and Exploitability

analysis of industry structure, organizational structure, IP issues, appropriability, and the planned market approach. The most desirable investment opportunities are those with both a large viable market size and a high likelihood of value capture [4]. 7.5.2

Initial Market Scan for Potential Applications for Al Foams

Aluminum foams have several unusual features, among them, exceptional energy absorbed per unit volume and, particularly, energy absorbed per unit weight [5]. Potential applications are those in which these functions are important; those that also exploit secondary attributes of metal foams (such as flame resistance, heat dissipation, noise reduction, water resistance, blast amelioration) are particularly attractive. The strongest opportunities for short-term take up of aluminum foam lie with substitution into existing markets, since for these the design requirements are well known. Radically new designs taking best advantage of their properties are slowed by lack of designer awareness and confidence, and by current manufacturing difficulties with achieving high tolerances. There are existing aerospace and automotive applications that require high energy absorption per unit volume. The large-scale production of aluminum foams cannot yet meet the tolerances required for aerospace applications (other than the expensive Duocel, which finds a market in defense and space vehicles); thus, automotive applications are prioritized, specifically, the ªA-pillarº designed for occupant safety, and the redesigned hood and front bumper regions to meet new pedestrian protection legislation. 7.5.3

Material Assessment Technical Performance The stress strain curve of aluminum foams (Fig. 7.5-2) approximates the idealized stress strain curve for energy absorption, suggesting their use in energy-absorbing applications. As a screening mechanism to eliminate prototyping and testing with uncompetitive materials, a range of aluminum foams was compared with all other materials along combinations of technical parameters. IMM utilizes CES (Cambridge Engineering Selector) software for this purpose [6]. Once a material is established as a non-dominated candidate for an application, prototyping and testing are required to substantiate technical viability. This technique is explained in detail in published books and papers [7,8]. 7.5.3.1

347

348

7.5 Applying the Investment Methodology for Materials (IMM) to Aluminum Foams

Figure 7.5-2.

(Duocell).

Stress strain curves of closed-cell Alporas and open-cell ERG metal foams

Cost of Production Economic analysis aims to establish the manufacturing cost differential between a component made with a novel process or material and the incumbent processes and materials. To this purpose, technical cost models were constructed for three processes for manufacturing aluminum foam. 7.5.3.2

x x x

Liquid-state foaming of aluminum, TiH2 expansion via powder metallurgical processing as a batch process, TiH2 expansion via powder metallurgical processing as a continuous process.

The cost models themselves include sub-models to capture the effect of component size on production rate, the die and equipment costs, allowance for scrap, die-life,

Figure 7.5-3.

Production costs for processing aluminum foam by three methods.

7 Service Properties and Exploitability

and capital write-off. The output of the models (Fig. 7.5-3) shows the way in which the cost of the manufactured component depends on production volume. Cost drivers can also be determined. In this instance the batch powder metallurgical process is the most economical option for annual production volumes of up to 20 000 parts [2,9]. By comparing the cheapest aluminum foam component (at the required production volume) with an incumbent material for any given application, the cost differential between a new and an incumbent material solution can be established. This provides input into the value assessment.

Co-Minimizing Volume and Cost in Energy-Absorbing Applications In most applications cost is a strong consideration and this raises the issue of cominimizing two objectives: volume and cost (or mass and cost). Used as an energy absorber in the form of a simple panel or slab application, the cost C of the finished block of foam is essentially that of the foam itself, CmM, where Cm is the cost per kg of the foam and M ˆ Vr is the mass of the panel, where r is the foam density and V is the panel volume. Modeling the production cost of shaping is discussed elsewhere [9]. The co-minimization is best done by constructing trade-off plots. This method reveals that the cheapest solution is polystyrene foam with a density of 0.05 Mg/ m3, but the volume (and thus thickness) required is large. The solutions with the lowest volume are offered by the Hydro (liquid-state) or the Alulight (PM) aluminum foams, both with densities of about 0.25 Mg/m3 (Fig. 7.5-4). 7.5.3.3

Figure 7.5-4.

Selection of metal foams and polymer foams by volume and cost with s pl ˆ 3.5 MPa.

349

350

7.5 Applying the Investment Methodology for Materials (IMM) to Aluminum Foams

7.5.4

Market Forecast

A technical assessment indicates that metal foams are technically viable as energy absorption elements within the A-pillar [8]. The next step is to examine the market size and rate of take-up.

Market Size for Aluminum Foam A pair of A-pillar energy absorbers made of aluminum foam weighs about 1 lb (0.4 kg). Assuming 1 lb of aluminum foam per car for a mass-produced passenger car at a finished cost of $10/lb ($25/kg) allows an estimated market size of $5 million annually if installed in a single, large-volume model of passenger car; if it becomes the industry standard, the market size increases to some $100 million annually. The substitution mode is either lower cost/higher performance, or higher cost/higher performance. The former mode would be followed when the displaced energy absorption element is complex, where minimizing volume is a priority, and when flammability is a concern, eliminating most polymer foams. In some other A-pillar designs, the Al foam would be replacing a cheaper existing solution that is unable to meet new occupant safety legislation. 7.5.4.1

Market Timing for Aluminum Foams A method of comparison with historical substitutions, such as Abernathy and Clark's transilience map [10], aids a substitution-timing forecast. Aluminum foam for energy absorbing automotive applications is a revolutionary innovation, in that it overturns established technical and production competencies, but does not overturn customer linkages nor require a company to sell into different markets. Thus the substitution timing of aluminum foam for A-pillars can be modeled on the historical examples of a revolutionary innovation in the automotive industry that was both lower in cost and higher in performance. Historical examples of these include SMC (sheet molded compound) hoods (bonnets) and polymer composite fenders. SMC hoods are lighter than those made of steel, and are cheaper to design and manufacture for low-volume platforms; substitution has occurred for these and for vehicles that are close to the legislated CAFE (corporate average fuel economy) limit, where weight saving is highly valued [11]. Polymer composite fenders are lighter than those made of steel and better able to resist impact without damage. For these, substitution has followed a similar curve to that for SMC hoods [12]. If aluminum foams in energy absorption automotive applications follow a similar substitution pattern, they could expect to capture 50 % of their potential market within 12 years (see Fig. 7.5-5). Automotive platforms with a flexible Body-In-White structure exact less demanding constraints on the A-pillar energy absorber. For these, metal foams, with their ease of shaping, offer aesthetic design improvements (for example, thinner A-pillars with improved lines of sight), but cost more than cheaper alternatives: a higher 7.5.4.2

7 Service Properties and Exploitability

Figure 7.5-5.

Scenarios for aluminum foam substitution into A-pillar market.

cost/higher performance mode of substitution. Historical examples of these include aluminum alloy wheels and air bags. With aluminum wheels, a combination of aesthetic qualities and lighter weight drove substitution in sporty platforms to a 50 % take-up after 18 years [13]. In the case of airbags, consumer safety concerns, the viability of the innovation, and automotive regulation drove substitution much more quickly [13]: an unlikely scenario in the case of metal foams in the A-pillar. We conclude that, if all other conditions are favorable, the time to 50 % take-up would be in the range 12 18 years. 7.5.5

Value Capture

In this investment assessment, we consider the position of a small firm, producing medium quality, medium priced, 3D, aluminum foam parts by a powder metallurgical process. The viability assessment and market assessment indicate a potential future market for aluminum foams in the automotive market starting at $5 million per annum and going to $100 million per annum. In this section, tools to assess industry attractiveness, appropriability, and organizational structures are utilized to predict the likelihood of the small companies who are at present in the process of commercializing the material capturing the value created by this innovation.

Industry Structure Porter's methodology for assessing industry attractiveness [12] directs attention to the competitive threats and to buyer/supplier pressures that might reduce valuecapture by the innovating firm. In the present context we find that several companies are able to make metal foams and that none of them has tight control of the 7.5.5.1

351

352

7.5 Applying the Investment Methodology for Materials (IMM) to Aluminum Foams •

Few potential entrants but weak IP position

•

Substitutes for metal foams: polymeric foams, shaped aluminium sections, fibre reinforced polymer composites, wood

•

Strong buyer power in most mass applications (e.g., automotive)

•

Overall, medium-low attractiveness

Figure 7.5-6.

Potential Entrants

Suppliers

Competitive Rivalry

Buyers

Substitutes

Porter's ªfive forcesº as a means of assessing industry attractiveness.

rights to the process, which is not difficult to reproduce. Their position is made less attractive because they must fight both against competitors who are commercializing alternative processes for making metal foams (the lower end liquid aluminum foam process, for instance) and against substitutes for energy absorption in automotive applications, such as polymeric foams, shaped aluminum sections, and fiber-reinforced polymer composite sections. Additionally, the automotive companies exert very strong buyer power that will be difficult for the small producer to counter (Fig. 7.5-6).

Appropriability of Profits Teece's concept of appropriability [14] is useful in establishing the potential for value capture. Here we seek to establish the appropriability position of a small company seeking to sell metal foam automotive components. The intellectual property (IP) position does not appear to be strong. Specialized assets exist with the process, but most could be assembled by a die-casting competitor without excessive difficulty. There is a possibility for co-specialized assets, if certain methods of automotive design propagate. Aluminum foam for energy absorbing automotive applications is a revolutionary innovation, in that it overturns established technical and production competencies, but does not overturn customer linkages nor require a company to sell into different markets. New product cycle time is slow, giving a longer period over which to appropriate value, and the structure of the automotive industry allows for protection of IP. The conclusion is that the appropriability position is not strong, but might be classified as medium. 7.5.5.2

7 Service Properties and Exploitability

7.5.6

Conclusions: Applying IMM to Aluminum Foams x

x

x

x

x

Target market: energy absorption in automotive applications: the A-pillar, and front-end pedestrian protection. Viability: yes, in energy absorption applications in the automotive industry. No in pedestrian protection applications currently. Market assessment: market size of up to $100 million annually, with 50 % takeup in 12 18 years. Competitive position: poor, uncertain IP protection, vulnerable to extreme buyer power. Value capture: medium to low chance.

As the chances of value capture are relatively low and the payback period is relatively long, a small firm would be disadvantaged in commercializing this innovation unless as a joint venture with a metal supplier or automotive producer. A larger company might be interested in pursuing this opportunity if it was in a good position to capture the value created. Alternatively, a government-sponsored initiative for pedestrian or occupant safety might subsidize the commercialization of such an innovation.

Acknowledgements

We wish to acknowledge the support of the KoÈrber Foundation, the Cambridge Canadian Trust, the UK EPSRC through the support of the Engineering Design Centre at Cambridge, and Granta Design, Cambridge, who developed the software illustrated in this article.

References

1. D. Wield, R. Roy, ªR&D and corporate strategies in UK materials-innovating companiesº Technovation 1995, 15(4). 2. E. M. A. Maine, ªInnovation and Adoption of New Materialsº PhD Thesis, Cambridge University 2000. 3. C. Freeman, L. Soete, The Economics of Industrial Innovation, 3rd ed, Pinter, London 1997, p. 237. 4. E. M. A. Maine, M. F. Ashby, ªAn investment methodology for materials. Part 1: The methodologyº Mater. Design, Elsevier 2002 in press.

5. M. F. Ashby, A. Evans, N. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wadley, Metal Foams: A Design Guide, Butterworth-Heinemann, Oxford 2000. 6. CES, The Cambridge Engineering Selector, Granta Design, Cambridge 1999, http:// www.granta.co.uk 7. M. F. Ashby, Materials Selection in Mechanical Design, Pergamon Press, Oxford 1992. 8. E. M. A. Maine, M. F. Ashby, ªAn investment methodology for materials. Part 2: Applications of the methodologyº Mater. Design, Elsevier 2002 in press.

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354

7.5 Applying the Investment Methodology for Materials (IMM) to Aluminum Foams 9. E. M. A. Maine, M. F. Ashby, ªCost estima- 12. M. E. Porter, Competitive Advantage: Creattion and the viability of metal foamsº in Proc. ing and Sustaining Superior Performance, Harvard Business School Press, Boston, MA Int. Conf. Metal Foams and Porous Metal 1985. Structures, MIT-Verlag, Bremen 1999, Vol. 1, 13. R. Grant, Contemporary Strategy Analysis, p. 63 70. Blackwell, Oxford 1998, p. 245. 10. W. J. Abernathy, K. B. Clark, ªInnovation: mapping the winds of creative destructionº 14. D. J. Teece, ªProfiting from technological innovation: implications for integration, Research Policy 1985, 14, 3 22. collaboration, licensing and public policy.º 11. E. M. A. Maine, ªFuture of Polymers in Research Policy, 15, p. 285±305. (Elsevier) Automotive Applicationsº Master's thesis, 1986. MIT 1997.

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

8 Strengths, Weaknesses, and Opportunities H. P. Degischer

The research interest in cellular metals and the activities of manufacturers in various market sectors illustrate the appeal of these materials: they are attractive because of their unusual specific properties and appealing property profiles. Expectations for so-far unachievable metallic light-weight structures have created ideas for the substitution of existing materials in weight-sensitive components such as floating metals, light stiff panels for automotive and aerospace applications, crashabsorbing safety components, electromagnetic shielding, structural components with low absorption for nuclear particle radiation, housings with high acoustic damping, and decorative design objects. Many different markets have been addressed, but how long will it take for a market breakthrough? Tables 8-1 8-3 resulted from a discussion at the end of the Symposium ªMetallschaÈumeº in Vienna, 29 February 2000. The tables show the advantages of cellular metals and the achievements of research as well as their disadvantages, and the remaining unanswered questions: i. e. cellular metals' strengths, weaknesses, and opportunities. 8.1

Processing

The formation of porous aluminum in welding zones of conventionally pressure die-cast components is well known, but very much unwanted, requiring special efforts to be suppressed. The controlled production of porous structures and the architecture of cellular metals appeared to be complicated. The processing of semiproducts and shaped parts requires additional efforts resulting in higher cost of production for cellular structures than for the parent metal. Even more complex processing techniques have to be developed to improve the regularity of cell structures with reasonable reproducibility. A rule of thumb became apparent: that the price per unit volume of the material remains at least the same! Therefore specialty products may find the appropriate market for the introduction of industrial production of cellular metals. In Table 8-1, achievements in various production routes (see Chapter 2) are listed for the general categories of cellular metals. Structures with open porosity can have

355

8.1 Processing Table 8-1.

Type

Achievements in the processing of cellular metals and remaining questions. Achievements in production

Open cell structures (sponges)

x

x

x

x

x

x

x

x

x

Foamed metals

356

x

x

x

x

x

x

Mass densities in the range 10 1 10 2 of the bulk metal; liquid metal replication, deposition, and solid compaction processes; some brands of different metals commercially available; uniformity of architecture and good reproducibility; net-shape production is possible, machining with some precautions; integrated massive-cellular components can be cast or sintered; recyclability about 80 %. Mass densities about 10 1 of the bulk metal (mainly aluminum alloys); powder compact foaming and melt foaming processes; various brands of foamed aluminum available; complex net-shape products with skin in dimensions between 5 and 2000 mm possible in series up to thousands; reproducible semi-product blocs of relatively uniform, foamed Al melts available; products with foamed cores (sandwich, filled profiles, inserts) in prototype stage; various joining techniques and machining feasible; recyclability about 80 %.

Subjects of concern, R&D demand x x x

x x

x

x x

x

x x

x

x

x

x

x

x

x

Rather slow processes; no large series production; specifications not yet generally established; rather small dimensions; joining techniques in development, specific system solutions are required; damage hazard due to handling and machining.

Other metals only in laboratory scale; relation of processing parameters with cell architecture not fully understood, therefore unsatisfactory control of uniformity of cell architecture; permeability to be quantified (cells not tight); poor surface quality (skin not tight); tolerances in shape and skin quality not specified; mold technology not optimized; large series or continuous production not yet realized; pore-size variation is limited, generally irregular distributions, occasionally oversized pores and high density clusters; control of bonding for integrated parts to be improved (junctions, brazing, welding); foaming of hollow long products desirable; joining techniques in development, specific system solutions required; damage hazard in handling and machining; remnants of blowing agents tolerable?

8 Strengths, Weaknesses, and Opportunities Table 8-1.

With closed cell substrates

Type

Continues Achievements in production x

x

x

Industrial production

x x x x x

Mass densities about 10 1 of the bulk metal are realized; melt, coating, and solid compaction techniques available; controllable architecture with preform technology. Duocel open-cell aluminum; Incofoam deposited nickel sponge; Alporas foamed aluminum melt; Cymat foamed aluminum melt; venture status: Alulight, Alufoam, Foaminal foamed powder compacts; AFS sandwiches with Al-foam core; replication technique ªm-poreº; Gasar eutectics; LDC, LBM solid-state processed.

Subjects of concern, R&D demand x x x x

x

Ceramic inclusions; no process industrially realized; consistence and stability of substrates; recycling requires separation from substrate. Various other techniques mostly in laboratory status for research and prototype production (for instance COMBAL).

very low densities with the highest degree of regularity and reproducibility of cell architecture. They seem to be only appropriate for small volume components for high-tech and high-price applications. Foaming of metals in the liquid state promises the most economic processing route with the drawback of difficult control of cell architecture. Products of remarkable size and complexity have been made for structural applications. Although foaming produces closed bubbles in the liquid, during solidification the cell walls are usually damaged giving the components a certain permeability and negligible mechanical stiffening. Even the characteristic surface skin of foamed metal parts can not be considered as defect-free and sufficiently protective. Processing of closed-cell structures with enclosed hollow substrates or sintered hollow spheres is still in the prototyping stage. There are no defined specifications for cellular metals. They are essentially characterized by their processing method. The dependence of material properties on the different techniques of production remain the subject of research and development. There is great potential in improving reproducibility by scaling-up production, allowing better control of processing parameters. Some successful examples of industrial production are quoted in Table 8-1. The chances of any of the cellular metals being used in components depends mainly on the availability of appropriate bonding and joining techniques. Secondary processing like forming, machining, bonding, and surface treatment require further technological developments, which have to be governed by the service requirements of each case. A significant advantage of cellular metals compared with polymers is their recyclability and the potential of up-grading scrap metal, which may gain increasing importance in the future.

357

8.2 Properties

8.2

Properties

The processing method for a cellular metal component defines the achievable property profile in the first instance. The density achieved by a given production route determines the magnitude of the properties. Physical principals govern those property relations, which reveal the limits as well. The introduction of pores into a metal cannot improve its mechanical properties even when related to the specific mass. Tensile strength is limited by fracture mechanics due to inhomogeneous stress distributions within the cellular architecture containing many crack-initiation sites. Properties depending nonlinearly on the dimension of the part offer benefits for design application, for example specific stiffness for bending of beams or plates. The close relation between processing and properties is enhanced by the importance of the mesoscopic 3D-structure formed by the metal matrix with its specific microstructure. The scatter of material properties is assumed to be caused by irregularities in the cellular architecture of real products. Some of these can be tolerated, but there is still the ambiguity of extremely poor property values not yet correlated with structural parameters. Sensitivity studies are required to relate the influence of meso- and microscopic defects to the properties. Consequently the reliability of the properties needs verification by testing series of products. The properties depend on the variations in cellular architecture and their uniformity. The actual achievements are contrasted in Table 8-2 with the deficiencies still existing for most of the available cellular metals. The average density does not seem sufficient for the characterization of a cellular component. The properties of cellular materials are not only determined by the matrix metal, but essentially

Table 8-2.

Topic

Achieved properties and characterization methods compared with demands. Available property data x

x

x

Cellular structure

358

x

x x x

Average mass densities in the range 10 1 10 2 of the bulk determined by classic densitometry; medium and high resolution 2Dmicroscopy; thermo-acoustic nondestructive test methods applicable; radiography or 3D X-ray computed tomography (for light metals human tomography applicable) determining local mass distribution; center of gravity; die-penetrant testing of surface skins; permeability determination for open porosity character.

Characterization deficiencies x

x

x

x

x

Uniformity only for cellular structures with porous substrates, and solid state processed; architectural defects' assessment required; oversized pores as well as mass concentrations cause degradation of specific properties; labor intensive and time consuming determination of 3D pore-size distributions; architectural quality criteria to be developed; quantified nondestructive test methods to be established.

8 Strengths, Weaknesses, and Opportunities Table 8-2.

Topic

Continues Available property data x

x

Mechanical properties

x

x

x

x

x

x

Static and dynamic compression behavior generally tested; high specific crash energy absorption of high efficiency; synergy in crash energy efficiency for filled folding hollow structures; definitions of initial stiffness, peak stress, plateau stress, densification strain available; high specific stiffness for beams and plates; some data on fatigue, crack growth, and creep behavior published; brittle and ductile cellular metals available; properties mainly related to average mass density.

Characterization deficiencies x

x

x x x x

x

x

x

x

x

x

Physical properties

x

x x

Environmental properties

x

x

x

x

x

High internal surface; open cell structures beneficial for heat transfer and catalytic functions; potential for acoustic absorption; low electrical and thermal conductivity, but higher than of polymers and ceramics; electromagnetic shielding effects. Thermal stability usually better than that of bulk metal; not inflammable; space compatibility of open-cell structures, no radiation damage; no low-temperature embrittlement for thermally stable alloys; corrosion resistance similar to that of bulk metal.

x x

x x

x

x

x

x

Dependence on test procedure and specimen geometry; scatter of properties to be related to irregularities of the material; limited reliability of properties; sensitive to load introduction; tensile properties very poor; multi-axial load conditions to be considered; elastic behavior depends on architecture (stiffness of cellular structure); matrix of Poisson ratio to be determined for elastic and plastic load cases; specification of test procedures and evaluation required; life-time predictions for components not yet established; properties of the solid material in the cellular structure difficult to determine; dependence on thermomechanical treatment to be investigated. Higher reproducibility required; controversial frequency dependence for sound absorption; not suitable for isolating functions. frequency and intensity dependence on material conditions not fully understood. High thermal gradients due to low conductivity; high initial desorption rate of foamed metals; closed-cell structures entrap gas; high specific surface and high capillarity enhances corrosive attack (high sensitivity to galvanic corrosion); protective coating rather complicated.

359

360

8.3 Design and Application

by the local material distribution: the architecture of the cell structure. X-ray computed tomography offers the possibility of 3D characterization, but requires significant effort. Nondestructive testing is one of the main activities of the research necessary to correlate properties with cellular architecture. Furthermore, the properties of the matrix metal itself cannot be simply transferred from bulk material, but need to be investigated for each processing technique. In the case of age-hardening metals, the influence of thermal treatments during production has been indicated, but may offer chances for further material development. Table 8.2 lists the most appealing properties, especially attractive in relation with the low specific mass. The potential of cellular metals depends on combinations of these specific properties according to particular service requirements. The mechanical properties for structural applications have to be defined specifically for these cellular structures. Elastic properties, for example, have to be considered as the stiffness properties of the architecture of the metal; similarly plastic deformation and damage mechanisms. Complications arise from the internally multi-axial load transfer, which require special attention regarding the test conditions providing material data. Both test conditions and the significance of the results have to be defined properly for cellular metals. Life-time predictions require further research to complete the achieved results for exposure conditions simulating long-term service. Damage mechanisms are revealed qualitatively and first attempts of quantification need verification in use. The physical properties deserve considerable attention to underline the perspectives of multi-functional application. They have to be determined quantitatively individually for each type of cellular metal, based on the principally existing potential. There are essential advantages of cellular metals in comparison with polymers regarding environmental properties. Of course, the environmental service conditions have to be considered for specific cases. The high fire resistance and the space compatibility have not yet been exploited for aerospace applications.

8.3

Design and Application

The technical advantages of cellular metals cannot be fully exploited just by substitution of materials, but require material-appropriate engineering solutions and design concepts. The simulation of the performance of components relies on the material laws and constitutive equations appropriate to cellular metals and their loading conditions. The actual situation in modeling of cellular metals and in designing components thereof is summarized in Table 8-3. Material models for cellular metals are required, which have to reflect the 3D behavior of the highly porous, compressible material. Theoretical studies help to identify the important parameters. The transfer of the theoretical results to real architectures requires experimental calibration of the material laws. As stated before, even micromechanical computations require the appropriate metal matrix properties, which are very difficult to determine in the processing condition of cells. Reasonable approximations

8 Strengths, Weaknesses, and Opportunities Table 8-3.

products. Topic

State of applicability of modeling, simulation, and design methods for different

Actual achievements x

x

x

Modeling

x

x

x

x

x

3D-models for geometrically perfect periodic cell structures for elastoplastic behavior; scaling laws related to apparent mass densities for estimation of stiffness, plateau stress and densification strains; mesomechanical methods based on continuum mechanics of multi-phase material structure to predict elastoplastic behavior of real cellular parts; finite element methods applied to simulate the micro-/meso-/marcoscopic material behavior; micromechanical studies of elastoplastic deformation of cell elements; models for crush behavior of regular cell structures; sensitivity studies on defects in regular cell structures; rules for qualitative crash behavior of real parts.

Potential for improvements x

x

x

x

x

x

x

x

x

Design and simulation

x

x

Design based on macroscopic behavior according to experimental tests; design methods for phase and shape optimization for non-uniform cellular structures in development.

x

x

x x

x

x

Only for regular microgeometrics (processed by replication, LBM ...) applicable; neglect local non-uniformities (depletion or concentration of mass) of real cellular structures; deformation concentrations not predictable by models of regular structures; prerequisite for mesoscopic simulations is the existence of a common cell architecture and uniform properties of the solid metal; averaging procedure has to represent the characteristic microgeometry in each volume element; size of FEs have to reflect cellular material of known material laws; constitutive equations restricted to idealized prerequisites; input data for material behavior and constitutive equations not fully available; calibration by macroscopic testing necessary; micromechanical procedures only for a few cells applicable owing to the excessive computing time. No safety margins established coping with inhomogenities of real products; sensitivity studies on tolerable defects are to be developed; reliable material data for design incomplete; life time prediction rules not available; mechanical properties for multi-axial load conditions not available; appropriate design experience is missing; conflict between optimization and realization; joining solutions not yet verified for transfer into design rules.

361

8.3 Design and Application Table 8-3.

Topic

Continues Actual achievements x

x

x

Application

x

x

x

x

x

x

x

Market

362

x

x x x

Light-weight structural parts of high bending stiffness; crash energy absorption by light weight components; additional requirements of thermal stability or/and non-inflammability; light weight components exhibiting acoustic absorption and mechanical damping; open porosity for heat exchangers, catalysts and filters; multi-functional applications exploiting as well physical properties; compounds with face sheets (AFS) or inserts in hollow sections of extrusions or castings; a multitude of prototypes offered. Applications where the value of weight saving is high (means of transport, highly accelerated machine parts and sporting goods); aerospace applications; small series rail, public transport and utility vehicles; selective use of cellular metals; value of recyclability; chances for learning curve effects on processing and price.

Potential for improvements x

x

x

x x

x

x

x

x x x

x

x

No service experience; service tests required; integration of cellular metals into systems unsatisfactory; established alternative solutions available; special small series cases; multi-functional benefits required (functional integration, reduction of parts, assembling advantages); processing too complicated and of limited reproducibility.

Price estimations actually more than 15 U/kg or 5 U/liter (which is more than the automotive market is prepared to pay); advanced material image to be improved; additional benefits required; increased importance of recycling; experience in part integration required; no large series production existing, therefore price estimations difficult; price mainly governed by processing effort. specialty markets with progressive demands to be selected.

based on averaged or characteristic structures are available. The hierarchical approach of macro-, meso-, and micromechanical simulations according to the local sensitivity of a structural feature in relation to the load case of the component seems very promising. The close interaction of development of models with experimental determination of properties is leading to useful interpretations of the general material behavior. The access to the material data required for input to the different models is a specific topic of research. Finite-element calculations have to take care of the appropriate choice of mesh geometry owing to the generic heterogeneous structure dealt with, whether for the micromechanical considerations or for the mesomechanical

8 Strengths, Weaknesses, and Opportunities

approach, where representative cellular material volumes have to be found. Design optimization for cellular metals refers not only to shape, but also to the arrangement of the varying structures to be interpreted as different material phases. Load transfer from the surrounding is an essential design element for which experience has to be broadened and solutions unconventional for metals may be beneficial. The influence of scatter in material properties locally within a part and between different samples of the same component needs further attention in design and simulation. The sensitivity to irregularities in the cellular architecture has to be known in order to establish tolerance margins and service-related quality criteria for products. The discussion on ªhow uniform a cellular metal has to be to be reliableº needs quantified arguments related to the intended application. Progress is expected by performing case studies that enable correlation of processing parameters, material properties, modeling requirements, performance simulation, and service experience. The expected general benefits are listed in Table 8.3. Various prototypes exist for testing service performance, but unfortunately most of them are designed for substitution of existing material solutions and the systems are usually not optimized for cellular metals. Any how, each practical case increases the experience in potential application of cellular metals. Prototypes of specialty products, like open-cell Duocel or Incofoam electrodes, or noise-damping Alporas plates, may serve to demonstrate the potential of tailored property profiles for specific requirements. Multifunctionality and part integration increase the chances for industrial application of high-value materials. The market is mainly governed by cost benefit relations. Applications experiencing frequent accelerations, where weight savings are of interest, are indicated in Table 8-3. The question of what price can be paid for such weight savings, has to be asked periodically. The answer depends mainly on the changing economic boundary conditions like energy costs and ecological restrictions. Global trends seem to support further efforts for weight reductions. Opportunities in small-series specialty applications should be seized because they provide means of gaining experience in all aspects: engineering, processing, performance, and service assessment. The first series product for automotive applications has been announced and a successful market introduction is expected. The introduction of a learning curve in the whole production chain seems to stimulate the most important progress step necessary for the development of market-penetrating innovations made of cellular metals.

363

Handbook of Cellular Metals: Production, Processing, Applications. Edited by H.-P. Degischer and B. Kriszt Copyright c 2002 Wiley-VCH Verlag GmbH & Co. KGaA ISBNs: 3-527-30339-1 (Hardback); 3-527-60055-8 (Electronic)

Index

a

A-type ATPases 387 ABC (ATP Binding Cassette) 77 ABC secretion 184 ff diversity of proteins secreted 186 ABC secretion pathway, schematic representation of 191 ABC subunit, sequence 97 ff ABC systems, definition 79 ABC transporters 77 ff associated proteins 84 binding proteins 85 ff components of 85 ff composition of 80 ff crystal structure 88 ff integral transmembrane domains (TMDs) 91 ff listing of 89 metal- 316 ABC-type efflux permeases 13 ABC-type nickel transporter 407 ABC-type uptake permeases 12 Acidithiobacillus ferrooxidans 332 ACR (arsenic compounds resistance) family 393 ACR genes, in yeast 393 aerolysin 215 ff Aeromonas hydrophila, channel formation by aerolysin 216 AFT1 in yeast 466 alignment studies, on TonB-dependent receptors 282 alkaliphilic Bacillus 50 ALLBP 89 a-toxin 217 a-type channels 5 d-aminolevulinic acid, transport of 154

anion-stimulated ATPase 380 anthrax protective antigen 218 anthrax toxin 218 antimonite transporters 377 ff antiporters 8 ff aquaglyceroporins 251 aquaporin AQP1 248 aquaporin Z, of E. coli 250, 255 aquaporin 1 254 aquaporins 247 ff MIP-related- 248 plant- 249 AraF 89 Archaeoglobus fulgidus 49 ARN1 transporter 469 ars operon in bacteria 392 of E. coli 378, 391 arsA 379 ATPase activity of 380 crystal structure of 389 DTAP domain 386 nucleotide binding sites 381 ff of E. coli 388 unisite and multisite catalysis in ArsAB pumps 392 arsB 379, 390 ArsC 379, 391 arsenite efflux 392 arsenite resistance 392 arsenite transporters 377 ff ArsR 379 asperchrome B1 470 asperchrome D1 470 ATP hydrolysis 98 ff by FhuC 298 ATP synthases 23 ff

384

481

482

Index copA 368 copB 368 cop operon of Enterococcus hirae 368 copY 368 copZ 368 CopA, in copper uptake 369 b CopB, in copper excretion 369 b-barrel porins 6 CopB copper ATPase, of Enterococcus Bacillus stearothermophilus 49 hirae 363 Bacillus subtilis, CitM protein 404 copper ATPases saturable Mn permease 330 of Helicobacter pylori 373 Bacillus thuringiensis Cry toxins 223 of Listeria monocytogenes 373 bacterial copper transport 361 ff copper chaperones 366 bacterial cytochrome c oxidases 436 copper excretion, CopB 369 bacterial iron transport 289 ff copper ion transport, mitochondrial- 419 ff bacterial zinc transport 313 ff copper resistance binding protein-dependent Zn2‡ uptake in Escherichia coli 371 in gram-negative bacteria 320 plasmid-encoded- 374 in gram-positive bacteria 316 ff copper transport 361 ff Bradyrhizobium japonicum (HupN) 413 copper transport system, in S. cerevisiae 426 Bsd2p and manganese ions 453 copper uptake, CopA 369 coprogen transporter 472 c Ca2‡ -ATPase, of sarcoplasmic reticulum 364 CopY repressor protein 370 CorA Ca(II) ATPase 428 of Methanococcus jannaschii 353 Ca-ATPase calcium pump, structure of 428 of Salmonella typhimurium 352 ff Caloramator fervidus 49 CorA magnesium transporter 351 ff Candida albicans peptide transport gene Corynebacterium glutamicum 53 (Ca Ptr2) 155 COS16 457 carbon monoxide dehydrogenases [Ni] 399 Cox polypeptides 425 catalysis within the F1 complex 27 ff Cox1 polypeptide 424 cation diffusion facilitator 315 Cox2 subunit 424 Ccc1p: a manganese homeostasis protein Cox11 sequences 434 456 Cox17 metallochaperone 429 Ccc2 P-type ATPase transporter 427 Cox17 sequences 430 CCC2, intracellular transporter of copper CPx motif 364 449 CPx-type ATPases 362 Ccc2p 456 sequence motifs 365 CDC1 gene product 456 crystal structures of DtxR 305 cell surface permease FTR1 449 CTR1, cell surface copper permease 449 channel formation steps 212 ff Ctr1/Ctr3 system 426 channel forming colicins 222 Cu metallation, of cytochrome c channel forming protein toxins 209 ff oxidase 431 ff a-toxin 217 Cu metallation, of mitochondrial cytochrome c aerolysin 215 ff oxidase 441 channel forming proteins 209 ff Cu-specific ATPase pumps 428 classification of 211 CxxC motifs 366 cholesterol-dependent toxins 219 cytochrome c oxidase, structure of 424 CitM protein of Bacillus subtilis 404 cytochrome c oxidase citrate fermentation 51 Cu metallation of 431 ff classes of transporters 4 ff Cu metallation of mitochondrial- 441 Clostridium fervidus 49 mitochondrial- 422 ff Cnr (cobalt nickel resistance) 406 cytochrome c oxidases, bacterial- 436 coenzyme F430 399 Czc (cobalt zinc cadmium resistance) 406 colicins 222

ATPase activity of ArsA 380 ATPases, phylogram 363 Atx1 metallochaperone 427 Atx2p 456

Index

d

des(diserylglycyl)ferrirhodin 470 dipeptide permease (Dpp) 144 diphtheria toxin 304 DMT1 329 Dpp-type 159 DppA 89 DTAP domain, in ArsA 386 DtxR, crystal structures 305 DtxR/IdeR family 338

e

EI 118 enantio-ferrichrome 470 enantio-rhizoferrin 468 ENB1 transporter 472 energy transduction, ATP synthase 31 ff enteric bacteria, peptide transport in 143 ff Enterococcus hirae cop operon 368 Enterococcus hirae CopB copper ATPase 363 Escherichia coli HlyA 221 aquaporin Z 250, 255 ars operon 378, 391 ABC transporters 80 ff ArsA 388 ATP synthase 24 ff, 36 ff ATP transporter binding proteins 90 copper transport in 371 FhuABCD activities 292 FhuD protein 297 LamB 240 MalK 105 melibiose transporter 54 Na‡/melibiose transporter 58 Na‡/proline transporter 55, 59 ff, 65 ff Na‡/substrate transport in 52 Nik system 407 OmpF 234 peptide transport 143 ff Tat pathway in 174 TolC trimer 242 extracellular loops in FepA 270 ff in FhuA 270 ff

f

F1 subunits 25 ff F1/FO interface 31 ff F1FO ATP synthase 23 ff model of energy transduction 39 ff FO subunits 33 ff proton translocation pathway 42 F-ATPases 23 ff

F-type ATPases 23 ff families of transporters 1 ff, 5 ff Fe3‡ -citrate 306 Fe3‡ -dicitrate 300 Fe3‡ regulatory mechanism 306 Fe3‡ -siderophore transport 291 ff Fe-enterobactin transporter 473 FecI and FecR proteins 306 feo genes 304 FepA 264 ff b-barrel 265 ff conserved residues 284 extracellular loops 270 ff N-terminal domain 267 ff ribbon diagram 264 structure determination of 275 FepA mutants 285 Ferric Uptake Repressor (Fur) 337 ferric citrate transport system 306 ferrichrome 470 ferrichrome A 470 ferrichrome transporter 471 ferrichrysin 470 ferricrocin 470 ferrirhodin 470 ferrirubin 470 ferrous iron transport system 304 FET3 448 FET4 450 FET5 450 FhuA 264 ff barrel structure 266 conserved residues 284 extracellular loops 270 ff N-terminal domain 267 ff structures with ligand 272 ff FhuA protein 265, 292 FhuABCD activities, of E. coli 292 FhuB transport protein 298 FhuC, ATP hydrolysis by 298 FhuD 89, 295 ff crystal structure 297 Fibrobacter succinogenes 50 FRE genes, of Saccharomyces cerevisiae 448 FRE reductases, in siderophore transport 474 ff FRE1 447 FRE2 447 FRE3 448 FRE4 448 FTR1 448 fungal ornithine-N5 -oxygenase 466 fungi, siderophore transport in 463 ff

483

484

Index

g

GATA family of transcription factors 466 GBP 89 General Diffusion Porins 234 GlnBP 89 GlpFs 251 glucose transport 115 ff glutathione transport 154 glycerol conducting channels 247, 256 glyoxalase I 399 group translocation 115

h

iron metabolism, in eukaryotic cells 305 iron transport 261 ff, 289 ff Saccharomyces cerevisiae genes involved in 458 regulation of 451 iron transporters, in yeast 447 ff iron uptake, low-affinity- 450 iron-dependent regulatory protein (IRP) 305

k

Klebsiella pneumoniae citrate fermentation in 51 melibiose transporter 54 Na‡/citrate transporter 56, 59, 61, 69

H‡ cycle 52 Haemophilus influenzae ATP transporter binding proteins 90 heme transport systems 301 hFBP 297 Halobacteriales 50 Halobacterium 50 HbpA 89 heavy metal ATPases 362 heavy metals, transport of 452 Helicobacter pylori, nickel/cobalt transporters 409 Helicobacter pylori copper ATPases 373 heme, bacterial use of 300 heme transport systems 301 ff hexahydroferrirhodin 470 HgAtx1 complex, structure of 427 high-affinity nickel uptake systems 406 HisJ 89 HoxN 410 hpCopA 373 HPr 118 hydrogenases [NiFe] 399 hydroxamate reductases 476

lactic acid bacteria, peptide transport in 148 ff Lactobacillus plantarum 328 Lactobacillus plantarum MntA, gene 331 Lactococcus lactis ABC transporters 81 ff peptide transporters 148 ff lactoferrin 299 LamB, of E. coli 240 LamB channel 238 LAO 89 LbpA 299 LbpB 299 lipid bilayer membranes 231 Listeria monocytogenes, copper ATPase 373 LivJ 89 LivK 89 low-affinity iron uptake 450 low-affinity Zn2‡ uptake systems 321 Lys7 metallochaperones 429

i

m

IIA 118 IIAGlc subunit 120 regulatory role 131 IIB 118 IIC 118 IICBGlc mutants 124 ff listing of 125 ff IICBGlc subunit 121 ff regulatory role 132 topology of 122 insecticidal crystal (Cry) proteins 223 integral transmembrane domains (TMDs) ABC transporters 91 ff sequence 96 ion selectivity of porins 233

l

magnesium transporters 347 ff CorA 351 ff MgtE 350 Major Intrinsic Proteins (MIPs) superfamily 247 malK dimer, asymmetry within 105 ff MalK from Thermococcus litoralis 101 ff maltoporin 237 maltose binding protein from E. coli 90 maltose binding protein MBP or MalE 239 manganese, in bacteria 326 manganese accumulation 325 ff manganese homeostasis 452 manganese homeostasis protein, Ccc1p 456

Index manganese transport Saccharomyces cerevisiae genes involved in 458 in Saccharomyces cerevisiae 452 ff in bacteria 330 ff manganese transport ATPase, Pmr1p 455 manganese transporters, in yeast 447 ff manganese uptake, in bacteria 325 MBP 89 MBP (MalE) 89 melibiose transporter of E. coli (EcMelB) 54, 62 ff melibiose transporter of K. pneumoniae (KnMelB) 54, 62 membrane topology of CPx-type ATPases 363 metal ABC transporters 316 metalloenzymes, nickel as cofactor 398 ff Methanobacterium thermoautotrophicum 49 Methanococcus jannaschii 49, 353 MFS-type nickel exporter (NrsD) 406 Mg2‡ transporter families: MgtE, CorA, and MgtA/B 347 MgtA/MgtB Mg2‡ transporters 355 ff MgtC protein 357 MgtE magnesium transporters 350 microbial nickel transport 397 ff microbial siderophores 465 MIP-like channel genes 252 MIP-related aquaporins 248 MIP-related sequences, phylogenetic tree 252 mitochondrial copper ion transport 419 ff mitochondrial cytochrome c oxidase 422 ff MMT1 451 MMT2 451 Mn(II) ABC transporters 328 Mn(II) as a Fur co-repressor 338 Mn(II) primary transporter 328 Mn(II) permeases 328 Mn(II) transport in S. aureus 330 MntABC uptake system 333 MntH 329 MntH proteins 336 ModA 89 molecular recognition templates (MRT) 156 ff molecular recognition templates (MRTs), optimal features of 159 MRP1 (multidrug resistance-associated protein) 393 multi-copper oxidase 448 Mycobacterium tuberculosis (MtNicT) 413

n

N-terminal domain of FepA 267 ff of FhuA 267 ff Na‡ cycle 52 Na‡/citrate transporter (CitS) of K. pneumoniae 56, 59, 61, 69 Na‡/H‡ antiporter 52 Na‡/K‡ ATPase 23 Na‡/melibiose transporter of E. coli 58 Na‡/proline transporter 53 Na‡/proline transporter (PutP) of E. coli 59 ff, 55, 65 ff Na‡/substrate transport in Escherichia coli 52 Na‡/substrate transport systems 48 ff Natural Resistance-Associated Macrophage Protein (Nramp1) 329 Ncc (nickel cobalt cadmium resistance) 406 NhlF 410 Nic1p, of Schizosaccharomyces pombe 412 nickel, as a cofactor of metalloenzymes 398 ff nickel/cobalt transporter family 408 ff hydropathy profile alignment 409 in Bradyrhizobium japonicum 412 nickel homeostasis 403 ff nickel resistance 401 nickel toxicity 401 nickel transport 397 ff nickel transporter (UreH, UreI) of thermophilic Bacillus sp. 412 nickel transporters, ABC-type- 407 nickel uptake, high-affinity systems 406 nickel/cobalt transporters, metabolic functions 410 NiCoT in Bradyrhizobium japonicum, nickel/cobalt transporter in 412 Nik system, Escherichia coli 407 Nik-related transporters 408 nikABCDE operon 407 nikR gene 407 nitrous oxide reductase (N2OR), in P. stutzeri 439 NixA 410 (Nramp)/Divalent Metal Transporter (DMT) 329 Nramp family 452 Nramp1 protein 339 Nramp2 329 nucleotide binding sites, in ArsA 381 ff

485

486

Index

o

oligopeptide permease (Opp) 145 ff oligopeptide transport in sporulation 151 oligopeptide transporter family (OPT) 142 OmpF of E. coli 234 Opp-type 159 OppA 89 ornithine-N5 -oxygenase, fungal- 466 osmoregulator 53 osmosensor 53 osmotic stress 53

p

P-type ATPase, superfamily 331 P-P-bond-hydrolysis-driven transporters 12 P-type ATPase superfamily 355 P-type ATPases 315, 362 sequence motifs 365 P. aeruginosa exotoxin A 304 Pelobacter venetianus porins 235 PepT family 141 peptide-acetyl-CoA transporter (PAT) family 142 peptide transport 139 ff in eukaryotic microorganisms 155 peptide transport systems, classification of 140 ff peptide-uptake permease (PUP) family 142 perfringolysin O 219 periplasmic Zn2‡/Mn2‡/Fe? binding proteins 319 peroxide stress regulator PerR 338 pertussis CyaA 221 phage adsorption sites 293 Phosphotransferase System (PTS) 115 ff components 117 ff PTS proteins 118 PTS transporters 119 ff regulation of 129 ff plant aquaporins 249 plasma membrane ferric reductase 447 plasma membranes, transport systems in 403 plasmid-encoded ars operon of E. coli 391 plasmid-encoded copper resistance 374 Pmr1p: a manganese transporting ATPase 455 pore-forming toxins 6 porin channels, function of 230 ff porin pores, reconstitution of 232 porins 227 ff Rhodobacter capsulatus 234 ff ion selectivity of 233 isolation of 229

of Pelobacter venetianus 235 solute selectivity of 230 specific- 237 ff Porphyromonas gingivalis, heme transport system 302 porters 8 ff PotD 89 PotF 89 Propionigenium modestum, ATP synthase 36 ff, 40 protein export 165 ff Sec pathway 168 ff Tat pathway 173 ff protein secretion 165 ff pathways found in gram-negative bacteria 167 Sec-dependent pathway 178 ff Sec-independent pathways 184 ff type III secretion pathway 192 ff type IV secretion systems 198 ff proton motive force (pmf) 48 proton-dependent manganese transporter 329 proton-dependent oligopeptide transporter family (POT) 141 PsaA and TroA proteins 332 Pseudomonas stutzeri, nitrous oxide reductase (N2OR) 439 PstS 89 PTR (Peptide Transport) 155 PTR2 transporter 155 PUP (peptide-uptake permease) 152 Pyrococcus furiosus 86 ATP transporter binding proteins 90 Pyrococcus horikoshii 49

r

Ralstonia eutropha, nickel/cobalt transporters 409 Ralstonia eutropha (HoxN) 413 RbsB 89 reconstitution, of porin pores 232 reduction of arsenate 391 regulation by Fe3‡ 306 by Fe3‡ -siderophores 306 repressor protein CopY 370 rhizoferrin 468 Rhodobacter capsulatus porin 234 ff Rhodococcus rhodochrous, nickel/cobalt transporters 409 RND family of exporters 313 ff RND-type Ni2‡ export systems 406 RTX toxins 220

Index

s

S. gordonii ScaABC system 333 S. marcescens cytotoxin 304 Saccharomyces cerevisiae FRE genes 448 copper transport system 426 genes involved in iron and manganese transport 458 iron transport in 447 ff manganese transport in 452 ff Salmonella SitA periplasmic protein 334 Salmonella typhimurium 52, 88, 352 ff peptide transport 143 ff sap (sensitivity to antimicrobial peptides) 152 sarcoplasmic reticulum, Ca2‡ -ATPase 364 SBP 89 ScaABC system, of S. gordonii 333 Schizosaccharomyces pombe, Nic1p 412 Sco protein sequences 432 Sec-dependent pathway:type II secretion pathway 178 ff Sec pathway 168 ff schematic representation of 171 Sec proteins 166 Sec translocase 169 ff secretion proteins 166 Selenomonas ruminantium 50 SfuA 300 Shigella toxin 304 shuttle mechanism 295 siderophore classes 464 ff Siderophore Iron Transport (SIT) family 463 siderophore receptors 261 ff genetic and biochemical studies on 276 ff mechanism 279 ff siderophore transport FRE reductases 474 ff in fungi 463 ff siderophores, representative microbial- 465 SIT1 transporter 468 SitA periplasmic protein, of Salmonella 334 Smf1p 452 Smf2p 452 SMF3 451 Smf3p 452 sodium motive force, (smf) 48 sodium/substrate transport 47 ff solute selectivity, of porins 230 specific porins 237 ff SRE 467 SREA 467 SREP 467

Staphylococcus aureus, Mn(II) transport 330 staphyloferrin 468 Streptococcus bovi 50 Streptococcus pyogenes 328 subunit g rotation 29 ff subunits IIAGlc and IICBGlc 119 ff subunits IIABMan, IICMan and IIDMan 119 Sulfolobus solfataricus, ABC transporters 81 ff superoxide dismutases [Ni] 399 symporters 8 ff synechococcal copper ATPases 372

t

TAF1 transporter 469 Tat (twin arginine transfer) pathway 173 ff Tat pathway, in Escherichia coli 174 Tat proteins 175 Tat signal peptide 176 TbpA 299 TbpB 299 Thermococcus litoralis 86 ATP transporter binding proteins 90 MalK 101 ff Thermoplasma acidophilum 332 TIM complex 421 TMBP 89 TolC, of E. coli 241 TOM complex 420 TonB, functions of 281 TonB box 294 TonB-dependent phages 294 TonB-dependent transport 281 Tpp-type 159 transferrin 299 transport, of Fe3‡ -siderophores 291 ff transport proteins, for heme 301 ff transport systems, in bacterial and eukaryotic plasma membranes 403 transporter, for ferrichromes 471 Transporter Classification (TC) 1 ff transporter for coprogens 472 Treponema, TroA protein 332 tripeptide permease (Tpp) 147 TroA protein from Treponema 332 type I secretion pathway 184 ff schematic representation of 191 type II secretion pathways 178 ff schematic representation of 183 type III secretion pathway 192 ff schematic representation of 197 type IV secretion pathways, schematic representation of 200 type IV secretion system 198 ff

487

488

Index

u

ubiquinol oxidase 436 uniporters 8 ff Urbs1 in Ustilago 466 ureases 399 Ustilago, Urbs1 466

v

Vibrio alginolyticus 50 Vibrio parahaemolyticus 50 virulence factors 304 vitamin B12, binding of 294

w

Walker A and B sequences 98 Walker A sequence 386 water channels 247 Wilson copper ATPase (ATP7B) 367

y

yeast ACR genes 393 AFT1 in 466 iron transporters 447 ff manganese transporters 447 ff yeast oxidase complex 422 yeast vacuole and manganese 457 Yersinia pestis YfeABCD system 334 YfeABCD system, of Yersinia pestis 334

z

Zinc transport 313 ff Zinc uptake, low-affinity systems 321 ZIP transporters 405 Zn2‡ export 314 Zn2‡ transport systems, regulators of 323 Zn2‡ uptake, binding protein-dependent316 ff znuA (zinc uptake) gene 321