An Insight Into Metal Based Foams: Processing, Properties and Applications [1st ed.] 9789811590689, 9789811590696

Table of contents :
Front Matter ....Pages i-xiii
Introduction to Metallic Foams (Dipen Kumar Rajak, Manoj Gupta)....Pages 1-20
Applications of Metallic Foams (Dipen Kumar Rajak, Manoj Gupta)....Pages 21-37
Manufacturing Methods of Metal Foams (Dipen Kumar Rajak, Manoj Gupta)....Pages 39-52
Materials Selection and Design Considerations (Dipen Kumar Rajak, Manoj Gupta)....Pages 53-80
Yielding, Fatigue, and Creep Response of Metal Foams (Dipen Kumar Rajak, Manoj Gupta)....Pages 81-98
Acoustic, Damping, Thermal and Electrical Properties of Metal Foams (Dipen Kumar Rajak, Manoj Gupta)....Pages 99-120
Concluding Remarks and Future Directions (Dipen Kumar Rajak, Manoj Gupta)....Pages 121-124
Back Matter ....Pages 125-133

Citation preview

Advanced Structured Materials

Dipen Kumar Rajak Manoj Gupta

An Insight Into Metal Based Foams Processing, Properties and Applications

Advanced Structured Materials Volume 145

Series Editors Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Germany Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Porto, Portugal Holm Altenbach , Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

Common engineering materials reach in many applications their limits and new developments are required to fulfil increasing demands on engineering materials. The performance of materials can be increased by combining different materials to achieve better properties than a single constituent or by shaping the material or constituents in a specific structure. The interaction between material and structure may arise on different length scales, such as micro-, meso- or macroscale, and offers possible applications in quite diverse fields. This book series addresses the fundamental relationship between materials and their structure on the overall properties (e.g. mechanical, thermal, chemical or magnetic etc.) and applications. The topics of Advanced Structured Materials include but are not limited to • classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforced plastics) • metal matrix composites (MMCs) • micro porous composites • micro channel materials • multilayered materials • cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere structures) • porous materials • truss structures • nanocomposite materials • biomaterials • nanoporous metals • concrete • coated materials • smart materials Advanced Structured Materials is indexed in Google Scholar and Scopus.

More information about this series at http://www.springer.com/series/8611

Dipen Kumar Rajak Manoj Gupta •

An Insight Into Metal Based Foams Processing, Properties and Applications

123

Dipen Kumar Rajak Department of Mechanical Engineering Sandip Institute of Technology and Research Centre Nashik, Maharashtra, India

Manoj Gupta Department of Mechanical Engineering National University of Singapore Singapore, Singapore

Formerly at Department of Mining Machinery Engineering Indian Institute of Technology (ISM) Dhanbad, Jharkhand, India

ISSN 1869-8433 ISSN 1869-8441 (electronic) Advanced Structured Materials ISBN 978-981-15-9068-9 ISBN 978-981-15-9069-6 (eBook) https://doi.org/10.1007/978-981-15-9069-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

For about the last two and half decades, with the field of engineering evolving at a fast pace, there has been widespread research interest in development and improvement of metal foams with particular objective to enhance their properties. The enhancement of mechanical, chemical, acoustics, electrical, and thermal properties ensures good performance and reliability of the end product. Metal foams exhibit a structure comprising a solid metal with a large volume fraction of gas-filled pores. Metal foams can be multifunctional when compared to its parent solid metal depending on how they are engineered. Over the years, applications of metal foams have been significantly growing and diversifying in different fields of engineering and beyond. The primary focus of this book, accordingly, is to provide insight into the fundamentals, applications, manufacturing aspects, and properties (mechanical, thermal, electrical, etc.) of metal foams. Their potential applications in various small- as well as large-scale industries are highlighted. The present book also focuses on aspects of designing simple structures by taking into account loading conditions under tensile, compressive, or torsional stress for metals and their foams. In view of theoretical analysis, clear explanation is provided as how metal foams can exhibit better structural properties when compared to their parent metal. It is hoped that the present book, in view of significant application potential of metal foams in near future, will be extremely useful for students and academicians in tertiary institutes and researchers working in research labs who are attempting to find lightweight solutions. Nashik, India Singapore, Singapore

Dr. Dipen Kumar Rajak Dr. Manoj Gupta

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Acknowledgments

We would like to take this opportunity to express our heartfelt thanks to the people who have helped with and contributed to the publication of this book, in particular, to our families for their unflagging love and understanding and to co-workers, friends, and students for their encouragement. We would also like to express our special gratitude to the following individuals (in alphabetical order): Professor (Dr.) S. Das, Former Director, Advanced Materials and Processes Research Institute, Bhopal, India, and Associate Professor (Dr.) L. A. Kumaraswamidhas, Head of Department, Department of Mining Machinery Engineering, Indian Institute of Technology (ISM), Dhanbad, India. Manoj Gupta will also like to acknowledge the funding from Ministry of Education Academic Research Funding (WBS# R 265 000 684 114) for the financial support.

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Contents

1 Introduction to Metallic Foams . . . . . . . . . . . . . . . . . . . . . 1.1 History of Metal Foam Development . . . . . . . . . . . . . . 1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Classifications of Foams . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Based on Materials and Structures . . . . . . . . . 1.3.2 Classification of Metal Foams Based on Manufacturing Processes . . . . . . . . . . . . . . 1.3.3 Classification of Foams Based on Applications 1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Applications of Metallic Foams . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 2.2 Applications . . . . . . . . . . . . . . . . . . . . . 2.2.1 General Considerations . . . . . . . 2.2.2 Structural Applications . . . . . . . 2.2.3 Noise/Sound Management . . . . 2.2.4 Aerospace/Space Industry . . . . . 2.2.5 Ship Building . . . . . . . . . . . . . 2.2.6 Railway Industry . . . . . . . . . . . 2.3 Building Industry . . . . . . . . . . . . . . . . . 2.4 Machine Construction . . . . . . . . . . . . . . 2.5 Biomedical Industry . . . . . . . . . . . . . . . 2.6 Functional Applications . . . . . . . . . . . . 2.6.1 Filtration and Separation . . . . . . 2.6.2 Support for Catalysts . . . . . . . . 2.6.3 Storage and Transfer of Liquids 2.6.4 Silencers . . . . . . . . . . . . . . . . . 2.6.5 Fluid Flow Control . . . . . . . . . 2.6.6 Battery Electrodes . . . . . . . . . .

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Contents

2.6.7 Spargers . . . . . . . . . . . . . 2.6.8 Flame Traps . . . . . . . . . . 2.6.9 Water Decontamination . . 2.6.10 Electrochemical Functions 2.6.11 Acoustic Control . . . . . . . 2.7 Summary . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . .

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3 Manufacturing Methods of Metal Foams . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Foam Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Air Bubbling . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Decomposition of Gas-Releasing Particles in Melt 3.2.3 Decomposition of Gas-Releasing Particles in Semi-solids . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Metal Deposition on Cellular Preforms . . . . . . . . 3.2.5 Casting Using a Polymer or Wax Precursor as Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Entrapped Gas Expansion . . . . . . . . . . . . . . . . . . 3.2.7 Co-compaction . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8 Hollow Sphere Structures . . . . . . . . . . . . . . . . . . 3.2.9 Gas–Metal Eutectic Solidification Method . . . . . . 3.3 Challenges in Metal Foam Production . . . . . . . . . . . . . . . 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Materials Selection and Design Considerations . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Foam Structure . . . . . . . . . . . . . . . . . . . 4.2 Properties of Foams . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Mechanical Properties . . . . . . . . . . . . . . 4.2.2 Thermal Properties . . . . . . . . . . . . . . . . . 4.2.3 Electrical Properties . . . . . . . . . . . . . . . . 4.3 Design Analysis for Material Selection . . . . . . . . 4.3.1 Materials Selection Procedure . . . . . . . . . 4.3.2 Method of Single-Objective Optimization 4.3.3 Significance of Material Indices for Metal 4.4 Designing of Simple Structure . . . . . . . . . . . . . . . 4.4.1 Constitutive Equations . . . . . . . . . . . . . . 4.4.2 Moments of Various Sections . . . . . . . . . 4.4.3 Elastic Deflection of Beam and Panels . . 4.4.4 Failure of Beams and Panels . . . . . . . . . . 4.4.5 Buckling of Columns . . . . . . . . . . . . . . . 4.4.6 Torsion of Shafts . . . . . . . . . . . . . . . . . .

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4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Yielding, Fatigue, and Creep Response of Metal Foams . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Integral Standard for Metal Foams . . . . . . . . . . . . . . . 5.2.1 Yield Conceptualization of Solid Metals . . . . 5.2.2 Review of Yielding Nature of Metal Foams . . 5.3 Structural Insight into Fatigue of Metal Foams . . . . . . 5.3.1 Introduction to Fatigue Terms . . . . . . . . . . . . 5.3.2 Fatigue Behavior of Metal Foams . . . . . . . . . 5.3.3 S-N Curves of Metal Foams . . . . . . . . . . . . . 5.4 Introduction to the Concept of Creep . . . . . . . . . . . . . 5.4.1 Creep of Metallic Foams . . . . . . . . . . . . . . . 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Acoustic, Damping, Thermal and Electrical Properties of Metal Foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Properties of Metal Foams . . . . . . . . . . . . . . . . . . . 6.2.1 Acoustic Properties . . . . . . . . . . . . . . . . . . 6.2.2 Damping Properties . . . . . . . . . . . . . . . . . . 6.2.3 Thermal Properties of Metal Foams . . . . . . . 6.2.4 Electrical Properties . . . . . . . . . . . . . . . . . . 6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Concluding Remarks and Future Directions . . . . . . . . . . 7.1 Types of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Materials Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Properties of Foams . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Analysis of Foams Under Different Types of Loading 7.5 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Appendix A: Manufacturers of Metallic Foams . . . . . . . . . . . . . . . . . . . . 125 Appendix B: List of Suppliers of Metallic Foam . . . . . . . . . . . . . . . . . . . 127 Appendix C: List of Research Groups Working on Metal-Based Foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Chapter 1

Introduction to Metallic Foams

Abstract In this chapter, metal foams are introduced and fundamentally described. Their unique structure and properties which made them different from conventional materials are introduced. For enhancing their appreciation, this chapter systematically and chronologically summarizes the origin and history of metal foams highlighting the efforts of researchers from prehistoric to modern times. The differentiation of metal foams when compared to conventional materials is highlighted. Different manufacturing methods to develop metal foams are described while simultaneously highlighting the need of optimizing the processing parameters. Finally, their applications originating due to their unique physical and mechanical properties in various industrial sectors are described succinctly.

1.1 History of Metal Foam Development Metal foams are cellular materials comprising a predominant volume occupied by the pores. Naturally occurring cellular materials such as pumice stone, wood, cork, bone, etc. due to their unique properties were instrumental in exciting researchers to fabricate cellular materials artificially [1]. Wood artifacts, for example, have been used in Egypt almost 5000 years back [2]. Wood is a multifunctional natural cellular material which not only provides physical support to tree but also carries out important functions such as circulation of water and nutrients [3]. Engineered cellular materials include honeycomb and foam structures. Cell formations in honeycombs are in a two-dimensional array whereas in foams it is a three-dimensional array of hollow polygons [4]. The matrix material of foams can be a polymer, glass, ceramic, or metal. In 1943, Benjamin Sosnick [5] first attempted to fabricate metal foam of aluminium using mercury vapors. Initially, a mix of aluminium and mercury was melted in a closed chamber under high pressure. Further release of pressure led to mercury vaporization at the melting point of aluminium, forming Al–Hg metal foam. In 1950s, it was revealed that liquid metals can be converted into metal foam by oxidizing the melt or by adding oxide particles; it was less hazardous process and enhanced the viscosity of material. Elliott in 1951 [6] developed an aluminium © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 D. K. Rajak and M. Gupta, An Insight Into Metal Based Foams, Advanced Structured Materials 145, https://doi.org/10.1007/978-981-15-9069-6_1

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1 Introduction to Metallic Foams

foaming process for the U.S. Navy at Bjorksten Research Laboratories (BRL). BRL then started to develop foamed aluminium for commercial use signing an agreement with the LOR Corporation. Stuart Fiedler from LOR Corp. in 1957 [7, 8] proposed another method of manufacturing metal foam comprising of an alloy and ground metal hydride (titanium and zirconium hydride). Metal foams for other potential applications, such as car bumpers, were also investigated during these years. BRL also continued to investigate several other metal foaming processes for foaming metals like lead and zinc. Numerous small companies also attempted to produce metal foams targeting properties enhancement and it is still an ongoing research. Erb et al. [9] in 1971 created the method for shaping products made of foam metal by progressive localized crushing. In this process, it was possible to accurately fit a metal part such as a wall partition, doctor blade, and the like to a ribbed surface. The localized heat of friction enhanced the ductility of the metal in the areas where crush forming results. Berry et al. [10] in 1972 synthesized cellular structured metal foam by melting and adding the dross. Niebylski et al. [11] in 1974 disclosed the synthesis of good quality lead zinc foams through a US Patent. Thornton et al. [12] in 1975 concluded that the increase in resistance to fracture under compression in the case of foams will be instrumental in long-column compression utilization. Niebylski et al. [13] in 1975 optimized the crushing force to form the foamed metal structure. They observed that if the foam consists of cells of small size, the crushed profile of the metal body complies more uniformly with the shape of the shaping plate. They advocated that pore size of foams should be between 1/32 to about 1/78 of an inch. They also indicated that foams with ordinary pore sizes moderately greater or smaller than this scale can also be utilized in applications. Till this time, aluminium is the most popular research material for metal foam production. For unknown reasons, popularity and the level of research and development activities in the field of metal foam declined after 1975 [14]. Niebylski et al. [15] in 1976 improved a process for the production of fiberreinforced metal foam. In this method, fibers and reinforced materials were placed into one vessel and stirred around 1200–10,000 rpm depending on the weight of the fiber and metal. The foam manufactured by this method exhibited a small pore size and more uniform length. Kendall et al. [16] in 1980 reported the synthesis of copper foams with exceptional potential for vacuum applications. Davies et al. [17] in 1983 reviewed the various approaches for the formation of metallic foams like casting, powder metallurgy, and metallic deposition. He suggested that casting metal around the granules is most recommended for the preparation of metallic foam because it allows casting parts with intricate shapes. He also noted that the investment casting can only be used when the metal exhibits a low melting point and identified the applications of metal foams in petrol engine exhaust, afterburner, and other devices. Cocks [18] in 1984 developed hyper-ballistic protection material for the fabrication of metal foams for the applications associated with space and rockets. Resurgence in metal foam manufacturing industry happened during the end of 1980s when Japanese engineers at Shinko Wire Co. developed Alporas process in 1986 where foamed aluminium was manufactured successfully using a batch casting process [19]. Marracino et al. [20] in 1987 introduced the new dormant

1.1 History of Metal Foam Development

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matrices for volume electrodes using metallic foams which present high specific surface areas and thus could be used for the electrolytic processing of dilute solutions. German physicist Joachim Baumeister in 1990 re-discovered the old powder-compact foaming route developed by Benjamin Allen in 1950s. This brought a significant level of sophistication and a fertile environment for new alternatives in lightweight material designs [21]. Jin et al. [22] in 1990 described a method for fabricating the metal foam in which gaseous bubbles were preserved inside a mass of the molten metal throughout foaming. In this method, there was neither a necessity to provide a controlled foaming temperature limit nor processing time. Only the condition was to finely separate solid stabilizer particles beyond the liquidus temperature of metal matrix and discharging the gas bubbles in the molten metal composite under the surface to form the metal foam with closed cells. Chen et al. [23] in 1991 reported the elastic properties of the copper foam with the help of holographic interferometry technique. Jin et al. [24] in 1992 described a novel method to produce the stabilized metal foam by producing foamed metal in which gaseous bubbles were retained within a mass of molten metal foaming process in which it is not mandatory to add a gas-evolving mixture or to manage the foaming in the controlled melt temperature span and limited processing time. Clancy et al. [25] in 1994 developed a technique to fabricate the low-density hollow sphere metallic foam. The hollow oxide sphere of 2 mm diameter was prepared by the powder slurry technique and degraded to the metallic state in the hydrogen environment with the composition of NiO, Cu2 O, and NiO-Cu2 O. To enhance the strength, the metal foam was sintered and the density was reduced to between 0.8 and 1.6 g/cc of the nickel hollow sphere. Knott et al. [26] in 2005 used die-casting process for the production of metal foams. In this method, the objective was to provide easy fabrication of metal foam which will fit the mass production demand and industry oriented. The method involved combining a blowing agent to a metal melt, wherein the metallic melt is injected into the die cavity of a metal die-casting system and is foamed utilizing a blowing agent which delivers gases and is solid at room temperature. Knott et al. [27] in 2005 also invented a process for making the metal foam with reduced weight compared with other conventional materials. Dobesberger et al. [28] in 2006 invented a device for the production of free flow of metal foam with particular physical characteristics. Kretz et al. [29] in 2008 preferred the casting process for the production of lightweight and low melting point metal foams. Kattannek et al. [30] in 2009 applied layers of molten metal to an open-pore non-metallic substrate to form porous metal foam body. Dunand et al. [31] in 2010 adopted sintering process for the fabrication of metal foam. The invention involves creating metallic foam by a sintering method that comprises solid-state sintering and migrating liquid phase to create and then densify the wall arrangement of the metallic foam. This method was not only employed to create super elastic macro-porous NiTi materials but also for other porous alloy/metal foam with a large pore size of 0.05–5 mm and porosity in the range of 20–80%. Campagna et al. [32] in 2011 reported the metal foam used for the heat exchanger application as condenser fins. Jung et al. [33] in 2012 disclosed preparation of the coated opencell aluminium foams by a nano-crystalline nickel coating via an electro-deposition process to enhance the stiffness, energy absorption, and damping capacity. Klett

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1 Introduction to Metallic Foams

et al. [34] in 2013 introduced a technique for the preparation of metal-bonded graphite composite foam. Graphite foams were used in many applications like heat sinks, heat exchangers, brake disk components, clutch components, etc. but for thermal cyclers and other components, the graphite foam exhibited drawbacks like low mechanical properties. By considering the drawbacks, a technique was developed in which three operations like grinding, mixing, and consolidation were done one after the other to enhance the properties of the graphite by adding filler material to form metal-bonded graphite composite foam. Banhart et al. [35] in 2013 introduced a method for a powder metallurgical production of metal foam which contains one metal and one metal alloy. In this method to form a dimensionally stable semi-finished product, a mechanical pressure in the range of 200–400 MPa, temperature up to 400 °C, and gas pressure in the range of 1–50 bars was utilized. Cochran et al. [36] in 2014 described the powder metallurgy and casting process for the fabrication of syntactic foam. The syntactic foam comprised of hollow metallic shells with solid metal foam matrix. By using this process they reported some enhancement in the properties like strength and density. Babcsan et al. [37] in 2015 disclosed a novel manufacturing method to fabricate metal foam by customizing the size of the bubble by oscillations produced by longitudinal waves inside the formation of the bubble. This method circumvented the drawbacks of the uneven size of the bubble diameter by introducing the gas bubble by special agitating devices or by injecting means through nozzle orifice to ultrasonic waves. Reesink et al. [38] in 2016 developed a process for the formation of an opencell porous-shaped body for the heat exchanger. The assortment of thermomagnetic material is based on the compound of the general formula [(Ay B1-y )2 + δCw Dx Ez ]. The invention proved that any suitable organic binder can be used as a binder for thermomagnetic materials. Noraas et al. [39] in 2017 used dual investment solid mold technique for the manufacturing of reticulated metal foam. Wood et al. [40] in 2018 developed combination of metal foams and carbon foam to augment heat transfer and enhance acoustic absorption. They also improved the design of surface coolers employed in turbo machines. The surface cooler consisted of inner and outer layers, where the outer layer comprised of metal foam, carbon foam, and the combination of both which is configured to increase heat transfer with improvement in acoustic absorption. Aronsson et al. [41] in 2019 manufactured hybrid metal foams with the help of electroplating process. This work disclosed electroplating metal foam by placing metal foam to be plated into an electroplating chamber with a plating material source. An electrolyte through the chamber carried metal ions from the plating material source in a controlled manner to produce an even coating of plating material on surfaces of the metal foam.

1.2 Introduction Cellular materials are one of the most widely emerging materials due to their remarkable low densities, high strength-to-weight ratio, aspects of their structure, and mechanical and thermal properties. Cellular materials are naturally obtained or can

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5

be fabricated and these are compulsorily composed of two phases, one is solid and other is gaseous phase [42]. Pumice stone, human bones, wood, rubber, and cork are some examples of naturally occurring cellular materials as shown in Fig. 1.1. As a result of unique combination of properties exhibited by these materials, engineers were enticed to reproduce these structures artificially leading to formation of manmade cellular materials such as metallic foams. Metallic foams comprise of a cellular structure and are produced by introducing gas into the molten metal creating voids which on cooling results in porous structure. The methods of synthesizing metal foams using different manufacturing techniques are described elsewhere [43]. Metal foams exhibit novel combinations of physical, mechanical, thermal, electrical, and acoustic material properties while simultaneously providing high stiffness-to-weight ratio, gas permeability, and high thermal conductivity [44]. They offer remarkable performance in applications where requirements of light and stiff structures, efficient absorption of energy, thermal management, and acoustic control are required [45]. Considering cell structure, metal foams are preliminarily classified as opencell and closed-cell foams. Open-cell metal foams are composed of interconnected network of pores (Fig. 1.2a) similar to loofah sponge while the pores of closed-cell foams (Fig. 1.2b) are not interconnected instead they are sealed like cellulose kitchen sponge where each cell is separated by very thin metal cell wall. The dependency of

Fig. 1.1 Naturally occurring cellular structure materials

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1 Introduction to Metallic Foams

(a)

(b)

Fig. 1.2 a Open-cell b closed-cell metal foam (© D K Rajak)

selecting the material structure is based on its application. Closed-cell metal foams exhibit excellent mechanical properties but due to isolated pores it will not allow access to internal surface. Therefore, they are applied for structural and load-bearing applications [46]. Open-cell metal foam is generally manufactured with the help of powder metallurgy. Open-cell metal foam has very large surface area per unit weight. Open-cell metal foams are largely used in the heat exchangers and have limitations particularly in automobile sector due to high cost of the material. Lu et al. [47] in 1998 used open-cell metal foam in heat exchangers and prepared two models for the testing. Using these two models they analyzed the temperature distribution, cell size, and also the heat transfer parameters. They claimed suitability of two models for applications in heat sinks for high power electronic devices and multi-layered heat exchanger for aeronautical applications. Ozmat et al. [48] used the reticulated metal foam heat exchanger in place of previously used materials. Due to the use of metal foam in heat exchanger, enhancement in the performance was reported. Ambrosio et al. [49] investigated effect of strut shape on convection heat transfer and pressure in open-cell metal foams. It was reported that the volumetric convection heat transfer coefficient (HTC) rapidly decreases with porosity, subsequently surface-tovolume ratio and HTC decrease at increasing porosity. Fink et al. [50] proved that the open-cell porous metal contributes toward the exceptional possibilities to enhance the performance. Figure 1.3 shows the open-cell metal foam manufacturing process illustrated by Pinkhasov [51]. In this process, two electrodes are taken and in between the electrodes, the metal foam was attached. The chamber was connected with the vacuum pump and DC supply. Firstly, DC supply was switched on to deposit nickel on the metal foam. Subsequently, the metal foam was subjected to pyrolysis in the presence of air in an electric furnace leaving the nickel for openwork structures. Hereafter, the nickel open work was passed through a vacuum pump for the sintering process and based on requirement the metal foam was rolled or pressed [51]. Among the foams, for impact absorption closed-cell metal foams are favored, likewise to the polymer foams in a bicycle helmet but for higher impact loads. Fire resistance and recycling potential can also be realized by closed-cell foams. The manufacturing of closed-cell metal foams is done by injecting the gas into the

1.2 Introduction

7

Fig. 1.3 Open-cell metal foam manufacturing process (adapted from Ref. [51])

molten metal or by causing the gas formation in the liquid by gas-releasing blowing agents. Tan et al. [52] investigated compression behavior of closed-cell aluminium (Al) foam by a direct impact test. They reported that dynamic strength properties are affected by the inertia effects associated with the dynamic localization of crushing. Micro-inertial results are liable for the improvement of the dynamic initial crushing strength at the subcritical velocities. Jeon et al. [53] investigated the elastic modulus, yield stress, and power-law hardening exponent of the closed-cell Al foam using both experimental measurements and finite element analysis. They reported that the elastic limit stress of the cell wall significantly enhanced the magnitude of the peak force and the elastic stiffness but did not improve the displacement at the peak force. Figure 1.4 shows conventional closed-cell metal foam manufacturing process capable to manage the density of foam samples. In this process, the metals and its alloys containing the inert gases are heated above their melting temperature and held till all the entrapped gas expands within the molten metal body to form individual Fig. 1.4 Closed-cell metal foam manufacturing process (adapted from Ref. [54])

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Fig. 1.5 a Metal foam, b porous metal, c metal sponge (adapted from Refs. [55–57])

cells and to attain the desired reduced density. After the desired density is realized, the metal is again cooled below the melting temperature of the metal to form a foamed body (closed-cell foam) [54]. The difference between materials with porosities can be understood with Fig. 1.5. (a) Metal foam or a cellular metal is metal produced with foaming process, where pores are intentionally infused in its structure. (b) Porous metal is generally referred to a metal having large volume of porosities in it. It is a special class of cellular metal and normally its pores are round and isolated from each other. Porous metals are also popular in several structural applications due to the presence of small pores. (c) Metal sponges are materials with highly complex porous structure which cannot be defined as cell. Porous metals have large volume of porosity typically in range of 75–95% while for metal foams range of porosity can be similar but the pores are deliberately integrated into their structure like open or closed cell through the manufacturing and foaming process (temperatures, foaming agents, stirring and holding time, etc.) [45]. Metal foams and porous metals possess distinct combination of properties that dense polymers and ceramic foams cannot acquire. For example, porous metals and metal foams retain their mechanical properties in extreme environments such as hightemperature conditions. However, metallic foams are more attractive for thermal applications such as heat exchanger, heat sink, and heat pipes due to conductive and high surface area (only open-cell foams) [46]. Meanwhile, the electrical conductivity of metal foam is low compared to the base metal but it is commonly used as electrodes for batteries because of high surface area and for this application nickel foams are extensively used [45]. In current scenario, due to the inherent and unique capabilities of metal foams, they are being progressively required in many sectors such as automobile industry, construction and infrastructure, aerospace and defense, marine, biomedical, railway, consumer goods, and others.

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Fig. 1.6 Metal foams usage in various industries

Figure 1.6 shows the approximate percentages of metal foam used in the various industries till 2019

1.3 Classifications of Foams 1.3.1 Based on Materials and Structures This section provides a snapshot of the most commonly used materials and structures that are used to fabricate metal-based foams. (a) Aluminium: In the case of Al-based materials, blowing agents such as CaCO3 , MgCO3 , ZrH2 , and TiH2 are commonly used. On heating, they release gases for the formation of pores in molten Al. To note that Shinko Wire Co., Germany developed a technique to fabricate very popular Al foam named as Alporas [45, 58]. (b) Copper and Nickel: Alantum, a global manufacturing industry patented a powder metallurgy process where high-quality iron, copper, and nickel metal foams were produced. They used organic binder solution to apply a coat of powder alloy on pure polyurethane (PU) foam [58]. Open-cell nickel foams were fabricated by using carbon foam-based templates to produce mufflers, electrodes for batteries of electrical vehicles, and sound absorption applications [59, 60].

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(c) Stainless steel and Titanium: Stainless steel and titanium foams are fabricated by using powder metallurgy-casting and hot isostatic pressing (HIP) methods. Foam products are mainly employed for aerospace and sports applications [61]. (d) Iron foam: Despite that most of the metal foams are made of aluminium alloys, iron-based metal foams serve various advantages such as high strength, high energy absorption ability, low cost, and better weldability over aluminium alloybased foams. Due to the differences between the decomposition temperatures of conventional foaming agents and the melting point of iron, it is hard to manufacture iron-based foams [62]. Iron-based foams were successfully developed by introducing CO and CO2 as foaming gases over conventional foaming agents. This newly developed manufacturing technique comprised of preparing a precursor by cold pressing iron, graphite, and hematite powders. After heating the precursor, molten iron was foamed by reduction reaction. Spherical pore shape with maximum porosity of 57% was obtained at 1350 °C [63, 64]. (e) Amorphous metallic foams: Regardless of several advanced properties of amorphous metals such as high strength, resistance to wear, and corrosion, they lack in ductility [65]. Therefore, to overcome this drawback combination of amorphous metals and metal foams which is termed as amorphous metal foam (AMF) or porous metallic glass (PMG) was introduced. Magnesium-, zirconium-, or palladium-based bulk metallic glass (BMG) foams were fabricated which exhibit high energy absorption ability with compressive ductility better than Al foams [66–68]. (f) Metal foam-based composites: Metal foams are combined with other metal or an alloy by filling a hollow section with foam material or by producing sandwich structures with a core made of metal foam. This combination provides unique set of properties. Foamed metal is ex situ bonded between sheets of a metal or an alloy by adhesive bonding, brazing, or diffusion bonding [69]. Sandwich panel structure consisting of Al foam inside Al shell offers good damping and high stiffness properties with low weight [70]. (g) Metallic hollow spheres: Metallic hollow spheres (MHS) consist of highly homogeneous spherical cell structures with combination of open and closed porosity providing flexibility over cell diameter and cell-wall thickness. They provides good mechanical damping properties and increased heat capacity which can be useful for the application of thermal storage systems and designing heat exchangers [71]. (h) Wire mesh structures: Wire-woven bulk Kagome is a new type of cellular metal structure which was assembled by using continuous helical wires systematically assembled in six different directions. As structures was periodic and uniform it exhibited very high compressive strength compared to Al foam materials. Their compressive strength and stiffness can further be increased by specific heat treatments or by selecting different wire materials [72, 73].

1.3 Classifications of Foams

11

1.3.2 Classification of Metal Foams Based on Manufacturing Processes Metal foams can be classified according to their manufacturing processes as shown in Fig. 1.7. Classification is done on the basis of pressure requirement and the physical state of metal during the process, viz., molten, vapor, powder, or ions.

1.3.2.1

Classification Based on Melt

(a) Using blowing agents: Blowing agents consist of hydrides of metal, carbonates, oxides such as TiH2 , CaCO3 , MgCO3 , ZrH2 , etc., which release gases on heating which are mixed and stirred with molten metal for specific period of time to form a metal foam [42, 45]. (b) Using space holders: Woven wire mesh, salt beads, hollow spheres, ceramics, or polymers could be used as a space holding fillers in which molten metal

Fig. 1.7 Classification of metal foams based of manufacturing techniques (adapted from Refs. [44, 74])

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is added and it is then removed after solidification of molten mass of metal resulting in a homogeneous interconnected porous structure [75]. (c) Metal gas injection: In this method, a pressurized gas (air, nitrogen, argon, etc.) is injected into molten metal while viscosity is controlled by adding ceramics or by varying melt temperature. For closed-cell metal foams and extensively for Al alloys, this technique is employed, where by controlling process parameters complex shapes can be fabricated with precision [45, 76]. (d) Foam replication for melt: Highly porous open-cell metal foams are created with this process, where a mold pattern of different material is prepared and reproduced with immersion of desired metal slurry in it and mold pattern is removed after solidification [77]. 1.3.2.2

Classification Based on Metal Powder

(a) Space holder techniques for metal powder: Metal powders are mixed with the space holder materials like TiH2 , carbamide, ammonium bicarbonate, dolomite, etc. followed by compaction to form a pellet which is then subjected to heat treatment process designed for the removal of space holder. Further, it is treated with sintering process which helps to remove leftover space holder particles resulting in metal foam porosity up to 90%. It is one of the most economical powder metallurgical processes offering flexibility over complex structures [78–80]. (b) Sponge replication for metal powder: Sponge replication is an efficient method for manufacturing ultralight metal foam with very high porosity, but the challenges are to control the process parameters such as pH, viscosity, binder, dispersant, and particle size and shape. Bakan et al. [81] fabricated 316 L steel foam using sponge replication method and obtained 98% porosity. They also validated that titanium carbonitrides (TiC0.7 N0.3) particles mixed with 2–4 wt% as reinforcement help retaining good strength. Moreover, Li et al. [82] studied the influence of process parameters on rheological properties of the Ti and Ti-alloy slurry for biomedical application. Figure 1.8 shows the schematic flowchart of polymeric sponge replication method for making a biomedical porous titanium scaffold. They further investigated the influence of powder shape for metal foam fabrication and indicated that the binder system should consist of at least two ingredients which will decompose at diverse temperature during the production of foam. (c) 3D-printing process: It is a successful process for producing a sacrificial template and template is printed (3D) using a CAD model for desired shape and size. It can be used for metal coating by using metallic slurry or loose powder filling the template followed by sintering [82]. Li et al. [82] introduced 3D-fiber deposition rapid prototyping technology. This technology was further successfully used to produce a novel 3D porous Ti6A14V scaffolds with fully interconnected porous network and highly controllable porosity and pore size.

1.3 Classifications of Foams

13

Fig. 1.8 Schematic flowchart of polymeric sponge replication method

(d) Loose powder sintering: This is simple and economical process where pressure is not required. A negative replica of desired structure is developed and metal powders are filled into it followed by sintering [83]. 1.3.2.3

Classification Based on Metal Vapors

In this method, polymeric sponge is made electrically conductive by coating it with electrically conductive materials such as graphite, and then deposition of metal is done by evaporation, chemical vapor deposition, or by electro-deposition [84].

1.3.2.4

Classification Based on Metal Ions

Shin et al. [85] fabricated copper foams with highly porous nano-structured cell walls using electrochemical deposition process. The foams produced showed a minimal interfacial electrical impedance due to their large surface area and nano-compactness. Because of nano-porous structure, these metal foams have a huge potential in various sectors (like biomedical, aerospace, and marine engineering). Therefore, these foams are getting more attention from researchers worldwide. Efforts are currently made to reduce the investment cost.

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Fig. 1.9 Classification of metal foam materials based on their applications (adapted from Refs. [86–90])

1.3.3 Classification of Foams Based on Applications Materials deployed for the desired applications of metal foams are classified as shown in Fig. 1.9. (a) Biomedical applications: 3D open-cell porous magnesium (Mg) is used in tissue engineering as bone scaffolds [91]. Titanium (Ti) scaffold is also commonly used for orthopedic and dental applications. In addition, for bone tissue engineering, alloys of Ti, Zr, Nb, Sn, Mo, and Si are found to be promising candidates as porosity of metal foams are adjusted with natural bone accordingly [92]. (b) Mechanical applications: Porous nickel, bronze, and stainless steels are widely used as mechanical filters in liquid streams such as streams of oil, gasoline, refrigerant, etc. In the rotating generator of gas turbine engines, Ni-Cr alloy foam contact seals are used [93]. Open-cell metal foams employed for the application of heat exchangers showed six times higher heat transfer rate [94, 95]. Karmann [45] introduced aluminium foam for automobile body structures where they achieved 50% reduction in weight with improvement in material stiffness and cost-effectiveness. Shinko Wire Company Ltd. developed and deployed ALPORAS as sound-absorbing material to reduce noise pollution near highways [45]. They also claimed their material to be fire resistant, durable, and resistant to weathering. Nickel cadmium (Ni-Cd) and nickel metal hydride (NiMH) batteries that are very popular and most widely used in automobile sector use Ni foam as an electrode [45]. Steel foams find applications in lifting

1.3 Classifications of Foams

15

arm and the support of a crane [69] as energy-absorbing material and in cars as a crash absorber [46, 96]. (c) Aerospace/space applications: Metallic foams have found applications in aerospace sector. As an example, DUOCEL has deployed foamed aluminium composite sunshade for an optical telescope satellite [45]. Aluminium foams are also used as reinforcements for load-bearing structure in satellites, clamping parts for supporting outer shell of an aircraft wing panel, and missile nose support [97]. (d) Civil applications: Metal foams are also used in infrastructural applications. Both aluminium and steel foams can be used. Aluminium foams can be replaced by steel foams in construction industry for the manufacturing of bars, rods, sandwich plates [98], walls, floors [69] balcony platform, and parking floor slab fabrication equipment for high-speed rail applications. Compared to aluminium foams, steel foam manufacturing and application are at their initial stage. Fundamental advantages for using steel instead of aluminium as base metal are due to their high elasticity, strength, yield stress, and better weld ability. However, for making a steel foam, manufacturing process is challenging due to high melting point of iron when compared to aluminium [99]. Applications where multifunctionality is considered as an important aspect, metal foams are replacing polymer foams as they function as a structural component in a sandwich panel providing acoustic damping as well [100].

1.4 Summary This chapter introduces the concept of metals foams and provides its history of development. Classifications of metallic foams based on different considerations while simultaneously providing their applications in a wide array of industrial sectors like automobiles, aerospace, biomedical, and marine engineering are provided so that the reader understands the viability, applicability, and importance of these unique materials. The work done so far globally has also indicated that aluminium-based materials are currently most widely used in industry for making metallic foams and apart from aluminium other materials like copper, steel, nickel, iron, magnesium, and zinc have also found applications in industry but their presence remains low when compared to aluminium. This chapter further highlights that much work needs to be done to develop foams of different materials and using manufacturing processes that are industrially viable, reproducible, and cost-effective.

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51. Pinkhasov, E. (1990). U.S. Patent No. 4,975,230. Washington, DC: U.S. Patent and Trademark Office. 52. Tan, P. J., Harrigan, J. J., & Reid, S. R. (2002). Inertia effects in uniaxial dynamic compression of a closed cell aluminium alloy foam. Materials Science and Technology, 18(5), 480–488. 53. Jeon, I., Katou, K., Sonoda, T., Asahina, T., & Kang, K.-J. (2009). Cell wall mechanical properties of closed-cell Al foam. Mechanics of Materials, 41(1), 60–73. 54. Patten, J. W. (1978). U.S. Patent No. 4,099,961. Washington, DC: U.S. Patent and Trademark Office. 55. Image retrieved from https://en.wikipedia.org/wiki/Metal_foam (Assess on 10/07/2019). 56. Image retrieved from http://www.porous-aluminum.com/sinteredmetal.html (Assess on 10/07/2019). 57. Coxworth, B. (2018). Hybrid foam combines strengths of wood and metal. Image retrieved from https://newatlas.com/wood-metal-foam/56577/ (Assess on 10/07/2019). 58. Walther, Gunnar, Kloeden, Burghardt, & Kieback, Bernd. (2010). A new pm process for manufacturing of alloyed foams for high temperature applications. Proceedings of the World Powder Metallurgy Congress and Exhibition, World PM, 2010, 4. 59. Wen, C. E., Yamada, Y., Shimojima, K., Chino, Y., Asahina, T., & Mabuchi, M. (2002). Journal of Materials Science Materials in Medicine, 13(4), 397–401. 60. Queheillalt, D. T., Katsumura, Y., & Wadley, H. N. G. (2004). Synthesis of stochastic open cell Ni-based foams. Scripta Materialia, 50(3), 313–317. 61. Salimon, A., Brechet, Y., Ashby, M. F., & Greer, A. L. (2005). Potential applications for steel and titanium metal foams. Journal of Materials Science, 40(22), 5793–5799. 62. Murakami, T., Akagi, T., & Kasai, E. (2014). Development of porous iron based material by slag foaming and its reduction. Procedia Materials Science, 4, 27–32. 63. Murakami, Taichi, Ohara, Kensuke, Narushima, Takayuki, & Ouchi, Chiaki. (2007). Development of a new method for manufacturing iron foam using gases generated by reduction of iron oxide. Materials Transactions, 48(11), 2937–2944. 64. Murakami, T., Omameuda, G., & Kasai, E. (2010). Effect of Cr2O3 and WO3 addition on pore formation and microstructure in iron foam. ISIJ International, 50, 307–313. 65. Schroers, J., & Johnson, W. L. (2004). Ductile bulk metallic glass. Physical Review Letters, 93(25). 66. Brothers, A. H., Dunand, D. C., Zheng, Q., & Xu, J. (2007). Amorphous Mg-based metal foams with ductile hollow spheres. Journal of Applied Physics, 102(2), 023508. 67. Brothers, A., & Dunand, D. (2005). Plasticity and damage in cellular amorphous metals. Acta Materialia, 53(16), 4427–4440. 68. Wada, T., Kinaka, M., & Inoue, A. (2006). Effect of volume fraction and geometry of pores on mechanical properties of porous bulk glassy Pd42.5Cu30Ni7.5P20 alloys. Journal of Materials Research, 21(04), 1041–1047. 69. Banhart, J., & Seeliger, H.-W. (2008). Aluminium foam sandwich panels: Manufacture, metallurgy and applications. Advanced Engineering Materials, 10(9), 793–802. 70. Leitlmeier, D., Degischer, H., & Flankl, H. (2002). Development of a foaming process for particulate reinforced aluminum melts. Advanced Engineering Materials, 4, 735–740. 71. Goehler, H., Jehring, U., Meinert, J., Hauser, R., Quadbeck, P., Kuemmel, K., et al. (2013). Functionalized metallic hollow sphere structures. Advanced Engineering Materials, 16(3), 335–339. 72. Lee, M. G., Hoang, V. M., Yoon, J. W., Han, S. M., Suh, Y. S., & Kang, K. J. (2014). Compressive strength of wire-woven bulk kagome with various orientations. Procedia Materials Science, 4, 209–214. 73. Lee, Y. H., Lee, B. K., Jeon, I., & Kang, K. J. (2007). Wire-woven bulk Kagome truss cores. Acta Materialia, 55(18), 6084–6094. 74. Korner, C., & Singer, R. F. (2000). Processing of metal foams-challenges and opportunities. Advanced Engineering Materials, 2(4), 159–165. 75. Kennedy, A. (2012). Porous metals and metal foams made from powders. Powder Metallurgy. https://doi.org/10.5772/33060.

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76. Babcsan, N., Banhart, J., & Leitlmeier, D. (2003). Metal foams-manufacture and physics of foaming. Retrieved from https://www.kfki.hu/anyagokvilaga/tartalom/2005/jan/03_Babcsan. pdf. 77. Ryan, G., Pandit, A., & Apatsidis, D. (2006). Fabrication methods of porous metals for use in orthopaedic applications. Biomaterials, 27(13), 2651–2670. 78. Bram, M., Stiller, C., Buchkremer, H. P., Stover, D., & Baur, H. (2000). High-porosity titanium, stainless steel, and superalloy parts. Advanced Engineering Materials, 2(4), 196–199. 79. Banhart, J., Baumeister, J. & Weber, M. (1995). Powder metallurgical technology for the production of metallic foams. In European Conference on Advanced PM Materials (Euro PM’95). 80. Asavavisithchai, S., & Kennedy, A. R. (2006). The effect of compaction method on the expansion and stability of aluminium foams. Advanced Engineering Materials, 8, 810–815. 81. Bakan, H. I., & Korkmaz, K. (2015). Synthesis and properties of metal matrix composite foams based on austenitic stainless steels-titanium carbonitrides. Materials and Design, 83, 154–158. 82. Li, J. P., de Wijn, J. R., Van Blitterswijk, C. A., & de Groot, K. (2006). Porous Ti6Al4V scaffold directly fabricating by rapid prototyping: Preparation and in vitro experiment. Biomaterials, 27(8), 1223–1235. 83. Butev, E., Yeni, E., Yilmaz, E., Esen, Z., & Bor, S. ¸ (2014). Effect of alkali treatment parameters on surface structures and mechanical properties of porous Ti6Al7Nb scaffolds. IMMC, Istanbul, Turkey. 84. Banhart, J., & Baumeister, J. (1998). Production methods for metallic foams. MRS Proceedings, 521, 121. 85. Shin, H.-C., & Liu, M. (2004). Copper foam structures with highly porous nanostructured walls. Chemistry of Materials, 16(25), 5460–5464. 86. Singh, S., & Bhatnagar, N. (2017). A survey of fabrication and application of metallic foams (1925-2017). Journal of Porous Materials, 25(2), 537–554. 87. Omnia, M. F. G. (2019). Composite metal foams and their applications. retrieved from https://www.omniamfg.com/mechanical/2018/4/16/composite-metal-foams-and-theirapplications (Assess on 13/07/2019). 88. Kalveram, S. (2017). Advances in metal foams. Retrieved from https://www.advancedscie ncenews.com/advances-metal-foams/ (Assess on 13/07/2019). 89. http://www.alantum.com/en/view.php?mn=116 (Assess on 13/07/2019). 90. https://amcetec.com/ (Assess on 13/07/2019). 91. Tan, L., Gong, M., Zheng, F., Zhang, B., & Yang, K. (2009). Study on compression behavior of porous magnesium used as bone tissue engineering scaffolds. Biomedical Materials, 4(1), 015016. 92. Nouri, A., Hodgson, P. D., & Wen, C. (2010). Biomimetic porous titanium scaffolds for orthopedic and dental applications. In Biomimetics learning from nature. 93. Dai, Z., Nawaz, K., Park, Y., Chen, Q., & Jacobi, A. M. (2012). A comparison of metal-foam heat exchangers to compact multilouver designs for air-side heat transfer applications. Heat Transfer Engineering, 33(1), 21–30. 94. Huisseune, H., De Schampheleire, S., Ameel, B., & De Paepe, M. (2015). Comparison of metal foam heat exchangers to a finned heat exchanger for low Reynolds number applications. International Journal of Heat and Mass Transfer, 89, 1–9. 95. Cardoso, E., & Oliveira, B. (2019). Study of the use of metallic foam in a vehicle for an energy economy racing circuit. Materialwissenschaft und Werkstofftechnik, 41, 257–264. 96. Liu, P. S., & Chen, G. F. (2014). Porous materials: Processing and applications. ButterworthHeinemann. https://doi.org/10.1016/C2012-0-03669-1. 97. Kremer, K„ Liszkiewicz, A., & Adkins, J. (2004). Development of steel foam materials and structures. US DOE and AISI final report DE-FC36-97ID13554 performed by Fraunhofer USA-Delaware Center for Manufacturing and Advanced Materials, Newark, DE.

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98. Neugebauer, R., Hipke, T., Hohlfeld, J., Thümmler, R. (2005). Metal foam as a combination of lightweight engineering and damping. In R.F. Singer, C. Koerner, V. Alstaedt, H. Muenstedt (Eds.), Cellular metals and polymers 2004 (pp. 13–8). 99. Smith, B. H., Szyniszewski, S., Hajjar, J. F., Schafer, B. W., & Arwade, S. R. (2012). Steel foam for structures: A review of applications, manufacturing and material properties. Journal of Constructional Steel Research, 71, 1–10. 100. Harte, A., Fleck, N. A., & Ashby, M. F. (2000). Sandwich panel design using aluminum alloy foam. Advanced Engineering Materials, 2, 219–222.

Chapter 2

Applications of Metallic Foams

Abstract This chapter cites multiple applications where metal foams are actively utilized. These applications broadly relate to structural, biomedical, chemical industry, and functional areas due to the outstanding properties metal foams exhibit when compared to parent metals. Applications of metal foams strongly depend on whether they are open-cell or closed-cell foams. Essentially, aluminium, steel, and iron foams are used in structural and aerospace industry. For biomedical applications, steel, cobalt–chromium, titanium, copper, and foams are popular for implants and tissue engineering. For chemical industry, nickel- and copper-based foams are extensively used. To note that the current scenario is attractive for metal foams to be used in various other engineering application that are not mentioned here and open to the imagination of engineers and researchers.

2.1 Introduction In the technologically fast-paced modern world, metal foams have emerged as lightweight material solution for several applications. Since 1990s, applications of metal foams are widening significantly. This class of materials exhibit extraordinary mechanical, physical, electrical, and structural properties coupled with low density [1, 2]. These unique properties make them popular in various engineering applications such as structural, functional, biomedical, and chemical requirements (Fig. 2.1) [1–3]. To note that properties of metal foams critically depend on fabrication process and their structure (open cell or closed cell). To this end, much focus is placed on scale-up of fabrication processes and to introduce new techniques for continuous production with better quality and low cost. Besides this, it is always desirable to investigate new materials which can be further used to fill the current gaps. Alantum is a global company that works on nickel, iron, and copper foams and produces high-quality open-cell foams, whereas Shinko Wire Company uses titanium hydride (TiH2 ) as a foaming agent in melts (using base metals like aluminium, copper, zinc, gold, etc.) to fabricate open- and closed-cell foams in large scale [1, 2]. Similar applications based on other materials, such as porous concrete, are also quite popular in © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 D. K. Rajak and M. Gupta, An Insight Into Metal Based Foams, Advanced Structured Materials 145, https://doi.org/10.1007/978-981-15-9069-6_2

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Fig. 2.1 Schematic of metal foams’ applications

industry. Applications of metallic foams in industry are still limited due to their comparatively high cost. One of the main constraining factors is the availability of suitable low-cost manufacturing process for mass production of metal foams. From the current perspective, when global warming has become an issue of serious concern to mankind, metal foams are actively sought for weight-critical structural applications and lightweight design where target is to select materials with high specific mechanical properties. The functional applications of metal foams are based on the parent metal property and are quite wide and promising as illustrated in subsequent sections.

2.2 Applications 2.2.1 General Considerations Applications of metal foams have seen a noticeable rising trend from 1990s for several applications in various sectors. However, suitable porous metals or metals foams can further be used for non-conventional applications such as in home appliances and furniture items (Fig. 2.2). The use of metal foams in both conventional and unconventional applications depends on several factors listed as follows [1, 2]:

2.2 Applications

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Fig. 2.2 Aluminium open-cell foam tea-table stand used as home appliance (adapted from Ref. [5])

• Porosity: This includes open- or closed-cell structures and pore sizes. • Metallurgical aspects: The type of material or microstructure. • Processing ability: This includes shapes of foams to be created or sandwich structures and machinability. • Economical aspects: This includes cost-effectiveness and mass production suitability. • Functionality suitability: This includes its functionality such as structural, biomedical, chemical, thermal, and any other special requirements. Figure 2.3 shows applications of metal foams with respect to their degree of openness or closed character in metal foams [1]. For investigating the capability to manufacture metal foams from metals or alloys, the problem statement is equally important. Metals (solid), composites, and alloys can be used for making foams. Traditionally, pure metals or alloys of titanium, copper, aluminium, nickel, and magnesium are favored for making metal foams [2]. Titanium is used for medical applications as it is bio-inert and compatible with tissues. Titanium or steels are preferred instead of other reactive or bio-toxic elements which may otherwise jeopardize the purpose of application. Heat resistance is another point of consideration and other issues such as processing, treatment, userfriendliness, and monetary considerations are also taken into account to decide on applicability of metal foams. There are several techniques to shape the foams prior to application. Cost factors again are important for choice of the method. A method to produce porous cellular metal structures will be unsuitable if it is not economical [3–5]. The following sub-sections briefly discuss about structural and functional applications of metal foams. The structural applications mostly involve closed-cell structures.

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Fig. 2.3 Applications of cellular metallic materials and metal foams based on degree of openness (adapted from Ref. [1])

2.2.2 Structural Applications 2.2.2.1

Automotive Industry

The requirement of higher safety in vehicles necessitated increased weight of the vehicle in the past. This, on the other hand, compromised on the fuel efficiency, which requires lighter weight of automobiles. Small cars are more in demand these days to reduce the travel cost and greenhouse gas emissions without compromising on passengers’ comfort. As a result, compact-sized engines and modified structures and designs have been introduced. Nevertheless, this creates problem regarding temperature in the engine section as all the parts are compactly placed or they are fitted with collision safeguard measures, requiring shortened dimensions. Moreover, acoustic emissions have to be controlled as well. These issues necessitated the development of multifunctional materials and among them metal foams are one of the viable options. Figure 2.4 shows reasons for use of foams in automotive structures. Generally, aluminium-based foams meet most of the requirements [6–8].

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Fig. 2.4 Reasons for use of metal foams in automotive and weight-critical sectors (adapted from Refs. [6–8])

2.2.2.2

Energy Absorption

Aluminium foams can outdo the conventional polymer foams for crash energy absorption in vehicles. Figure 2.5 shows a crash box used in vehicles designed for absorbing energy in an event of collision. There could be several types of collisions, such as head-on collision, rear-end collision, side-impact collision, etc., besides

Fig. 2.5 Crash box for domestic vehicles (adapted from Ref. [7])

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rollover accidents. To deal with all these situations, the absorber in vehicle requires various properties. The following features are necessary in good energy absorbers: a. The foam should have a very high yielding point. Yielding should begin only when the utmost tolerable stress is attained and just prior to distortion at the plateau stress, i.e., rectangular stress–strain curve. b. The foam should have immense energy absorption capability per mass, volume, or length. c. The foam should exhibit uniformity in energy absorption. Homogeneous aluminium foams are good energy absorbers and satisfactorily fulfill all these conditions [8, 9].

2.2.2.3

Lightweight Construction

The use of metal foams for lightweight construction depends on two major factors: a. high-stiffness-to-mass ratio and b. quasi-elastic deformation behavior, which reflects the sustainability of foams’ strength and life cycle. Foam-based structures can be used in lightweight structures because of the following reasons [8–11]: • Complex design can be possible to manufacture by melt route process. • Metal foams are more robust and tend to fail less catastrophically. • Metal foams exhibit multifunctional properties due to its base metals or alloys.

2.2.3 Noise/Sound Management For control and management of noise, metal foams are preferred material [12]. A passenger in a car may be exposed to high-decibel external and internal noises (noisy machine). In such cases, aluminium foams, such as Alporas, can be suitably used for noise reduction and control. If coupled with polymeric foam, metal foams can be capable of high-intensity sound absorption up to 99% with regard to certain frequencies in the range of 1–5 kHz [1].

2.2.4 Aerospace/Space Industry Like the automotive sector, lightweight materials and structures are important for aerospace industry as well. Foam-filled structures are used to substitute expensive honeycomb structures as the former increases efficiency and reduces cost. Metal foams are advantageous because they give higher buckling and crippling resistance.

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They also ensure isotropic mechanical properties and freedom to design composite structures without using any adhesive agent. The fire-resistant property also plays an important role in ensuring integrity of a structure. Boeing (USA) used massive titanium foam sandwich parts and aluminium sandwich structures with aluminium cores, for tail booms in airplanes and helicopters. Sandwich structures can be produced according to the required curvature and for three-dimensional profiles in contradiction with honeycomb structure. Due to these advantages, metal foam sandwiches are being increasingly used by aerospace industry [4, 13, 14]. They can be used in turbine blades where high stiffness is required with enhanced damping as well as in engine seals. Aluminium foams are also finding new applications in spacecraft as well as in energy absorber components and in satellites. Due to their lightweight and their isotropic properties, metallic foams have proved to be much suitable for use in satellites and space stations [15, 16].

2.2.5 Ship Building As in any structural application, low-weight and high-strength components are essential for shipbuilding also. Ships these days are basically constructed with aluminium sheets and honeycomb structures. Aluminium foam cores are important in shipping structures because they act as rigid core, supporting top layers. These layers are responsible for carrying load. Foams, sandwiched with polyurethane, can make stiff and light structures with low-frequency damping behavior. While comparing with massive plates, aluminium foam core materials have lower density but the same loadcarrying ability. Hence, sandwich products are always lighter and therefore preferred. Cellular metallic materials or metals foams can also be used for structural bulkheads, antenna, and elevator platforms as well as pyrotechnic lockers [8]. Most importantly, they are corrosion-resistant.

2.2.6 Railway Industry Similar to automotive industry, metal foams, particularly, aluminium-based foams are suitable for use in locomotive industry. Figure 2.6 shows the use of metal foam in German high-velocity train. The use of foam in this application was for following three reasons: a. Energy absorption. b. Lightweight construction. c. Noise/sound management. The only difference is that locomotive structures are huge as compared to regular automotives. The initial target is to use metal foams particularly for smaller trains and trolley cars which ply in city zones and where risk of collision is greater. As

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Fig. 2.6 Aluminium foam sandwich panel for prototype German high-velocity-intercity express train (adapted from Ref. [15])

an example, Japanese trains are using energy absorbers, which are made of 2.3 m3 Alporas aluminium foam block.

2.3 Building Industry There are numerous ways in which metal foams are used in construction industry. Concrete is an important material for building constructions. Of late, metal foams are finding applications in concrete for buildings. For example, building frontages are covered by decorative sheets of thin marbles, granite, or other types of stones so as to cover the concrete and enhance show of a building shown in Fig. 2.7. Metal foams can be used in building frontages as light, stiff, and fire-resistant structures by replacing expensive honeycomb structures. Moreover, for fire protection in building materials, aluminium foams are widely used nowadays. In elevators or lifts, use of aluminium foams reduces energy consumption because metal foams ensure lightweight even though safety regulations stipulate a certain weight for certain structures. Metal foams in lifts or elevators also work as energy absorbers which can reduce impact of shocks and regulate acceleration of lift. Metal foam sandwich panels in doors and hatches can reduce stiffness as well as facilitate fire protection particularly if aluminium foams that have low thermal conductivity are used. Aluminium melts at temperature of about 660 °C, which is substantially low. Still it can be unexpectedly steady when subjected to flames.

2.4 Machine Construction

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Fig. 2.7 Footsteps on the lower section made from aluminium foam (adapted from Ref. [17])

2.4 Machine Construction For construction of machines, there are several uses of metal foams. Foam-filled pillars or stiff foamed parts of machinery components enhance damping capacity and reduce inertia that could be used to substitute axles or platforms made with conventional metals. They can be used in fixed drilling and milling machines. Intrinsic damping in foamed housing used in hand-held drilling and milling machine gives advantage over traditional housings. Foamed housing also provides electromagnetic shielding ensuring efficient functioning of electrical machines. Aluminium foams can also be used to make operational part of grinding disk with the grinding material attached to edge. Partly open permeability would serve as material pool for material minced and enables intrinsic damping within disk and helps supress strong vibrations. For certain applications, floaters need to have very buoyant filling materials of high strength to measure level of corrosive or hot media. Polymers cannot be used in such cases while titanium welded sheets are suitable for such applications but they tend to be expensive. Aluminium foams, with dense outer skin, are found to be very suitable to replace expensive floaters [16].

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Fig. 2.8 Biomedical implant (adapted from Ref. [19])

2.5 Biomedical Industry Biomedical applications involve use of steels, cobalt–chromium, and titanium alloys shown in Fig. 2.8. These materials are used in bone replacement or dental implants as these are the most biocompatible metals or alloys while providing the necessary stiffness, strength, and biocompatibility. For instance, dental implants need the same strength as jaw. This is possible with titanium or cobalt–chromium foams. As regard to biomedical implants in general, due to close connection between density and modulus of metal foams, together with improved stiffness and biological compatibility, metal foams with open permeability promote bone growth. Biodegradable implants can be made from magnesium foams as well. Due to their high energyabsorbing capacity, metal foams are finding increasing application in sports industry also as protective gears [2, 3, 18].

2.6 Functional Applications Just as traditional powder metallurgical process has wide applications in the manufacture of sintered porous materials, metal foams also have growing applicability provided they have a definite extent of openness in functional applications.

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2.6.1 Filtration and Separation Conventionally, filters are of two kinds: those with separate dense particles or with fibers disseminated in fluid (suspension). The second type has filters that separate liquid or solid elements spread in gaseous fluid (smoke or fog). The first kind is used for eliminating impurities in oil, for separating yeast in beer, etc. The necessary qualities for such filters include increased filtering rate, corrosion resistance, maximum particle retention, and good mechanical properties at a minimal cost. Metal foams can ensure these qualities [2, 3].

2.6.1.1

Heat Exchangers and Cooling Machines

Copper and aluminium foams can be used for making high-conductivity components. For this purpose, open-cell structures are needed. Heat exchange process can be carried out in foams by passing liquid or gases through them [20]. Pressure drop can also be minimized in it. Coefficient of performance can be improved in metal foams if stream resistance can be kept low and thermal conductivity is kept higher, which can be difficult to achieve because they are contradictory. Another application of metal foams is in transpiration cooling. High surface area, good thermal conductivity, and low resistivity make foams more suitable component for manufacturing heat exchangers and cooling machines [21–23, 25–30]. Copper and aluminium foams can also be used in heat sink application (Fig. 2.9) for microelectronic components requiring higher rate of heat dissipation for power electronics, circuit boards, and computer chips [31, 32]. Generally, pin-fin array is employed for this purpose.

(a)

(b)

Fig. 2.9 Heat sink a copper foam (adapted from Ref. [32]), b aluminium foam (adapted from Ref. [33])

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2.6.2 Support for Catalysts Catalysts (aluminium, nickel, nickel–chromium, and Fe–Cr alloy foam) are used for accelerating rate of chemical reactions. Efficiency of a chemical process can be improved by using catalysts while avoiding generation of unwanted by-products. Efficacy of catalysis is determined by the maximum interaction between the catalytic agent and the concerned liquids or gases. One such application of catalyst involves lean sheets of corrosion-resistant metal foam, which is filled with slurry of catalyst and then treated at higher temperature. It ensures considerable structural and mechanical integrity. In other words, the catalyst will stick to foams even after passing through a number of temperature cycles. They can be used for eliminating nitrous oxide (NOx ) from the stack of power plants and automobile emissions [22].

2.6.3 Storage and Transfer of Liquids Metal foams can be used for fluid storage also. Self-lubricating bearings are one of the major products manufactured through powder metallurgy (P/M) in which oil is filled and allowed to slowly flow out of the bearings. Open-cell metal foam can be used for such applications. These bearings are advantageous than the conventional ones because of their high volume capacity. Such application is not only limited to oil but even water can be filled up and discharged for moisture regulation. Also it is used for storing fluid under cryogenic conditions. Anti-sloshing may be reduced with metal foams in partially filled tanks [24].

2.6.4 Silencers Due to their porosity, metal foams (NiCrAl, NiFeCrAl, FeCrAl, STS by Alantum) can be used for damping vibrations, sound, and pressure pulses. Metal foams can be tailored for producing dampening effect at certain frequencies as per requirement. They can absorb sudden pressure changes in pneumatic or hydraulic compressors. Metal foams are also cost-effective [25].

2.6.5 Fluid Flow Control Metal foams are used to control flow pattern of liquid and gaseous fluids (Fig. 2.10). They are used in flow distributors in valves and in wind straighteners in wind tunnels [6–12]. Because of indeterminate degree of openness in metal foams, one can tailor them as per requirement and make the product more effective.

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Fig. 2.10 Numerically simulated view for a heat transfer (adapted from Ref. [34]), b fluid flow and heat transfer (adapted from Ref. [35])

2.6.6 Battery Electrodes Another use of metal foams is in battery electrodes. Lead foams are being used to replace conventional lead gratings in lead–acid batteries. Electrochemically active lead oxide paste can be filled in voids of metal foam, which reacts with sulfuric acid (electrolyte). The foam used (lead based) works as an extremely good conducting matrix with nominal resistance offered by internal components of battery. In nickel– cadmium (Ni-Cd) batteries, nickel foams are used, which exhibit lightweight and high energy density. Nickel battery systems are being used by some of the leading automobile companies of the world such as General Motors, Toyota, and Honda for their next-generation hybrid and electric vehicles.

2.6.7 Spargers For certain purposes, it is necessary to use homogenized mixture of liquid and gas at a constant rate. Porous metals are required in such operations which generate bubbles. It is also suitable for preventing heat, vibration, and corrosion. Metal foams ensure optimum results for such applications as compared to various other materials [4].

2.6.8 Flame Traps Metal foams due to their higher thermal conductivities are used for retarding flame. Long running pipes transporting combustible fluid have to be kept away from the

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Fig. 2.11 Water filtration filter made from metal foam (adapted from Ref. [36])

source of ignition. Metal foams are also used in manufacture of such pipes. The working principle of flame arrester is quite simple. The flames propagating from one end of a pipe are exposed to open-cell metal foam. Due to higher thermal conductivity and open pores, flames at high velocities get neutralized as they come into contact with foams. It results in a pressure drop which obstructs flame from spreading to another end of the pipe. Flame arresters are important where there are fire hazards.

2.6.9 Water Decontamination Open-cell metal foams can be used to decrease ion accumulation in water (Fig. 2.11). Contaminated and turbid water is passed through highly porous metallic structures. During the process, undesirable ions react with the matrix material or as electrodes for zinc- and nickel-based batteries [28, 29]. Ions react to metallic structure leading to electroless reduction of chromium ions Cr (VI) by cast aluminium foam and this results in redox reaction and purification of water [21, 30, 31].

2.6.10 Electrochemical Functions In electrochemical reactors, nickel foams are often used as electrodes to enhance the performance [29, 30]. Filter-press electrode comprises quarantined stack of metallic overlays. These overlays are paired with turbulence promoters’ network of polymer which creates mesh of plastic and shielding membranes. Nowadays, this is replaced with sheets of nickel foams while keeping the turbulence promoters for the benefit of getting greater surface area for electrodes [28]. Another application of nickel foams is to make electro-catalytic processes more effective, while ensuring compactness of the reactor.

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2.6.11 Acoustic Control Metal foams can be used for acoustic control. The sound absorption device could be made with the prism-shaped part of metal foams. The incident sound waves are absorbed and transmitted by this apparatus. Research is underway to find effectiveness of closed-cell foams to absorb ultrasonic sound from impedance sources [37].

2.7 Summary This chapter described applications of metal foams in various industrial sector based on their unique properties. The open literature shows that metal foams are one of the most promising materials for fulfilling the increasing demands where certain properties such as weight reduction, specific mechanical properties, and certain thermal characteristics are required. Metal foams are emerging progressively for commercialization and widening its applications since 1990s. The work done so far globally has also shown that aluminium-based materials are currently most widely used in industry for making metallic foams and apart from aluminium other materials like steel, copper, nickel, magnesium, zinc, cobalt, and composites have also found applications in industry but their presence remains low when compared to aluminium. This chapter also highlighted the individual application under the flagship of structural, biomedical, chemical, and aerospace industries.

References 1. Lefebvre, L.-P., Banhart, J., & Dunand, D. C. (2008). Porous metals and metallic foams: Current status and recent developments. Advanced Engineering Materials, 10(9), 775–787. 2. Metal foams: Fundamentals and applications. (2012). DEStech Publications, Inc. 3. Banhart, J. (2013). Light-metal foams-history of innovation and technological challenges. Advanced Engineering Materials, 15(3), 82–111. 4. Banhart, J., & Weaire, D. (2002). On the road again: Metal foams find favor. Physics Today, 55(7), 37–42. 5. https://en.wikipedia.org/wiki/Metal_foam#/media/File:Metal_foam_Coffee_table.jpg (Access on 19/05/2020). 6. Simancik, Frantisek. (2001). Metallic foams-ultra light materials for structural applications. Inzynieria Materiałowa, 5, 823–828. 7. https://en.wikipedia.org/wiki/Metal_foam#/media/File:Metal_foam_-Crash_box_1.JPG (Access on 19/05/2020). 8. Banhart, John. (2005). Aluminium foams for lighter vehicles. International Journal of Vehicle Design, 37(2/3), 114. 9. Srinath, G., Vadiraj, A., Balachandran, G., Sahu, S. N., & Gokhale, A. A. (2010). Characteristics of aluminium metal foam for automotive applications. Transactions of the Indian Institute of Metals, 63(5), 765–72.

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10. Banhart, J., & Seeliger, H-W. (2008). Aluminium foam sandwich panels: manufacture, metallurgy and applications. Advanced Engineering Materials, 10(9), 793–802. 11. Claar, T. D., Yu, C.-J., Hall, I., Banhart, J., Baumeister, J., & Seeliger, W. (2000). Ultralightweight aluminum foam materials for automotive applications, pp. 2000-01–0335. 12. Jones, M., Tony, P., Daniel, S. & Christopher, H. (2009). Assessment of soft vane and metal foam engine noise reduction concepts. In 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference). Miami, Florida: American Institute of Aeronautics and Astronautics. 13. Liu, Hanru, Wei, Jinjia, & Zhiguo, Qu. (2012). Prediction of aerodynamic noise reduction by using open-cell metal foam. Journal of Sound and Vibration, 331(7), 1483–1497. 14. Read, S., & Peter, R. B. (2010). Aerofoils for gas turbine engines. U.S. Patent No. 7,753,654. Jul. 13. 15. García-Moreno, F. (2016). Commercial applications of metal foams: Their properties and production. Materials, 9(2), 85. 16. Ryan, S., Christiansen, E., & Lear, D. (2011). Shielding against micrometeoroid and orbital debris impact with metallic foams (pp. 267–269). Houston, TX, USA: NASA. 17. Sasan F., Dorsa, K., & Shervin, Z. (2019). Review of aluminium foam applications in architecture. In International Conference on Applied Research in Science, Technology & Knowledge, Rotterdam, Netherlands. 18. Salimon, A., Bréchet, Y., Ashby, M. F., & Greer, A. L. (2005). Potential applications for steel and titanium metal foams. Journal of Materials Science, 40(22), 5793–5799. 19. https://commons.wikimedia.org/wiki/File:Pseudoachondroplasia._02.jpg (Access on 19/05/2020). 20. Boomsma, K., Poulikakos, D., & Zwick, F. (2003). Metal foams as compact high performance heat exchangers. Mechanics of Materials, 35(12), 1161–1176. 21. Ejlali, A., Arash, E., Kamel, H., & Hal, G. (2009). Application of high porosity metal foams as air-cooled heat exchangers to high heat load removal systems. International Communications in Heat and Mass Transfer, 36(7), 674–679. 22. Gancarczyk, A., Sindera, K., Iwaniszyn, M., Pi˛atek, M., Macek, W., Jodłowski, P. J., et al. (2019). Metal foams as novel catalyst support in environmental processes. Catalysts, 9, 587. 23. ERG Inc. Oakland, USA. Duocel® Aluminum Foam–ERG Aerospace. (http://www.ergaerosp ace.com) (Access on 13/03/2019). 24. SEAC International B.V., Krimpen (Netherlands). (1998). Product data sheet of “Recemat”. (http://www.seac.nl) (Access on 13/03/2019). 25. Eisenmann, M. (1998). Metal powder technologies and applications. In ASM Handbook, 7, ASM International, 1031. 26. Metzger, W., Westfall, R., Hermann, A., & Lyman, P. (1998). Nickel foam substrate for nickel metal hydride electrodes and lightweight honeycomb structures. International Journal of Hydrogen Energy, 23(11), 1025–1029. 27. Xue, Y., Jun, L., Hao, C., Ruigang, W., Dingqiang, L., Jia, Q., et al. (2012). Nitrogen-doped graphene foams as metal-free counter electrodes in high-performance dye-sensitized solar cells. Angewandte Chemie International Edition, 51(48), 12124–12127. 28. Montillet, A., Comiti, J., & Legrand, J. (1993). Application of metallic foams in electrochemical reactors of filter-press type part I: Flow characterization. Journal of Applied Electrochemistry, 23(10), 1045–1050. 29. Cognet, P., Berlan, J., Lacoste, G., Fabre, P. L., & Jud, J. M. (1996). Application of metallic foams in an electrochemical pulsed flow reactor Part II: Oxidation of benzyl alcohol. Journal of Applied Electrochemistry, 26, 631–637. 30. Langlois, S., & Coeuret, F. (1989). Flow-through and flow-by porous electrodes of nickel foam. II. Diffusion-convective mass transfer between the electrolyte and the foam. Journal of Applied Electrochemistry., 19, 51–60. 31. Kim, S., & Lee, C.-W. (2014). A review on manufacturing and application of open-cell metal foam. Procedia Materials Science., 4, 305–309.

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32. https://en.wikipedia.org/wiki/Metal_foam#/media/File:Heat_sink_copper_foam.jpg (Access on 19/05/2020). 33. https://en.wikipedia.org/wiki/Metal_foam#/media/File:Design_heatsink.JPG (Access on 19/05/2020). 34. https://en.wikipedia.org/wiki/Metal_foam#/media/File:Mousse_aluminium_-_transfert_the rmique.png (Access on 19/05/2020). 35. https://en.wikipedia.org/wiki/Metal_foam#/media/File:Numerical_simulation_on_an_open_ cell_metal_foam._Velocity_and_temperature_fields.gif (Access on 19/05/2020). 36. https://commons.wikimedia.org/wiki/File:Aquarium_Sponge_Filter_foam_1.jpg (Access on 19/05/2020). 37. Iida, K., Mizuno, K., & Kondo, K. (1998). US Patent 4,726,444.

Chapter 3

Manufacturing Methods of Metal Foams

Abstract This chapter succinctly presents manufacturing processes for metallic foams. Nine manufacturing process are patented but only five major processes are successfully deployed for commercial purposes. Several manufacturing companies are tirelessly working on conventional and non-conventional approach targeting primarily for more efficient, reliable, reproducible, and low investment production system. These manufacturing systems target separately open-cell and closed-cell metal foams. As historically established in the area of materials science, metal foam properties depend critically on the type of base metal and manufacturing process. The present chapter also provides the glimpse of role of processing parameters which are critical in reproducing the structure and properties of foams. Present chapter also highlights the challenges in the production of metal foams.

3.1 Introduction Metal foam can be defined as an evolved structure from a parent metal containing a considerable amount of pores filled with gases that may be of different types. The pores can be sealed (closed-cell foam) or interconnected (open-cell foam). Aluminium is one of the most commonly used metals to produce foam [1–9]. However, other metals, viz., tantalum, copper, nickel, titanium, and even composites of metals, can be used to make foams. The most defining characteristic of a metal foam is the presence of high level of porosity which ensures its light weight. Also, metal foam, to an extent, retains physical properties of its base material. As indicated earlier, metal foam is a broad term. One can make several distinctions of metal foams on the basis of certain parameters: (a) Metal foam: This is a special class of cellular material, originating from liquid metals. In this structure, gas bubbles are finely dispersed in a liquid and it has a restricted morphology. It has closed, rounded, polyhedral cells, distinguished by degree of openness. (b) Porous metal: It refers to a structure having voids, which are usually circular and separated. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 D. K. Rajak and M. Gupta, An Insight Into Metal Based Foams, Advanced Structured Materials 145, https://doi.org/10.1007/978-981-15-9069-6_3

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(c) Metal sponge: In this structure, space is filled by pieces of metal that have interconnected network. Over the years, evolution of metallic foams from the conventional materials has proved to be a boon for the society [3–5]. New developments are creating wider scope of foam utilization and creating new areas of research [1–3]. Besides being light in weight, metal foams also display good energy absorption property, resistance to thermal cracks, good acoustic behavior, low relative density, high cell edge thermal conductivity, and larger surface area per unit volume. Even though metal foams generally have similar physical properties as that of the base metal, their thermal conductivity reduces due to their porous structure. Researchers have found that energy-absorbing capacity of the material increases when honeycomb materials are combined with metal foam as filler material. It may be noted here that metal tubes are largely used in energy-absorbing devices in cars, trains, and ships for protection against crash handling [6–13]. The process route chosen for the production of foam decides the structure, its corresponding properties, and applications. The properties of foams also depend upon pore size and relative density, i.e., its micro/macrostructure [14–19]. Metal foams serve to both structural and functional applications. Metal foams can be characterized/tested both microscopically and macroscopically. For characterizing metal foams, both destructive and non-destructive methods are used [20–34]. The properties of foams are characterized using conventional characterization tests such as tensile, compression, fatigue tests, etc. Microscopically, field emission scanning electron microscope (FESEM), energy dispersive X-ray (EDX), transmission electron microscopy (TEM), X-Ray powder diffraction (XRD), and Fourier transform infrared spectroscopy (FTIR) are used. Such characterizations help to get an overview of mechanical, physical, and other properties of metal foams [35–46]. This chapter aims to provide comprehensive description of manufacturing process commonly used for producing metal foams. Table 3.1 describes structural aspects, density ranges, and the corresponding processes for producing metal foams. Some of the processes are practically feasible and cost-effective while some other processes Table 3.1 The range of cell size and relative density for different metal foam manufacturing methods [21] Cell size (mm)

Relative density (–)

Cell-producing process (–)

0.01–0.1

0.01–0.1

Closed cell—HSC, PDISS, GME, EGE, PDM

00.1–1.0

0.1–1.0

Open cell—VEDCP, Partly open—MGI, PDM

1–10

Closed cell—MGI

where HSC hollow sphere consolidation, PDISS particle decomposition is semi-solid, GME gas–metal eutectic, EGE entrapped gas expansion, PDM particle decomposition in melt, VEDCP vapor of electro-deposition on open-cell polymer, MGI melt gas injection

3.1 Introduction

41

are still largely at experimental stage. To note that some of these processes produce open-cell foams while others produce closed-cell foams depending upon the processing conditions during the formation stage.

3.2 Foam Formation The first and the most important step in any investigation of metal or alloy foam is the preparation of specimen. Production of metal foam is a difficult task as the material is available in all three states, i.e., solid, liquid, and gaseous, at varying temperatures [6– 11]. Non-uniformity or randomness of the porous structure diminishes mechanical properties of the material. Hence, it is important to control the structure of foams to make them more stable. Nine different processes have been developed and patented for making metal foams. These processes are divided into two main groups: (i) Direct foaming. (ii) Indirect foaming. In direct foaming methods, the metal, which is in a liquid phase, is stirred with a blowing agent. Upon coming in contact with gas, the metal develops into foam. Indirect foaming method has an aluminium precursor with zirconium hydride and titanium as dispersed blowing agent particles. Upon heating above its melting point, the precursor expands, thereby turning into foam. Figure 3.1 illustrates five major production methods of metal foam (Alulight, Gasar, Foamcast, Hydroalcan, and Alporas). The nine processes which are commonly used for production of metal foams are as follows: 1. Air bubbling (direct foaming). 2. Deposition of gas-releasing particles in melt and by controlling pressure while cooling (direct foaming). 3. Deposition of gas-releasing particles in semi-solids (direct foaming). 4. Metal deposition on cellular preforms (indirect foaming). 5. Casting with a polymer or wax precursor as template (indirect foaming). 6. Entrapped gas expansion. 7. Co-compaction or casting of two materials. 8. Hollow sphere structures. 9. Gas–metal eutectic solidification.

3.2.1 Air Bubbling It is difficult to form foam of pure metals by infusing bubbling gas into them as the melt drains down the walls of bubbles, thereby reducing possibilities of forming a foam structure. However, 10–30% of tiny and gradually dissolving particles enhance

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Fig. 3.1 Five major production methods of metallic foams

the viscosity thereby stabilizing the foam. Pure aluminium is melted while stabilizing ceramic particles, like alumina, silicon carbide, and titanium diboride, etc., are added. Various gases can be used to form bubbles in liquid aluminium. The most commonly used gases are CO2 , O2, and various inert gases. Water can also be injected to form bubbles in the liquid metal. The process requires a gas injector-cum-stirrer through which the gas is injected into the melt and stirred continuously as shown in Fig. 3.2. Once, the gas bubbles rise up to the surface level of the liquid melt, the melt starts solidifying. Controlled and uniform flow of gas plays an important role in producing closed-cell foam structures. Various techniques can be adopted to float up the foam and up to 1-m-long and 0.2-m-thick slabs can be produced made up of closed-cell pores with diameter ranging from 5 to 20 mm. This is by far the least expensive method and is commonly used for commercial purposes [6–12].

3.2.2 Decomposition of Gas-Releasing Particles in Melt Figure 3.3 shows the process that involves melting of aluminium and stabilizing it between 670 and 690 ◦ C. Titanium hydride (TiH2 ) is the most commonly used foaming agent which is added into melt. TiH2 decomposes and releases hydrogen (H2 ) gas when heated above 465 ◦ C. Addition of TiH2 produces large volume of H2 gas, thereby creating bubbles, which can lead to formation of closed-cell foamed

3.2 Foam Formation

43

Fig. 3.2 Air bubbling process (CYMAT and HYDRO processes) (adapted from Refs. [1, 6, 9, 21])

Fig. 3.3 Particle decomposition in liquid (Alporas process) (adapted from Refs. [11, 21])

structure. Shinko Wire Company, Japan has developed aluminium foam, under the brand name Alporas using this method. The Alporas process was patented in the United States of America in 1987. Since the patent expired, several companies and research centers, such as Foamtech (Daegu, Korea) and Shanxi Putai Aluminum Foam Manufacturing (Linfen, China) have successfully used this method. It typically takes 10 min to decompose TiH2 completely. The cell size varies in the range of 0.5– 5 mm, primarily depending upon the TiH2 and cooling conditions. Relative densities from 0.2 to 0.07 can be attained with this process. Although very small amount of TiH2 and calcium is used in it, this process is found to be costlier than air bubbling as it happens to be a batch process which entails routine use of the expensive materials. Nowadays, only aluminium is used for this process because TiH2 decomposes too quickly in case of high melting point metals and hydrogen embrittles many metals including steels [13–18].

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Fig. 3.4 Particle decomposition in semi-solid (Fraunhofer & Alulight processes) (adapted from Refs. [17, 21])

3.2.3 Decomposition of Gas-Releasing Particles in Semi-solids In this method, the material with which foam is to be made is kept in semi-solid condition during foaming process. It begins by combining particles of a foaming agent (typically TiH2 ) with an aluminium alloy powder [19–24]. Gas particles are released for formation of bubbles, thereby obtaining a foamed structure. At around a temperature of 465 ◦ C, the decomposition process of TiH2 starts whereas the melting point of pure aluminium and its alloys is around 660 ◦ C. Initially, the materials, thoroughly mixed and cold compacted, are in powder form. This precursor material is cut into small pieces, placed inside a sealed split mold, and heated slightly above the solidus temperature of the alloy. TiH2 then decomposes, creating voids under high internal pressure. The expanded volume of semi-solid flow and the aluminium creates foams that fill up the mold. The process results in the formation of structures in the same shape as that of the container and exhibit relative density as low as 0.08. The foam has closed cells with diameter ranging from 1 to 5 mm. A schematic diagram of the manufacturing sequence is shown in Fig. 3.4.

3.2.4 Metal Deposition on Cellular Preforms Chemical vapor deposition (CVD) by evaporation or by electro-deposition is a process by which various metals can be deposited in the open-cell polymer foams which serve as a template (Fig. 3.5). The INCO process is an approach in which an open-cell polymer is kept inside the CVD reactor and nickel carbonyl is introduced, which decomposes into nickel and carbon monoxide when heated above 100 ◦ C and coats the heated surfaces in the reactor entirely. Infrared radiations are used to heat and remove the polymer from the reactor, leaving behind cellular structure of the metal with hollow ligaments. The limitation of this process is that nickel carbonyl is a highly toxic material, which has to pass through an expensive procedure for environmental control before being suitable for manufacturing any product. As a result of this, USA and a few other countries have banned nickel carbonyl or have made

3.2 Foam Formation

45

Fig. 3.5 CVD process to create open-cell nickel foam (INCO process) (adapted from Refs. [18, 21])

the treatment procedure prohibitively expensive in order to restrict its use. The CVD process has the advantage of producing lower electrical resistant material compared to that produced by other electrode methods. The pore diameter can vary in size from 100 to 300 µm The lowest relative density achieved is between 0.02 and 0.05 and the method is restricted to pure metals like nickel or titanium due to the complexity in the process of CVD or electro-deposition of alloys.

3.2.5 Casting Using a Polymer or Wax Precursor as Template Any metal, which is suitable for investment casting, can be considered feasible for this process. Duocel process developed by ERG Aerospace Corporation, Oakland, CA, (USA) (Fig. 3.6) is an example of this type. In this process, polymer is selected in the first place to make a precursor structure by injection molding of wax or polymeric lattices. Thereafter, a ceramic coating is applied to the polymer. Baking process is carried out in order to remove moisture and gain rigidity, creating a negative image of foams in the precursor as template. The mold is then slowly filled with the metal

Fig. 3.6 Manufacturing method for open-cell foam (Duocel process) (adapted from Refs. [15, 21])

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3 Manufacturing Methods of Metal Foams

or an alloy as per the requirement. Application of moderate pressure to overcome resistance to the flow is permissible in order to guarantee uniform distribution. This step is followed by directional solidification and cooling process to regain the original polymer foam. After the cooling process, an open-cell foamed structure is formed with the pore size ranging from 1 to 5 mm and with relative density at around 0.05. Figure 3.6 shows the processing steps used in Duocel process.

3.2.6 Entrapped Gas Expansion In this manufacturing technique, powders are compressed to a dense precursor material (Fig. 3.7). Gas is allowed to get entrapped in the material. This creates enormous pressure inside, resulting in expansion of the gas. The pore diameter ranges from 10 to 100 µm. One can expect to attain around 50% porosity with this technique. Powder metallurgy processes have been developed for manufacturing of materials by means of dispersion of small pores containing an inert gas, which tends to show very low solubility. A rolling process is commonly utilized to improve the structure and obtain greater uniformity. At the end, the material is kept at a high temperature of around 900 ◦ C, which raises the internal pressure to about 10–16 MPa. This causes reduction in the density of the material. The expansion of gas results in foam formation.

Fig. 3.7 Process steps used to manufacture titanium alloy sandwich panels with highly porous closed-cell cores (adapted from Refs. [1, 21])

3.2 Foam Formation

47

Fig. 3.8 Co-compaction processes (adapted from Ref. [21])

3.2.7 Co-compaction This process is used to produce metal foams (Fig. 3.8) of relative density between 0.3 and 0.5. Double connected structures of both phases are made by mixing and compacting two powders with volume fraction not less than 25%. Suitable solvent is used to leach out one powder type. The cell size in this process ranges between 10 µm and 10 mm.

3.2.8 Hollow Sphere Structures A few methods have been recently developed to synthesize hollow metal spherebased structures. One such method is shown in Fig. 3.9. These processes can further be differentiated by flotation methods and consolidation by hot isostatic pressing method, liquid phase sintering, or by vacuum sintering. Liquid phase sintering (LPS) is a favored method for certain alloys as it enables to avoid distortions due to compression. Moreover, with this method, prolonged high-temperature treatments are possible to ensure strong bonds between the particles. One of the methods developed at IFAM, Germany, helps to produce metal spheres of high uniformity by coating polystyrene spheres with slurry of metal and subjecting the spheres to sintering process.

3.2.9 Gas–Metal Eutectic Solidification Method Solid metals foamed by gas–metal eutectic solidification are termed as GASARs and apparatus required for this method is shown in Fig. 3.10, which means gas-reinforced materials. Certain liquid metals are suitable for eutectic system with hydrogen gas. When metals are melted under high pressure of up to 50 atm in a hydrogen atmosphere, certain changes take place in the melt, and that is homogeneous in nature. When temperature is lowered, the melt has a eutectic transition to a heterogeneous solid plus gas system. This solid plus gas system must have eutectic concentration,

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3 Manufacturing Methods of Metal Foams

Fig. 3.9 Schematic diagram of hollow sphere structure method (adapted from Ref. [47])

which causes a segregation reaction at a specific temperature. The melt begins to solidify causing gas pores to precipitate and get entrapped in metal. Mostly elongated pores are formed which are oriented along the solidification direction. The process includes melting of a material in the presence of a gas to densify it with hydrogen. It also entails directional solidification under controlled kinetic and thermodynamic constraints. The resultant material obtained out of this process has a monolithic matrix and proper geometrical shapes of the pores, thereby providing GASARs with comparatively higher strength, thermal and electrical conductivities, and plasticity as compared to other porous materials. Applications of GASARs include filters, bearings, metal-matrix composites, etc.

3.3 Challenges in Metal Foam Production Metallic foams can be used in a huge number of applications in various sectors as has been described in Chap. 2. However, it is open to all researchers, scientists, practicing engineers, and academicians to develop new technologies or accessories and attachment to reduce the manufacturing costs in order to gain more attention and

3.3 Challenges in Metal Foam Production

49

Fig. 3.10 Schematic illustration of apparatus used for gas eutectic solidification method (adapted from Ref. [48])

widespread application. Some of the following constraints as per open literature [49, 50] are as follows: a. Choice of materials: Only a limited number of metals and alloys are used to make foams, which can be expanded for even better mechanical, thermal, and other targeted properties. b. Control of foam structure: It is still a challenge to produce metallic foams in large scale with uniform pore size and wall thickness. To note that if foams are produced with inhomogeneous structure then the mechanical properties such as energy absorption during loading will be compromised. The research conducted so far also indicated that it is difficult to produce uniform structure of cell pores, layer by layer surrounded with solid surface due to lack of manufacturing process, which is always required for heavy load-bearing applications. c. Development of manufacturing processes: There is a strong need to further develop existing manufacturing processes which can reliably synthesize metal foams with reproducible structures at large scale and low cost. d. Properties Characterization: There is still insufficient knowledge required for foam property characterization and identification of the material behavior at micro- and nano-level. This information can be very critical in determining the characteristics of foams under various conditions and must be further explored. e. Transfer of research findings to design engineers: A wide gap between these two segments often thwarts further development of a specific type of metal foam due

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to lack of clear and detailed knowledge about the metal foam being used and their manufacturing process. f. Cost factor: Using the current methods available, metal foams are more expensive when compared to their base elements. A reduction in this gap will enhance the further use of metal foams in many industrial sectors.

3.4 Summary This chapter broadly highlights various manufacturing techniques that are used to synthesize metal foams and five major production methods which are commonly used commercially. These processes are described, wherever possible, with the help of schematic diagrams. The present chapter also highlights different parameters that need to be optimized and crucial for processing of foams with best possible structure. Some of these parameters include temperature, foaming agents, thickening agents, stirring time, holding times, and other reinforcement materials. To note that the demands of cellular metallic materials or metallic foams are lacking due to high manufacturing cost and insufficient knowledge of properties. It is extremely important that the existence of manufacturing processes should be improvised by integrating them with new technologies or through further rectification of present processing methodology. To note that such improvisation must ensure and target to enhance the end properties of foams.

References 1. Banhart, J. (2001). Manufacture, characterization and application of cellular metals and metal foams. Progress in Materials Science, 46(6), 559–632. 2. Banhart, J. (1999). Metal foams and porous metal structures. Berlin: MIT-Verlag. 3. Banhart, J., Ashby, M. F., & Fleck, N. A. (2001). Cellular metals and metal foaming technology. Berlin: MIT-Verlag. 4. Banhart, J., Fleck, N. A., & Mortensen, A. (2003). Cellular metals: Manufacture, properties, applications. Berlin: MIT-Verlag. 5. Degischer, H.-P., & Kriszt, B. (2010). Handbook of cellular metals: Production, processing, applications. Wiley-InterScience. 6. Jin, et al. (1990). Method of producing lightweight foamed metal. US Patent No. 4,973,358. 7. Jin, et al. (1992). Stabilized metal foam body. US Patent No. 5,112,697. 8. Jin, et al. (1993). Lightweight metal with isolated pores and its production. US Patent No. 5,221,324. 9. Kenny, et al. (1994). Process for shape casting of particle stabilized metal foam. US Patent No. 5,281,251. 10. Niebyski, et al. (1974). Preparation of metal foams with viscosity increasing gases. US Patent No. 3,816,952. 11. Miyoshi, T., Itoh, M., Akiyama, S., & Kitahara, A. (1998). Aluminum foam, ALPORAS, the production process, properties and applications. Shinko Wire Company, Ltd. 12. Thomas, et al. (1997). Particle-stablilized metal foam and its production. US Patent No. 5,622,542.

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13. Akiyama, et al. (1987). Foamed metal and method of producing same. US Patent No. 4,713,277. 14. Elliot, J. C. (1956). Method of producing metal foam. US Patent No. 2,751,289. 15. ERG Inc. Oakland, USA. Duocel® Aluminum Foam–ERG Aerospace. (https://www.ergaer ospace.com) (Access on 13/03/2019). 16. Schwartz, D. S., & Shih, D.S. (1998). Titanium foams made by gas entrapment. In D. S Schwartz, D. S. Shih, A. G. Evans, & H. N. G. Wadley (Eds.), Porous and cellular materials for structural application. Materials Research Society Proceedings, 521, MRS, Warrendale, PA, USA. 17. Sang, et al. (1994). Process for producing shaped slabs of particle stabilized foamed metal. US Patent No. 5,334,236. 18. Paserin, V., Marcuson, S., Shu, J., & Wilkinson, D. S. (2004). CVD Technique for inco nickel foam production. Advanced Engineering Materials, 6(6), 454–459. 19. Akiyama, S., Ueno, H., Imagawa, K., Kitahara, A., Nagata, S., Morimoto, K., et al. (1986). Foamed metal and method of producing same. U.S. Patent 4,713,277. 20. Baumeister J. (1991). Methods for manufacturing foamable metal bodies. US Patent 5,151,246. 21. Ashby, M. F., Evans, A. G., Fleck, N. A., Gibson, L. J., Hutchinson, J. W., & Wadley, H. N. G. (n.d.). Metal Foams: A Design Guide. 263. 22. Yu, C. J., & Eifert, H. (1998). Metal foams. Advanced Materials & Processes, 45–47. 23. MEPURA. (1995). ‘Alulight’ Metallpulver GmbH. Brannau-Ranshofen, Austria. 24. Quadbeck, P., Kümmel, K., Hauser, R., Standke, G., Adler, J., & Stephani, G. (2010) Open cell metal foams-application-oriented structure and material selection, 10. 25. Bart-Smith, H., Bastawros, A.-F., Mumm, D. R., Evans, A. G., Sypeck, D. J., & Wadley, H. N. G. (1998). Compressive deformation and yielding mechanisms in cellular Al alloys determined using X-ray tomography and surface strain mapping. Acta Materialia, 46(10), 3583–3592. 26. Kottar, A., Kriszt, B., & Degisher, H. P. (1999). Shear test in flatwise plane of flat sandwich constructions or sandwich cores. Philadelphia, PA: American Society for Testing and Materials. 27. ASTM E8 / E8M-16ae1. (2016) Standard Test Methods for Tension Testing of Metallic Materials, ASTM International, West Conshohocken, PA. 28. Andrews, E., Sanders, W., & Gibson, L. J. (1999). Compressive and tensile behaviour of aluminum foams. Materials Science and Engineering: A, 270(2), 113–124. 29. Andrews, E. W., Gioux, G., Onck, P., & Gibson, L. J. (2001). Size effects in ductile cellular solids. Part II: Experimental results. International Journal of Mechanical Sciences, 43(3), 701–713. 30. Bastawros, A., & McManuis, R. (1998). Case study: Use of digital image analysis software to measure non-uniform deformation in cellular aluminum alloys. Experimental Techniques, 22(2), 35–37. 31. Brigham, E. O. (1988). The fast Fourier transform and its applications. Prentice Hall. 32. Chen, D. J., Chiang, F. P., Tan, Y. S., & Don, H. S. (1993). Digital speckle-displacement measurement using a complex spectrum method. Applied Optics, 32(11), 1839. 33. Instron. (1997). Surface displacement analysis user manual. 34. Deshpande, V. S., & Fleck, N. A. (2000). Isotropic constitutive models for metallic foams. Journal of the Mechanics and Physics of Solids, 48(6–7), 1253–1283. 35. Gioux, G., McCormack, T. M., & Gibson, L. J. (2000). Failure of aluminum foams under multiaxial loads. International Journal of Mechanical Sciences, 42(6), 1097–1117. 36. Hutmacher, D. W. (2001). Scaffold design and fabrication technologies for engineering tissuesstate of the art and future perspectives. Journal of Biomaterials Science, Polymer Edition, 12(1), 107–124. 37. Banhart, J., & Seeliger, H. W. (2012). Recent trends in aluminum foam sandwich technology. Advanced Engineering Materials, 14(12), 1082–1087. 38. Neugebauer, R., & Hipke, T. (2006). Machine tools with metal foams. Advanced Engineering Materials, 8(9), 858–863. 39. Baumeister, J., Banhart, J., & Weber, M. (1997). Aluminium foams for transport industry. Materials & Design, 18(4–6), 217–220.

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40. Schäffler, P., Hanko, G., Mitterer, H., & Zach, P. (2008). Alulight metal foam products. In Proceedings of the Porous Metals and Metallic Foams. The Japan Institute of Metals Kyoto, Japan, 7–10. 41. Eshraghi, S., & Das, S. (2010). Mechanical and microstructural properties of polycaprolactone scaffolds with one-dimensional, two-dimensional, and three-dimensional orthogonally oriented porous architectures produced by selective laser sintering. Acta Biomaterialia, 6(7), 2467– 2476. 42. Partee, B., Hollister, S. J., & Das, S. (2006). Selective laser sintering process optimization for layered manufacturing of CAPA® 6501 polycaprolactone bone tissue engineering scaffolds. Journal of Manufacturing Science and Engineering, 128(2), 531–540. 43. Truscott, M., de Beer, D., Vicatos, G., Hosking, K., Barnard, L., Booysen, G., & Ian Campbell, R. (2007). Using RP to promote collaborative design of customised medical implants. Rapid Prototyping Journal, 13(2), 107–114. 44. Faustini, M. C., Neptune, R. R., Crawford, R. H., & Stanhope, S. J. (2008). Manufacture of passive dynamic ankle-foot orthoses using selective laser sintering. IEEE Transactions on Biomedical Engineering, 55(2), 784–790. 45. Fukuda, A., Takemoto, M., Saito, T., Fujibayashi, S., Neo, M., Pattanayak, D. K., et al. (2011). Osteoinduction of porous Ti implants with a channel structure fabricated by selective laser melting. Acta Biomaterialia, 7(5), 2327–2336. 46. Wang, Y., Shen, Y., Wang, Z., Yang, J., Liu, N., & Huang, W. (2010). Development of highly porous titanium scaffolds by selective laser melting. Materials Letters, 64(6), 674–676. 47. Gohler, H., Jehring, U., Kuemmel, K., Meinert, J., Quadbeck, P., Stephani, G., et al. (2012). Metallic hollow sphere structures—Status and outlook. In Proceedings of Cellular Materials— CellMat 2012, 07.09. November 2012, Dresden. 48. Shapovalow, V. I. (1993). US Patent 5,181, 549. 49. Banhart, J. (2000). Metallic foams: Challenges and opportunities (pp. 13–20). Berlin: MITVerlag. 50. Korner, C., & Singer, R. F. (2000). Processing of metal foams—Challenges and opportunities. Microstructural Investigation and Analysis: Wiley-VCH Verlag GmbH, Weinheim.

Chapter 4

Materials Selection and Design Considerations

Abstract This chapter describes material selection in relation to design considerations using open literature resources. The mechanical, thermal, and electrical properties underlined by fundamental knowledge of design analysis for materials selection is succinctly described. More specifically, the elastic deformation and constitutive equations for failure, buckling, and torsion phenomena are presented. Failure mechanism of dense and metallic foams is explained in relation to materials and design prospective. The chapter also focusses on procedure, function, objectives, constraints, free variable along with single optimization methods, and significance of materials. Additionally, the chapter also addresses the indices for metal foam design of simple structures and constitutive equations for the same are highlighted.

Nomenclature E G Et Ec R Rs L B T F S* I B1 , B2 M x dA T

Young’s modulus or modulus of elasticity Shear modulus Tensile modulus Compression modulus Resistance of parent metal Resistance of metal foam Length of panel Breadth of panel Thickness of panel Force per unit width Desired bending stiffness Second moment of area of section Constant depending upon the distribution of load Mass of the panel Distance of fiber from neutral axis The cross section of fiber Torque exerted by the fiber on beam after loading

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 D. K. Rajak and M. Gupta, An Insight Into Metal Based Foams, Advanced Structured Materials 145, https://doi.org/10.1007/978-981-15-9069-6_4

53

54

ym J M b1 , b2 Ff Mf C Fcrit N K T

4 Materials Selection and Design Considerations

Normal distance of outer surface from neutral axis Polar moment of inertia Moment Constants depending upon the type of loading and the supports of the beam Failure force Failure moment Constant value which depend upon the support and type of loading Critical force required to buckle the beam loaded axially Half wavelength in buckled shape Stiffness Torque applied on cross–section

Greek Letters ρ ρs ρ/ρs υ εD σp1 σts λ λs

δ

σy σ1 , σ2 , σ3 1 δθ  θ τs

Density of foam Density of parent metal Relative density of metal foam with respect to parent metal Poison’s ratio Densification strain Plateau stress Ultimate tensile strength Thermal Conductivity of parent metal Thermal Conductivity of metal foam Density of panel Tensile strength Principle stresses Strain in fiber An angle subtended by fiber at the center Deflection of the beam End slope Shearing stress

4.1 Introduction Everything that exists in the world which we can see, touch, and sense is defined as matter Matter exists in three forms: solid, liquid, and gas. Nature has always maintained a balance of all these three forms to arrive at best possible properties. The best example is the human body, which consists of solids (skin, bones, organs, etc.), liquids (blood, saliva), and gasses (respiratory system comprising inhalation

4.1 Introduction

55

of oxygen and exhalation of carbon dioxide, etc.). Metal foam is a porous material having a cellular structure comprising of metal and gas bubbles [1]. The presence of gas bubbles in metal makes the foam lighter than the parent material. There are closed-cell foams (bubbles sealed from each other) or open-cell foams (bubbles interconnected) [2]. Closed-cell metal foams find applications mainly for the purpose of energy absorption due to their outstanding compressive properties. Investigation into the history of metal foams takes one to the era of the Second World War. In 1943, Benjamin Sosnick made an attempt to make foam of aluminum and mercury [3]. With the development of a new technology, less hazardous methods evolved in the decade of 1950. Commercial use of metal foam was started by the US Navy around the same time. However, there was a pause in R&D activities related to metal foams after 1975, due to issues concerning quality degradation, safety, recycling, etc. However, research on metal foams resumed in the late 1980s, and then onwards there have been extensive research activities, especially in countries like Japan, Norway, Canada, as well as in various other parts of the world [1, 4]. Metal foams find tremendous applications in dust and fluid filters, heat exchanging devices, automobile sector, mufflers at engine exhausts, porous electrodes, shock and impact absorbers, high-temperature gaskets, flame arresters, abradable seals, acoustics, load-bearing sectors, marine, building construction, and high-performance engineering applications, etc., as discussed in Chap. 2 [5–12]. The unique combination of lightweight, high thermal stability, good electrical insulating property, air and water permeability, unusual acoustic properties, energy absorption, good environmental and corrosion properties, etc., justifies the wide range of applications of metal foams [5, 13, 14]. In spite of its wide applications, metal foams are not yet extensively used for commercial purposes. The primary reason is the high production cost of metal foams. Nevertheless, the scenario is changing [2, 6]. The characteristics of metal foams depend upon the material from which it is made. The properties are generally determined by four factors listed below [2, 6]: a. Relative density of foam (ρ/ρs ratio of density of foam and density of parent metal). b. Structure of metal foam that is whether it is open- or closed-cell foam. c. Anisotropy. d. Defects (buckled or broken cell walls). The material selection is the first and very crucial part of the design procedure. Wrong material selection leads to premature failure of the components leading to accidents and causing financial, as well as human life losses. It is said that “Well begun is half done”. In other words, the selection of correct material contributes to correct designing of the required component. It can be an overwhelming task due to the wide availability of materials and processes in the open literature. The present chapter addresses material selection techniques for the designer and computation of material indices taking into account various functions, objectives, and constraints. In the designing procedure, material selection is followed by the determination of dimensions and type of loading of components. The dimensions are generally ascertained by the type of failure that the material may encounter. For

56

4 Materials Selection and Design Considerations

example, shafts are used for transmitting power and are subjected to torsional load while horizontal beams are subjected to bending leading to deflections and vertical columns are subjected to compressive loads and buckling loads, etc. If appropriate dimensions are not selected, the components may fail in the application in spite of correct material selection. Hence, it necessitates the designer to study failure characteristics for optimized design. A detailed study of bending failure, buckling, etc., is carried out emphasizing on various ways of supporting. In addition, a comparison is also made between the properties of metal and its foam at the end of each study.

4.1.1 Foam Structure Metallic foams comprise of small/medium/large voids and cell walls which depend on their base metals/alloys and manufacturing technique. Metallic foams are classified based on the degree of openness of pores, i.e., open-cell and closed-cell foams. The foam structures can be better explained using metal foams developed by Cymat (Al-SiC), Mepura (Alulight) and Shinko (Alporas) as they are globally recognized foams manufacturing companies with patented technologies. Figure 4.1 shows the polyhedral structure of foams that is similar to soap films with thin cell faces and thick plateau borders. Figure 4.1 shows foams of different relative densities. Relative density of Cymat is between 0.02 to 0.2 (Fig. 4.1a), whereas for Alulight (Fig. 4.1b), the relative density ranges between 0.08 and 0.2, and for Alporas (Fig. 4.3c), relative density lies in the range of 0.1–0.35. All three manufacturers produced foams that are unique such as in terms of relative density where the relative density follows the order as Cymat (0.05) < Alulight (0.09) < Alporas (0.25). Cymat foams are composed of large voids with large volume, and hence exhibit lower relative density and thinner cell walls. Wherein Alporas and Alulight foams show small voids with decreasing volume with thicker cell walls leading to relatively higher relative density [6].

Fig. 4.1 Microstructural images showing the pores size and cell-wall thickness of: a Cymat, b Alporas, and c Alulight foams (adapted from Ref. [6])

4.2 Properties of Foams

57

4.2 Properties of Foams 4.2.1 Mechanical Properties 4.2.1.1

Compression Properties

The properties of metal foams depend upon whether it is open-cell or closed-cell foam. The compression property of a metal foam is important, especially for energy absorbing applications. Figure 4.2 shows the stress–strain curves under compression loading for metal foams (open-cell and closed-cell). The compressive stress–strain curve of metal foam generally consists of three different states, i.e., linear elastic deformation, plateau, and densification region [15–17]. According to the Hooke’s law, stress is directly proportional to strain in the elastic region. Hence, in the elastic region, the stress and strain shows linear relation, i.e., the stress–strain curve is a straight line. This law holds good for many metals, however, the stress–strain relation is not completely linear in the elastic region for metal foams. The reason behind the presence of nonlinearity is the breaking of cell walls in the metal foams even under the application of small load, which cannot be reversed during unloading. Therefore, the modulus of elasticity obtained during initial loading is less than the real modulus of elasticity E. The slope of the unloading curve gives the real Young’s Modulus. Modulus of elasticity (E), for open-cell (Eq. 4.1) and closed-cell (Eq. 4.2) foams, modulus of rigidity (G) (4.3) and poison’s ratio (υ ≈ 0.3) are related to relative density for open- and closed-cell structure as follows [6, 10]: E ≈ (0.1 − 4)E∗s (ρ/ρs )n

Fig. 4.2 A typical compressive stress–strain diagram exhibited by metallic foams

(4.1)

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4 Materials Selection and Design Considerations

Fig. 4.3 Typical tensile behavior of metal foams (adapted from Ref. [6])

  E ≈ (0.1 − 1)E∗s 0.5(ρ/ρs )n + 0.3(ρ/ρs )

(4.2)

G ≈ (3/8)∗ E

(4.3)

The value of “n” varies between 1.8 and 2.2. To note that the tensile modulus Et of metal foam and compression modulus Ec differ from each other. The tensile modulus is greater than the compression modulus by ~10%. In the case of an open-cell foam, the compressive stress increases very rapidly with an increase in strain until a particular stress point is reached, which is the plateau stress. With further loading, the stress remains constant and strain keeps increasing until the point of densification strain (εD ) [15]. Up to the point of densification strain, the density of metal foam continuously increases and pores collapses at εD . Hereafter, from this point, strain increases rapidly due to semi-dense form [6]. The stress–strain behavior of closed-cell foam is different from that of the open-cell foam to a certain extent. Since the thickness of cell walls of closed-cell foam is greater as compared to open-cell foams, the cell material of closed-cell foam is more prone to tensile failure rather than bending failure. Hence, the stress in case of close cell foam keeps on increasing with an increase in strain. As a result, we do not get a clear distinct plateau stress as exhibited by open-cell foams [6, 18, 19]. The plateau stress σp1 and the densification strain εD are related to relative density as follows:   ∗ σp1 ≈ (0.25 to 0.35)∗ σy,s (ρ/ρs )n , εD ≈ 1 − α∗1 (ρ/ρs )

(4.4)

For the currently available metal foams, the value of “n” varies between 1.5 and 2.0 and “α1 ” between 1.4 and 2.0. Experiments have revealed that for metal foams, the strain rate does not have considerable effect on the value of plateau stress [2, 20–23].

4.2 Properties of Foams

59

The deformation behavior of metal foam under compression loading also depends upon the ductile property of foam. It is observed that the ductile foams exhibit smooth and constant curve in the plateau region, while the brittle foam has zig-zag nature in the plateau region [24]. The behavior of metal foam under compression also depends upon the relative density. The compression behavior remains almost constant for all metal foams of different relative density in the linear elastic deformation state. However, the initial peak-stress at the end of the linear elastic deformation state goes up with an increase in the relative density. In the plateau state, an increase in the relative density of metal foam causes the plateau stress to increase because the increase in relative density causes thickening of cell walls, resulting in an increased resistance to buckling and bending [25]. The behavior for densification strain is slightly different from that of the plateau stress. An increase in relative density causes thickening of the cell walls, and hence reduces the voids inside the foam. Hence, at the densification strain, the whole foam (cellular) structure compacts early into the solid structure (~80% can be compressed) [18]. With an increase in relative density, the densification strain reduces for foam [18]. The mechanical properties of metal foams are affected by the temperature of the working environment. With an increase in the temperature of the surrounding, a softening effect can be observed in foam, causing a decrease in its compressive strength [26, 27].

4.2.1.2

Tensile Properties

For a design engineer an insight into the tensile response of a material is always important. Figure 4.3 shows the tensile behavior of a typical metal foam. The stress increases very rapidly with a very small increase in strain, reaching subsequently to the maximum value which is commonly known as the ultimate tensile strength (σuts ). Metal foam hardens up to this point and after this point, metal foam fails and stress begins to reduce with an increase in very small strain [6]. Open-cell foams shows mechanical properties inferior to that of closed-cell foams. Mechanical properties of open-cell foam can be enhanced by: a. Heat treatment [28, 29]. b. By reinforcing another metal inside the foam matrix. c. By combining with another material to create a composite [30–32]. Diameter of the foam can also be increased at the cross section and height can be reduced [33, 34], by changing cell diameter, shape, and distribution [35, 36].

4.2.2 Thermal Properties It has been validated experimentally that metal foams exhibit far superior thermal properties when compared to their parent metals with respect to specific heat, effective thermal conductivity, coefficient of thermal expansion, etc. Hence, metal foams

60

4 Materials Selection and Design Considerations

are potential candidates for multiple applications in nuclear fuel casks and other thermal shielding applications ensuring excellent thermal isolation, fire retardancy, energy absorption capacities at lightweight, etc. [37]. It is evident that the thermal conductivity of air is very low as compared to the metals. As metal foams are primarily made up of voids which are filled with air, naturally they have a low thermal conductivity in comparison to their parent metals. In a study conducted by Chen et al., aluminum-steel composite metal foam (Al-S CMF) was found to have a thermal conductivity of 32.1 ± 1.61 W/m °C and that of aluminum was 205 W/m °C at 300 °C [37]. The coefficient of thermal expansion (CTE) was determined for 316 L stainless steel (S–S) and S–S composite metal foam (S–S CMF) over a temperature range of 0–400°C. It was observed that the foaming process reduced the CTE of CMF by about 80% as compared to the parent material. CMF was found to be more thermally stable since its CTE was nearly constant over the given temperature range while the CTE of 316 L SS, on the other hand, was found increasing [37]. The flame test was also carried out on 304 L SS and S–S CMF (316L stainless steel matrix). The results showed that four minutes were required for 304L SS to reach equilibrium, while it took eight minutes for S–S CMF to reach equilibrium. The reason was again attributed to low permeability and high resistance of air in voids of CMF [37]. The presence of gas bubbles change the thermal conductivity (λ) of metal foams when compared to metals [6, 10], according to the following equation: λ ≈ λs ∗ (ρ/ρs)q

(4.5)

where ρ = density of foam, ρs = density of base metal, the value of “q” ranged from 1.65 to 1.8.

4.2.3 Electrical Properties Gas bubbles occupy a large volume of metal foams and electrical resistivity of gas is more than that of metal. Hence, electrical resistance in case of metal foams increases as compared to that of metal. The relation is expressed as [6, 10] R ≈ Rs∗ (ρ/ρs)−r where R = electrical resistivity, “r” ranges from 1.6 to 1.85.

(4.6)

4.3 Design Analysis for Material Selection

61

4.3 Design Analysis for Material Selection Every material consists of certain properties which are unique to it. Diamond has high hardness and crystallographic structure, while plastics normally exhibit high level of plasticity. A complete list of properties of a material, which determine the applicability of that material, is called “Property Profile” [6]. For instance, gold is highly ductile, less stiff, and exhibit lower strength as compared to steel. However, gold has high luster, shine, and a very noble material in both dry and wet atmospheric conditions. Hence, for thousands of years, gold has remained the most precious material for making jewellry and ornaments, while steel remains one of the basic components in building infrastructure, tools, ships, automobiles, machines, appliances, and weapons. For a particular application, a material is selected only if its property profile matches the requirements of the end application. There are about 80,000 materials and about 1,000 processes to produce components with materials through joining, shaping, and finishing. This can be an overwhelming and time-consuming task, and hence requires an optimized and strategic procedure [38]. Only a proper study of application requirements, property profile of materials, constraints, etc., can ensure successful material selection and subsequent designing of an engineering structure. For selecting materials for any application, there are three important parameters to consider, i.e., (1) its function, (2) objective, (3) constraints. All these three parameters are related to the material index. By changing any of these parameters, material index can be changed. Hence, it is important to find a relationship between the objectives and material index with the help of constraints and functions [39–42]. The generalized procedure for material selection consists of the steps as shown in Fig. 4.4.

4.3.1 Materials Selection Procedure 4.3.1.1

Function

The initial and most important part of the procedure is to find out primary functions for which the material is required. For example, an electric wire is required to carry the current, a knuckle pin is required to sustain the shear forces, and a shaft is required to transmit the torque [44, 46, 47, 51]. This forms the first step in materials selection.

4.3.1.2

Objective

This is perhaps the most important parameter. The designer has to determine which variable to maximize or minimize. It may be weight, cost, environmental impact, energy storage, etc. Objectives always vary. When designing a resistive wire for a bulb, the objective may be the maximum illumination. On the other hand, when

62

4 Materials Selection and Design Considerations

Fig. 4.4 Steps in material selection (adapted from Refs. [43–52])

designing a damper, it would be the damping capacity [6, 43, 45, 47, 50]. For automotive sector, aerospace, space, defense, and sports sectors, specific material properties are very important.

4.3.1.3

Constraints

This factor is important to ensure satisfactory performance of the component during service. The constraining factors such as dimensions of the component, the load capacity, the strength and stiffness, etc., determine objectives of the component. Constraints can be multiple and contradictory to one another, as well as conflicting with the objective. For instance, when designing a shaft, the objective is to minimize the weight, while torsional rigidity, cost, dimension are the constraints [6, 43–52].

4.3.1.4

Free Variable

Sometimes, there could be certain dimensions of a component, which do not have rigid specifications and which can be varied by the designer according to his/her convenience to meet the required performance standard [6, 48, 49]. This is considered as free variable.

4.3 Design Analysis for Material Selection

4.3.1.5

63

Material Indices

There are a few specific steps to ascertain the material index [6, 42–52]: (a) Write the equation of objective. (b) Find the free variable in the objective function. (c) Find the equation of free variable depending upon the strength or stiffness criterion. (d) Substitute the value of free variable in the equation of objective. Many parameters in the objective equation are known, which are provided by the design.

4.3.2 Method of Single-Objective Optimization This method is explained taking an example of a panel that has to be designed to support an electronic equipment. It has to be subjected to bending failure. Let us consider that the length and breadth of the panel are L and b as shown in Fig. 4.5. Therefore, the mass of the panel will be [6] m = b∗ L∗ t∗ ρ

(4.7)

where t = thickness of panel in meters, ρ = density of material (kg/m3 ). Case-1: Panel Design on the Basis of Specified Stiffness and Minimum Mass In this case, the force per unit width and the desired bending stiffness (S) are specified. From the equation of mass, it is clear that the mass of the panel is directly related to thickness, hence mass can be directly reduced by reducing the thickness. However, with a decrease in thickness, the deflection, and therefore, the stiffness gets compromised. Hence, the desired stiffness limits the minimum value of thickness and thereby the mass [6].

Fig. 4.5 Panel of thickness (t), length (L), and width (b) loaded with force F per unit width

64

4 Materials Selection and Design Considerations

B1 ∗ E I Fb = ≥ S∗ δ L3

S=

(4.8)

where S* = Desired bending stiffness, E = Young’s modulus, I = Area moment of inertia of the section, Fb = load, and δ = deflection. The panel has rectangular cross-sectional area b * t [6] b ∗ t3 12

(4.9)

B1 ∗ Ebt 3 12 ∗ L 3

(4.10)

12 ∗ L 3 ∗ S ∗ B1 ∗ Eb

(4.11)

I = S∗ ≤ t3 ≥  t≥  m ≥b∗ 

12 ∗ S ∗ B1 ∗ Eb 12 ∗ S ∗ B1 ∗ Eb

m≥

12 ∗ b2 ∗ S ∗ B1 ∗ E



 13

m≥

12 ∗ b2 ∗ S ∗ B1

 13  13  13

∗L

(4.12)

∗ L2 ∗ ρ

(4.13)

∗ L2 ∗ ρ

(4.14)

 ∗ L2 ∗

ρ 1

E3

 (4.15)

This is the equation for performance metric (m). All the terms in the above equation are already known as input data, except for the quantities in the last bracket, which are unknown. These terms are referred to as material index. Case-2: Panel Design on the Basis of Designated Strength and Minimum Mass For this case, the tensile strength σy and failure load (F f ) per unit width of material are already specified [6] Ff =

B2 ∗ σ y I ≥ Ff ∗ b∗t ∗L

(4.16)

where B2 is a constant, whose value is determined by the distribution of load [6] I =

b ∗ t3 12

(4.17)

4.3 Design Analysis for Material Selection

65

B2 ∗ σ y bt 3 12 ∗ b ∗ t ∗ L

(4.18)

B2 ∗ σ y ∗ t 2 12 ∗ L

(4.19)

12 ∗ L ∗ F f ∗ B2 ∗ σ y

(4.20)

Ff ∗ ≤ Ff ∗ ≤ t2 ≥  t≥

12 ∗ L ∗ F f ∗ B2 ∗ σ y

 21 (4.21)

m ≥ b∗t ∗l ∗ρ  m ≥b∗  m≥

12 ∗ L ∗ F f ∗ B2 ∗ σ y

12 ∗ L ∗ b2 ∗ F f B2

Here, the material index is

ρ 1

σy 2

∗

 21

(4.22)

∗l ∗ρ 

21 3 2

∗L ∗

(4.23)

ρ 1

σy 2

(4.24)

.

Some of the material indices along with the functions, objective, and constraints are listed in Table 4.1.

4.3.3 Significance of Material Indices for Metal Foams (1) The material index Eρ characterizes stiffness of the panel at a low weight. As we know that the density of metal foams is low as compared to their parent material, hence metal foam panel provides better stiffness at a low weight. In general, by using metal foam as the sandwiched material, superior properties of components can be realized. (2) The material index σρy characterizes the strength of a panel at a low weight. As the metal foam is less dense than the parent material, foam panels provide better strength at a low weight [6, 46, 49, 50]. (3) As the metal foam consists of several hollow regions, it can absorb a lot of energy in crushing the foam up to the densification region, which is characterized by σ pl ∗ ε D . Therefore, the metal foam has excellent energy absorbing properties [6, 52].

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4 Materials Selection and Design Considerations

Table 4.1 Material indices for various combinations of requirements, objectives, and constraints [6, 43–52] Function

Objective

Constraint

Material index

Tie (Cable supported tensile structure)

Minimize the weight

Stiffness given

ρ E ρ σy

Tie (Cable supported tensile structure)

ρ

Beam (Beams of roofs, car chassis elements)

E2

Beam (Suspension arm of car)

σy

1

ρ

2 3

ρ

Panel (Car door panel)

1

E3 ρ

Panel (Bumpers of car)

σy

Column (Legs of table)

Buckling load given

1 2

ρ

1

E2

Spring (Springs for clutches)

Given energy storage

Precision devices (Gauges)

Minimize the distortion

Given temperature gradients

Heat sinks (Cooling systems)

Maximum thermal flux

Thermal expansion given

Electromagnet (High-speed electric motors)

Maximize the field

Temperature rise and strength given

ρE σy 2 α λ α λ 1 k ∗ Cp ∗ ρ

4.4 Designing of Simple Structure During the design of any component, the first and the most important step is material selection. This aspect has already been discussed in the previous section. After proper material selection, the next step in designing is to determine appropriate dimensions of the component. When the components are put into application, they may be subjected to different types of loads such as torsion, bending, compression, contact stresses, etc. Therefore, to decide on appropriate and optimum dimensions, one needs to have adequate knowledge of all these loading types and most possible failures. In the present section, a detailed study of failures of components (beams, tube, disks) has been attempted along with the discussion on different types of component supports such as simple support, cantilever, hinges, etc. At the end of each sub-topic, the behavior of metal foams under loading is also compared with that of dense solids [6, 53–57].

4.4 Designing of Simple Structure

67

4.4.1 Constitutive Equations A constitutive equation expresses the relation between two or more physical quantities which indicates how a particular material is going to behave when an external stress or forces are applied on it. The constitutive equation changes if the nature of force is changed. The constitutive equation will not be the same for torsion and tensile stress [6]. Certain properties of a material also appear in the constitutive equation. For instance, the Modulus of Rigidity (G) is present in the equation of torsion force, while the modulus of elasticity (E) and Poison’s ratio appears in the equation of tensile force [6, 53–55]. The equations for elastic and plastic loading for dense solids and metal foams are summarized in Table 4.2. Constitutive Equations for Metal Foams Figure 4.6 shows that when a very small force is applied at small strains, stress becomes proportional to the strain conforming to Hooke’s law. Hence, for elastic deformation, the constitutive equation for metal foam is the same as that of dense solids. However, with an increase in load, metal foams plastically deform rapidly as it largely consists of hollow volume. Hence, the plastic flow equation for metal foams is different [6]. Table 4.2 Constitutive equations for isotropic solids and metal foams under uniaxial and general loading [6, 43] Constitutive equation for Elastic Deformation (ED) Isotropic solids Uniaxial loading

1 =

General loading

1 =

σ1 E σ1 E

−

ϑ E

∗ (σ2 + σ3 )

Metal foams Uniaxial loading

Same as the dense solids

Constitutive equation for Plastic Deformation (PD) Isotropic solids Uniaxial loading

σ1 ≥ σ y

General loading

σ1 − σ3 = σ y σ1 ≥ σ2 ≥ σ3 (Tresca) σe ≥ σ y (von mises) with σe 2 = 21 [(σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ3 − σ1 )2 ]

Metal foams Uniaxial loading

σ1 ≥ σ y

General loading

σ1 ≥ σ y Where σ1 2 = Also σm =

1 3

1 (1+( α3 )2 )

∗ [σe 2 + α 2 ∗ σm 2 ]

∗ [σ1 + σ2 + σ3 ]

σ y = Yield strength, α = Yield constant, E = Modulus of elasticity, ϑ = Poison’s ratio

68

4 Materials Selection and Design Considerations

Fig. 4.6 Beam of the uniform cross-sectional area showing parallel elastic fiber throughout the cross section

4.4.2 Moments of Various Sections Moment of section refers to the resistance of the cross section against bending. In the present case, a beam is considered to be made up of a number of elastic fibers parallel to the neutral axis as shown in Fig. 4.7. When the beam gets loaded in bending each of the fibers in the beam gets curved. Now, considering that the fibers are at a distance of x from the neutral axis, the fibers at the outer part of the central axis get elongated,and the fibers at the inner part get compressed. Hence, the strain in fiber can be expressed as in Eq. 4.25 [6] ε=

x R

(4.25)

Therefore, the stress induced under normal force on the plane can be represented as σ (x) = E ∗

x R

(4.26)

where E = modulus of elasticity. Considering that the fiber subtends an angle δθ at the center, the length of the selected fiber is (R + x) × δθ. The length of the fiber at the neutral axis is (R × δθ). The difference in length of fibers causes a torque to be applied on the cross section. Considering that dA is the cross section of fiber, the torque exerted by the fiber on the beam after loading is [6] τ=

Fig. 4.7 Beam when loaded at one end, gets bend and forms a part of a circle of radius R

E x∗E∗x ∗dA = ∗ x2 ∗ d A R R

(4.27)

4.4 Designing of Simple Structure

69

The integration of the Eq. (4.27), from the neutral axis to the outermost fiber gives a combined torque exerted by one side of the beam on the other side [6]. τtotal =

E ∗ R

τtotal =

x 2d A EI R

(4.28) (4.29)

where I is the second moment of area. “I” represent the resistance of the beam to bending. The flexural equation is expressed as [6] M σ E = = I y R

(4.30)

Similarly, ym = normal distance of the outer surface from the neutral axis, J = polar moment of inertia, which represents the resistance of the section to twisting. The section modulus is presented by following equation [6, 58–60]: Z=

I ym

(4.31)

where ym = normal distance of the outer surface from the neutral axis. It is used to detect surface stress as [6, 60] σ =

M Z

(4.32)

The moment H of a beam is defined by [6, 58–60] y ∗ b(y) · dy

H=

(4.33)

section

This measures the resistance of a beam to full plastic loading. The common moments of this section are enlisted in Table 4.3.

4.4.3 Elastic Deflection of Beam and Panels As available in the open literature, when the load is applied to a beam within its elastic limit, elastic fibers are bent into curvature. The bending of the beam under the applied load is called deflection. Bending can be measured in degrees or meters. The deflection of a beam depends upon the following factors:

Section

π 64

  ∗ do 2 − di 2

π 4

b ∗ (h o − h i )

b∗h

π 64

∗ d4

π 4

b 12

  ∗ ho 3 − hi 3

b∗h 3 12

  ∗ do 4 − di 4

∗ d4

I (m4 )

A(m2 )

−

16 3

π 32

π 32

∗ h ∗ b3 1 −

  ∗ do 4 − di 4

∗ d4

K (m4 )

Table 4.3 Second moment of area for various cross sections of solids [43, 58–60]

0.58∗b h



∗ d3

b 12∗h o

b∗h 2 6

  ∗ do 4 − di 4

  ∗ ho 3 − hi 3

π (32∗do )

π 32

I 3 y m (m )

  ∗ do 3 − di 3

∗ d3

b 4

(continued)

  ∗ ho 2 − hi 2

b∗h 2 4

1 6

1 6

H (m3 )

70 4 Materials Selection and Design Considerations

Section

Table 4.3 (continued)

π 4

π ∗a∗b

√ a4 ∗ 3 80

K (m4 )

∗ a ∗ b3

π ∗a 3 ∗b3 a 2 +b2

  ∗ bo ∗ h o 3 − bi ∗ h i 3 −

a 4√ 32∗ 3

1 12

∗ a2

I (m4 )

h o ∗ bo − h i ∗ bi

3 4

√

A(m2 )

π 2

  ∗ bo ∗ h o 3 − bi ∗ h i 3

∗ ab2

1 12∗h o

a3 32

I 3 y m (m )

−

1 4

−

  ∗ bo ∗ h o 2 − bi ∗ h i 2

H (m3 )

4.4 Designing of Simple Structure 71

72

(a) (b) (c) (d) (e)

4 Materials Selection and Design Considerations

Modulus of elasticity, i.e., stiffness. Resistance of cross section to bending, i.e., second moment of area. Free or unsupported length of beam. Magnitude and types of force applied. Supporting of beam.

The deflection of beam (δ) and end slope (θ) are formulated by following equations [6, 53–56]: δ=

M ∗ l2 F ∗ l3 = b1 ∗ E I b1 ∗ E I

(4.34)

θ=

Fl 2 M ∗l = b2 ∗ E I b2 ∗ E I

(4.35)

where b1 and b2 are constants and their values depend upon the type of loading and the supports of the beam. Several values of b1 and b2 are depicted in Table 4.4. Table 4.4 Values of b1 and b2 for different types of supports and loading [6, 53–56]

TYPES OF SUPPORTS

b1:192, b2: --

b1:384, b2: --

b1:2, b2: 1 b1:3, b2: 2

b1:8, b2: 6

b1:

, b2: 24

b1:48, b2: 16

4.4 Designing of Simple Structure

4.4.3.1

73

Elastic Deflection for Metal Foams

Elastic deflection of beams is being discussed, which refers to the stiffness of beams and panels placing emphasis to working with minimum mass. For stiffness of beams, the mass scales are calculated as ρ1 and for panels the mass scales are calculated as E2

ρ

. Therefore, for the same stiffness, metal foam beams or panels will have lesser E weight as their densities are lower when compared to that of their parent metals. To note that metal foams in sandwich structures give the best results [6]. 1 3

4.4.4 Failure of Beams and Panels Whenever a beam is loaded, the stress formed in the outer fibers of that beam can be represented as [6] M σ =E∗ = ym I



1 1 − R Ro

 (4.36)

where Ro is the radius of curvature for beam before the moment of load application and R is after the load has been applied. Whenever a beam is loaded in bending, there can be three possibilities of failure. Tables 4.5 and 4.6 show the relevant equations and loading conditions for failure analysis. Following guidelines need to be noted: 1. When the stress in the outer fiber of the beam reaches the yield stress, the plastic or permanent deformation of the metal fibers sets in. The beam, at that point, is said to be failed and small zones of plasticity appear on the surface. 2. Toughness is another important property for any component. Toughness is defined as the amount of energy absorbed by the material prior to fracture. Fracture toughness of metals is very high. Hence, most of the metals generally undergo yielding failure. However, materials like ceramic have lower fracture toughness. Such materials undergo brittle fracture when loaded. 3. Plastic hinge is the last part of surface plastic deformation. When the surface plastic deformation extends through the entire cross section of a beam, plastic bending initiates. Table 4.5 Case of failure and formulae for failure force and failure moment [6, 53–56]

Case

Failure force (Ff )

For the first two case of failure

Ff =

For plastic hinge

Ff =

C×



I ym

L C H σy L



×σ ∗

Failure moment (Mf )

 M f = yIm × σ ∗ M f = H × σy

74

4 Materials Selection and Design Considerations

Table 4.6 Value of constant “C” for various ways of loading and types of supports [6, 53–56]

C=1

C=1

C=1

C=8

C=16

C=4

C=8

C=2

In Table 4.5, I = second moment of area, m4 , σ y = yield strength, N/mm4 , σ f = modulus of rupture, N/mm4 , σ * = σ y (Plastic material), and σ f (Brittle material), C = constant value, which depends upon the support and type of loading. These parameters are also shown in Table 4.6. The relation of plateau stress (σpl ) is presented as [10]  σ pl ≈

ρ ρs

n (4.37)

where “n” varies in 1.5–2.0 range. When higher bending strength at a low weight of the beam is sought, the mass scales are calculated as ρ 3 for beams and ρ 1 for panels. Therefore, it signifies that σy 2

σy 2

for the same value of yield stress, the beams or panels made up of metal foam are lighter in weight as compared to their parent metals [6].

4.4.5 Buckling of Columns When a component is axially loaded it undergoes compressive failure. However, if the longitudinal dimensions of the components are larger than the lateral dimensions, instead of undergoing compressive failure, the components undergo buckling failure at a critical load, Fcrit . Buckling failure of a component is a type of bending failure. Hence, Fcrit depends upon the stiffness (modulus of elasticity E) and the second moment of the area (I). Depending on the types of support of the component, there can be one of the following cases [6, 53–56]: (a) A column is simply supported at both ends. (b) A column is hinged on both ends.

4.4 Designing of Simple Structure

75

(c) A column is simply supported at one end and hinged at another end. (d) A column is simply supported at one end and hinged roller at the other end and so on. The critical force, required to buckle the beam, loaded axially is [6] Fcrit =

n2 ∗ π 2 E I L2

(4.38)

where, F = Force (N), M = Moment (N-m), n = Half wavelength in buckled shape, k = stiffness (N/m), L = Length of beam (m), I = Second moment of area (m4 ). Various values of “n” are presented in Table 4.7, for several kinds of support of buckling and their causes. For the columns of the same dimensions and made up of metal foam and parent metal, the second moment of the area will also be the same. Hence, the only variable left is the modulus of elasticity. For open-cell foam (OCF) and closed-cell foam (CCF), modulus of elasticity “E” can be given as [6] Table 4.7 The value of half wavelength “n” in buckled shape for various types of supports with axial loading in buckling [6, 53–56]

TYPES OF SUPPORT

n=2

n= Case

n=

n=1

Equation of critical force When the bending moments is applied over the buckling column in the direction of buckling, it reduces the critical force required for column to buckle. The pressure applied to the beam under axial loading in lateral direction, reduces the critical force required for buckling.

76

4 Materials Selection and Design Considerations

Fig. 4.8 A round metal bar subjected to torsion on both the end

 OCFE = (O.1 − 4)E s ∗

ρ ρs

n

 n   ρ ρ CCFE = (O.1 − 1)E s ∗ 0.5 + 0.3 ρs ρs

(4.39) (4.40)

where “n” varies between 1.8 and 2.2. For elastic buckling resistance at the minimum weight, the mass of components are calculated as ρ1 for beams and ρ1 for panels. Hence, for the same elastic buckling E2 E3 resistance, metal foam columns will have lesser weight as compared to that of the parent metal [6].

4.4.6 Torsion of Shafts When a torque is applied over a shaft at any cross section, shearing stress is induced at the shaft (Fig. 4.8). The magnitude of the shearing stress is zero at the axis of the cross section and it is the maximum at the surface of the shaft [6]. In such case, the shearing stress induced at the cross section is presented by torsional formula as follows [6]: Gθ τ T = = J L r

(4.41)

where, T = Torque applied on the cross section (N-m), J = Polar moment of the area in (m4 ), G = Modulus of rigidity (N/m2 ), L = Length of shaft (m), τ = Shearing stress (N/m2 ), r = Radius of cross section from neutral axis (m). The maximum shear stress τmax and the maximum bending stress σmax are calculated using the following equation [6, 53–57]: τmax = σmax =

Gθ do T ∗ do = 2∗k 2∗L

(4.42)

In case of circular cross sections, the maximum stress induced is at all points of the outer surface of the shaft. However, in case of shafts of other cross sections

4.4 Designing of Simple Structure

77

(triangular, rectangular, elliptical, square, etc.), the maximum shear stress is induced at the surface of the points closer to the centroid of the section. In such case, one can imagine a circle passing through midpoints of larger sides while shear stress is induced at the surface of the circular shaft. The shear modulus G of metal foam is given as [6, 10] 3 G ≈ (O.1 − 4)E s ∗ 8



ρ ρs

n (4.43)

where n ranges from 1.8 to 2.2. This means that the modulus of rigidity of metal foam is always less than the modulus of rigidity of solid metals. However, when the modulus of rigidity at a low weight is sought, we calculate the mass of beam scales as Gρ and panel mass scales as ρ1 . Hence, for the same modulus of rigidity, the weight of metal foam panels or G2 beams will be lighter when compared to that of the parent metals [6].

4.5 Summary This chapter described the material selection process and design consideration aspects of metallic foams and explained about various loading conditions based on the moment of sections. The chapter also highlights the mechanical, thermal, and electrical properties of foams. The constitutive equations and deformation behavior of fully dense and metallic foams are systematically described. Utilizing fundamental concepts of failure mechanisms, buckling and torsion response of metal foams is discussed. Finally, this chapter emphasizes that metallic foams owing to their unique properties are very attractive and potential materials for fulfilling the increasing demands in many application where certain properties such as mechanical, electrical, and certain thermal characteristics coupled with low weight are required. To note that metallic foams exhibit quite extraordinary suitable cellular structure leading to their multi-functionality and are likely to be used very aggressively in various engineering sectors in near future.

References 1. Banhart, J., & Weaire, D. (2002). On the road again: Metal foams find favor. Physics Today, 55(7), 37–42. 2. Rajak, D. K., Kumaraswamidhas, L. A., & Das, S. (2017). Technical overview of aluminium alloy foam. Reviews on Advanced Materials Science., 48, 68–86. 3. Sosnick, B. (1943). Process for making foamlike mass of metal. US Patent 2,434,775. 4. Banhart, J. (2006). Metal foams: Production and stability. Advanced Engineering Materials, 8(9), 781–794.

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5. Davies, G. J., & Zhen, S. (1983). Metallic foams: Their production, properties and applications. Journal of Materials Science, 18(7), 1899–1911. 6. Ashby, M. F. (Ed.). (2000). Metal foams: A design guide. Butterworth-Heinemann. 7. Baumeister, J., Banhart, J., & Weber, M. (1997). Aluminium foams for transport industry. Materials & Design, 18(4–6), 217–220. 8. Degischer, H.-P., & Kriszt, B. (2003). Handbook of cellular metals: Production, processing, applications. Wiley-InterScience. 9. Wang, Y., Liew, J. Y. R., Lee, S. C., Zhai, X., & Wang, W. (2017). Crushing of a novel energy absorption connector with curved plate and aluminum foam as energy absorber. Thin-Walled Structures, 111, 145–154. 10. García-Moreno, F. (2016). Commercial applications of metal foams: Their properties and production. Materials, 9(2), 85. 11. Das, S., & Prasad, B. K. (2012). Al and Mg based lightweight metallic material for automobile applications. Invertis Journal of Science and Technology, 5(3), 147–156. 12. Banhart, J. (2005). Aluminium foams for lighter vehicles. International Journal of Vehicle Design, 37(2/3), 114. 13. Banhart, J. (2000). Manufacturing routes for metallic foams. JOM Journal of the Minerals Metals and Materials Society, 52(12), 22–27. 14. Davis, J. R. (Ed.). (1999). Corrosion of aluminum and aluminum alloys. ASM International. 15. Luo, Y., Yu, S., Liu, J., Zhu, X., & Luo, Y. (2010). Compressive property and energy absorption characteristic of open-cell SiCp/AlSi9Mg composite foams. Journal of Alloys and Compounds, 499(2), 227–230. 16. Rajak, D. K., Kumaraswamidhas, L. A., & Das, S. (2014). An energy absorption behaviour of foam filled structures. Procedia Materials Science, 5, 164–172. 17. Rajak, D. K., Kumaraswamidhas, A., & L., & Das, S. . (2015). Energy absorption capabilities of aluminium foam-filled square. Advanced Materials Letters, 6(1), 80–85. 18. Edvige, C., Alexander, N. C. (2019). Handbook of Graphene, volume 1: Growth, synthesis, and functionalization. Wiley. ISBN: 978-1-119-46861-5. 19. Heydari, A. A., Shahverdi, H. R., & Elahi, S. H. (2015). Compressive behavior of Zn– 22Al closed-cell foams under uniaxial quasi-static loading. Transactions of Nonferrous Metals Society of China, 25(1), 162–169. 20. Ruan, D., Lu, G., Chen, F. L., & Siores, E. (2002). Compressive behaviour of aluminium foams at low and medium strain rates. Composite Structures, 57(1–4), 331–336. 21. Paul, A., & Ramamurty, U. (2000). Strain rate sensitivity of a closed-cell aluminum foam. Materials Science and Engineering: A, 281(1–2), 1–7. 22. Patel, A., Das, S., & Prasad, B. K. (2011). Compressive deformation behaviour of Al alloy (2014)–10wt.% SiCp composite: Effects of strain rates and temperatures. Materials Science and Engineering: A, 530, 225–232. 23. Hall, I. W., Guden, M., & Yu, C.-J. (2000). Crushing of aluminum closed cell foams: Density and strain rate effects. Scripta Materialia, 43(6), 515–521. 24. Gibson, L. J., & Ashby, M. F. (1997). Cellular solids: Structure and properties (2nd ed.). Cambridge University Press. 25. Park, C., & Nutt, S. R. (2000). PM synthesis and properties of steel foams. Materials Science and Engineering: A, 288(1), 111–118. 26. Aly, M. S. (2007). Behavior of closed cell aluminium foams upon compressive testing at elevated temperatures: Experimental results. Materials Letters, 61(14–15), 3138–3141. 27. Dilley, D. C. (1974). Mechanical and Production Engineering, 125, 24. 28. Zhou, J., Gao, Z., Cuitino, A., & Soboyejo, W. (2004). Effects of heat treatment on the compressive deformation behavior of open cell aluminum foams. Materials Science and Engineering a, 386(1–2), 118–128. 29. Wang, Z., Li, Z., Ning, J., & Zhao, L. (2009). Effect of heat treatments on the crushing behaviour and energy absorbing performance of aluminium alloy foams. Materials & Design, 30(4), 977–982.

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30. Cheng, H. (2003). Compressive behavior and energy absorbing characteristic of open cell aluminum foam filled with silicate rubber. Scripta Materialia, 49(6), 583–586. 31. Orbulov, I. N., & Ginsztler, J. (2012). Compressive characteristics of metal matrix syntactic foams. Composites Part A: Applied Science and Manufacturing, 43(4), 553–561. 32. Harte, A.-M., Fleck, N. A., & Ashby, M. F. (2000). Energy absorption of foam-filled circular tubes with braided composite walls. European Journal of Mechanics—A/Solids, 19(1), 31–50. 33. Chino, Y., Mabuchi, M., Yamada, Y., Hagiwara, S., & Iwasaki, H. (2003). An experimental investigation of effects of specimen size parameters on compressive and tensile properties in a closed cell al foam. Materials Transactions, 44(4), 633–636. 34. Caner, F. C., & Bažant, Z. P. (2009). Size effect on strength of laminate-foam sandwich plates: Finite element analysis with interface fracture. Composites Part B: Engineering, 40(5), 337– 348. 35. Han, F., Cheng, H., Wang, J., & Wang, Q. (2004). Effect of pore combination on the mechanical properties of an open cell aluminum foam. Scripta Materialia, 50(1), 13–17. 36. Jiang, B., Wang, Z., & Zhao, N. (2007). Effect of pore size and relative density on the mechanical properties of open cell aluminum foams. Scripta Materialia, 56(2), 169–172. 37. Chen, S., Marx, J., & Rabiei, A. (2016). Experimental and computational studies on the thermal behavior and fire retardant properties of composite metal foams. International Journal of Thermal Sciences, 106, 70–79. 38. Ashby, M. F., Brechet, Y. J. M., Cebon, D., & Salvo, L. (2004). Selection strategies for materials and processes. Materials & Design, 25(1), 51–67. 39. Shanley, F. R. (1960). Weight-strength analysis of aircraft structures. New York: Dover Publications. 40. Gordon, J. E. (1978). Structures, or why things don’t fall through the floor. Harmondsworth: Penguin Books. 41. Siddall, J. N. (1982). Optimal engineering design: Principles and applications. M. Dekker. 42. Johnson, R. C. (1962). Optimum design of mechanical elements. XIV + 535 S. New York/London 1961. Wiley. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 42(10–11), 514–514. 43. Ashby, M. F. (1999). Materials selection in mechanical design (2nd ed). ButterworthHeinemann. 44. Budinski, K. G., & Budinski, M. K. (1999). Engineering materials: Properties and selection (6th ed). Prentice Hall. 45. Charles, J. A., Crane, F. A. A., & Furness, J. A. G. (1997). Selection and use of engineering materials. Butterworth Heinemann. https://site.ebrary.com/id/10190866. 46. Ashby, M. F., & Cebon, D. (1999). Case studies in materials selection. Cambridge, UK: Butterworth-Heinemann. 47. Farag, M. M. (1989). Materials selection for engineering design. Prentice Hall. 48. Ashby, M. F., & Johnson, K. (2014). Materials and design: The art and science of material selection in product design (3rd ed.). Butterworth-Heinemann. 49. Lewis, G. (1990). Selection of engineering materials. Englewood Cliffs, NJ, USA: PrenticeHall. 50. Dieter, G. E. (1983). Engineering design: A materials and processing approach. McGraw-Hill. 51. Dieter, G. E. (Ed.). (1997). Materials selection and design (10th ed). ASM International. 52. Ullman, D. G. (2003). The mechanical design process (3rd ed). McGraw-Hill. 53. Timosenko, S. P. (1979). Elements of strength of materials. Van Nostrand Reinhold. 54. Beer, F. P. (2015). Mechanics of materials (7th ed). McGraw-Hill Education. 55. Hibbeler, R. C. (2017). Mechanics of materials (10th ed). Pearson. 56. Nash, W. A. (2014). Schaum’s outlines: Strength of materials (6th ed). McGraw Hill Education. 57. Den Hartog, J. P. (2012). Advanced strength of materials.

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58. Gere, J. M., & Timosenko, S. P. (1985). Mechanics of materials. London: Wadsworth International. 59. Timosenko, S. P., & Gere, J. M. (1961). Theory of elastic stability. London: McGraw-Hill Koga Kusha Ltd. 60. Weaver, P. M., & Ashby, M. F. (1996). The optimal selection of material and section-shape. Journal of Engineering Design, 7(2), 129–150.

Chapter 5

Yielding, Fatigue, and Creep Response of Metal Foams

Abstract In this chapter, yielding, fatigue, and creep are introduced and fundamentally described for metal foams. Metallic foams deforms differently from solid metals. This chapter highlights and describes yielding, fatigue, and creep behavior of metallic foams. The difference between yielding and plastic response of metal foams and the base metal is explained. Similarly, fatigue response of metallic foam is explained using constitutive laws placing emphasis on strength degradability under cycling loading. The chapter also addresses the creep response of metal foams.

5.1 Introduction Metallic foams exhibit diverse and unique properties leading to their use in diverse applications over the decades. They exhibit the inherent capability to withstand large strain along with near constant stress, allowing a high degree of energy absorption without affecting the hump stress. Energy absorption is the ability of a material to gain and retain energy/force under various mechanical conditions such as apex crushing, mid-point crushing, and specific energy absorption are commonly used to ascertain energy absorption capacity of a material [1]. During the axial compressive force, metallic foams can sustain a great amount of crushing energy through the collapse of foam pores [2, 3]. However, mechanical properties of metal foams depend on two basic factors: the cell boundary material and the presence of fluid or gas inside the cell [4, 5]. Although yield, fatigue, and creep behavior of the metal foams and necessary design properties also significantly depend on their base material. Plastic deformation of metallic foams is different from that of the fully dense metals. Therefore, a comparison of their constitutive equation plays an essential role in designing metal foams. Deshpande et al. developed a practical constitutive law for multiaxial yielding of metallic foams. It was observed that yield surface is of quadratic shape in effective stress versus mean stress space and plastic flow is normal to the yield surface, whereas strain hardening is quite effective to the direction of stress path under hydrostatic loading [5]. In terms of fatigue, it can be seen that the fatigue response of metal foams is different from solid metal due to its unique structure © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 D. K. Rajak and M. Gupta, An Insight Into Metal Based Foams, Advanced Structured Materials 145, https://doi.org/10.1007/978-981-15-9069-6_5

81

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5 Yielding, Fatigue and Creep Response of Metal Foams

containing voids. It is also important to understand the degradation of strength under cycling loading for sandwich panel application of metallic foams. In order to examine the reaction to the cyclic loading and loading at enhanced temperatures, numerical and analytical methods are used to evaluate the crack growth behavior within the metallic foams. Crack growth occurs in cell faces firstly and then progresses into the cell edge in closed-cell metallic foams [2]. Accordingly, the main aim of this chapter is to discuss yielding, fatigue and creep behavior of metallic foams and to compare them with solid metals.

5.2 Integral Standard for Metal Foams The plastic deformation characteristics of metal foams show different manifestation from the dense metals because foams get compacted when held under compression and the yield phenomenon also depends upon pressure. However, the application of metal foams requires the development of design methods based on engineering constitutive laws. One can find very few investigations and experimentations over the years on metal foams. As a result, it is difficult to gather much information and data on yield surfaces [4, 6–8].

5.2.1 Yield Conceptualization of Solid Metals Yield-stress is the stress when a material begins to permanently deform. Before reaching the yield point, the material deforms elastically and then returns to its original shape when the applied stress is removed. Once the yield point is crossed, the deformation becomes permanent and nonreversible. As a result, the material tends to remain in that state. On progressive application of load and beyond uniform plastic zone (UTS onwards), necking sets in and the material starts to deform in a non-uniform mode. For instance, uniaxial state of stress turns into multiaxial stress state once the necking starts. Figure 5.1 shows the schematic diagram depicting (1) true elastic zone, (2) proportionality limit (3) elastic zone, and (4) yield strength [9]. Von Mises criterion: It is also known as the maximum distortion energy theory (study) of failure. It addresses the yielding of a material that is initiated when the second deviatoric stress invariant J2 extends to a critical value. It is a part of the plastic theory that applies to ductile materials. Mathematically, the Von Mises criterion is formulated as: J2 = k2 , where k is the yield stress of the material in pure shear. Completely dense metals start deforming plastically at a changeless volume which, in turn, results in making the yield behavior independent of the mean stress [2–5, 7, 9–12]. The average plastic response can be measured by the von Mises criterion. As per this criterion, yield befalls when the von Mises effective stress σe attains the yield (gain) value Y. Effective stresses in terms of principle stresses (σa, σb, σc ) can

5.2 Integral Standard for Metal Foams

83

Fig. 5.1 Tensile stress–strain curve shows elastic zone and yield–stress

be written as [2–4] 2σe2 = [σa − σb ]2 + [σb − σc ]2 + [σc − σa ]2

(5.1)

While the stress σ is resolved on the arbitrary Cartesian axes which is not aligned properly to the principal axes of stress. σ has three direct components (σ11 , σ22 , σ33 ) and three shear components (σ12 , σ23 , σ31 ), which can be expressed as a symmetric 3 × 3 matrix with components σij . The mean stress (σm ), which is invariant with respect to a rotation of axes [2–4] σ = 1/3(σ11 + σ22 + σ33 ) = 1/3 σk

(5.2)

The stress can be broken down cumulatively into its mean parts and the stress component in the system can also be obtained by subtracting mean stress from each principle stress. The outcome can be expressed as [2–4] σij = Sij + σm δij

(5.3)

In the above equation, σij is a Kronecker delta symbol. The von Mises effectual stress becomes [2] e2 = 3/2Sij Sij

(5.4)

In a similar way, the strain rate (ε) has three direct components (ε11 , ε22 , ε33 ) and three shear components (ε12 , ε23 , ε31 ). The volumetric strain can be put forward by the following equation [2–4]:

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5 Yielding, Fatigue and Creep Response of Metal Foams

εm ≡ ε11 + ε22 + ε33 = εkk

(5.5)

The strain rate can be broken down into its volumetric parts and the stress divisional parts, and thus the equation can be modified to get the final outcome. Thus, for fully dense metallic solids, the plastic flow develops slip with no change of volume. Accordingly, the volumetric plastic strain rate εm = εkk equals zero [2]. εe2 ≡ 2/3εij εij

(5.6)

In the above equation, the factor 2/3 has been introduced so that ε2e is equal to the uniaxial plastic strain rate in tension or compression test on the solid, which is incompressible. In conventional Prandtl–Reuss J2 flow theory, the yield criterion is formulated as [2]  ≡ σe −Y ≤ 0

(5.7)

Effective strain scales with the effectual stress rate are the parameters upon which the hardening rate is determined [2]. εe = σe /h

(5.8)

where, h is the hardening modulus, assuming true expedient of stress and strain in all the above conditions.

5.2.2 Review of Yielding Nature of Metal Foams The yielding theory can be simply modified to take account of the significance of porosity in the yield criterion and also in the strain hardening law for the metal foams. The immediacy of experimental diversions in this study has made it difficult to conduct a study on the shape of the yielding surface. The yield criterion can be modified as foam can yield under the hydrostatic loading and also under the deviatoric loading [9, 10, 13]. The equation can be written in the following form [2]:  ≡ σ∗ − Y ≤ 0

(5.9)

The equivalent stress (σ∗ ) can be written as [2] 

  2 1 2 2 ∗≡   α 2  σe + α σm 1+ 3

(5.10)

In the above equation (α), the aspect ratio of the ellipse in the limits of (α) = 0 and the flow theory is reintroduced also. Therefore, two properties get mixed like the

5.2 Integral Standard for Metal Foams

85

pressure sensitivity coefficient α and uniaxial yield strength Y. The property Y can be measured with a simple compression test along with α in the manner described earlier. The basic yielding surface was determined using Alporas and Duocel foams by probing each of the specimens over a range of stress path. The probing of the foams is shown in Fig. 5.2. Thus, to get a better idea of the elliptical behavior of foams, the yield surfaces for both types of foams (Alporas and Duocel) under the compressive stress state are shown in Fig. 5.3 [2, 5]. In the following case of uniaxial compression, the values of σe = 1 and σm = σm = 1/3 and the data has been normalized by the action of uniaxial compressive yield strength. The value of aspect ratio lies in the range of 1.35–2.08. The effect of yield surface shape can be portrayed in the measurable plastic Poisson’s ratio under the uniaxial compression test. The ratio of transverse strain to that of axial strain υp is presented in Fig. 5.4. The yielding surface shape [Eqs. (5.9 and 5.10)] is comparatively simple to determine, which is derivable for υp in terms of α. It is expressed as [2, 4] ν =

1 2

p

−

1+

 α 2 3

 α 2

(5.11)

3

With the inversion, the equation is formed in terms of α as [2, 4] 

− νp α=3 1 + νp 1 2

2 (5.12)

For determining the value of α, the easiest path is to obtain the measurements of υp for uniaxial compression test. The yield surface shape can also be determined

Fig. 5.2 Probing of the yield surfaces for the foams of Alporas and Duocel (adapted from Refs. [4, 5])

86

5 Yielding, Fatigue and Creep Response of Metal Foams

Fig. 5.3 Yield surface nature for Alporas and Duocel foam and the surface layers are elliptical as mentioned in the Eqs. (5.9) and (5.10) (adapted from Refs. [2, 5])

Fig. 5.4 Relation between plastic poisson ratio (υp ) and the constant (α). The marks on the graph denote the uncertainty in experimental measures as mentioned in the Eqs. (5.11) and (5.12) (adapted from Refs. [2, 5])

5.2 Integral Standard for Metal Foams

87

with the following results. Previous experimentations suggest that the measures of υp are best done by compressing the available sample [5, 12, 13]. Once the yield surface shape is defined, the next task would be to ascertain whether the yield surface will grow with strain or not. For a better understanding of the proposition, it should be assumed that the yielding surface grows in a geometrically similar way as that of the strain (which is technically termed as isotropic hardening). In the case of Alporas, with the basic relative density of about 0.16, the yield surfaces are portrayed for the initial stage of state and 10 and 30% are the uniaxial pre-strains. The plastic strain rate (špij ) is again considered to be normal to the yield surface (φ) and also the relationship that can be formed is as follows [2]: (5.13) where the identical strain rate (›) is the conjugate of (σ’), and hence [2] (5.14) The above equation can also be written as [2] (5.15) The uniaxial compressive stress–strain is used to define the (σ’) − › relation. The true stress (σ) to the logarithmic plastic strain šp curve in the uniaxial compression towards the increasing order is expressed as follows [2]: (5.16) where h develops gradually with the increasing stress level σ. The above-mentioned definition of σ’ and that of › establishes that σ’ is the uniaxial stress and › is the uniaxial plastic strain rate. Thus, the hardening law [2, 5] can be presented as (5.17) The above relation holds good for general multiaxial loading. Figure 5.5 shows the compressive measure, as well as tensile and shear stress–strain plotted curve for Alporas and Duocel foams [2]. The two outcomes can be deduced from the above observation. The experimental analysis that is presently available is insufficient to have a comprehensive concept of isotropic hardening law. Even though one can get an idea about isotropic hardening from a few available studies that is not sufficient to arrive at a conclusion. There are some evidences and proofs that the rate of hardening for the hydrostatic compression is greater than that in the simple compression process. Most of the experiments are conducted with Alporas and Duocel. One of those experimental results related to the measurement of the hydrostatic and uniaxial compression response of Alporas

5 Yielding, Fatigue and Creep Response of Metal Foams

True Uniaxial stress (Mpa)

88

35

Hydrostatic compression

30

Uniaxial compression

25 Alulight 30%

20

15 10

Alporas 13%

Alporas 8%

5 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

True volumetric or Axial strain Fig. 5.5 Stress–strain curve for compression, tension, and shear response (adapted from Ref. [2])

and Duocel foams validated that the hardening rate is much quicker in hydrostatic compression [2, 5, 12, 13].

5.3 Structural Insight into Fatigue of Metal Foams In recent years, the demand for foams has progressively increased. Especially, in demand are aluminum alloy foams because they are lightweight and can be developed with better quality. They are extensively used in many structural applications where weight reduction is the main objective [14, 15]. Sandwich panels with foam layers with metallic face sheet are effectively used in the aerospace and automobile industries. However, it should be noted that during such structural applications of metal foams, the strength degrades under cyclic loading conditions or due to continuous loading effect. In various applications, the foam core is loaded in compression or shear. The deformation leads to nucleation of cracks within the foam structure. The deformation in the structure after loading initiates from the cell face and then gradually moves towards cell edges in case of closed-cell foams. The effect of loading on the structure in tension and compression is shown in Fig. 5.6. It shows that the cumulative fatigue mechanism operates within the cyclic deformation of foam, i.e., cyclic creep known as ratcheting [2]. When the metallic foam goes under cyclic loading, the cell walls gradually bend under compression and straighten under tensile mean stress. On the other hand, in case of metallic alloy, the material lengthens under the tensile mean stress and reduces in size under compressive mean stress.

5.3 Structural Insight into Fatigue of Metal Foams

89

Fig. 5.6 Deformation effect on the cell wall and cell edges under the loading conditions of tension–tension and compression–compression (adapted from Refs. [1, 2, 22])

Deformation is an essential feature of metallic foams requiring high damage tolerance capacity [16–20]. Instead, the focus should be on the size of the cracks or circular holes for a better understanding of the deformation pattern [1]. Assessment of the crack size helps clearly understand the change from ductile to brittle form during tensile part of loading. However, there is limited research conducted on the fatigue behavior analysis for metallic foams and sandwich panel structures on this aspect [21, 22].

5.3.1 Introduction to Fatigue Terms Figure 5.7 shows the basic terms used in fatigue using an example of a cylindrical member loaded uniaxially by stress (σ), which varies from the least absolute value (σmin ) to the highest absolute value (σmax ). The number of cycles (N) is plotted as x-axis [1, 22]. To note that Fig. 5.7a, shows a normal tension–compression curve for fatigue, and Fig. 5.7b, fatigue under tension–tension and compression–compression loading. Thus, within the span of low cycles (typically in the range of 103 to 104 ), the foam begins to show strong yielding and is strained by a certain amount (in mm). Later, after the initial phase of yielding, the rate of straining slows down but the damage and deformation of foam continues. As regards to fixed life of aluminum foams, the reduction in strength is directly related to mean stress of the fatigue cycle. It is then normalized by the ultimate tensile strength of alloy [2].

90

5 Yielding, Fatigue and Creep Response of Metal Foams

Fig. 5.7 Basic fatigue loading terms used for: a tension–compression, b tension–tension, and c compression–compression loading

5.3.2 Fatigue Behavior of Metal Foams Fatigue life of a component can be summed up in two important parts: number of loading cycles that a component goes through for initiation of a crack and the number of cycles that the crack takes to propagate till failure. Thus, in the structural application of metallic foams, it is essential to understand about the degrading strength of the structure with cyclic loading. When the foam comes under tension–tension loading (Figs. 5.7 and 5.8), gradually it starts to lengthen at a plastic rate of around 0.5% along with the gradual increase of the fatigue cycle until failing at an axial extension of 1–2%. Towards the end of the fatigue life, a visible crack initiates that runs down progressively across the specimen. In case of the compression–compression fatigue, on the other hand, the outcome turns out to be different. After a specific interval of time, large plastic strains develop, and eventually, the specimen starts to behave in a quasi-ductile manner. Figure 5.9 shows behavior of metallic foam in compression–compression fatigue at fixed stress values [2]. Basic occurrences in the compression loading are: (a) Sequential formation of crush bands. (b) Continuous shortening with increasing cycles and widening of single crush band.

5.3 Structural Insight into Fatigue of Metal Foams

91

Fig. 5.8 Successive lengthening in tension–tension fatigue of Alporas with variable fixed stress cycle (R = 0.1, relative density = 0.11 and gauge length = 100 mm) (adapted from Ref. [22])

Fig. 5.9 a Gradual shortening by thickening of a single crush band with multiple number of cycles, b sequence wise formation of the crush bands (adapted from Refs. [2, 18, 22])

(c) Gradual shortening leading to widening of the band and compression of the specimen to the extent of final deformation. (d) Progressive crushing of cells. To note that both compression–compression and tension–tension fatigue lead to gradual crushing of the cells or actual continuous deformation of the cell structure. The deformation may start to begin from the face of the structure and gradually

92

5 Yielding, Fatigue and Creep Response of Metal Foams 0.1 0

0

Nominal compressive strain

Nominal compressive strain

0.1

1.2 σmax / σpl =2

-0.1

1.1

1.0

-0.2

-0.3

0.49

-0.1 0.95

-0.2

0.58

-0.3 1.4 -0.4

-0.5

-0.4 1

10

102

103

104

Number of Cycles

(a)

105

106

10

1

10

102

103

104

105

106

107

10

Number of cycles

(b)

Fig. 5.10 Gradual shortening behavior in compression fatigue for a Duocel Al-6101T6 foam having a density of 0.08. b Alcan foam which possess a relative density of 0.057, (adapted from Refs. [1, 2, 23]), (dotted line in the figure: R = 0.1 and the continuous lines denote R = 0.5 (adapted from Ref. [23])

spread to the cell edges. However, three deformation patterns develop due to the compression–compression fatigue loading. These are described as follows: Type 1: Due to the loading, a uniform strain accumulates in the foam without any crush band development. This accumulation of the compressive strain at constant stress rate can be observed in Fig. 5.10a with regard to Duocel foam Al-6101T6. The data pertain to numerous values of maximum stress of fatigue cycle normalized by the plateau value of the yield strength. Type 2: The crush bands are formed at random spots causing strain to gather as plotted in Fig. 5.9b. The crush bands form with gradual loading upon the surface. The band forms at location (1) is the weakest part of the foam. The crush band sustains strain up to a certain level and then the normal strain in the band reaches a saturated level, the value of which is about 30% of the nominal strain. Once reaching this value of strain, the new crush bands start to form elsewhere like location (2) or location (3). Sometimes this phenomenon can be observed in monotonic tests as well. The crush bands detected in the test results depend upon the stress level when the density gradient is in the loading direction. The total number of crush bands consequently keeps increasing in the material with increasing stress. Type 3: A single crush band is formed, as shown in Fig. 5.9a, which gradually keeps widening with multiple stress cycles. This behavior resembles the propagation of stable state drawing by the neck as in case of a polymer. The crush bands keep widening and then finally take over the entire specimen. Then again contraction behavior can be observed in a uniform manner. Such behavior is observed in Alulight, which is a composite of Al-1 Mg-0.6Si with a relative density of 0.30. In case of Alporas, relative density is of 0.11, the strain rate in the band is inclined to an angle of about 20° to the axially as shown in Fig. 5.9a.

5.3 Structural Insight into Fatigue of Metal Foams

93

A significant drop in the elastic modulus can occur during fatigue. This drop in the elastic modulus is very similar to what is observed in the static loading condition. This may be a result of geometric changes in the cells with strain and with deformation of the cell wall. Comparisons made between Fig. 5.10a, b, show that the contraction behavior has a similar outcome. As the system goes under gradual load cycles, the contraction becomes directly proportional. A huge amount of compressive strain is generated in a progressive manner. Figure 5.10b shows the different contraction behavior under compression fatigue for Alcan foams. Different fatigue failure factors help in designing metal foams under the conditions of tension–tension and compression–compression loading. Material separation or bifurcation of material is an important factor in the tension–tension loading. In case of compression–compression loading, on the other hand, one has to take note of the initiation of the progressive shortening of the specimen [24–32].

5.3.3 S-N Curves of Metal Foams S-N curves of aluminum alloy foams are shown in Fig. 5.11. The plotted curves show the sensitivity of different metal foams and how they react to the behavioural changes that occur during the tension and compression loading. The tests were carried out in a stable stress range. The extent of fracture of the specimens under the tension–tension fatigue and initiation of progressive shortening in case of compression–compression loading was found to depend upon the number of cycles. The following broad conclusions were drawn from these results: 1. The endurance limit can be stretched and can be at 107 cycles as it is the case for solid metals. The number of cycles to failure increases by reducing stress levels. 2. The fatigue strength under tension–tension fatigue is lower than the compression– compression fatigue [2]. 3. The fatigue life of meal foams is more interrelated to σ max (maximum stress) then 107 cycles in comparison with the stress range σ. When R = 0.5, the compression strength is greater than when the value of R is 0.1, with the maximum stress being used as the main parameter [2]. The fatigue strength of aluminum foam is apparently similar to that of the completely dense aluminum alloys if the fatigue strength is neutralised by uniaxial compression strength. To note that there is no perfect trend as far as fatigue strength and the density of foam are concerned [1, 2].

5.4 Introduction to the Concept of Creep Creep refers to the time-dependent deformation of materials under the action of mechanical stresses. The tendency to creep increases when the material is subjected

94

5 Yielding, Fatigue and Creep Response of Metal Foams

Fig. 5.11 a S-N curve for compression–compression and tension–tension fatigue in Alporas foam (relative density having a value of 0.11). b S-N curve for compression fatigue in Alulight foam (value of R = 0.1), c S-N curves for compression and tension fatigue in Duocel Al-6101-T6 foam with a relative density of (0.08) (adapted from Refs. [1, 2, 22, 23])

to higher temperatures [33–38], for a longer duration of time. As this phenomenon is dependent on the magnitude of the load and the duration for which it is applied, deformation may gradually start to spread, and eventually, the material (component) may no longer perform its functions properly. Creep is not an instantaneous development as in case of other fractures. It is totally a time-dependent deformation process. The three stages of creep are typical as shown in Fig. 5.12. The process is divided into three different stages: stage 1-primary creep, stage 2-secondary creep, stage 3-tertiary creep. In the first stage, the strain rate diminishes to the minimum and becomes nearly constant. In the secondary stage, the creep rate is nearly constant due to a balance between strain hardening and recovery. In the tertiary stage, creep is in an accelerated mode eventually leading to tensile rupture and the time period required for this stage to initiate is the amount of time required for the rupture to occur.

5.4 Introduction to the Concept of Creep Stage 2

Stage 3

Rupture point

Strain ε

Stage 1

95

Transition point

Time (t)

Fig. 5.12 Schematic diagram of a typical creep curve

5.4.1 Creep of Metallic Foams The creep behavior of metallic foams depends upon the relative density of the material from which the foam is made. Two factors, i.e., temperature [37–40] and stress, play the most important role in creep phenomenon. The creep strain response of open-cell Duocel foam under compression load is shown in Fig. 5.13. In case of tension, the primary stage (creep) is short and the secondary stage is extended followed by the tertiary creep. The final stage is that of failure or rupture. For compression of the

Fig. 5.13 Compression creep behavior of Duocel Al-6101T6 foam (adapted from Refs. [2, 37])

96

5 Yielding, Fatigue and Creep Response of Metal Foams

open-cell foams, the graphical plot varies and one can observe a difference in the foam behavior at the end of the secondary stage with the strain increasing at the start and slowly decreasing. The increase in the strain is directly proportional to the collapse of the layers of the cell upon which the test was carried out [37, 38], and this process goes on. Until the remaining cells are deformed, they keep on getting affected by the secondary and the initial tertiary creep rate. For the compressive loading behavior, the time of failure is defined as the time at which the strain rate is five times as that for the secondary creep. In case of tensile loading, the time for failure is considered to be the time when the final rupture sets in [37–40].

5.5 Summary This chapter briefly introduces the concept of yielding, fatigue, and creep phenomena for fully dense metals and metallic foams. These concepts are illustrated using the investigations conducted on Alulight, Alporas, and Duocel foams using limited open literature. This chapter highlights the characteristic features of metallic foams such as strengthening capabilities with high-stiffness-to-mass ratio due to the presence of porosity. Further, the effect of porosity on the yield criterion, strain-hardening law, constitutive law, fatigue, and creep response is presented. To note that the current scenario is attractive for metal foams due to the unique physical and mechanical properties they exhibit. To note that metal foams make an extraordinary combination with metal sheet structures such as sandwich panels and the outer shell of metal in various engineering applications.

References 1. Banhart, J. (Ed.). (1999). Metal foams and porous metal structures. Verl: MIT Publ. 2. Ashby, M. F., Evans, A. G., Fleck, N. A., Gibson, L. J., Hutchinson, J. W., & Wadley, H. N. G. (2000). Metal foams: A design guide. 3. Davies, G. J., & Zhen, S. (1983). Metallic foams: Their production, properties and applications. Journal of Materials Science, 18(7), 1899–1911. 4. Deshpande, V. S., & Fleck, N. A. (1999). Multi-axial yield of aluminium alloy foam,. 8. 5. Deshpande, V. S., & Fleck, N. A. (2000). Isotropic constitutive models for metallic foams. Journal of the Mechanics and Physics of Solids, 48(6–7), 1253–1283. 6. Gibson, L. J., & Ashby, M. F. (1997). Cellular solids: Structure and properties (2nd ed.). Cambridge University Press. 7. Gioux, G., McCormack, T. M., & Gibson, L. J. (2000). Failure of aluminum foams under multiaxial loads. International Journal of Mechanical Sciences, 42(6), 1097–1117. 8. Miller, R. E. (2000). A continuum plasticity model for the constitutive and indentation behavior of foamed metals. International Journal of Mechanical Sciences, 42(4), 729–754. 9. Collins, J. A. (1980). Failure of materials in mechanical design. New York: Wiley. 10. Khan, A. S., & Huang, S. (1995). Continuum theory of plasticity. New York: Wiley. 11. Rajak, D. K., Kumaraswamidhas, L. A., & Das, S. (2016). Technical overview of aluminum alloy foam, 19.

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12. Motz, C., & Pippan, R. (2001). Deformation behaviour of closed-cell aluminium foams in tension. Acta Materialia, 49(13), 2463–2470. 13. Peroni, L., Avalle, M., & Peroni, M. (2008). The mechanical behaviour of aluminium foam structures in different loading conditions. International Journal of Impact Engineering, 35(7), 644–658. 14. Rajak, D. K., Mahajan, N. N., & Emanoil, L. (2019). Crashworthiness performance and microstructural characteristics of foam-filled thin-walled tubes under diverse strain rate. Journal of Alloys and Compounds, 775, 675–689. 15. Rajak, D. K., Kumaraswamidhas, L. A., Das, S., & Senthil Kumaran, S. (2016). Characterization and analysis of compression load behavior of aluminium alloy foam under the diverse strain rate. Journal of Alloys and Compounds, 656, 218–225. 16. Zettl, B., Mayer, H., & Stanzl-Tschegg, S. E. (2001). Fatigue properties of Al-1 Mg-0.6Si foam at low and ultrasonic frequencies. International Journal of Fatigue, 23, 565–573. 17. Ashby, M. F., & Jones, D. R. H. (1997). Engineering materials, 1 (2nd ed.). Oxford: Butterworth-Heinemann. 18. Sugimura, Y., Rabiei, A., Evans, A. G., Harte, A. M., & Fleck, N. A. (1999). Compression fatigue of a cellular Al alloy. Materials Science and Engineering A, 269(1–2), 38–48. 19. Vendra, L., Neville, B., & Rabiei, A. (2009). Fatigue in aluminum–steel and steel–steel composite foams. Materials Science and Engineering A, 517(1–2), 146–153. 20. Fleck, N. A., Kang, K. J., & Ashby, M. F. (1994). Overview no. 112: The cyclic properties of engineering materials. Acta Metallurgica et Materialia, 42(2), 365–381. 21. Fuchs, H. O., & Stephen, R. I. (1980). Metal Fatigue in Engineering (p. 102). New York: Wiley. 22. Harte, A.-M., Fleck, N. A., & Ashby, M. F. (1999). Fatigue failure of an open cell and a closed cell aluminium alloy foam. Acta Materialia, 47(8), 2511–2524. 23. McCullough, & Fleck. (2000). The stress-life fatigue behavior of aluminium alloy foams. Fracture of Engineering Materials and Structures, 23(3), 199–208. 24. Olurin, B. (1999). Fatigue of an aluminium alloy foam, 7. 25. Schwartz, D. S. (1998). Porous AND Cellular materials for structural applications: Symposium held April 13–15, 1998, San Francisco, California, U.S.A. Materials Research Society. 26. Bao, G., & Suo, Z. (1992). Remarks on Crack-bridging concepts. Applied Mechanics Reviews, 45(8), 355–366. 27. Suresh, S. (1992). Fatigue of materials (1st with corrections and exercises). Cambridge University Press. 28. Bergara, A., Dorado, J. I., Martin-Meizoso, A., & Martínez-Esnaola, J. M. (2017). Fatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM). International Journal of Fatigue, 103, 112–121. 29. Banhart, J., & Brinkers, W. (1999). Fatigue behavior of aluminum foams. Journal of Materials Science Letters, 18(8), 617–619. 30. Veale, P. J. (2010). Investigation of the behavior of open cell aluminum foam. University of Massachusetts Amherst. 31. Kolluri, M., Mukherjee, M., Garcia-Moreno, F., Banhart, J., & Ramamurty, U. (2008). Fatigue of a laterally constrained closed cell aluminum foam. Acta Materialia, 56(5), 1114–1125. 32. Boller, C., & Seeger, T. (1987). Materials data for cyclic loading. Part. B, Part. B. http://site. ebrary.com/id/10988893. 33. Evans, H. E. (1984). Mechanisms of creep fracture. Elsevier, Applied Science, London: Fracture mechanics. 34. Frost, H. J., & Ashby, M. F. (1982). Deformation mechanism maps: Plasticity and creep of metals and ceramics. Elsevier Science Limited: Technology & Engineering. 35. Anon. (2000). Design for creep with metal foams. In Metal foams, pp. 103–12. Elsevier. 36. Burteau, A., Jean-Dominique, B., Yves, B., & Samuel, F. (2014). On the creep deformation of nickel foams under compression. Comptes Rendus Physique, 15(8–9), 705–718. 37. Andrews, E. W., Huang, J.-S., & Gibson, L. J. (1999). Creep behavior of a closed-cell aluminum foam. Acta Materialia, 47(10), 2927–2935.

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38. Couteau, O., & David, C. D. (2008). Creep of aluminum syntactic foams. Materials Science and Engineering A, 488(1–2), 573–579. 39. Diologent, F., Conde, Y., Goodall, R., & Mortensen, A. (2009). Microstructure, strength and creep of aluminium-nickel open cell foam. Philosophical Magazine, 89(13), 1121–1139. 40. Haag, M., Wanner, A., Clemens, H., Zhang, P., Kraft, O., & Arzt, E. (2003). Creep of aluminumbased closed-cell foams. Metallurgical and Materials Transactions A, 34(12), 2809–2817.

Chapter 6

Acoustic, Damping, Thermal and Electrical Properties of Metal Foams

Abstract In this chapter, acoustic, damping, thermal and electrical properties of metallic foams are introduced. Particular emphasis is placed to highlight how the unique structure and properties of metal foams make them different from dense and conventional materials. To note that like other properties, the non-mechanical properties of metal foams also strongly depend on whether metallic foams are opencell or closed-cell types. Further, this chapter highlights the underlining concepts governing sound absorption, damping, and electrical properties of metal foams. These properties are explained using limited sources available in public domain.

6.1 Introduction The discovery of metal foams, as discussed in earlier chapters has been a revelation in the engineering field and beyond. They exhibit low density and novel mechanical, physical, thermal, and electrical properties. Lately, various new features have been added to metal foams. For instance, foams are being made of alternative and new structural, as well as functional materials that are even more cellular, lightweight, and porous for vibration reduction, sound absorption, high specific strength, thermal resistance, etc. They have potential application in acoustic liners, flame arresters, heat exchangers and heaters, filters, energy absorbers, catalytic supporters, etc. Their field of application is growing steadily [1]. Materials that are capable of damping vibrations and that have high strength and stiffness along with lightweight are high in demand. Product quality of a component enhances if it offers more than what are its primary functions. For example, for a bulkhead, carrying loads is its primary function, however, its product quality and durability increases if it further provides greater acoustic absorption and damping vibration. For most materials, a high loss factor (η) is necessary for high damping capacity. Metal foams exhibit higher damping characteristics as compared to their parent materials. The capacity of acoustic absorption by metal foam and its parent metal is another distinctive quality determining their acceptability and applicability. Acoustic absorption is a process of energy absorption

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 D. K. Rajak and M. Gupta, An Insight Into Metal Based Foams, Advanced Structured Materials 145, https://doi.org/10.1007/978-981-15-9069-6_6

99

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6 Acoustic, Damping, Thermal and Electrical Properties of Metal Foams

in which a material or structure absorbs acoustic energy when infused with sound wave through [2] a. b. c. d.

Mechanical damping by the material itself. Aerodynamic vortex-shedding from shrill boundaries. Reduction of frictional viscous as pressure wave propagates to and fro in voids. Thermo-elastic damping.

Sound is measured on a logarithmic scale and in decibels with accord to human ear. In terms of human audibility level, 0.5 sound-absorption coefficient indicates absorption of only half energy. Absorption coefficient exceeding 0.9 is considered to be really effective. Sound absorption coefficient around a range of 0.85 in metal and metal foam is decent but not comparable to what it is in felt or fiber glass. As far as sound absorption is concerned, the relationship between metal foams and their pore size is uncertain yet [3–5]. Metal foams also have high natural vibration frequencies due to high flexural stiffness and low mass. It is hard to trigger vibration in metal foams. As a result, metal foam panels are much in demand for vibration suppression and sound management. Closed-cell metal foam has lower thermal conductivity with a factor of 8–30 compared to the fully dense parent metal. Metal foams act as a buffer in stiff structure and varying temperature field. Due to higher surface-to-volume ratio, they can be used for reducing the area of Heating, Ventilation, and Air Conditioning & Refrigeration (HVAC&R) systems. Open-cell foams are used for heat transmission in various apparatus, such as heat shields, heat sink in electronic applications, regenerators, etc. [6, 7]. In general, metal foams also exhibit low electrical conductivity. Due to their morphology and microstructure, cell interiors of foams are gas filled and they are nonconducting. Although conductivity and relative density of various metal foams vary linearly, their reliability for electrical resistance is ensured. Due to reduced electrical conductivity, metal foams ensure decent electrical grounding and protection against radiation. They can be used as electrodes for batteries that have open cells with a large surface area. Nickel foams serve the purpose most. Most batteries are too bulky and costly. Their volume, as well as cost, can be reduced using porous foam structures [8–10]. Subsequent sections will describe these properties in more details.

6.2 Properties of Metal Foams Metal foams exhibit very unique acoustics, damping, thermal and electrical properties. These properties are reviewed systematically in the following sections.

6.2 Properties of Metal Foams

101

6.2.1 Acoustic Properties Vibration in an elastic medium causes sound. Propagation of sound relies on the characteristics of the medium. Sound travels with a speed of about 343 m/s at sea level and at a temperature of 21.1 °C. In solid materials, on the other hand, it travels at a considerably faster rate. In iron and steel, for instance, at a temperature of 21.1 °C, the speed of sound is approximately 5182 m/s. The velocity of sound depends on the material it travels through. The relation for wave velocity (υ) is expressed by equation υ = λf, where λ is the wavelength and f is the frequency of a given wave. The audible range for humans is 20 to 20 kHz with respect to wavelengths in the range of 17 mm to 17 m. In terms of auditory perspective, 500–4000 Hz frequency is considered suitable [2]. Sound pressure is measured using unit Pascal (Pa). However, if it is in the audible range, the pressure would be in the array of power 6, which would be measured with the unit of decibels (dB) due to convenience as it uses a logarithmic scale. This scale is not absolute as it compares different sound levels [9]. The sound pressure level (L p ) is the most commonly used scale, as presented in Eq. (6.1) [2, 10]  L p = 10 log10

pr ms pr e f

2

 = 20 log10

pr ms pr e f

 (6.1)

where pr ms = root mean square (rms) sound pressure in a given source (Pa) and pr e f is reference pressure that is usually 2 × 10–5 Pa. The reference pressure is chosen as 2 × 10–5 Pa because it has been found that an average adult with normal hearing capacity can perceive only 1000 Hz tone at this pressure. Therefore, this is often referred to as the threshold of hearing at 1000 Hz. Sound power level refers to acoustic power radiated by a given source per unit time with respect to reference sound power. It is presented in Eq. 6.2 [2, 10] as  L w = 10 log10

W Wr e f

 (6.2)

where W = sound power level of given source and Wref = 10–12 W. Both measures are correlated as sound power is proportional to the square of root mean square pressure. Commonly sound pressure level scale is used [11–13]. Table 6.1 shows the sound levels (in dB) associated with different devices and operations. A part of the sound energy in a flat sound wave originating from a given source is absorbed when it is exposed on a material. It is expressed by the sound absorption coefficient. For example, if a substance has a coefficient of about 0.8, then it will take in 80% of the incident sound energy, which would translate into a sound level of 20 dB. Table 6.2 shows the values of the sound absorption coefficient in various building materials.

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6 Acoustic, Damping, Thermal and Electrical Properties of Metal Foams

Table 6.1 Sound levels for various components (in dB) [12]

Source of sound

dB

Boeing 747

140

Civil defense siren

130

Jack Hammer

120

Rock concert

110

Lawn mower

100

Motorcycle

90

Garbage disposal

80

Vacuum cleaner

70

Normal conversation

60

Light traffic

50

Background noise

40

Whisper

30

Table 6.2 Sound absorption coefficients for various materials for different frequencies [14] Materials

Absorption coefficients by frequency (Hz) 125

250

500

1,000

2,000

Acoustic tile (Ceiling)

0.80

0.90

0.90

0.95

0.90

Brick

0.03

0.03

0.03

0.04

0.05

Carpet over concrete

0.08

0.25

0.60

0.70

0.72

Heavy curtains

0.15

0.35

0.55

0.75

0.70

Marble

0.01

0.01

0.01

0.01

0.02

Painted concrete

0.10

0.05

0.06

0.07

0.09

Plaster on concrete

0.10

0.10

0.08

0.05

0.05

Plywood on studs

0.30

0.20

0.15

0.10

0.09

Smooth concrete

0.01

0.01

0.01

0.02

0.02

Wood floor

0.15

0.11

0.10

0.07

0.06

In case of metal foams, plane wave impedance tube is used for measuring the absorption coefficient. In case of incident flat sound wave on the right angle to an acoustic absorber, a part of the energy is absorbed and part of the energy is echoed back [15]. Figure 6.1 show the principle of impedance tube. If the pressure of the incident ( pinc ) wave is represented by Eq. 6.3 [2] pincident = X cos(2π f t)

(6.3)

And that of the reflected wave ( pr e f lected ) is expressed by Eq. 6.4 [2] pr e f lected

   2a = Y cos 2π f t − s

(6.4)

6.2 Properties of Metal Foams

103

Fig. 6.1 Representation of plane wave impedance tube for sound absorption (adapted from Ref. [2, 11])

Then, for obtaining total pressure inside the plane wave, impedance tube microphone is used and total pressure will comprise of the incident and reflected pressure. Here, X and Y are amplitudes, f = frequency (Hz), t = time (s), a = distance from sample surface (m), s = speed of sound (m/s) and from this sound, absorption coefficient α is defined as in Eq. 6.5 [2]  α =1−

Y X

2 (6.5)

The sound absorption coefficient is part of incident energy from any given sound source, which is absorbed by a given material [11]. Experiments helped to determine the value of the absorption coefficient in glass wool. For frequencies greater than 1000 Hz, the absorption coefficient is around 1, signifying that sound is fully absorbed by the material. Experiments were also conducted on sound absorption by Alporas foam (aluminum foam) in a virgin state (without any structural modification). They revealed that α increases to about 0.9 at 1800 Hz. It was also seen that if the Alporas sample is compressed by 10%, several cell walls are ruptured in the foam increasing the sound absorption [2]. From Eq. 6.6, one can find a 10 dB drop in noise level if the sound absorption coefficient is 0.9 and can be measured the drop sound level (L P ) in decibels [2]. From this, we can conclude that metal foams possess restricted sound absorbing capability, which can be improved by compressing it. However, such compression may affect other properties in metal foams. Moreover, in materials like glass wool, felt, etc., absorption is much better. Nevertheless, due to multifunctional applications of metal foams, often they are the preferred choice [16–19]. Decibel (dB) scale is used for measuring relative sound levels while dealing with noise [2,

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6 Acoustic, Damping, Thermal and Electrical Properties of Metal Foams

11, 13].  L P = −10 log10

Y X

2 = −10 log10 (1 − α)

(6.6)

6.2.2 Damping Properties Metal foams exhibit higher damping characteristics than their parent metals. Consider a single degree of freedom spring mass system as shown in the Fig. 6.2a. The mass is fastened to base with the support of a spring and viscous (using fluid in the cylinder) damper. The base oscillates at single frequency ω and has an amplitude of X, the displacement of the base will accordingly be expressed as x = X eiωt . Therefore, the relative displacement of the supported mass is expressed by y = Y eiωt [2, 18]. The transfer function (F(ω)) is represented by Eq. 6.7 [2] F(ω) =

Y (ω/ω1 )2 = X 1 − (ω/ω1 )2 + iη(ω/ω1 )

(6.7)

where ω1 = undamped natural frequency of spring mass oscillator and η = damping factor. Transfer function for various (ω/ω1 ) values is shown in Fig. 6.2b.

Fig. 6.2 a Schematic diagram of a single degree of freedom spring mass oscillator system. b Approximate transfer function for relative displacement y of mass (adapted from Ref. [2])

6.2 Properties of Metal Foams

6.2.2.1

105

Solitary Low Frequency and Undamped Input

Considering the diminutive values of (ω/ω1 ) and undamped conditions, Eq. 6.8 [2] is expressed as |Y | = (ω/ω1 )2 |X |

(6.8)

From the equation, one can infer that response Y can be curtailed if its undamped natural frequency ω1, yielded as maximum is feasible. Practically, the oscillating system would show ample mode of vibrations provided the condition necessitating maximization of ω1 is unaltered. Material index can be expressed by Eq. 6.9 [2] as Mu = ω1

(6.9)

For limiting the response to solitary low frequency undamped input, material index (M u ) should be maximized. By enhancing ω1 to the maximum for the circular plate, one gets the lowest frequency of flexural oscillation as in Eq. 6.10 [2] ω1 =

C2 2π



Et 3 m 1 R 4 (1 − ν 2 )

1/2 (6.10)

where C2 is constant, E is the modulus of elasticity, R is the radius of the plate, m 1 is the mass per unit area, and ν is the Poisson’s ratio. If this plate is to be transformed into foam, there has to be an increment in the thickness t as relation (ρ/ρs )−1 and reduction in modulus by amount (ρ/ρs )2 , giving us the scaling law Eq. 6.11 [2], as ω1 = ω1,s



ρ ρs

−1/2 (6.11)

The higher the natural vibration frequency, the lower would be the density. Even if the density of the core is reduced at a constant mass, the flexural stiffness would increase, which would be effective in the sandwich panel as a core element.

6.2.2.2

Material Damping

Hysteresis damping is a form of internal damping in which energy is dissipated within a material as the material is cyclically stressed. The dissipation occurs via internal friction as the particles within the material slip and slide at internal planes during deformation. The damping capacity of metal foams is larger than that of the parent metals by up to a factor of 10 [21–23]. It is important to consider damping aspect while subjecting an element to input frequency which is near or at the resonating frequency of the material. Material damping is characterized in various ways. One can assume that a material is loaded elastically to a stress of σmax . Loss of coefficient η is

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6 Acoustic, Damping, Thermal and Electrical Properties of Metal Foams

Fig. 6.3 Stress–strain cycle for loss coefficient measurement (adapted from Ref. [17, 24])

used in relation to energy dissipation. In a cycle elastic strain, energy is stockpiled by the material with respect to unit volume, which is dispelled as it dissipates, expressed as U as shown in Fig. 6.3 [17, 24], and can be formulated [2, 17] as  σmax 2 1 σmax and U = σ dε σ dε = U= 2 E

(6.12)

0

η=

U 2πU

(6.13)

Thus, loss coefficient (η) [2, 17] is a ratio of energy dissipated per radian to limiting elastic strain in body or absolute energy. The loss coefficient depends upon temperature, amplitude of stress and strain, as well as the frequency of cycling. There are other parameters as well for measuring damping, such as logarithmic decrement δ, damping ratio ξ (see Table 6.3), Quality factor Q, loss angle ψ, and energy loss per cycle. When a system is under-damped and excited near resonating frequency, ξ = 0.01. The following relations (Eq. 6.14), are hence established [2, 17]: η=

δ 1 D = 2ζ = = tan ψ = 2π π Q

(6.14)

When damping in a system is large, there would not be any empirical relations. As in other materials, cyclic loading causes fatigue damage in metal foams. Fatigue tests help to measure fatigue limit σe (σe is the range in which a material survives 107 cycles) [23].

6.2 Properties of Metal Foams Table 6.3 Representative damping ratios [20]

107 System

Viscous damping ratio (ξ)

Metals (in elastic range)