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Development of steel foam processing methods and characterization of metal foam
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Development of steel foam processing methods and characterization of metal foam
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INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send U M I a complete manuscript and there are missing pages, these w ill be noted. Also, if unauthorized copyright material had to be removed, a note w ill indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6’ x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UM I directly to order. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, M l 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEVELOPMENT OF STEEL FOAM PROCESSING METHODS AND CHARACTERIZATION OF METAL FOAM by Chanman Park A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Materials Science) December 2000 © 2000 Chanman Park Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. U M I Number: 3041506 UMI’ U M I Microform 3041506 Copyright 2002 by ProQuest Information and Learning Company. A ll rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, M l 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PAM LOS ANGELES, CALIFORNIA S O M ? This dissertation, written I n f ^ . ^ . ^ . ^ . ^ . . . .0 ? : ^ ............................ under the direction of H ..L S Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of re quirements for T h e degree of DOCTOR OF PHILOSOPHY D im o f Graduate Studios Date pecemher.18^ 2 0 0 0 DISSERTATION COMMITTEE Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements I am deeply grateful to my advisor, Professor Steve R. Nutt, for his continuous support and valuable guidance throughout the program. His enthusiasm and encouragement made my achievement today possible, and will continue to be the inspiration in by career ahead. I would like to thank my thesis committee for taking the time to review and evaluate my work. The committee members include Professor Edward Goo and Professor Charles G. Sammis. I wish to thank Dr. Terry S. Creasy for his help in operating some of the laboratory equipment and for very fruitful discussions throughout the program. I would like to thank Professor E.J. Lavemia of the Chemical and Biochemical Engineering and Materials Science Department of University of California at Irvine for granting me access to some of his equipment. I would like to acknowledge Capstain Pacific for allowing me use their pressing machine and dies. I would also like to thank Mr. Evans of PESCO metal Powder Company for providing all kinds of steel powder. Finally, I wish to thank my wife, Julia Park, for her numerous encouragement and stimulating discussions during the duration of this research work, and my daughter, Angela Park, for her support. This work was supported by the T.R.W. and M.C. Gill Co. ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Acknowledgements Page ii List of Figures vi Glossary xii Abstract xiv 1. Introduction I 2. Literature review 6 2.1 Definition of cellular solids 6 2.2 Relative density 7 2.3 Methods of producing metallic foams 9 2.3.1 Foams made form metallic melts 9 2.3.1.1 Casting metal around syntactic foams 9 2.3.1.2 Direct foaming of melts 10 2.3.1.3 Foaming agents technique 12 2.3.1.4 GASAR process 15 2.3.1.5 Incorporating granules in the melts 17 2.3.1.6 Investment casting 18 2.3.2 Powder metallurgy 18 2.3.2.1 Particle deformation during cold isostatic pressing 18 2.3.2.2 Foaming of slurries 21 2.3.2.3 Loose powder sintering 22 2.3.2.4 Metallic deposition techniques 23 2.3.2.5 Powder metallurgical (PM) process 24 2.3.2.6 Sputter deposition 27 2.4 Mechanical properties of foams 29 2.4.1 Linear elasticity 31 2.4.2 Plastic collapse 35 2.4.3 Densification 37 2.4.4 Deformation mechanisms in foams 38 2.5 Energy Absorption 39 2.5.1 The Janssen factor, J 42 2.5.2 The Cushion factor 43 2.5.3 The Rush curves 46 2.5.4 Energy absorption diagrams 49 2.5.5 Optical selection of foamed materials 53 iu Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3. Experimental procedures 55 3.1 Outline for experimental procedures 55 3.2 Steel powder 59 3.3 Foaming agents 59 3.4 Mixing methods 6 1 3.5 Isostatic cold pressing 62 3.6 Foaming process 66 3.7 Mechanical testing 68 3.8 Structural observation 72 3.8.1 Optical microscopy 72 3.8.2 Transmission electron microscopy 74 4. Powder metallurgy (PM) synthesis of steel foam 76 4.1 Introduction 76 4.2 Foam synthesis 77 4.2.1 Foaming agents 77 4.2.2 Carbon content 78 4.2.3 Microstructure analysis 79 4.3 Effects of process parameters on steel foam synthesis 83 4.3.1 Introduction 83 4.3.2 Experiments 86 4.3.3 Mixing methods 87 4.3.4 Melting time 88 4.3.5 Mechanical behavior 92 4.4 Interlayer membranes method 93 4.5 Conclusion 97 5. Mechanical properties of steel foam 100 5.1 Introduction 100 5.2 Annealing effects 101 5.2.1 Compression strength 101 5.2.2 Collapse mechanism 106 5.2.3 Energy absorption of steel foams 108 5.2.3.1 Energy absorption efficiency 108 5.2.3.2 Energy absorption capacity 113 5.2.3.3 Energy absorption diagrams 116 5.2.4 Conclusion 118 5.3 Anisotropy of mechanical properties 118 5.3.1 Introduction 118 5.3.2 Experiments 120 5.3.3 The compression test results 122 5.3.4 Comparing the measured values with the predicted values 128 5.3.4.1 Predicted by power law 128 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.3.4.2 Determination of the distribution constant 133 5.3.5 Deformation mechanism 133 5.3.6 Conclusion 139 5.4 Effect of different strain rates and morphological defects 143 5.4.1 Introduction 143 5.4.2 Experiments 145 5.4.3 Yield strength with strain rate 146 5.4.4 Variation of energy absorption capacity with strain rate 151 5.4.5 Morphological defects 153 5.4.6 Conclusion 162 6. Metallographic study of GASAR porous magnesium 165 6.1 Introduction 165 6.2 Experimental procedures 166 6.3 Porosity and pore size distribution 167 6.3.1 Porous Mg 167 6.3.2 Porous AZ31 168 6.4 Microstructure 176 6.4.1 Porous Mg 176 6.4.2 Porous AZ31 176 6.5 Conclusion 187 7. Summary and conclusion 188 References 192 V Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures Page Figure 1.1. Example of cellular solids: (a) two-dimensional honeycomb (b) three-dimensional foam with open cells (c) three-dimensional foam with closed cells. 3 Figure 2.1 Direct foaming of melts (MMC foams). 11 Figure 2.2 Foaming agent method. 14 Figure 2.3 The processing steps for PM method. 26 Figure 2.4 Aluminum foam made from metal powder. 28 Figure 2.5 Schematic compressive stress-strain curves for foams, showing the three regimes of linear elasticity, collapse and densification. 30 Figure 2.6 Schematic of closed-cell foams and stretching of the faces of a closed-cell foam in compression. 32 Figure 2.7 Plastic stretching of the cell faces of a closed-cell foam. 34 Figure 2.8 The yielding of a plastic foam. 36 Figure 2.9 Stress-strain responses for an elastic solid and a foam made form the same solid, showing the energy absorbed at stress o p . 40 Figure 2.10 The Janssen factor, J, is used to characterize energy absorption in foams. 44 Figure 2.11 The cushion factor, C, is used to characterize energy absorption in foams. 4S Figure 2.12 The typical Rusch curve. The curves constructed from the stress-strain equations of Rusch. 48 Figure 2.13 Stress-strain responses are measured at a single strain rate. 50 Figure 2.14 The energy is plotted against stress. The energy and stress are normalized by the solid modulus. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.15 The envelope is replotted on the same axes, and marked with density points. The density points are connected to give a family of intersecting contours of constant density. Figure 3.1 Flow chart of the experimental proced. Figure 3.2 PM Manufacturing Process. Figure 3 3 Twin shell dry blender. Figure 3.4 Drill mixing method. Figure 3.5 Ball-milling method. Figure 3.6 Cryomilling method. Figure 3.7 The Lindberg 1700°C Box Furnace (Model 51314). Figure 3.8 (a) The picture of graphite crucibles (b) schematic illustration of the crucible. Figure 3.9 The compression tests were performed by Instron 1331. Figure 4.1 Pore structures of steel foams: (a) MgCC> 3 forming agent (b) SrCOa foaming agents. Figure 4.2 Metallography of foam microstructure: (a) Pre-annealed sample (75X) (b) Annealed sample (75X). Figure 4.2 Metallography of foam microstructure: (c) High magnification of (b) (500X). Figure 4 3 Cross section of steel foams resulting from powder blended by (a) drill mixing (b) ball-milling (c) cryomilling. (Mixing time: 2 hours). Figure 4.4 Steel foams produced by foam expansion at 1330C using melting times (tm) of (a) 3.5 min, (b) 5 min, (c) 6 min, and (d) 8 min. Crack-like features arise from pore collapse during melting (powders were blended by ball-milling for 30 min). Figure 4.5 Compression stress-strain curves for three foam samples. The powders were blended by drill mixing, ball milling, and cryomilling in samples 1-3 respectively. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.6 Schematic illustration showing the use of interlayer membranes. Figure 4.7 Cross sections of steel foams showing the effects of using interlayer membranes (a) Foam structure produced without interlayer membranes, (b) Foam structure with 20 interlayer membranes (powders were blended by drill-mixing). Figure 5.1 Stress-strain response of steel foam and A1 foam. Figure 5.2 Stress-strain response of low-density and high-density steel foam. Figure 5 J Compression strength of a series of the steel foams as a function of relative density. Figure 5.4 The effect of annealing treatment on the stress-strain response of steel foam. Figure 5.5 Comparison of real and ideal energy absorbers. Figure 5.6 Compressive stress-strain response and energy absorption efficiency of annealed steel foam (density = 3.56 g/cm). Figure 5.7 Compressive stress-strain response and absorption efficiency, of pre-annealed foamed steel (density = 4.96 g/cm). Figure 5.8 Energy absorbed by various steel foams after compression strains o f20,30, and 50% (annealed samples). Figure 5.9 Energy absorbed by various steel foams after compression strains of 20,30, and 50% (pre-annealed samples). Figure 5.10 Compression behavior of three steel foams of different densities. The various areas correspond to equivalent amounts of absorbed energy, W. Figure 5.11 Schematic of the loading and foaming directions: (a) Longitudinal direction (b) Transverse direction. Figure 5.12 Cell structures of steel foam showing (a) elliptical shape cells, and (b) spherical shape cells. Figure 5.13 Stress-strain response for compression in the longitudinal direction. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.14 Stress-strain response for compression in the transverse direction. Figure 5.15 Comparing yield strength versus density for transverse and longitudinal directions. Figure 5.16 Relative yield strength versus relative density for longitudinal and transverse directions. Figure 5.17 (a) The distribution constant for steel foam as function of relative density (longitudinal direction). The dotted lines are predictions given by equation (46). Figure 5.17 (b) The distribution constant for steel foam as a function of. relative density (transverse direction). The dotted lines are predictions given by equation (46). Figure 5.18 Deformation banding during a typical compression test (a) s = 0% (b) e * 20% (c) e = 30% (d) e = 50%. Figure 5.19 Schematic for cell collapse model. Figure 5.20(a) Mechanical response for a foam with uniform pore size (about 1.5-2 mm): (a) Foam structure, (b) Stress-strain curve of the compression test (density: 3.52 g/cm'3 ). Figure 5.20(b) Mechanical response for a foam with a wide range of pore size: (a) Foam structure, (b) Stress-strain curve of the compression test (Density: 4.63 g/cm3 ). Figure 5.21 Stress-strain curve of steel foam and A 1 foam. Figure 5.22 Yield strength (<?*) with different strain rates (sec*1 ). Figure 5.23 Energy absorbed (W) by various strain rates (sec'1 ). Figure 5.24 Method for measuring cell wall curvature. Figure 5.25 Curvature distribution for steel foam sample A. Figure 5.26 Curvature distribution for steel foam sample B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.27 Relative strength versus relative density for steel foam sample A and B (density = 3.78 g/cm3 ). The solid line represents the prediction of closed cell with ^=0 .8. 160 Figure 5.28 Three samples with different cell wiggles: (a) Type I (drill mixing) (b) Type II (Ball-milling) (c) Type III (Cryomilling). 161 Figure 5.29 The yield strengths for three samples: type I (•), type II (■), and type III (▲). 163 Figure 6.1 Sectioning of samples. 166 Figure 6.2(a) Picture of transverse section and fraction of pore diameters: sample number 1. 169 Figure 6.2(b) Picture of transverse section and fraction of pore diameters: sample number 2. 170 Figure 6.2(c) Picture of transverse section and fraction of pore diameters: sample number 3. 171 Figure 6.2(d) Picture of transverse section and fraction of pore diameters: sample number 4. 172 Figure 6 J(a) Pictures of transverse section of AZ31 Mg alloy: sample 1. 173 Figure 6 .3(b) Pictures of transverse section of AZ31 Mg alloy: sample 2. 174 Figure 6.3(c) Pictures of transverse section of AZ31 Mg alloy: sample 3. 175 Figure 6.4(a) Micrographs showing pores in porous Mg. 177 Figure 6.4(b) Micrographs showing micropores in porous Mg. 178 Figure 6.4(c) Micrographs showing porous AZ31 Mg alloy. 179 Figure 6.5(a) TEM pictures: peripheral region. 181 Figure 6.5(b) TEM pictures: Near the pores. 182 Figure 6.6(a) TEM pictures: large gas track. 183 Figure 6.6(b) TEM pictures: Vein-like network of fine gas track. 184 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 6.7 TEM picture: (a) The boundary between coarse- and fine-grain regions (b) SAD ring pattern for coarse-grain regions (c) SAD ring pattern for fine-grain regions. Figure 6.8 The ternary intermetallic phases Mgu((Zn,Al)49) and MgsZ^Afe. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Glossary Symbols • P Density of foamed material P m Density of the cell wall material t Cell wall thickness I Cell edge length Q Constant (/ = 1,2,3,4.....) t. Cell edge thickness '/ Cell face thickness n Average number of edges per face on a single cell f Number of faces on a single cell Z f Number of faces that meet at an edge * Distribution constant P Compacting pressure s Deflection of cell edge F Compression force E m Young’s modulus of cell wall material I Second moment of area of cell edge £* Young’s modulus of foamed material Yield strength of the cell wall material • a Yield strength of foamed material ” , Plastic moment e. Strain at which densification starts £c Strain at which densification complete J Janssen factor Deceleration m Mass V Velocity h Height of the cushioning material W Energy absorption per unit volume A Area of the cushion C Rush curve (s) Shape factor e Strain e D Densification strain Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Maximum permitted stress by a given application Shape function of the stress-strain curve Integral of k(e) over strain Initial collapse stress Lagrange function Tm Melting temperature Td Decomposition temperature p ni Relative density 7 Energy absorbing efficiency A,. . Ideal energy absorption Real energy absorption a, Constant (cr^, y : Yield strength of the metal at OK 9 e Strain rate * ( * ) k,(£) f(o) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract Steel foam was synthesized by a powder metallurgical route, resulting in densities less than half that of steel. Process parameters for foam synthesis were investigated, and two standard powder formulations were selected consisting ofFe- 2.5% C and 0.2 wt% foaming agent (either MgC03 or SrC03). Compression tests were performed on annealed and pre-annealed foam samples of different density to determine mechanical response and energy absorption behavior. The stress-strain response was strongly affected by annealing, which reduced the carbon content and converted much of the pearlitic structure to ferrite. Different powder blending methods and melting times were employed and the effects on the geometric structure of steel foam were examined. Dispersion of the foaming agent affected the pore size distribution of the expanded foams. With increasing melt time, pores coalesced, leading to the eventual collapse of the foam. Inserting interlayer membranes in the powder compacts inhibited coalescence of pores and produced foams with more uniform cell size and distribution. The closed-cell foam samples exhibited anisotropy in compression, a phenomenon that was caused primarily by the ellipsoidal cell shapes within the foam. Yield strengths were 3x higher in the transverse direction than in the longitudinal direction. Yield strength also showed a power-law dependence on relative density (n = 1.8). Compressive strain was highly localized and occurred in discrete bands that extended transverse to the loading direction. The yield strength of foam samples showed stronger strain rate dependence at higher strain rates. The increased strain rate xiv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dependence was attributed to microinertial hardening. Energy absorption was also observed to increase with strain rate. Measurements of cell wall curvature showed that an increased mean curvature correlated with a reduced yield strength, and foam strengths generally fell below predictions of Gibson-Ashby theory. Morphological defects reduced yield strength and altered the dependence on density. Microstructural analysis was performed on a porous Mg and AZ31 Mg alloy synthesized by the GASAR process. The pore distribution depended on the distance from the chill end of ingots. TEM observations revealed apparent gas tracks neat the pores and ternary intermetallic phases in the alloy. XV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1. INTRODUCTION It is the definition of porous material that the solid has the clusters o f cell structures like cellular solid. The cell means a small compartment or an enclosed space. The porous materials are an interconnected network of cells and packed together. There are two kinds of porous materials: one is the natural porous material such as wood, cork, coral, bone and sponge etc [1-4]. The other is the artificial porous materials such as honeycomb structure and foamed materials. Long time ago, man had used the natural porous materials like wooden artifacts, bungs in wine bottles, etc. Because of the special properties of the porous material, the artificial porous materials are developed by mankind [5-8]. The most common porous material is the polymeric foam, which are used in everywhere from packing materials to the crash padding of an aircraft cockpit. Now the other materials are used for making foamed materials (porous materials) such as metals, ceramics and glasses. These newer foamed materials are increasingly used for engineering materials because the porous structure, offered by porous materials. The metallic foams have many attractive properties, such as energy absorption capacity, air and water permeability, acoustic absorption properties, good electrical insulating properties, and low thermal conductivity. Therefore, the metallic foams have been developed in the last 20 years and the applications are increased as new engineering materials. The examples of their applications are shock and impact absorbers, engine l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. exhaust mufflers and valves, high temperature gaskets and abradable seals, dust and fluid filters, flame arresters, porous electrodes, etc [9,10]. There are three typical porous structures that are shown in figure 1. The figure 1.1 (a) shows the honeycomb structure that is two-dimensional porous materials. Three- dimensional porous materials are called foamed materials. If the foamed materials are contained in the cell edges only, the foam is called as open cell foams (figure 1.1 (b)). If cells are divided each other cells by faces, it is called as closed ceil foams (figure 1.1 (c)). Man-made honeycomb structures are produced from metal, polymer and ceramic. They are used in a various areas of applications. Polymer honeycombs are used as the cores of sandwich structures in everything from cheap doors to advanced aerospace components. Metal honeycombs structures are mainly used as energy absorbing applications. Applications of ceramic ones are the high-temperature processing as catalyst carriers and heat exchangers. Three-dimensional porous materials are produced out of polymers, metals, ceramics, and even glasses. Artificial foamed materials are used for absorbing the energy of impacts, such as packaging and crash protection, and lightweight structures, for instance the cores of sandwich panels. Also the foamed materials can be used for thermal insulation, or flotation, or as a filter. Without a detailed understanding o f the mechanical behavior, the foamed materials can not be used efficiently [11-13]. Porous or cellular materials, commonly known as foams, exhibit novel properties and afford great potential for weight savings [14]. Polymer foams have long been used to absorb vibration, noise, and impact energy (e.g., packing materials). However, structural applications of polymer foams generally have been limited to low-stress components 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (C) Figure 1.1. Example of cellular solids: (a) two-dimensional honeycomb [14,21] (b) three-dimensional foam with open cells [26] (c) three-dimensional foam with closed cells [21]. 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. because of the relatively low strength compared with other engineering materials. This also limits the amount of energy that can be absorbed by polymer foams during deformation. For these reasons, considerable attention has been devoted recently to the synthesis and properties of metallic foams, which offer the prospect of much higher strength, stiffness, and energy absorption during deformation, and substantial weight savings relative to conventional metallic components [15-19]. However, the process technology for making such materials is not yet mature, and a full understanding of structure-property relations is only beginning to emerge [20]. One method for synthesizing metallic foam is the so-called Fraunhofer process [16]. In this process, metal powder is mixed with a granular foaming agent and compacted to yield a fully dense semi-finished product. The compact is expanded to foam by heating the compact to the melting point, whereupon gas evolves from decomposition of the foaming agent. The product typically is a closed-cell foam with a relative density that depends on several key process parameters. Although this process has been successfully employed to aluminum foam synthesis [16], there have been few attempts to apply the process to steel [17], which poses special difficulties stemming from higher melting points and lower melt viscosity. Steel foam offers several potential advantages over aluminum foam (in principal), including - increased strength and specific stiffness. - lower raw material cost 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - higher melting temperature. • compatibility with steel structures. The inherent strength of steel combined with the reduced density of foam could yield an attractive material with reasonable strength, greatly reduced density, and highly efficient energy absorption. Potential applications include cores for beams and sandwich panels, weight-critical components, and energy absorbing components and structures. However, process control is critical for achieving uniform, controlled pore structures and consistent properties, and this is currently a formidable challenge. Nevertheless, if the process technology can be sufficiently developed, the inherent advantages of steel foams will undoubtedly open doors to innovative structural applications. The purpose of the present work is to demonstrate a feasible synthesis route for steel foams and to report the basic mechanical properties. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2. LITERATURE REVIEW 2.1 Definition of Cellular solids The cell means a small compartment or an enclosed space and the word “cell” comes from the Latin cella. A cellular solid is one made up of an interconnected network of solid struts or plates which form the edges and faces of cells. There are two kinds of cellular materials: one is natural cellular material such as wood, cork, bone, etc and the other is man-made cellular material [6, 7]. The simplest man-made one is honeycombs structure that is two-dimensional cellular material. The three-dimensional cellular materials are called foams. There is no clear-cut and generally accepted definition for the term “foam”[11, 12]. The foams can be existed in two kinds of structures that are open-cell and closed cell structure. The open-cell structure is contained in the cell edges only so those cells connect through open faces. However, the closed-cell structure is consisted o f cell faces and edges so that each cell is sealed off from its neighbor. Some foams are partly open and partly closed. The geometry and characterization of cells is very important subject. The single most important feature of a cellular solid is its relative density (p* / p ,). The definition of relative density is the density of the cellular material (p*) divided by that of the solid from which the cell walls are made (p s) [21-23]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.2 Relative Density The properties of a foamed material strongly depend on its relative density. The relative density is expressed as the density of the foamed material, p , divided by that of the solid from which the cell walls are made, ps- The relative density for honeycombs is calculated by [21, 22] £ = c'7 where p \ Density of honeycombs ps: density of the cell wall material t: cell wall thickness /: cell edge length For all open cell foamed materials with edges of length / and thickness /: i-iil (2) And for all closed cell foamed materials with faces of side I and uniform thickness /: ^ = (3) Pm 1 where C/, Cj, and Cj are constants (near unity) that depend on the cell shape [21,22]. The cell edges are thicker than the cell faces for the most closed cell materials. It is another important parameter that is the volume fraction of the solid (distribution constant), The distribution constant is expressed by [2,21-25] Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where Cell edge thickness if. Cell face thickness /: Cell edge length n : Average number of edges per face on a single cell /. Number of faces on a single cell Zf Number of faces that meet at an edge. Also the relative density can be calculated by From equation (4) and (5), equations for tj l and t/l are obtained in terms of the distribution constant and relative density [21,26]. C4 [2 Z ,l2 2 / L\-*L+L‘ j. (5) (6) { n f P J (7) 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3 Methods of Producing Metallic Foams 23.1 Foams Made from Metallic Melts 23.1.1 Casting Metal around Syntactic Foams This method produces an interconnected cellular structure light-weight metals by casting around inorganic granules or by hollow spheres of low density or by infiltrating such materials with a liquid melt These granules can be some loose bulk of expanded clay, foamed glass spheres of aluminum oxide hollow spheres, hollow corundum spheres, etc [27-29]. Granules can also be soluble, such as sodium chloride which is later leached out to leave a porous metal [30]. Then the granules are introduced into the melt or the melt is poured over the bulk of filler material. The heat conductivity and capacity of the granules is very low so it does not disturb the flow of the metal too much. However, the high surface tension of most metals, especially aluminum, prevents the metal melt from immediately flowing into the interstices. Creating a slight vacuum in the bulk or exerting a slight external pressure upon the melt facilitates infiltration significantly. Some superheating of the melt or preheating of the granules can also improve the infiltration. A wide range o f metals can be produced by using this method including aluminum, magnesium, zinc, lead, tin etc. Parts with intricate shapes can be fabricated by designing a mould of the appropriate geometry. Sandwich panels can also be produced. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23.1.2 Direct Foaming of Melts The metal foams can be produced directly under certain circumstances by injecting gases into the liquid metals. The gas bubbles are tending to rise to surface quickly due to the high buoyancy forces in the metallic melt. Increasing the viscosity of the molten metal can impede this rise. Increasing viscosity can be achieved by adding fine ceramic powders or alloying elements, which form particles in the melts. For foaming aluminum and aluminum alloys, silicon carbide, aluminum oxide or magnesium oxide particles are used to enhance the viscosity of the metallic melt. Therefore, the first step consists of making an aluminium melt containing one of these particles. The next step is the foaming the liquid melt by blowing gases, such as air, argon, and nitrogen, into metallic melt using specially designed rotating impellers. These impellers are very important one because they can produce very fine gas bubbles in the melt and distribute gas bubbles homogeneously [31]. The foam that is generated this way floats up to the surface of the liquid where it can be pulled off. This processing method is schematically showed in figure 2.1. Without care, shearing the semi-solid foam too much can damage the foam structure. The foamed material is cut into the required shape after foaming or can be used as the state it comes out of the casting machine having a closed outer surface. The machining of the foamed metals is difficult because of the high content of ceramic particles. Another possible disadvantage is the brittleness of the foamed metal due to the reinforcing particles contained in the cell walls. In order to remove one of these disadvantages, attempts for making shaped parts by casting the semi-liquid foam into 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Addition of reinforcing particles (5-20% SiC or AI2 O3) i Melting the A 1 1 Air Rotating air injection shaft Solidified f t l Aluminum melt with SiC particles Figure 2.1 Direct foaming of melts (MMC foams) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. moulds or by shaping the emerging foam with rolls have been performed. The advantage of the process is the ability of producing large volumes at a rather low cost and the low density that can be achieved. This process is probably the least expensive ones compared to other metallic foams [32,33]. 2 3 .1 3 Foaming Agents Technique In 1924, Adolth Miller proposed a method for making foamed lead: the vaporization of mercury in lead [34], In 1943, Benjamin Sosnick invented the method that produced foamed aluminum, magnesium and their alloys by using vaporization of mercury and zinc [35. 36]. These methods are highly unsatisfactory as the materials utilized have a deleterious effect on each other. Also the amount o f gas evolved in the reaction is difficult to control. The reaction must be carried out in a pressurized chamber that exerts high pressure being on a mixture of metals to build up a high vapor pressure of the volatile metal. Lowering the applied pressure causes foaming. Another method proposed for the manufacture of metal foam involves the addition of an alloy containing ground metal hydride directly to the surface of the metal matrix. In 1951, John C. Elliott subsequently developed this idea and successfully produced foamed aluminum and magnesium. According to the process, adding a blowing agent to a molten metal and heating the mixture to decompose the blowing agent to evolve gas produces foamed metals. The blowing agents are usually a metal hydride such as titanium hydride (Tith) or zirconium hydride (ZH 2) [37]. The molten metal is foamed by the gas expansion. After foaming, the resultant material is cooled to form a foamed 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. solid. This processing method is schematically showed in figure 2.2. The alloy is prepared by grinding together metal hydride and one or more molten metals and then cooling and reducing the resultant product to a powder. Finally, the metal is melted and then the hydride mixture powder is added to the surface of the metal matrix. Addition of the hydride creates a difficulty due to the tendency of the powder to float to the top of the metal matrix and oxidize. Another problem is rather difficult to control and the foamed metal produced has a non-uniform cellular structure. Large gas bubbles are concentrated at the center and there is increasing density near the chilled surface. There are several ways to improve the above problems. Changing the processing methods can improve the problems o f the non-uniformity of distribution and undesirable large size at the center. The first method is increased the viscosity of the molten metal by adding the viscosity-increasing agents. Increasing the viscosity of the molten metal can prevent the escape of bubbles [38]. The viscosity-increasing agents can be either solids, liquids, or gases such as siliceous non-metallic aggregate, dross, air, oxygen, nitrogen, carbon dioxide, argon and water [39-41]. When molten metals treated with a viscosity- increasing agent a much thicker melt is produced. The thicker molten metal can produce the more uniform structure and the smaller pore size. For example, to make aluminum foam, it is necessary to stabilize bubbles in molten aluminum. The most important factor for stabilizing the bubbles in the molten aluminum is to increase its viscosity as shearing resistance acting on a fluid, and prevent the occurrence of bubble floatation. The Ca 1 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Impeller 1.5% Calcium Melting the A1 Thickening i Displaced air Foaming Figure 2.2 Foaming agent method 1.6% Titanium Hydride Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (1.5%) is used as thickening agent. The sequential expansion can produce better results for zinc forms [42]. This can be achieved by foaming with an intermediate product or by making more than one addition of blowing agent to the molten metal. It is another way that the applying agitation to collapse the foam and allowing it to expand again. The second method is the addition of particulate solid oxidizing agent, such as Mn0 2, to the molten aluminium mixture. This can produce the greater uniformity of cell size, cell distribution and cell shape because of the formation of cell nuclei of AI2O3 particles [43]. The third method is the high speed mixing particles of the foaming agent. The more uniform mixing can produce the better foam without exception. Therefore, by using high speed mixing can be dispersed throughout the molten metal mass in a very short time. The above three methods can prevent the non-uniformity and undesirable size of cells in foamed metals. However, the problem arises because of the relatively short time interval between adding a foaming agent to the molten metal and foam formation. This makes the casting operation particularly difficult. 23.1.4 GASARS (Solid-gas eutectic solidification) Process A novel solid-gas eutectic solidification process that was developed some years ago in Ukraine can produce porous metals [44, 45]. This method exploits the fact that some liquid metals form a eutectic system with hydrogen gas. A liquid metal that hydrogen gas has been introduced is cooled through the eutectic point. The solidification of the metal and nucleation of pores occur simultaneously resulting from the diffusion of IS Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. gaseous hydrogen out of the melt as it freezes. The porosity of the resulting metals can be controlled by manipulation of the pressure of the hydrogen gas in the casting chamber because the position of the eutectic point depends on the pressure of the system. By solving hydrogen in liquid metals under high pressure, a melt is pore free with the hydrogen completely solved in the metal. The melt is forced the metal to go through the two-phase regions by reducing the pressure and temperature. Beneath the eutectic temperature the metal arrives at a two-phase region corresponding to a solid plus the gas. If the cooling rate and pressure are correctly chosen then the gas will accumulate in fine gas bubbles in the solid. The temperature of melt must be coordinated with the hydrogen pressure to match the solubility of the hydrogen in the melt with the weight percent hydrogen at the eutectic point since the solubility of hydrogen significantly depends on the temperature. If the temperature and pressure are not properly coordinated, cooling will not pass through the eutectic and a pro-eutectic phase with a non-uniform microstructure will be formed. By changing the cooling rate, the size of the pores can be controlled. For bigger pore size, the cooling rate is decreased because of increasing the distance the hydrogen can diffuse. Also the orientation of the pores can be controlled by the direction of cooling. The directional solidification yields pores that are elongated in the direction of the movement of the front because the hydrogen gas tends to diffuse to pores that have been nucleated on the solidification front. The unidirectional cooling from the bottom plate of the mould can produce cylindrical pores. The cooling from the sides of a cylindrical mould produces the radial pores. The pressure pulsing in the casting chamber 1 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. during unidirectional cooling results in spherical pores [46]. The changing the process control variables during solidification produces the porous layers and materials with a graded porosity. Various types o f pore morphologies are shown in Fig.l [19]. The diffusion coefficient of hydrogen is the important factor for determining the pore size and the porosity depends on the solubility of hydrogen in the materials. The GASAR process has been used to produce porous metals such as nickel, magnesium, beryllium, chromium, tungsten, steel, molybdenum, copper, aluminum, stainless steel and cobalt. The maximum porosities that can be produced by this process are not very high but the metals with medium and high melting points can be foamed. The pore structure of such foams have some problems so that further improvement is necessary [47,48]. 2.3.1.5 Incorporating Granules in the Melt Granules can also be incorporated into metal melts in steady of casting molten metal around them. The metal is melted in a crucible and the granules are introduced therein in this process. Then vigorously mixing is applied for disperse uniformly the granules in the metal mass. During continuous mixing, the mass may be permitted to cool until the mixture is sufficiently viscous as to prevent segregation or stratification. Then the mixing is stopped and the mass is permitted to solidify with the granules embedded [49]. Also hollow metallic spheres can be added in the melt [50]. The phenolic plastic microballoons are utilized which are heated in an inert atmosphere until the plastic cokes, forming hollow carbon microspheres. The carbon spheres are then coated with metal by 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vapor deposition and the carbon is removed by vaporization leaving the hollow metal microspheres. This process is most applicable to refractory metals such as tungsten. 2.3.1.6 Investment Casting Metallic foams can be made without directly foaming the metal. A unique investment casting technique has been used to produce metallic foam [51]. In investment casting, voids of open pore plastic are filled with fluid refractory material, e.g. a mixture of mullite, phenolic resin and calcium carbonate. Then, this plastic-refractory material is heated so as to vaporize the plastic component and a mould having open lattice pores is made. Molten metal is cast into this mould and allowed to cool and solidify. After removing of the mould material, metallic foam is obtained that is the same open pore form as the original open pore plastic. Complex shaped parts can be made by pre-forming the plastic-refractory foam. The metals that are fabricated in this process are those having comparatively low melting points, such as copper, aluminum, lead, zinc, tin and their alloys. The plastic-refractory foam determines the densities and foam morphologies and the cost is high. The typical porosity is range from 80 to 97% [52]. 2J.2 Powder Metallurgy 23.2.1 Particle Deformation During Cold Isostatic Pressing of Metal Powders It is important to understand the deformation during cold isostatic pressing of metal powders. Densification of powder body is depended upon powder characteristics. Metal powders have different metallurgical and geometrical characteristics. The 1 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. metallurgical and structural features are hardness, response to plastic deformation, work- hardening, and adhesion of the particles. The geometrical features are particle size, shape, and distribution. Also lubricant additions effect interparticle movement and interlocking during pressing. Generally, there is a number of identifiable stages that are undergone by a metal powder during cold pressing [53-55]. The initial stage is the transitional restacking that is a certain amount of interparticle movement at low pressure. The initial stage is followed by more defined elastic-plastic deformation at interparticle contact areas. Then a further stage o f bulk compression is reached at higher pressures. At this stage, pore closure becomes very difficult and plastic deformation is very restricted. Accurate analysis of the densification process is extremely difficult because of the relative influence of each of the variables. However, using formulae, the densification process is described by the relationship between pressure and density or porosity level [56,57]. During compaction, the pressure is the major process variable and is the most operationally effective variable for determining the density level. Also compacting pressure significantly affect mechanical properties. Shapiro and Kolthoff proposed one formula which is widely used [58,59]. This formula is expressed as In - ^ = KP + A (8) where D: Relative density P: Compacting pressure K, A: Constants 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It had proposed by Heckel that the Konopicky-Shapiro slope factor K was inversely proportional to the yield stress of the materials [60]. While Greenspan had suggested that particle strain hardening was more dominant and he also confirmed that a change of slope occurred at higher pressures [61], By some experiments, it is confirmed that plastic deformation of metal powders occurs very rapidly beyond the initial stage of compaction where a high proportion of interparticle movement occurs [62,63]. As pressure increases, the rate of deformation diminished and proceeds to the stage where pore closure and elimination of porosity limits further particle deformation. At this point further compacting pressure would only serve to deform the system elastically by bulk compression. The softer powders can be deformed more extensively and densified to relatively higher levels than their harder powders. The application o f the Konopicky- Shapiro equation indicates that densification rate is related to the yield stress of the material in the early stages of plastic deformation. Also the densification rate is depended on material’s work-hardening capacity at higher compacting pressures. The harder materials with low work-hardening capacities would be more difficult to densify at intermediate pressure ranges. It is difficult to analysis that the effects of particle shape during the densification. According to the dodecahedron model, the regular particle shape allows deformation to proceed more homogeneously than for the irregular particle shape. Particularly, in the initial stage of compaction, the surfaces of irregular particle are subjected to more local pressure intensification against neighboring particles. Therefore, pressure transmission would be expected to be more irregular and particle work-hardening would vary 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. considerably within the compact during deformation. At high compacting pressure, the microhardness of hard powder, such as nickel and steel powder, has the slight upward trend. As a consequence the higher pressures are still effective in allowing some work- hardening to proceed with particle flattening, which in turn would be governed by the respective work-hardening capacity of powders. Generally, irregular powders are to be compacted better than more regular powders because of mechanical interlocking effects and the involvement of higher specific surface area. Finally, under isostatic compaction, plastic deformation happens more homogeneously in the spherical powders. The transmission of forces over the particle surface area created uniformity in particle flattening. In the early stages of compaction, particle flattening is less homogeneous for the irregular powders. At particle surface inregularities, the irregular powders are subjected to local intense particle deformation. 23.22 Foaming of Slurries Preparing slurry of metal powder mixed with a foaming agent can produce metallic foams. A slurry is consisted of a fine metal powder and a foaming agent is dispersed in an organic vehicle [64]. After mixing, the slurry is poured into mould and fired the mould at elevated temperatures. The slurry becomes more viscous and starts to foam as gas begins to evolve. If the expanded slurry is dried completely then a porous metals are produced. This process has been used for producing aluminum foam because aluminum is an inexpensive metal with many attractive properties. The aluminum foam is produced from slurry consisting o f fine aluminum powder using orthophosphoric acid 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with aluminum hydroxide or hydrochloric acid as a foaming agent. The mixed slurry is poured into mould for making the required shapes. The aluminum foam produced by the slurry technique has a relatively low strength because the aluminum oxide exists at the temperature of sintering. The other problem is cracks in the foamed materials [65]. Also this technique can use powders of more common metals such as nickel, copper, bronze, iron, and stainless steel powders. Loose Powder Sintering The loose powder sintering technique can be explained that mixtures of metal powders and spacing agents can be extruded then heat treated to produce the porous metals. According to mechanisms of sintering, contacts between powder particles are established and grow by the action of capillary or surface tension forces during the time that the powder particles are being heated in contact with each other. Application of pressure is not necessary for sintering. Therefore, the metal powder can be used to fill a mould and then sintered [66, 67]. The loose powder sintering can produce the porous metallic materials, such as bronze filters, and porous nickel membranes used as electrodes for alkaline storage batteries and fuel cells. The addition to the charge of a spacing agent can achieve the high degrees of porosity because a spacing agent decomposes or evaporates during sintering. Also a spacing agent can be removed by sublimation or dissolution [67]. The ammonium tetrachloride is the spacing agent for the manufacturing of filters from iron, copper or nickel and their alloys. 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The other method is the sintering slurry saturated sponge. A sponge-like organic material, such as a natural or synthetic plastic sponge, is cut to the desired shape and then saturated or soaked with slurry containing the desired metal powder. This sponge-like materials are used as a temporary support structure for producing uniform high porosity metallic foams [68,69]. Then the saturated sponge is dried to remove an organic liquid or water which is the slurry vehicle and the resulting dried saturated sponge is heated to a temperature sufficiently high to decompose or to pyrolyse the organic sponge-like material. After cooling a highly porous structure with interconnected pores is obtained. In an alternative process a metal compound is used instead of metal powder [70]. The metal compound, for example metal lactic acid salt or two-hydroxycarboxylic acid salt, can be converted to the corresponding metal by heating to its decomposition temperature when simultaneously the support structure is destroyed by combustion. 23.2.4 Metallic Deposition Techniques This technique use of a metallization process to apply a metallic cover to polyurathane strands and the process consists of three steps, rigidization, electroless preplating and electroplating [71]. The first step is the rigidization which can provide the necessary rigidity of polymeric foam with a thin epoxy layer coating. The polymeric foam is flexible foam so it must be made more rigid prior to metallic deposition in order to avoid distortion of the metal shape produced. The second step is electroless deposition. The polymer foam surface is made conductive by electroless deposition of a thin metal film because the deposition on polymer foam requires some electrical conductivity of the 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. initial polymer foam. This can be achieved by dipping the polymer foam into graphite solutions or by coating it with a thin conductive layer by metal vaporization. In order to improve the adhesion of the subsequently-deposited metal layers, the surface must be treated with a strongly oxidizing acidic solution which converts the surface to the water- receptive condition and selectively etches it to produce micro-roughening [72,73]. In the final operation, the preplated polymer foam is electroplated to the desired thickness. The preferred metal is nickel and nickel-chrome alloy, but copper foams can also be fabricated. After the final operation, the polymer can be removed from the metal/polymer composite by thermal decomposition. Metal foams produced be metallic deposition are characterized by their exceptional uniformity and high degree of porosity. The problem is the high production cost so their applications are restricted. 23.2.5 Powder Metallurgical (PM) Process Powder metallurgical (PM) process is used for production of foamed metals. In 1959, Benjamin used PM method to make porous aluminum [15]. According to his invention, a powdered structural metals, such as elementary metals, alloys or powder blends, are mixed with small quantities of a powdered foaming agents. The mixed powder is compacted to make a dense, semi-finished product. During compaction process, it ensures that the foaming agent is embedded into the metal matrix without any residual open porosity. The compaction process forms a foamable semi-finished product that can be worked into sheets, profiles, etc. by applying conventional deformation techniques. Examples for such deformation techniques are extrusion, swaging or rolling 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. in order to improve the flow conditions during foaming inside mould and it is chosen depends on the required shape of the precursor material. The extrusion is the preferred method because it seems to be the most economical method at the moment The rolling can produce thin sheets. Next step is the heat treatment When the semi-finished material, which has homogeneously distributed foaming agent within the dense metallic matrix, is heated in a controlled manner. The temperature should be near the melting point of the structure metal material then the foaming agent is released a substantial amount of gas. The released gas forces the compacted PM material to expand then highly porous structure is produced. Processing parameters such as temperature, amount of foaming agent, melting time, or mixing method can control the density of foamed metals. This processing method is schematically showed in figure 2.3. In 1991, the Fraunhofer-Institute for Applied Materials Research (IFAM) introduced a new powder metallurgical process for making foamed metals [16]. This method is similar to Benjamins’s except for the forming of the semi-finished product. When making semi-finished product, new PM method uses hot pressing in order to perfect embed the foaming agent in the metal matrix. Also a dense metal skin used at the top and bottom of the foamable material prevents the gas from escaping. The dense skin is layer metal powder alone and the foamable material is mixed metal powder with foaming agent. This method is very effective on aluminum foams but it is not restricted to this metal such as tin, zinc, brass, lead, and some other metals. PM method can also be applied on alloys by choosing appropriate foaming agents and process parameters. The 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Metal powder Foaming agent Mixing process i!!|!!i....... iiiji — H ii! i l l M l l l l i l [till: !::•= t ; | : i |r|r|s Axial compaction I Extrusion l a Foamable semi-finished product I Foamed material Figure 2 3 The processing steps for PM method Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. most common alloys for foaming are pure aluminum and alloys because of their low melting point and good foaming properties, while in principle virtually any aluminum alloy can be foamed by properly adjusting the process parameters. The figure 2.4 shows a typical cross section of a PM foam. The typical PM foam materials show the random distribution of cell size and shape. Foaming a piece of precursor material in a furnace results in a lump of metal foam with an undefined shape unless the expansion is limited in certain directions. Inserting the precursor material into a hollow mould and expanding it by heating does this. In this way near-net shaped parts can be prepared. Quite complicated parts can be manufactured by injecting the expanding foam into suitable moulds and allowing for final expansion there [74]. This PM technology will introduce a wider scope of applications which make use of the high temperature resistance, extreme strength and other properties of these materials. Due to their excellent biocompatibility, titanium foams could be used in prosthetical applications. Also it is now being extended to metals with higher melting points such as iron and steel [17]. 23.2.6 Sputter Deposition This is a new method for preparing foamed metals which have the closed cellular structures. Metals can be foamed without using a propelling agent by compressing powders to a precursor material and allowing gas to be entrapped in the metal structure during compaction [75-77]. A metal body containing atoms of entrapped inert gas evenly distributed throughout is prepared by sputtering the metal under a partial pressure of inert 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.4 Aluminum foam made from metal powder. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. gas, onto a substrate. Heating the precursor material then permits the entrapped gas to expand and form individual closed cell structures. It should be heated to a temperature above the melting point o f the metal for a period of time. The most common sputtering device is a triode sputtering apparatus in which the plasma is formed independently as the positive column of a discharge maintained between a thermionic cathode and an anode and which has a cooled substrate with a controllable negative bias. The pressure of the inert gas in the deposition chamber, the temperature of the substrate and the amount of negative bias voltage placed on the substrate can control the amount of entrapped gas in the sputtered body. The sputter deposition can produce foams from any material that contains uniformly distributed inert gas. This method is mainly used for making porous titanium structures. The titanium powder is filled into a can then this can is evacuated and refilled with argon gas. Hot isostatic pressing densities the filled can and finally appropriate heat treatment produces foamed structure. 2.4. Mechanical Properties of foams. The compressive stress-strain responses are shown in figure 2.5. There are basically three different foams that are elastomeric, elastic-plastic and brittle foam. From the compressive stress-strain responses, they show linear elastic deformation at low stresses (region I) flow by a long deformation plateau of almost constant stress. During a long collapse plateau (region II), the cell walls buckle and collapse. Finally, the plateau end and the stress begin to rise sharply (region III), as the flattened cell walls are 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Densification Plateau (Plastic Yielding) C O III Linear Elasticity Ed Strain (s) Figure 2.5 Schematic compressive stress-strain curves for foams, showing the three regimes of linear elasticity, collapse and densification [14,21] 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. completely collapse and impinge. The foamed metals are an example of elastic-plastic foam. For the closed cell foamed metals cell bending and cell face stretching control the linear elastic deformation at low stresses. The initial slope of the stress-strain curve is Young’s modulus, £*. The plateau is associated with collapse of the cells by the formation of plastic hinges in foam. When the cells have almost completely collapsed, the stress is rapidly increase at the densification stage. Increasing the relative density of the foam increases Young’s modulus (£*), raises the yield strength (cr) and reduces the densification strain (£p) [14,19,21,78,79]. 2.4.1 Linear Elasticity The stiffness of closed cell materials comes mainly from the cell edges bending and its moduli are identical with those of open cell materials [78-81]. A closed cell material is loaded with compression force then the bending of cell edge cause the cell faces to stretch as shown in figure 2.6. The deflection of cell edge, 5, is caused by the compression force, F. From elastic beam theory, Jean be calculated as [2] where Deflection of ceil edge F: Compression Force /: Cell edge length 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1 I i Tension t t I Figure 2.6 Schematic of closed-cell foams and stretching of the faces of a closed-cell foam in compression [2]. 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. £,: Young’s modulus of cell wall material /: Second moment of area of cell edge C\\ Constant The closed cell is linearly elastic, so work F5/2, is done against the restoring force caused by cell edge bending and force stretching as shown in figure 2.7. The cell edge bending is proportional to Stf/2 where S is the stiffness of the cell edges. Also S is proportional to EjI/13. The cell face stretching is proportional to Es^ V /2 where e is the strain caused by stretching of a cell face, and Vf is the volume of solid in a cell face. And e and F/can be expressed as 5 ( 10) e cc — I ( 11) Therefore, (12) (13) Also using equation (6) and (7), gives 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Plastic toendin Plastic stretching F Figure 2.7 Plastic stretching of the cell faces of a closed-cell foam. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (14) where A, B, A ' B', Cu and C? are simply constants of proportionality. The equation (14) describes the combined effect of cell edge bending and cell face stretching [2,21,79, 81]. 2.4.2 Plastic Collapse If the cell wall material is metals or many polymers that yields plastically then the porous material shows a plateau caused by plastic collapse. It occurs when the load is beyond the linear elastic regime and the moment on the inclined cell walls exceeds the fully plastic moment. It is creating plastic hinges as shown in figure 2.8 [26, 82, 83, 84]. For closed cell materials, plastic collapse causes the membranes to crumble in the compression direction but at right angel to this direction they are stretched. So the work done in an increment of deformation is the same as the plastic dissipation in bending and stretching the cell walls. A compressive plastic displacement 5 o f one cell allows the applied force / to do work F5. The plastic work done at hinges is proportional to MP &1 and the cell face is stretched by a distance that is proportional to S, doing work that scales as Oysdtjl. The fully plastic moment (Mp) is (15) And the moment is proportional to FI and the force (F) is proportional to < r ysl2. From these results 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F Plastic hinges i i i i F Figure 2.8 The yielding of a plastic foam [26,82-84]. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FS = AM m— + Bo„5t ,1 p I y j ( 16) where A and B are constants. Using equation (IS) a A (17) Finally, combining these results with equation (6) and (7), the plastic collapse, or plateau, stress < r (yield strength of foamed material) can be calculated where Cj and C< are constants. 2.43 Densification When the cell walls begin to touch, the plateau ended and the stress begin to rise sharply, as the flattened cell walls are completely collapsed and impinged. During elastic buckling or plastic collapse, there is almost no lateral spreading with axially compression load. Then simple geometry gives the relative density, p /p s, after compressive strain, £, where p /p , is the initial relative density. Densification starts at the strain at which the field of elastic buckling ends. The stress is rapidly increased with displacement. This starts when the folding of the cells is (18) as [2,26,78] (19) 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. so great that the walls begin to touch. When the foam has been compressed to a new relative density of about 0.5, the densification starts. The new relative density is the void space occupies half the volume. And the densification is completed when the new relative density is 1 (no porous space left). Then combining with equation (19), the strain at which densification starts [26,78] 2.4.4 Deformation Mechanisms in Foams The observation of the cell crushing of the foamed material reveals that crushing occurs in a layer of cells perpendicular to the compression load. The cell crushing can be deformation band. These results in stress concentration on the cells located round the crushed cell in the layer that contains the broken one and is perpendicular to the compression direction, and the cells in the layer break successively. As a result o f the crush, the stress in the crushed cells becomes free and the strain in the cells that is above and below the crushed cells is released. After a substantial crushing of the layer, the strain increases again, because the unbroken layers just above and below the crushed layer come into contact with each other due to the compression load. Therefore, crushing (20) And the strain at which densification is complete (21) explained by the following way. An individual weak cell is the initiation point for a 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of cell will propagate to the entire sample, by the cycle of strain storage and release. This deformation propagates through the foam by the transverse direction of a deformation band [3, 85, 86]. The maximum stress, that is the yield strength, during the cycle of crushing may be almost the same as the initiation stress of breaking, because the porous dimensions are nearly the same throughout the sample. Therefore, the compressive response of the foamed materials is expected to be nearly constant after a linear increase in the stress-strain curve. This mechanism is a good explanation of the observed the compression response of the foamed materials. The final sharply increasing stress is the result of a complete breaking of cells [86, 87, 88]. For samples with large distribution in porous size, the fluctuation of load is large but uniform porous has small fluctuation of load. 2.5 Energy Absorption Foams and honeycombs are most commonly used in packaging. The main idea of packaging is the ability to absorb energy for keeping the peak force on the packaged object below the limit that will cause damage or injury. These protective packaging materials convert kinetic energy into energy of some other sort like heat. Foamed materials (Cellular Materials) are especially good at this kind of applications. Figure 2.9 shows that their energy absorption capacity is compared to that o f the equivalent solid material. The foamed material usually shows a lower peak force than the solid material for the same energy absorption [21,89,90]. 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fully dense elastic solid Foam b Energy absorbed in dense solid Energy absorbed in foam Strain (e) Figure 2.9 Stress-strain responses for an elastic solid and a foam made form the same solid, showing the energy absorbed at stress op. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The absorbing energy of the foamed materials can be explained by consideration of the following steps, based on the deformation mechanism. First, energy is absorbed by elastic deformation before occurrence of crushing. Second, the stored energy is released partially by crushing of a layer, and energy is absorbed by deformation of uncrushed layers to the ultimate strain. On the assumption that one cell breaks at a time, the strain released in each layer that survives in one layer-crushing period is given by averaging the effective height of the porous space of one cell through which the top wall of the cell can traverse in one layer period. This partial strain-release occurs as long as the height of monolayer of cells is less than the ultimate strain of all survived layers. In the third stage, the strain of the specimen is released completely when the sum of the strain is less than the cell size [21,89,90]. The energy absorbed by the foam per unit volume at the strain e is simply the area under the stress-strain curve up to e. As figure 2.9 shows that the foamed materials have the long plateau in the stress-strain curve which allows large energy absorption at a near constant load. It is very important to understand that the cell wall material and relative density of foam. It is relatively simple to select the cell wall material. Selecting cell wall material depends on the application that the packaging material carries a static or repeated loading or whether it is subjected to serve environmental conditions such as high temperatures. If the load is applied repeatedly then an elastomeric cell wall material is suitable for packaging. However if the protection is needed only once, a plastic or brittle material is better because such cellular materials are more efficient. It is more difficult to choose the correct density for a given package. If the density is too low, the foamed 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. material will be crushed before enough energy has been absorbed. If the density is too high, the force exceeds the critical value before sufficient energy can be dissipated. The performance depends on the density of the foamed material. A number of methods have been suggested for characterizing energy absorption by foams. There are four main ways of characterizing absorption of foamed materials: the Janssen Factor, J, the Cushion Factor, C, the Rusch Curve, and the Energy Absorption Diagram [21,26,91-104]. 2.5.1 The JaDssen Factor, J The deceleration of an object packed in foam can be calculated by Newton’s Law a ,-- (22) m where F: Force ai : Deceleration m: Mass The force, F, is the area times the compressive stress. The area is the constant area that is between the packaged object and the foamed material. The efficiency of the absorbing impact energy can be estimated as the ratio of the maximum deceleration produced by the foamed material, ap, to the deceleration that is produced by an ideal absorber, a,. The value of a, is calculated by equating the kinetic energy to the work done by the constant force in the foam, acting through the height of the cushioning material. — mv1 - m ah (23) 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The Janssen Factor, J, that is the efficiency of a cushioning material at absorbing impact energy, can be defined by the ratio J = ^ (25) Therefore, the efficiency of different foams in energy absorption can be compared by using the J factor [105-107]. Usually J factor is plotted with the impact energy per unit volume, W, of the cushioning material and the typical curve is shown in figure 2.10. However, the energy absorption capacity does not relate the J factor and a large amount of data collection is the main requirement for the J factor because it is an empirical measure. 2.5.2 The Cushion Factor There exists a large amount of uniaxial stress-strain data for foamed materials. Using these stress-strain behavior, it can be calculated that the efficiency of a foamed materials in absorbing energy. According to Gordon, the cushion factor, C, is defined by using the above relationship such as the ratio of the energy stored, W, per unit volume of the cushion to the peak stress, < r p, developed in the cushion [106]. The figure 2.11 shows that the cushion factor is plotted against the peak stress of the foamed materials. In dynamic testing, the cushion factor is the same as the Janssen factor, J. 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. * 0 1 c o 1 (J o < Impact energy per unit volume, W (J/m3 ) Figure 2.10 The Janssen factor, J, is used to characterize energy absorption in foams [14,21,101]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. £ > I I u I I e o • p « J= t o 3 u Peak stress, c t p Figure 2.12 The cushion factor, C, is used to characterize energy absorption in foams [21,89,102]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where A : Area of the cushion h: Height of the cushioning material 2.53 The Rush Curve This method has suggested by Rush [97, 98]. He first suggests that an empirical shape factor, *F(e), is defined from the shape of the stress-strain curve for a foamed material. An empirical shape factor, *F (e), is calculated from this equation. a = E 'V W e (29) where *F (e): Shape factor er Compressive stress £*: Young’s modulus of foamed material c. Strain ¥(*) = ms-" + re' (30) 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where m, n, r, and s are constants of the foamed material. The equation (29) and (30) define a shape for the stress-strain curve of the foamed material. Rush further defines K, which is the energy-absorbing efficiency, as the maximum deceleration produced by an ideal foamed material to that packaged by the foam under investigation, dm : v2 1 K = ~ — = - (31) 2 hdm J Another dimensionless quantity, /, is calculated as the impact energy per unit volume of foamed material divided by the Young’s modulus of the foamed material. w / = - F (32) E The ratio UK is calculated as the peak stress generated in the foamed material normalized by the Young’s modulus of the foamed material. mv2 = f r (33) V v / AE E K 2AhE* The uniaxial stress-strain response of the foamed material is related to / and K through the shape factor *¥(e). The optimum foam for energy absorption for a given peak stress is determined by plotting UK against /. Figure 2.12 shows the typical plot of the Rush curve. Rush curve has greater generality than J factor but Rush curve depends on empirical function to describe the shape of the stress-strain curve. 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C O co s C O ■s a > a ■a .s ■ « I o Z Normalized energy per unit volume Figure 2.12 The typical Rusch curve. The curves constructed from the stress-strain equations of Rusch [90,97,98]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5.4 Energy Absorption Diagrams The Rush method is further improved by Maiti et al [26, 107]. This improved method is the energy absorption diagrams that offer a way of optimizing the choice of foamed material. From experimental stress-strain curves, figure 2.13,2.14 and 2.1S show the procedure for constructing the energy absorption diagrams. From compression test, the stress-strain curves are obtained as shown in figure 2.13. Then the energy absorption per unit volume, W, is calculated by measuring the area under each curve up to the stress O p . The stress and W are normalized by the Young’s modulus of the solid, E„ and the value of W is plotted against c r p for each curve. For given package, the best foam is the one that absorbs the most energy up to the maximum allowable package stress op. Figure 2.14 shows that the optimum choice of foam is defined by the heavy line. This heavy line shows the envelope of the shoulder by a relationship between W and ap. The envelope is replotted on the same axes and marked with the optimum relative density, p /p s as shown in figure 2.13. The above procedures are repeated at a series of different strain rates and the optimum energy absorption curves are build up. Finally, lines to give a family of intersecting connect the corresponding density points. By using the same way, a change of temperature can be applied. For closed cell foam, the bending, buckling and stretching of the cell walls produce the energy absorption during compression. The stress is vertically raised at the densification strain, E d, such as *D= 1 -1 .4 ^ - (34) P, 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.3 0.1 0.01 Increasing relative density j 0.03 Strain Figure 2.13 Stress-strain responses are measured at a single strain rate [14]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Normalized energy per unit volume 0.3 Envelope 0.03 0.03 0.01 / 0.01 Individual curve Shoulder Normalized peak stress Figure 2.14 The energy is plotted against stress. The energy and stress are normalized by the solid modulus [26]. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Normalized energy per unit volume 0.1 0.3 Relative density (p*/ps) 0.03 .01 Normalized peak stress Figure 2.15 The envelope is replotted on the same axes, and marked with density points. The density points are connected to give a family of intersecting contours of constant density [21]. 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In the linear-elastic region, the energy absorption per unit volume up to a stress ap is expressed by From the above equations, W/E, is a function of oj/£a and the relative density, p /p s, only. The plateau regime is the important part of the stress-strain curve because the most energy absorption is occurred at constant stress. 2.5.5 Optical Selection of Foamed Materials The purpose of packaging is to absorb the energy as much as possible without the damaging the packaged object. The energy absorption can be expressed by [89] (35) Applying equation (35), E* is (36) Then, W 1 a p (37) / J (38) 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. W = jade = £ f { p ' = /0 > ' K (e) (39) < * = A p )k(‘ ) (40) where p : Density of the foamed material pi. Density of the solid material (cell wall material) k(e): Shape function of the stress-strain curve ki(e): Integral of k(e) over strain f(p )\ Initial collapse stress, a op: Maximum permitted stress by a given application A Lagrange function shows as follows: L (p ',e ,i)= ir + A(<T-<T,)=/(p')k,(e)+Xl/(p-'lk(e)-<r,] (41) When the strain reaches the densification strain, E d, the partial derivatives of the Lamda function must all be zero. Then it gives (ff)=*2(f) (42) The maximum energy absorption is reached at the densification strain, ep. Then, by substituting the densification strain, the optimal density and the energy absorption can be calculated. Also the energy absorbed per unit volume is calculated as W = C ,op (43) where C/ is the energy absorption efficiency [89,107]. The initial part of the stress-strain curve has little contribution to the total energy absorbed so it is not considered here. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3. EXPERIMENTAL PROCEDURES 3.1 Outline for Experimental Procedures The brief summary of experimental procedures is schematically shown in figure 3.1. For this experiment the basic method for synthesizing steel foams is described in figure 3.2, while the effects of different process parameters is explored in this experiment As shown in figure 3.3, commercially available steel powder (an Fe-2.SC blend) was mixed with a small amount of a granular foaming agent for 75 minutes in a dry twin-shell blender. Addition to this mixing method, three different mixing methods, which will be described in chapter 4.3, was applied for finding out the best method. Mixing by this procedure achieved a homogeneous distribution of the granular foaming agent in the metal powder. The method of mixing was critical to achieving a homogeneous distribution within the blend because of the different densities of steel and the granular foaming agents. Blended powders were compacted by uniaxial cold-pressing. The resulting semi-finished samples were subsequently melted in a box furnace. Compression tests were conducted on both annealed and pre-annealed foams of different density at a crosshead speed of 2 mm/min. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 r TEM Mixing SEM Steel Powder Foaming Agents Optical Microscope Semifinished billet Compression Test Annealing Process Foaming Process Isostatic Cold Pressing Figure3.1 Flow chart of the experimental procedures Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Steel Powder (2.5 wt% carbon) + 8 ^ Foaming Agent (MgC03, SrC03) Mixing Machine (Dry twin shell blender) I Cold pressing -> semi-finished materials Melt @ ~ 1300C (Box furnace) Steel foam product with prc i of 0.38-0.64 Figure 3.2 PM Manufacturing Process Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Steel powder + Foaming agent Figure 3.3 Twin shell dry blender 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2 Steel Powder Carbon content had a marked effect on foaming behavior (and the resulting mechanical properties). Various amount of graphite powder was added into iron powder for controlling carbon content. Select amounts of carbon from 0.5-3% were added to steel compacts to determine the effects on foam expansion. Increasing the carbon content of the steel alloy to 2-3%C resulted in improved foamability and matrix strength, while reducing Tm (and foaming temperature) [108-110]. However, higher carbon contents compromised the compaction behavior, much like the effect of large amounts of foaming agent. In contrast, low carbon contents (0.77 wt%) produced no true foaming but resulted in a single large pore in the center of the sample. The carbon content for optimal foamability was found to be -2.5 wt%. Therefore, all samples were made with 2.5wt% carbon content steel powder. 3.3 Foaming Agents The first task of the effort to synthesize steel foam was to select a suitable foaming agent for the selected alloys, given the following constraints. The foaming agents must undergo thermal decomposition near Tm and generate gas pressure in the steel matrix sufficient to overcome atmospheric pressure and cause foaming. The gas foaming agents need a decomposition temperature near either the melting temperature of steel (around 1500°C) or inside the liquid and solid phase region (between 1250°C • 1450°C). The melting temperature of steel depends on the carbon contents. Seven 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. possible foaming agents for making foamed steel and stainless steel, their decomposition temperatures and processes are [111-115]: 1. MnS (Decomposition temperature: 1610°C) 2. Sn02 (Decomposition temperature: 1630°C) lsn02(s) - > ^Sn0{g) + ^02(g) 3. BaS04 (Decomposition temperature: 1500°C) Produces S0 2 gas at the decomposition temperature. 4. SrCC> 3 (Decomposition temperature: 1340°C) Produces CO2 gas at 1340°C 5. BaCCb: Barium Carbonate fuses with loss of carbon dioxide and dissociation is complete at 1600°C. The decomposition is much more easily effected in presence of carbon where it is completed at 1450°C. 6. WS2 (Decomposition temperature: 1250°C) 4WS2 (s)-> W (s) + W2S8 (g) 7. MgCC> 3 (Decomposition temperature: 1310°C) MgC(>3 (s) -> MgO (s) + CCh (g) The decomposition temperature (To) must lie between the solidus and liquidus temperatures for the steel alloys (generally between 1250°C and 1350°C). The two 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. foaming agents selected for the present work, strontium carbonate (SrCCh) and magnesium carbonate (MgCOa). Ideally, 7b for the foaming agent should be closely matched to the melting temperature of the steel alloy. If 7b is higher than the melting temperature, the foaming agent may dissolve in the melt or float to the liquid surface, while if 7b-is lower than the melting temperature of the steel, the sample may develop internal pressure and crack prematurely. If these general conditions are met, and the heating and cooling are carefully controlled, steel foam with acceptable porosity can be synthesized. The composition of the powder blend, including the amount of foaming agent and the carbon content, strongly affected the ultimate density and quality of the foam. To establish an understanding of the amount of foaming agent needed, foams were synthesized with selected amounts of S1 CO3 or MgCC> 3 foaming agent from 0.2 wt% up to 0.4 wt%. 3.4 Mixing Methods Commercially available steel powder was mixed with a small amount of a granular foaming agent in a dry twin-shell blender as shown in figure 3.3 [116, 117]. Addition to this mixing method, three different mixing methods was applied for finding out the best method. Mixing by this procedure achieved a homogeneous distribution of the granular foaming agent in the metal powder. (The method of mixing was critical to 6 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. achieving a homogeneous distribution within the blend because of the different densities of steel and the granular foaming agents.) Three methods of homogenizing the powder blend were employed. The first method was a simple and inexpensive technique known as drill mixing, illustrated in figure 3.4. Steel powder and foaming agent granules were placed into an empty can and agitated by the paddles on a rotating shaft. Ball-milling, shown in figure 3.5, was also employed. The milling machine consisted of a cylindrical vessel, impellers, and stainless steel balls about 5 mm in diameter. The shaft rotated at 200 rpm, and recirculating water flowing through the jacket cooled the vessel. Figure 3.6 shows the third method used, a high-energy ball-milling process known as cryo-milling [118,119]. In this method, a similar ball-milling machine was used, and liquid nitrogen was circulated to cool the vessel (rather than water). The shaft speed was maintained at 200 rpm, and typical blending times were 30 minutes. 3.5 Isostatic Cold Pressing Blended powders were compacted by uniaxial cold-pressing with one of four different pressures 276, 414, 552, and 827 MPa, yielding virtually non-porous, semi finished steel samples. The sizes of semi-finished steel samples were depended on the press die. There were two sizes of sample: one was 32 mm in diameter and 32 mm in height and the other was 25 mm in diameter and 30 mm in height. A slight variation of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. .• • • • • • • ' .•••••• ••*••••••••%••••••••»•%»% • • • • • • • • • • . * • • •• » “ • I * •*: • * . * » V • ‘ y ; <• ■ ’ • * W w w W w /-* • V 'V « V • .* • • • » V « v • /• < • • S • \ • S » V ■ % • % • S • • • ^ yy.'^ yyyyy . '1 v». • • • v* • • • *.* *. • T O > V w A n V » V * * ,A ,A . . . . . . ■ • * • •• • • • • • • ■ • % • • • • % • • » • • • • * . % ■ s • VI Vi Vi ',« », i . », • • . .. .. .. .. .ii(W .*i/iVi.mv«Viv* - *s “V • s ••• •% ^ is ■ % ••• i 'iT V '. •». •*. ••• •• V » V *V'.* *v « V «v •JiW /iV * /* v T » * ,v « V .V • V -V • • « v •• • • • • • • • ^ • .*• • • • .*• •• • •••••' • * s ' S *%v h 5i ■ % •% • •• •*. • * . » • % • • •. • « v ^ » .* » . * »y/^¥# i* r?; ■ * */».*» . » ♦ V»S*s »i\*V**»*%iS i %•%•%*%■*••%• V «% iV i*a*****B «* • » % • s ■ S •% •% » S » % • % • % ■ % •*. ■ % • % •% •*. •*. ■ • • * v c .* •!' ^yyy.* * V ^ • .* * V ^ •: • : ••%iSC#ftSWfiiMbkyklCi*S* i '^ ( i cS * S 'S * % * Figure 3.4 Drill mixing method 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Cold Water Figure 3.5 Ball-milling method Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.6 Cryomilling method 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the method described above was employed in an effort to limit pore coalescence in the melt during foaming. Before uniaxial cold-pressing process, thin sheets of low-C steel were inserted into the powder blend to create alternating layers of blended powder and steel sheet The steel sheets, which had a higher Tm than the powder, were intended to function as a non melting interlayer membrane, thereby limiting the pore size in the foam and improving uniformity. The thickness of the steel sheet was 3-5 pm, and the number of interlayer membranes was typically 15-20 in a compact that was 32mm in height. Foam expansion was accomplished as described below. 3.6 Foaming Process The Lindberg 1700°C Box Furnace (Model 51314) was used for foaming process. The picture of furnace is shown in figure 3.7. Generally, this furnace is designed for heating laboratory process applications and small production work loads to a maximum temperature of 1700°C. Also it can be reach a temperature of 1700°C in slightly more than 15 minutes. The complete furnace consists of the box furnace itself and a separate control console that is a digital display electronic controller. And other components are heating elements and insulator. The heating elements are the molybdenum disilicide and resistant to thermal shock. They can be subjected to extremely rapid heat-cool cycling for prolonged periods of time with no adverse effects. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.7 The Lindberg 1700°C Box Furnace (Model 51314) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The insulator is designed utilizes double shell construction and forced air-cooling. The graphite rod (EC12) was used as crucibles. The graphite rod was machined into special size and shape as shown in figure 3.8. For foaming process the resulting semi finished samples were subsequently melted in a box furnace at 1300°C to effect foam expansion. The heating rate was 30°C per min and the total heating time was about S min. The time at temperature was a critical factor affecting the foam density, as pore coalescence generally ensued rapidly after foam expansion. 3.7 Mechanical Testing After foam expansion, compression test samples were cut to approximately 20x18x17 mm. Cut samples were annealed for 1 hour at 950°C in air prior to compression testing. Compression tests were conducted on both annealed and pre annealed foams of different density at a crosshead speed of 2 mm/min. For characterizing anisotropy of mechanical properties, the loading direction was chosen in two directions: one is the longitudinal direction that is parallel to the direction of foaming. The other direction is the transverse direction that is perpendicular to the direction of foaming. These results were discussed in chapter S.3. For finding the effect of different stain rates the various strain rate experiments were performed on specimens in uniaxial compression. The experimental strain rates, which are calculated on the basis o f the initial specimen height and the crosshead displacement, were varied from 4.5x1 O '5 to 1.6x10' sec*1 . These results were discussed in chapter 5.4. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. / / 38 mm 32 mm, u> 00 3 3 0.7 mm 00 Figure 3.8 (a) The picture of graphite crucibles (b) schematic illustration of the crucible. 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The machine used for compression tests was Instron 1331 as shown in figure 3.9. The Instron 1331 is an advanced multiprocessor-based control console that provides full digital control of a testing system. It is closed-loop testing systems which supply static of dynamically changing forces to materials and test them by hydraulics, and can create forces up to 2.5 MN (560,000 lbs) or more at frequencies from 0 to 500 Hz or higher, depending on the force level. This machine consists of a closed load frame with a movable crosshead, a hydraulic actuator to apply a force and a load cell to measure the force. A displacement transducer measures the position of actuator piston. Load, position and strain are the basic parameters needed by a user of the system. The actuator piston is under closed loop control by controlling the hydraulic fluid flowing through a servovalve supplying the actuator. The load cell is a load measurement and control device that uses resistance strain gauging to convert a mechanical force into a proportional electrical signal which can be measured and processed by the control electronics. Load cells are available in a wide range of force capacities and sizes, and are selected on that basis as required by the test application. The Instron 1331 used the lOOKN-load cell for testing. The load frame provides a high stiffness support structure against which the test forces can react. It consists of a support base, a fixed, and a crosshead that moves on bylinderical vertical columns. The crosshead does not move during testing, but can be moved to increase or decrease the space between the load cell and the end of the actuator piston rod to accommodate 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.9 The compression tests were performed by Instron 1331. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. different lengths of test specimens. The load cell is mounted on the crosshead, with the actuator mounted under the frame table, with the end of the piston rod projecting through the table. Specimen plates are attached to the load cell and actuator piston rod. 3.8 Structural Observation 3.8.1 Optical microscopy The main purpose of the sample preparation is to prepare the sample surface for photographic examination at the microscopic level. An Olympus AH-3 research photomicrographic microscope was used to observe the microstructure of foamed materials. They were polished using SiC abrasive papers through 120,240,400,600,800 and 1200 grit and the next polishing step was conducted by using 4S, 30, IS, 6 and 1 pm polycrystalline diamond suspension on polishing cloth in order to get a mirror-like surface. The lowest number grit paper used to remove all scratches on the sample. The term "grit" refers to the number of tiny naps in the paper per inch. Lubricant was sprayed on the paper, the sample was placed face down on the paper and moved in a top to bottom, bottom to top fashion, for about five minutes. Then the surface was cleaned with ultrasonic cleaning machine, then examined under a microscope. Looking under the microscope, the quality of the surface is observed. Removing cutting marks was the problem encountered in the polishing procedure. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The unique properties of porous material make the sample preparation a procedure different from the preparation of conventional materials. For foamed materials the polishing debris filling up the pores was one of the biggest problem. It leads to ambiguity in defining the edges of the pore, which in turn leads to inaccurate data. Therefore, after each polishing step, samples were cleaned by ultrasonic cleaning machine. While the ultrasonic cleaning machine was on, hands had to be washed so that any particles form the previous polishing step would not carry over to the finer paper. A number of etchants for microexamination were tried and Nital was used for steel foam. Nital having the composition o f 5ml HN03 and 95 ml methanol was applied on the surface of sample for 20 to 40 sec at room temperature and then removed in stream of aceton [120]. For metallographic study of GASAR porous magnesium magnesium is a reactive element and the sample is easily corroded by water. Therefore, throughout the polishing, glycol was used as a lubricant. The ethanol bath was used for ultrasonic cleaning. Also a number of etchants for magnesium were tried and the best etchants having the composition of 15 ml Nitric Acid, 12g CrOj and 85ml water was applied on the surface for 10 to 20 sec at room temperature and then removed in streamed of methanol [120]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.8.2 Transmission electron microscopy Samples for transmission electron microscopy (TEM) were prepared by the following procedures. 1. Using a micro-cutting machine cut the slices of the porous sample with a thickness of 2mm. 2. The both sides of thin slices were polished using SiC abrasive paper from 600, 800, 1200 and 2400 grit and final thickness should be in the range of 100 pm. 3. Several disks with a diameter of 3mm were cutted. 4. Dimpling process: Dimpling produces an ultra thin region necessary for thinning while maintaining a robust peripheral thickness to prevent breakage when handling the specimen. Prethinning with the dimpling procedure also reduces specimen preparation time in an ion milling. Surface variations, including thermal effects, that are produced by long milling time are virtually eliminated. Typically, a specimen that has been cored to three millimeters in diameter is flatted from its bulk thickness. It is then waxed to a specimen platen surface which rotates. Four dimpling tools were used in succession on an ultra-precise rotating tool drive shaft Before finishing the dimpling process, the dimpling tool is wrapped with metallographic, napped pads that remove work hardening and scratches, creating specular surfaces on the specimen. The Dimpler Model D500I machine was used for dimpling process. By dimpling process the thickness of dimpling area was reduced from 100pm to 20pm. 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5. Ion polishing process: Ion polishing process can produce high quality TEM specimens that are exceptionally large, clean, electron transparent areas. Two ion guns were used for ion polishing process. The operating angle of each gun is independent of one another and both have the ability to accurately center the beam onto the specimen at any angle within ± 10° range. The operating angle is ±4° and this makes it possible to thin specimens. An optical microscope is used to inspect the specimen in its working position at anytime during the thinning process, and also to achieve very precise control over the final stage o f specimen thinning. The Model 691 PIPS is used for ion polishing process. 6. Finally, the TEM samples were washed using pure methanol and stored safely. Using a Philips EM 420 performed the TEM observations. The TEM was operated at accelerating voltage of 120 KV. The structural parameters, such as grain size and subgrain size, were estimated using the linear intercept technique. And also selected area electron diffraction (SAED) patterns were used in order to get information of specimens. The X-ray spectral analysis and EDS spectral analysis were used for analyzing chemical components of specimens. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. PM SYNTHESIS OF STEEL FOAM 4.1 Introduction Porous or cellular materials, commonly known as foams, exhibit novel properties and afford great potential for weight savings [14]. Polymer foams have long been used to absorb vibration, noise, and impact energy (e.g., packing materials). However, structural applications of polymer foams generally have been limited to low-stress components because of the relatively low strength compared with other engineering materials. This also limits the amount of energy that can be absorbed by polymer foams during deformation. For these reasons, considerable attention has been devoted recently to the synthesis and properties of metallic foams, which offer the prospect of much higher strength, stiffness, and energy absorption during deformation, and substantial weight savings relative to conventional metallic components [15-19]. However, the process technology for making such materials is not yet mature, and a full understanding of structure-property relations is only beginning to emerge [20]. Substantial effort was devoted to exploring the effects of process parameters, including powder blend composition, compaction method, blending routine, heating rate, and time at temperature. After numerous iterations, two standard powder formulations were selected consisting of 0.2 wt% foaming agent (either SrC03 or MgC03), and a carbon content of 2.5 wt%, as these appeared to give superior results. The results of this 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. effort are described in this chapter. Experiments were then performed to determine mechanical response and energy absorption behavior, as described in chapter S. 4.2 Foam synthesis 4.2.1 Foaming agents The first task of the effort to synthesize steel foam was to select a suitable foaming agent for the selected alloys, given the following constraints. The foaming agents must undergo thermal decomposition near Tm and generate gas pressure in the steel matrix sufficient to overcome atmospheric pressure and cause foaming. The decomposition temperature (To) must lie between the solidus and liquidus temperatures for the steel alloys (generally between 1250°C and 1350°C). The two foaming agents selected for the present work, strontium carbonate (SrCCh) and magnesium carbonate (MgCOj), undergo decomposition via [111-115]: 1. SrCO3(TD=1290°C) Produces CO2 gas at 1290C 2. MgCOj (Td = 1310°C) MgCOj (s) -> MgO (s) + CO2 (g) Ideally, To for the foaming agent should be closely matched to the melting temperature of the steel alloy. If To is higher than the melting temperature, the foaming agent may dissolve in the melt or float to the liquid surface, while if T d is lower than the melting temperature of the steel, the sample may develop internal pressure and crack prematurely. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The composition of the powder blend, including the amount of foaming agent and the carbon content, strongly affected the ultimate density and quality of the foam. To establish an understanding of the amount of foaming agent needed, foams were synthesized with selected amounts of S1 CO3 or MgC03 foaming agent (henceforth, S and M) from 0.2 wt% up to 0.4 wt%. With either foaming agent, the "best" results were obtained with 0.25 wt%, although foams synthesized with 0.2-0.3 wt% showed similar structures. Increasing the amount o f foaming agent beyond 0.3 wt% led to poor compaction behavior in the semi-finished material, and much of the gas that was evolved by decomposition escaped prior to expansion. Similar results were reported by Yu et al [17]. 4.2.2 Carbon content Carbon content also had a marked effect on foaming behavior (and the resulting mechanical properties). Select amounts of carbon from 0.5-3% were added to steel compacts to determine the effects on foam expansion. Increasing the carbon content of the steel alloy to 2-3%C resulted in improved foamability and matrix strength, while reducing Tm (and foaming temperature) [108-110]. However, higher carbon contents compromised the compaction behavior, much like the effect of large amounts of foaming agent. In contrast, low carbon contents (0.77 wt%) produced no true foaming but resulted in a single large pore in the center of the sample. The carbon content for optimal foamability was found to be -2.5 wt% [17]. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.23 Microstructure analysis Steel foams synthesized using magnesium carbonate and strontium carbonate foaming agents (designated foam M and foam S, respectively) are shown in figure 4.1. The pore structures are similar. Foam M has a relative density of 0.41 and an average pore size of 1.3mm, while foam S has a relative density of 0.45 and an average pore size of 1mm. The nominal carbon content of both foams is 2.5%. Foam M exhibits a slightly more uniform pore structure in which the pores are generally more spherical with more regular cell walls. The modest volume increase during foaming is attributed to the limited foamability of the steel alloys compared with, e.g., aluminum, in which foams with relative density of 0.2 are possible [16]. Examination of polished sections revealed a foam microstructure characterized by peariitic spheroids separated by semi-continuous films of ferrite with cementite (figure 4.2). The spheroids were similar in size to the starting powder, indicating that the spheroids were in fact prior powder particles. The heating schedule involved only a few minutes at the peak temperature, allowing only partial melting of the compact and resulting in capillary flow of the melt between the solid particles. This phenomenon is reflected in the microstructures shown in figure 4.2. Gas was evolved by decomposition of the foaming agent and was retained in the compact, forming pores. Annealing substantially altered the structure, as shown in figure 4.2(b) and (c). In these figures, the light “matrix” structure consists of a mixture of continuous ferrite and angular cementite inclusions [121,122]. The primary microstructural changes caused by 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (b) Figure 4.1 Pore structures of steel foams: (a) MgCOa forming agent (b) SrCOj foaming agents. 8 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.2 Metallography of foam microstructure: (a) Pre-annealed sample (75X) (b) Annealed sample (75X) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.2 Metallography of foam microstructure: (c) High magnification of (b) (500X) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. annealing were an increase in the amount of ferrite in the structure and a reduction of the average carbon content from 2.55% to 1.22% (determined by combustion analysis). In most regions of the foam, the ferrite films between spheroids were substantially thickened. In some other regions, pearlitic spheroids were replaced by ferrite containing cementite and other fine carbides. The decarburization that occurred during annealing undoubtedly facilitated the transformation to ferrite and reduced the proportion of carbide phases. 4.3 Effects of process parameters on steel foam synthesis 43.1 Introduction Metallic foams exhibit unusual mechanical properties and have potential for a wide variety of applications, such as ultra-lightweight structural components, core materials for sandwich structures, heat insulation, radiation shielding, and sound and energy absorption appliances [27, 50, 71, 83, 123-126]. However, few of these applications have been realized, primarily because the process technologies for manufacturing metallic foams are not fully mature and/or prohibitively expensive. Nevertheless, if affordable process technology can be sufficiently developed, the inherent advantages of metallic foams undoubtedly will find new and innovative applications in several industrial sectors. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Several methods for making metal foams have been reported in the literature [123, 128], including molten metal processes such as investment casting and direct foaming [129], as well as powder metallurgical (P/M) processes [130-132]. Most o f these processes have been devoted to the synthesis of aluminum foam, partly because of the low melting point of aluminum (Tm ~660°C) relative to most other structural metals, and the other properties that make aluminum a useful structural material. One of the more promising P/M methods for making metallic foam is the so-called Fraunhofer process, which has been successfully used to make closed-cell aluminum foams [16]. In this process, metal powder is blended with a granular foaming agent and compacted by conventional means, yielding a fully dense semi-finished product. The compact is expanded to foam by heating to the melting point, whereupon gas is evolved from the decomposition of the foaming agent. Foam expansion results in closed-cell foam with a relative density of 0.2-0.8, depending on the particular process parameters employed [133]. Process control is critical for achieving uniform pore structures and consistent properties, and this is currently a formidable challenge for producing metallic foam. While the Fraunhofer process has been successfully employed to synthesize aluminum foam [16], only recently has there been an attempt to produce steel foam by the same route [134, 135]. Steel foam synthesis poses special difficulty stemming from the much higher melting point (Tm ~1350°C) and the low melt viscosity. However, in a recent study, steel foam was made by a P/M method, and the resulting foams exhibited encouraging properties [134]. Indeed, the inherent property advantages of steel 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. compared with aluminum provide considerable incentive to develop processes for steel foam synthesis for certain applications. The present work is devoted to developing and investigating simple process parameters for making steel foam from metal powder. First, methods for blending the metal powder with the foaming agent are investigated. Ideally, the foaming agent should be homogeneously distributed and well dispersed throughout the semi-finished sample in order to achieve uniform pore distribution in the foam. However, the density of the foaming agent is typically much lower than that of the steel powder, and consequently the two tend to segregate to the top and bottom regions of the blend, respectively. Special attention is thus devoted to methods of uniformly distributing the powders of dissimilar density, including drill-mixing, ball-milling, and cryomilling. A second critical process parameter, the melting time, or foaming time above T m > is explored also. Pore coalescence proceeds rapidly in melts of low viscosity, and the melting time is one of the few means of limiting pore size. Finally, a novel alternative method is developed to limit pore coalescence. The method involves the use of low-carbon steel membranes to prevent pore coalescence across layers, thus affording additional control of cell size and distribution. The results of the different mixing methods are presented in chapter 4.3.3. Experiments were then performed to determine the effect of melting time, as described in chapter 4.3.4. The effect of melting time was assessed by comparing the characteristics of the resulting foams. Finally, the effectiveness of interlayer membranes in limiting pore 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coalescence is described in chapter 4.4. This approach produced what appeared to be the most uniform pore size distribution. 4.3.2 Experiments Samples of closed-cell steel foam were made according to the description in reference [134,135]. Steel powder (a Fe-2.5C mixture) was blended with 0.2 wt% foaming agent (MgCCb granules) by techniques described below. Selection of the powder composition was empirical [134]. Powder blends were compacted by uniaxial cold-pressing under a pressure of 827 MPa (120 ksi), yielding virtually non-porous, semi finished steel samples. The resulting semi-finished samples were subsequently melted in graphite molds in an air furnace at 1330°C to effect foam expansion. The heating rate was 30°C per min and the total heating time was about 5 min. Foam samples were annealed for one hour at 950°C in air. Foam expansion was accomplished by melting the cold-pressed compacts in a graphite mold. The compacts were melted at 1330°C and held for times o f210-480 sec before cooling (in air). Foam samples were sectioned and polished metallographically before examining. In Chapter 4.4, a slight variation of the method described above was employed in an effort to limit pore coalescence in the melt during foaming. Before uniaxial cold- pressing process, thin sheets of low-C steel were inserted into the powder blend to create alternating layers of blended powder and steel sheet. The low-C steel sheets had a higher 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Tm than the powder, and were intended to function as a non-melting "interlayer membrane," thereby limiting the pore size in the foam and improving uniformity. The thickness of the steel sheet was 3-5 jun, and the number of interlayer membranes was typically 15-20 in a compact that was 32mm in height. Foam expansion was accomplished as described above. 4 3 3 Mixing methods Three mixing methods were evaluated based on the pore size distributions in the resulting foams. Drill mixing resulted in foams with relatively large pores (>5mm), as shown in figure 4.3(a). Metallographic sections revealed pore shapes that were slightly oblate ellipsoids rather than spheroids. Measurements of the elliptical cross-sections of the pores resulted in a mean major axis of 2.93 ± 1.21mm, and a mean minor axis of 2.36 ± 0.66mm. Although the pore sizes were relatively large, the pores were well dispersed throughout the sample. The oblate character of the larger pores, which extended laterally, was attributed to gravitational forces, while the larger size was attributed to incomplete dispersal of the foaming agent granules during mixing. To obtain a more uniform pore size distribution in foams, better dispersal of aggregates of foaming agent must be achieved by milling prior to compaction. The second mixing method, ball-milling, is more effective in this regard, and involves refinement of the particles as well. Consequently, foams produced from ball- milled powder blends produced slightly smaller pore sizes (on the order of 2mm), as 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. shown in figure 4.3(b). These pores tended to be more ellipsoidal (and oblate) than the first foams, and the average major axis was 1.74 ± 1.2 mm, while the average minor axis was 1.03 ± 0.S7 mm. Note that the pores tended to be larger toward .the center of the section. This feature arose because the core region cooled more slowly than peripheral regions after foam expansion, thus affording more time for pore coalescence. Cryomilling produced ultra-fine, well-blended powders because of the reduced ductility of the powder particles at cryogenic temperatures. Consequently, foams produced from cryo-milled powder blends exhibited the smallest pore sizes (<2mm), as shown in figure 4.3(c). The pores are not equiaxed, and extend laterally more than vertically. The average major axis is 1.64 ± 1.20 mm, while the average minor axis is 0.78 ± 0.42 mm. Note that the cell walls are not uniformly convex, and exhibit reverse curvatures (irregular undulations). The undulations effectively comprise defects that diminish the mechanical properties of the foam, discussed in chapter 4.3.5. 43.4 Melting time Foam expansion (via melting of the compacts) was perhaps the most critical step in the process and revealed effects of other "upstream" process parameters. For example, the powder blending process strongly affected the foam density and pore distribution. The objective of the blending process was to embed each particle of foaming agent in a gas-tight steel matrix so that the released gas generated a closed pored structure. Foam expansion revealed that homogeneous distribution of the foaming agent granules was 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (C) Figure 43 Cross section of steel foams resulting from powder blended by (a) drill mixing (b) ball-milling (c) cryomilling. (Mixing time: 2 hours) (A:compaction direction, 1 :foaming direction) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. essential to achieve uniform pore size and distribution. On the other hand, compaction pressure had negligible effect on foam density. Foam characteristics were particularly sensitive to the heating schedule used for expansion, and the time at temperature was a critical parameter of this step of the process. At the melt temperature, the melt viscosity of the steel alloy was relatively low, and pore coalescence during foam expansion was consequently rapid and problematic. Thus, the time at the peak temperature was generally limited to a few minutes in order to reduce the likelihood of pore coalescence and still allow for foam expansion. These processing parameters were discussed in this chapter. The effect of melting times on foam structures is shown in figure 4.4. All of the foams were made from powders that were blended (ball-milled), compacted, and expanded under identical conditions, the only difference being the time tm spent above the melting point, Tm . In figure 4.4(a), where tm was 3.5 min, the number of pores is small and the pore sizes are relatively small, also, as tm is insufficient to allow complete expansion of the foam. However, when tm is increased to 5 min, the number and size of the pores is considerably larger, as shown in figure 4.4(b). The larger pores (about 8mm) result from the longer tm, which allows time for expansion (and coalescence) of pores in the melt If tm is increased to 6 min, the foam starts to collapse, as shown in figure 4.4(c). The lower portion of the sample is almost frilly collapsed to full density in a region that is about 12mm thick. This results simply because the lower portion supports a slightly greater weight which facilitates the flow of the melt as the foam collapses. The upper 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (C) (d ) Figure 4.4 Steel foams produced by foam expansion at 1330C using melting times (tm) of (a) 3.5 min, (b) 5 min, (c) 6 min, and (d) 8 min. Crack-like features arise from pore collapse during melting (powders were blended by ball-milling for 30 min). ( t :compaction direction, A:foaming direction) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. portion of the sample exhibits irregularly shaped pores in an earlier stage of coalescence and collapse. When tm reaches 6 min, the foam has almost completely collapsed, as shown in figure 4.4(d). There are no pores remaining in the lower portion of the sample and the density is high. Only a few pores remain in the upper portion, and these extend radially inward, indicating that the collapsing foam may in fact exert an inward pull while the pore gas is being expelled radially. The results indicate that the useful range of tm for steel foam expansion by this method is in the range of 3.5-6 min. 43.5 Mechanical behavior All of the foams described in the previous sections exhibited characteristic foam like mechanical response when loaded in compression, as described in the classic work of Gibson and Ashby [21]. The typical response, shown in Figure 4.S, includes a distinct knee at a critical stress where the slope of the stress-strain curve decreases to nearly zero. The critical stress is taken to be the compression yield strength, as it marks the end of linear elastic deformation and the beginning of (plastic) collapse o f the foam [21]. A long deformation plateau of almost constant stress ensues, during which the cell walls buckle and collapse. Finally, the plateau ends and the stress begins to rise sharply, marking the onset of densification. In this stage, the buckled cell walls are completely collapsed and impinge on one another. The method of powder blending had a pronounced effect on the mechanical response of the foam samples. Figure 4.5 includes three representative stress-strain 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. curves selected from twenty compression tests. The three foam samples were made similarly, and all three materials showed stress-strain behavior characteristic of foam. While all three samples had similar density, the powder and foaming agent were blended by different methods, as indicated in the figure, and the yield strengths differed substantially. For example, sample 3, made from a cryomilled powder blend, had the lowest yield strength. Recall that this foam exhibited irregular undulations in cell walls, which may effectively constitute defects that lead to premature buckling. Although further proof of this assertion is needed, recent studies conducted in our laboratory indicate that deformation of steel foam is often localized, and often initiates at cell wall irregularities [ 136]. The complex relationship between structural defects and the mechanical behavior of metallic foams requires an understanding of the mechanisms of foam deformation, as well as an understanding of edge effects, sample geometry, and sample size relative to pore size [137]. Deformation mechanisms depend on foam structure (both micro and macro), which is controlled by the process parameters employed. 4.4 Interlayer membranes method The structure of porous materials can be described in terms of geometrical structure and material structure. Geometrical structure includes the shape and size of the cells, the distribution of cell sizes, and defects or flaws in the cell wall configuration. Material structure is simply the nature and internal microstructure of the cell wall 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stress (MPa) 6 0 0 1 : D rill mixing (p*=3.59 g/cm3, o’ =84 MPa) 2: B allm iH in g (p'=3.52 g/cm3 . a =28 M Pa) 3: C ryom ilK n g (p’=3.65 g/cm3, c *22 M Pa) 500 - 400 - 300 - 200 • 100 - 0.7 0.2 0.4 0.6 0.0 0.3 0.5 0.1 Strain mm/mm Figare 4.5 Compression stress-strain curves for three foam samples. The powders were blended by drill mixing, ball milling, and cryomilling in samples 1-3 respectively. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. material. The overall mechanical properties of porous materials are determined by the interactions between these factors. When the macroscopic structure of metallic foam is produced, the geometric structure is determined by factors such as pressure difference across the cell walls, surface tension, fluid (melt) viscosity, and cooling rate. Pressure difference between adjoining cells gives rise to cell wall curvature, and this also is the main reason for cell coarsening through the diffusion of entrapped gases across the cell walls [138-141]. Clearly, controlling the cell size and distribution in steel foam requires a thorough understanding of these factors as well as careful control of the critical parameters. In practice, achieving the proper balance is problematic, and a simpler, alternative means of limiting pore coalescence would be useful. A new approach involving the use of "interlayer membranes" was devised for controlling the cell size and distribution in steel foams. The concept is illustrated schematically in figure 4.6. Sheets of high-Tm material (in this case, low-C steel) were inserted between layers of blended (drill-mixed) powder prior to compaction. These interlayer membranes were intended to limit the growth of pores in the vertical direction simply by remaining solid during foam expansion. The effectiveness of this concept is illustrated in figure 4.7. On the left is a foam (pR | = 0.43) expanded from a compact without interlayer membranes (figure 4.7a). The foam has large pores in the core region, and smaller pores in the shell region. As noted previously, the core region cools more slowly than the outer regions and remains molten longer, allowing more time for cell coarsening because of the high gas pressures in the cells. The sizes of the cells are 3- 7mm. 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Press Die Upper Punch Steel Powder _ + Foaming Agent Interlayer Membrane Lower Punch Figure 4.6 Schematic illustration showing the use of interlayer membranes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Introducing 20 interlayer membranes (3 pm thick) into the compact results in the foam shown in figure 4.7(b) which has pre i = 0.S3. Compared with the foam in figure 4.7(a), the cell size is smaller (2-5 mm) and the cell distribution is more uniform. The membranes are indistinguishable and have welded imperceptibly to the alternating layers of foam. Cells extend laterally, forming slightly elongated pores that are typically 1x2mm. Further experimentation is currently underway to determine optimal process parameters for foam synthesis using this approach. 4.5 Conclusion Steel foams with relative densities of <0.5 were synthesized by a PM process. Both the mixing process and the heating procedure (particularly the time at temperature above Tm ) had major effects on foam density, although the compaction pressure did not. The pore size distribution within the foam was somewhat coarse, and clearly greater process control will be needed to achieve more uniform pore structures. Steel foam synthesis requires careful control of process parameters to prevent pore coalescence during foam expansion. In the present work, two of these parameters were investigated and optimized. Superior results were obtained by blending the powders by ball-milling, and by limiting the melt time to 3.5-6 minutes. One of the critical processing challenges is preventing pore coalescence and collapse during foam expansion. Possible solutions include increasing the melt viscosity, extracting heat 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.7 Cross sections of steel foams showing the effects of using interlayer membranes (a) Foam structure produced without interlayer membranes, (b) Foam structure with 20 interlayer membranes (powders were blended by drill-mixing), (^com paction direction, ^rfoaming direction) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (freezing) more quickly, or, as shown in the present study, use of interlayer membranes to limit the coalescence of pores. The methods employed for producing steel foam were relatively simple, producing foams with somewhat coarse pore structures and thick walls. In spite of these features, the foams showed characteristic foam-type response to compressive loading, including the extensive stress plateau. The findings suggest that the development of more sophisticated processing methods may lead to considerable improvements in foam uniformity and mechanical properties. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5. MECHANICAL PROPERTIES OF STEEL FOAM 5.1 Introduction Steel foam samples showed a characteristic stress-strain behavior when loaded in compression (figure S. 1). The response typically included a distinct knee at a yield stress where the slope of the stress-strain curve changed from a high value to zero (see figure S.l). The critical stress, which marked the end of linear elastic deformation (region I) and the beginning of foam collapse, was taken to be the compression strength. A long deformation plateau of almost constant stress ensued, during which the cell walls buckled and collapsed (region II). Finally, the plateau ended and the stress began to rise sharply (region III), as the flattened cell walls were completely collapsed and impinged. Also plotted for comparison in Figure 3 is the typical response of an aluminum alloy foam (Al-4Cu) [16]. The steel and aluminum foams show almost identical response in figure 5.1, albeit on vastly different scales. (The stress scale for the aluminum foam is enlarged by a factor of 3 to allow comparison.) The relative densities are 0.45 and 0.2 for the steel and aluminum foams, while the absolute densities are 3.5 g/cm3 and 0.54 g/cm3. The similarity of the two curves is somewhat surprising given the vastly different pore structures of the two materials [16]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The duration (strain) of the three regions shown in figure S.l depended on the density of the steel foam. This phenomenon is shown in figure 5.2. If the foam density was high, then the constant-stress plateau was brief. On the other hand; a foam of lower density exhibits a longer, flatter plateau because the structure affords more opportunity for cell walls to collapse and deform. 5.2 Annealing effects 5.2.1 Compression strength As shown above, the compression strength of steel foam depends strongly on the relative density, defined as the ratio of the foam density to the material density [83, 142- 144]. The compression strength of open-cell foams can be predicted from a simple theory based on cubic unit cells [14]: where pj\s the density of the foamed material p, is the density of the massive material Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. — The high density (p‘=4.34 g/cm3 ) * • The low density (p’=3.52 g/cm3 ) 600 • 500 • « ■ 400 - 300 - 200 - 100 - 0.8 0.2 0.4 0.6 0.0 Strain Figure 5.2 Stress-strain response of low-density and high-density steel foam. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stress (MPa) 200 700 Steel foam (left scale) A l foam (right scale) 600 - 150 500 400 - 100 300 200 - 50 100 0.8 0.6 0.2 0.4 0.0 Strain Figure 5.1 Stress-strain response of steel foam and Al foam. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stress (MPa) O ja is the yield strength of the matrix material. a / is a constant that derives from the distribution of material in the foam. n is 1.5 For closed pore foams, the formula is more complicated, although the mechanical properties are controlled primarily by the thicker cell edges rather than the thinner cell walls (membranes). Therefore, the above equation has been used to approximate the strength of closed pore foams [14]. In figure 5.3, data for steel foam is plotted on a double log scale to test the relation (eqn. 44) and to determine the exponent. For the samples tested prior to annealing, the data are plotted as open circles, while data for annealed samples are plotted as closed circles. Both sets of data appear to be linear. The exponent n is determined by linear regression to be 1.8 for samples prior to annealing and 2.5 for annealed samples. These n values differ slightly from the value of 1.5 predicted by the cubic model for open-cell foams [14]. Because the model assumes cubic cell geometry and the steel foams are more irregular, some deviation between measured and predicted behavior is expected. Nevertheless, the cubic model describes with reasonable accuracy the relative variation of compression strength with density. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. b e I C 1 .5 ® O C S. 0. 6 • Sample with anneaing O Sample without annealing 0.7 0.9 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative density (p/p,) Figure S 3 Compression strength of a series of the steel foams as a function of relative density. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2.2 Collapse mechanism Compression test data from pre-annealed and annealed foams provided insight into the mechanism of cell collapse, an important indicator for steel foam applications (figure 5.4). The stress-strain curves from pre-annealed samples were typically serrated, particularly at the onset of plastic flow, and upper and lower yield points were often observed. The foam samples tended to fragment and shatter during compression testing, causing serrations in the o-e curve shown in figure 5.4. During compression, the cell walls tended to crack and fracture in a brittle manner, a probable consequence o f the high carbon content necessary to achieve foaming (2.5%). The brittle fractures of cell walls occurred locally and spread to the surrounding regions as compression proceeded. The implications of these results in terms of energy absorption are considered next, as cell wall collapse is the primary mechanism of energy absorption. In contrast, the stress-strain curve for the annealed foam deformed smoothly throughout the entire compression range (up to 75% strain). Cell walls buckled continuously during compression, providing the main structural collapse mechanism throughout the entire deformation range, and the buckling appeared to be uniformly distributed through the sample. The micro structural changes caused by annealing - decarburization and partial conversion to ferrite - profoundly affected the compression behavior, providing greater ductility of cell walls that permitted the buckling necessary for energy absorption. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 700 Annealed sample (p,=3.56 gtam3) Pre-annealed sample (p,=4.96 g/cm3) 600 500 ^ 400 « m 8 300 200 100 1.0 0.6 0.8 0.0 0.2 0.4 Strain Figure 5.4 The effect of annealing treatment on the stress-strain response of steel foam. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.23 Energy absorption of steel foam The majority of the absorbed energy is irreversibly converted into plastic deformation energy [26]. This occurs primarily in the broad stress plateau, which is typical of most metallic foams under compression loading, and imparts a large capacity for energy absorption. During the stress plateau, energy is absorbed largely by the buckling and collapse of cell walls in the foam. When this mechanism is exhausted, the stress begins to rise, and the material is densified. The magnitude (or "height") o f the stress plateau is strongly affected by the intrinsic yield strength of the metal. Thus, when compared to aluminum foams, steel foams afford greater energy absorption capability because of the much higher yield stress of steel. [145]. 5 3 3 .1 Energy absorption efficiency The energy absorption efficiency for a given strain value is defined as the ratio of the deformation energy absorbed by a real material to the deformation energy absorbed by an ideal energy absorber [26]. In figure 5.5, the area under the stress-strain curve represents the real amount of energy, which is converted into deformation work. An ideal absorber shows a rectangular stress-strain curve shape, the area of which is defined by the maximum stress and strain values (this is known as perfectly plastic behavior). Therefore the efficiency rj is given by the real absorbed energy after a compression strain s divided by the energy absorption of the ideal absorber [78]: 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 600 - 500 (0 (0 s 300 Ideal absorber to 200 100 Real absorber 0.0 0.2 0.8 0.4 0.6 Strain Figure 5.5 Comparison of real and ideal energy absorbers. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where Fm ^s) is the highest force occurring up to the deformation s. In figure 5.6, the stress-strain curve of the steel foam, which is annealed 1 hr at 950°C, is depicted as well as the numerically determined efficiency (right scale). As the applied stress changes during loading, so the calculated efficiency ( 7 7 ) changes during the deformation process. Thus, the energy absorbing efficiency is a function of the shape of the stress-strain curve. From figure 5.6, the energy absorption efficiency of this particular steel foam can go up to 90% within the plateau regime. In contrast, the stress-strain curve of pre-annealed steel foam is shown in figure 5.7, along with the numerically determined efficiency (right scale). The energy absorption efficiency is much lower than that of the annealed foam shown in figure 5.6, and is less than 50% in the stress plateau regime. When the flow stress increases, the mechanism of cell wall collapse is virtually exhausted, and the efficiency correspondingly decreases. The energy absorption efficiency is clearly a function of the duration of the plateau during compression, which is controlled by the relative density, the distribution and size of pores, and the cellular morphology. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 700 100 Stress-strain curve Effectiveness^) 600 - - 80 500 (0 ^ 400 - < 9 300 - - 60 (0 £ - 40 W 200 - - 20 100 - 0.8 0.0 0.2 0. 4 0.6 Strain Figure 5.6 Compressive stress-strain response and energy absorption efficiency of annealed steel foam (density = 3.56 g/cm) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Effectiveness (%) 700 100 Stress-strain curve Effectiveness(%) - 90 600 - 80 500 - 70 (0 ^ 400 (0 < / > 300 - 60 - 50 2 53 - 40 - 30 200 - 20 100 - 10 0.0 0.2 0.4 0.6 0.8 1.0 Strain Figure 5.7 Compressive stress-strain response and absorption efficiency of pre-annealed foamed steel (density = 4.96 g/cm) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Effectiveness (%) 5.23.2 Energy absorption capacity The energy absorption capacity is defined as the energy necessary to deform a given specimen to specific strains, and is used to compare foams of different density. Generally, a substantial increase in energy absorption is observed as the foam density is varied from low to high. Furthermore, the rate at which energy absorption increases with density increases with increasing strain. Figures 5.8 and 5.9 show the energy absorption after compression strains of 20%, 30% and 50% for annealed and pre-annealed foams. In figure 5.8, the energy absorption data for annealed samples show a dependence on density that ranges from weak to strong as the strain increases from 20% to 50%. In contrast, the data for pre-annealed samples (figure 5.9), show a relatively weak dependence on density at all strain levels, as well as substantially higher scatter in the absorbed energy values. The behavior of the pre-annealed samples stems from the unstable mechanism of cell wall collapse, manifest in serrations in the stress-strain curve after the onset of plastic flow. Like the annealed foams, the energy absorption capacity increases with foam density, although the dependence on density is never as strong. An important feature of the data in figures 5.8 and 5.9 is the maximum compressive stress, an important parameter affecting the utility of the material as an energy absorber. This parameter is needed to generate an energy absorption diagram, described below. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 0 Strain = 20% Strain = 30% Strain = 50% to E c o e- o U i Xi (0 a > c w 4 3 5 Density (g/cm ) 6 3 Figure 5.8 Energy absorbed by various steel foams after compression strains of 20,30, and 50% (annealed samples). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 o Strain = 20% & Strain = 30% • Strain = 50% 100 c o fr o M .O (0 2 k s > < u £ 20 6 5 4 3 Density (g/cm3) Figure 5.9 Energy absorbed by various steel foams after compression strains o f20,30, and 50% (pre-annealed samples). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5233 Energy absorption diagrams Maiti et. al. have proposed energy absorption diagrams as design tools for selecting appropriate foams for specific applications [78]. These diagrams are compression stress-strain curves for foams of different density, with indications o f peak stress experienced for equivalent amounts of energy absorbed (cf. figure S. 10). Thus, in order for a foam to absorb a specified amount of energy W during loading without exceeding a critical stress value, foam with a specific density should be used. The compression behavior of three steel foams with different densities is shown in figure 5.10. Wi, W2 , and W3 indicate equivalent energies absorbed (IV). The foam of highest density (pni= 0.56) shows a negligibe stress plateau and thus experiences the highest stress in the course of absorbing energy W. In contrast, the foams of medium density (aw=0.46 and 0.41)would be preferable in this case because they can absorb the same energy W with a much lower maximum stress. The steel foam (p^/=0.41) shows the lowest peak stress of the three foams, primarily because of the lengthy stress plateau. If the foam density is too low, however, foam densification occurs before the energy absorption specification is met, and the peak stress can exceed the critical value. Thus, such energy absorption diagrams can be useful for selecting a foam density that will absorb a specified energy without exceeding a critical stress. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stress 600 Density = 3.2 g/cm Density = 3.56 g/cm Density = 4.34 g/cm 500 400 300 200 100 0 0.0 0.2 0.4 0.6 0.8 Strain Figure 5.10 Compression behavior of three steel foams of different densities. The various areas correspond to equivalent amounts of absorbed energy, W. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2.4 Conclusion Despite the coarse and irregular pore structures of the foams, the compression stress-strain curves showed the distinctive stress plateaus characteristic of metallic foams with more uniform pore structures [146]. The stress-strain response was strongly affected by annealing, which reduced carbon content and replaced much of the pearlitic structure with ferrite. This appeared to enhance the ductility of the cell walls and altered the mechanism of cell wall collapse, thereby greatly increasing the energy absorption during compression loading. The response during compression loading indicated that substantial energy absorption capacity was possible in metallic foams, even with thick cell walls. Further substantial improvements in energy absorption behavior should be possible by reducing the cell wall thickness and density of the foam, and improving the pore size uniformity. 5.3 Anisotropy of mechanical properties 5.3.1 Introduction Metallic foams exhibit unusual mechanical and thermal properties, including energy absorption, vibrational and acoustic damping, and thermal insulation [123, 147]. Because of these unique properties, metallic foams may find applications in impact absorbers, ultralight sandwich structures, compact heat exchangers, and heat dissipation media. However, before these applications can be realized, two things are required - a 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mature and robust process technology for manufacturing metallic foams with consistent properties, and a knowledge amongst design engineers about the mechanical characteristics of metallic foams, their durability, and how to use them intelligently in structural applications. These requirements have not been met, although various molten metal and powder metallurgical processing methods have been reported [129*132, 148, 149], and the mechanical behavior of foams has been reviewed in the treatise by Gibson and Ashby [21]. The basic mechanical properties of metallic foams are not unlike polymeric foams, and both generally conform to the theory of cellular materials [21-]. However, there are notable deviations from theoretical predictions. For example, the elastic modulus and compressive strength of closed-cell aluminum foams is reportedly lower than predicted values [21, ISO], Insight into this discrepancy is provided by microstructural observations, which indicate that defects present in the cell structure may degrade mechanical properties [151]. Simple defects include cell wall curvature and non- equiaxed cell shapes. The latter defect can contribute to anisotropic mechanical properties, while the former can lead to localized deformation [152]. The present work focuses on mechanical anisotropy in steel foams synthesized by a powder metallurgical process. In this process, steel powder is blended with a granular foaming agent, compacted, then expanded to foam by heating the compact briefly above the melting point [134, 135]. Results from compression tests performed parallel and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. perpendicular to the foaming direction are compared with model predictions, and deformation mechanisms are observed and related to the measured response. 5.3J 2 Experiments A closed-cell steel foam material was synthesized by a P/M route and used for experimental testing [134]. Commercially available steel powder (Fe-2.5C blend) was blended with 0.2wt% of a granular foaming agent (MgCQ) or SrC<>}). Blended powders were compacted by uniaxial cold-pressing, yielding virtually non-porous, semi-finished steel samples. The resulting semi-finished samples were subsequently melted in an open graphite mold held in an air furnace at 1330°C to effect foam expansion. The heating rate was 30°C per min, and the total melting time (tm ) was about 5 min. The relative density of the foam samples was 0.4-0.65. Foams with anisotropic cells had an average major axis of ~5mm and an average minor axis of ~2mm. After foam expansion, compression test samples were cut to approximately 20x18x17 mm and annealed for 1 hour at 950°C in air. Compression tests were performed by loading in one of two directions: the longitudinal direction, parallel to the direction of foaming, and the transverse direction, perpendicular to the direction of foaming (figure 5.11 (a) and (b)). The crosshead speed was 2mm/min. The deformation mechanisms in steel foam were observed by interrupting compression tests at strains of 10%, 20%, 30%, and 50%, and examining cell structures metallographically. The anisotropy o f the 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Loading direction Loading direction I Foaming direction TT t (a) Foaming direction ► Ttt (b) Figure 5.11 Schematic of the loading and foaming directions: (a) Longitudinal direction (b) Transverse direction. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measured mechanical response is described in chapter 5.3.3 and 5.3.4, while the deformation mechanisms are described in chapter 5.3.5. 53 3 The compression test results Expanded foams were elongated in the foaming (vertical) direction, resulting in roughly ellipsoidal cells (figure 5.12(a)). During foam expansion, ellipsoidal cells evolve because of the microstructure of the pressed compact. During powder compaction by uniaxial cold-pressing, some flattening of the steel powder particles occurs, resulting in ellipsoidal shapes [152, 153]. As a result, prior particle boundaries (PPBs) tend to extend normal to the pressing direction, and foaming agent granules tend to reside on these PPBs. This distribution gives rise to ellipsoidal pores during foam expansion. Higher melting temperatures and/or longer melting time resulted in spheroidization and coalescence of the cells, as shown in figure 5.12 (b). Compression tests performed on steel foams in the longitudinal direction yielded typical foam-type behavior, as shown in figure 5.13. Typical stress-strain curves (longitudinal loading) show a relatively low yield point followed by a long stress plateau of nearly constant stress. During this long plateau, large plastic strain is achieved with little increase in the applied stress. The plateau is followed by a sharp increase in the applied stress, marking the onset of densification. These features are characteristic of most foams, and the yield stress is taken as the "knee" separating the elastic and plastic regions. Note that the yield stress for the foams represented in figure 5.13 is about 30-80 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (b) Figure 5.12 Cell structures of steel foam showing (a) elliptical shape cells, and (b) spherical shape cells. 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Strata (MPa) 500 1: Relative density = 0.456 2: Relative density - 0.410 3: Relative density = 0.271 400 - 300 - 200 - 100 - 0.8 0.6 0.4 0.0 0.2 Strain mm/mm Figure 5.13 Stress-strain response for compression in the longitudinal direction. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stress (MPa) 6 0 0 Relative density = 0.63S Relative density = 0.595 Relative density = 0.510 Relative density = 0.502 500 400 300 200 100 0 0.8 0.2 0.4 0.6 0.0 Strain mm/mm Figure 5.14 Stress-strain response for compression in the transverse direction. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MPa, and foams of higher density have slightly higher yield strengths. The length and height of the plateau is also density dependent, with foams of lower density having longer plateaus, albeit at lower stress levels. Typical densification strains are 0.7-0.8. The stress-strain response of foams loaded in the transverse direction is shown in figure 5.14. The yield stress in the transverse direction is 3-5 * higher (130-300 MPa) than in the longitudinal direction, and the stress level of the plateaus is 2-5 x greater. Also, the yield point drops are more pronounced in figure 5.14, and the stress plateaus are not nearly as long or as flat as in figure 5.13. The yield point drops and the stress variations after yielding are directly related to the deformation mechanisms, discussed in chapter 5.3.5. The data from figures 5.13 and 5.14 is summarized in figure 5.15, a plot of the compressive yield strength versus density for the two loading directions. In both cases, yield strength increases with foam density, although the density dependence is stronger in the transverse direction than in the longitudinal. The anisotropic mechanical response of steel foam stems from the geometry of the ellipsoidal cells. In the case of longitudinal loading, foam deformation involves the deflection of cell walls that extend normal to the applied load, much like beams and plates loaded in bending. Conversely, when loading is in the transverse direction, these same walls are loaded more like columns (or end-loaded beams and plates). "End- loading" of cell walls eventually causes buckling and a precipitous load drop, giving rise to the observed yield point drop shown in figure 5.14. However, unlike conventional 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Yield Strength (MPa) 300 • longitudinal direction — longitudinal direction regression ■ transverse direction • • transverse direction regression 250 - 200 - 150 - 100 - 50 - 5 3 4 2 D ensity (g/cm 3) Figure 5.15 Comparing yield strength versus density for transverse and longitudinal directions. 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. buckling, the load does not drop to zero. Buckled cell walls impinge and provide mutual support, arresting the load drop at a relatively high stress and abbreviating the stress plateau, as shown in figure S. 14. Consequently, the yield strength in the transverse direction is much higher than the yield strength in the longitudinal direction. 53.4 Comparing the measured values with the predicted values As noted above, the mechanical behavior of a cellular material depends strongly on density. Typically, lower density foams have longer stress plateaus and lower absolute yield strength [21]. This behavior derives from the mechanisms of cell wall collapse and the deformation mechanics of the porous structure [21, 85]. A simple theory is used to relate the density and yield strength o f cellular materials [21]. 5.3.4.1 Predicted by power law Conventional theory based on a cubic model and simple beam bending equations predicts that the yield strength for open cell and closed cell foams will exhibit a power law dependence on density given by the equation (44) [21,154]. The exponent n takes on different values for open and closed cell foams, and for different deformation mechanisms. For open cell foams, n =1.5, while for closed cell foams, n=l. However, equation (44) assumes deformation occurs primarily by beam bending. While this may be valid for open-cell foams, closed cell foams can deform by membrane stretching, beam bending, or mixtures of the two [21, 154, 155]. 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Recently, Gibson and Ashby proposed an alternative model to describe the behavior o f closed cell foams that recognizes the important contribution of cell wall stretching [21]. Their model describes foam structure as an array of cubic cells comprised of identical orthogonal struts joined at their ends to form cubes. While quite different from the actual geometry of cells in metallic foams, their model provides some insight into the basic physical processes that govern the deformation and structural stability of cellular materials. The predicted relationship between the yield strength and the relative density is given by where the distribution constant, 4 > , is defined as the fraction of solid in the foam which is contained in the cell edges [21]. The values of < j > are limited by The case of $=1 corresponds to an open-cell foam with material only in cell edges, while the lower bound of ^ corresponds to a foam with thick cell walls. The first term in equation (46) describes the contribution of the cell struts to the yield strength and is identical for closed- and open-cell foams. The second (linear) term includes the contribution of cell walls and would be absent for the case of open-cell foams. (Note that equation (46) does not include the internal gas pressure within the cells.) From equation (46), the three parameters controlling relative yield strength are the (46) (47) 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. relative density, the distribution of material within walls and struts, and the basic cell structure of the foam (open* or closed-cell structure). Despite the appeal of this simple model, the differences in the mechanical response of open- and closed-cell foams is not always so distinct Menges and Knipscheld pointed out that in most closed-cell foams, the majority of an imposed load is carried by the cell wall edges or junctions rather than the thin cell wall membranes [81]. They also identified cell wall bending as the principal mechanism of linear-elastic deformation for closed-cell foams. Consequently, they argued, open- and closed-cell materials can exhibit similar mechanical response. Indeed, closed-cell metallic foams of aluminum reportedly exhibit behavior described by equation (44) with n = 1.5-2, suggesting that some revision to the model may be needed to describe metallic foam behavior [153]. The relation between yield strength and density determined for steel foams is shown in figure 5.16. To allow for comparison of the measured yield strength with the prediction of the equations, the foam yield strength is normalized to the cell wall yield strength (taken as c y s=580 MPa), and the foam density is normalized to the cell wall density (ps =7.8 g/cm3) [156]. The exponent n expressed in the power-law relation described above is 1.9 for the transverse direction, 1.8 for the longitudinal direction. Similar measurements on steel foams of different density yielded values of n = 1.6 - 2.0. While these values are similar to those reported for closed-cell aluminum foams [153], neither value is close to the predicted values. 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Relative S trength 0.5 • longitudinal direction — longitudinal direction regression ■ transverse direction ■ transverse direction regression 0.4 0.3 0.2 0.1 0.7 0.6 0.5 0.4 Relative D ensity Figure 5.16 Relative yield strength versus relative density for longitudinal and transverse directions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The apparent discrepancy between observed dependence of strength on relative density stems from the unusual structure of steel foam and a clear understanding of the basis for the model. When foam strength is derived primarily from cell wall stretching and the contribution from bending of cell edges can be neglected, an exponent of n = 1 is expected [21]. On the other hand, when foam strength derives primarily from beam bending (as in the case of open cell foam), an exponent of n = 1.5 is expected. However, when the relative density range for foams here is high, and the strut thickness to length ratio is high (as it is here), the simple beam bending equations used to derive foam strength may no longer be valid. Indeed, both of these conditions are realized in the steel foam studied here. Ironically, an earlier theory of Gibson and Ashby predicted a quadratic dependence of strength on relative density for closed cell foams [82]. This theory was based on an assumption of foam deformation by cell wall bending, and appears to predict the power law dependence observed in the present work. However, the agreement may be fortuitous. While the cells within the steel foam structure are undoubtedly closed, the structure is distinctly different from most conventional foams. The steel foams here have substantially thicker cell walls than the typical polymeric foams on which relations (44) and (46) are based. Nevertheless, the power-law relation approximates the observed behavior, and both foam orientations yield similar exponents. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 3 3 .2 Determination of the distribution constant The distribution parameter $ can be estimated from comparisons of experimental data with predictions of equation (46). Figure 5.17 shows a log-log plot of relative yield strength versus relative density. Superimposed on the plot are the predictions of equation (46) using trial values of $. Comparisons indicate that the distribution constant, 4, is ~ 0.77 for the longitudinal direction and 0.75 for the transverse direction. That the distribution constants are nearly identical is not surprising, because the foams are nearly identical and thus have the same fraction of solid in the cell edges. However, $=0.75 is considerably lower than typical foams. For example, closed-cell A1 foams with thin cell walls and thick cell edges reportedly exhibit values of $=0.94 [146]. Consequently, aluminum foams can exhibit behavior similar to open-cell foam [146]. Thus, one of the distinguishing features of steel foam in the present study is cell walls that are much thicker than conventional foams. 5 J .5 Deformation mechanism Compression of steel foam resulted in the formation of a series of deformation bands comprised of collapsed cells. The bands extended normal to the direction of applied load, and developed sequentially with increasing strain, as shown in figure 5.18. The images show the evolution of plastic strain during a single compression test, interrupted at increasing strain levels. Figure 5.18(a) shows the sample prior to deformation, with 9 cells numbered. The relative density of the foam is 0.50, and the 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Relative Density (pVp^) Figure 5.17 (a) The distribution constant for steel foam as function of relative density (longitudinal direction). The dotted lines are predictions given by equation (46). 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Relative Density (p’/p^) Figure 5.17 (b) The distribution constant for steel foam as a function of relative density (transverse direction). The dotted lines are predictions given by equation (46). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. loading rate is 2 mm/min. After 20% strain, plastic yielding has occurred, and two discrete bands of deformation appear near the top of the field of view. Cells 1-4 within the bands have collapsed, while cells 5-9 remain undistorted. The evolution of strain localization is apparent in figure 5.18(c). Cell 5 has partially collapsed, and a third deformation band is extending across the sample. At 50% strain, cells 6-9 have begun to collapse, forming a fourth deformation band. Nearly all of the cells have collapsed at this point, and the stress is starting to increase sharply, marking the onset of foam densification. The process and mechanisms of foam deformation are illustrated in figure 5.19. The deformation sequence initiates with elastic deflection of the cell walls, followed by cell collapse and strain localization (cf. figure 5.19). However, instead o f cells collapsing independently and in isolated fashion, the cells collapse in discrete bands. Apparently, a weak cell wall serves as the initiation site for strain localization. This deformation then propagates rapidly through the foam in the transverse direction, resulting in a band of collapsed cells separating regions of elastically deformed cells. Once the strain capacity of a band is mostly exhausted, deformation begins anew with the formation of a new band. Globally, macroscopic strain is achieved by the sequential formation of deformation bands. Cell geometry can strongly influence the deformation mechanisms and plastic response of foams under compressive loading. Figures 5.20(a) and 5.20(b) show foams with different cell structures and their corresponding stress-strain curves. Both samples 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (C) (d) Figure 5.18 Defonnation banding during a typical compression test (a) e = 0% (b) e = 20% (c) e = 30% (d) e = 50%. 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Elastic deflection stage Initial state (undeformed) ooooo Elastic deflection stage Collapse and densification stage Collapse and densification stage Figure 5.19 Schematic for cell collapse model. 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. were tested in the transverse direction. The foam in figure 5.20(a) has uniform, equiaxed pores (~1.5-2mm), and the mechanical response shows a long, flat stress plateau with little fluctuation in stress. In contrast, the foam shown in figure 5.20(b) has a wide range of irregular (elongated) pores. As a result, the mechanical response shows a pronounced yield point drop, followed by a brief plateau in which the stress fluctuates substantially. Note that the density of this foam is higher than the one shown in figure 5.20(a), and the strength is also higher. The deformation sequence is somewhat different for foams with large variations in cell shape and size, but can be explained by a series of steps. The difference arises because strain localization takes place at discrete points simultaneously, and these points of localized strain subsequently connect to form an irregular deformation band that is not completely transverse to the applied load. The process by which collapsed cells are linked contributes to the observed variations in stress afier the yield point. More uniform cell sizes tend to minimize the post-yield oscillations in stress, as shown in figure 5.20(a). 5.3.6 Conclusion Steel foams fabricated by a P/M route show distinct anisotropy when subjected to uniaxial compressive loading. The foams are ~3x stronger in the transverse direction than in the longitudinal direction, and exhibit a more pronounced yield point drop. The anisotropic response is directly related to the foam structure, which is characterized by ellipsoidal cells with thick walls extending transverse to the foaming direction. In both 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S t r e s s (MPa) (a) 350 300 250 200 150 100 50 0 0.6 0.8 0.0 0.2 0.4 Strain mm/mm (b) Figure 5.20(a) Mechanical response for a foam with uniform pore size (about 1.5-2 mm): (a) Foam structure, (b) Stress-strain curve of the compression test (density: 3.52 g/cm'3 ) 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) 500 400 « Q . s 300 Collaps 200 Densificatio (0 Yield 100 0.7 0.4 0.5 0.6 0.0 0.1 0.2 0.3 Strain mm/mm (b) Figure 5.20(b) Mechanical response for a foam with a wide range of pore size: (a) Foam structure, (b) Stress-strain curve of the compression test (Density: 4.63 g/cm3 ) 141 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. orientations, behavior is described by a power-Iaw with a similar stress exponent (n = 1.8). The distinctly different structure of steel foam, with its thick cell walls and irregular cell geometry, will require a different model based on a more realistic relation between microstructure, deformation mechanisms, and plastic response. Plastic deformation of steel foam is characterized by strain localization and occurs in a characteristic sequence. The first step is elastic deflection of the cell elements, followed by localized deformation in a few cells. Collapse and densification of cells leads to the initiation of a deformation band, which gradually spreads across the sample. The deformation mechanism proceeds in a sequential manner with repeating cycles of yield, collapse and densification of cells. The anisotropic character of steel foam might one day provide design engineers greater freedom than possible with isotropic foams. For example, mechanical anisotropy should make it possible to soften structures selectively, thus forcing loads away from highly stressed areas. Similarly, strain localization might make certain manufacturing operations more tractable, such as repairs, joining, and machining. For example, strain localization might make it feasible to selectively density certain locations within a component, which could then be machined or welded more readily. In any event, both anisotropy and strain localization must be well understood to effectively implement steel foam into future engineering applications. The most likely applications are ones in which weight savings translate into significant performance gains, and those in which energy Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. absorption is important. Foreseeable applications in the automotive industry include engine valves, camshafts, wheel rims, and door intrusion beams. 5.4 Effect of different strain rates and morphological defects 5.4.1 Introduction Metal foams exhibit unusual mechanical properties not found in solid materials. In particular, the energy absorbed during deformation can be extremely high, a phenomenon that stems from the mechanisms of cell wall collapse. In addition, the density can be extremely low (relative density as low as 0.2). These special properties (and others) may lead to a variety of applications such as impact absorbers, ultralight structures, damping components, compact heat exchangers, and heat dissipation media. Impact absorbers are a natural application to consider, because the energy absorption capacity of metal foam is unusually high. However, before any such structural applications can be realized, two things are required - (1) a sound fundamental understanding of the mechanical response and deformation mechanisms, and (2) a mature process technology for synthesizing uniform foams with consistent properties [129-132, 134,148,149,157]. The present study addresses the first requirement, and deals with steel foams fabricated from metal powders. Fundamental understanding of structure-property relations in metallic foams is only beginning to emerge. Traditional models have been used to describe the behavior of cellular materials, as given by Gibson and Ashby in their classic treatise [21]. However, 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. several recent reports of metallic foam behavior indicate that some refinements to earlier models are needed to account for discrepancies between predictions and experimental observations. For example, experimental measurements of the Young's modulus and compressive strength of closed-cell A1 foams are substantially lower than values calculated from classical models [21, ISO, 158]. Furthermore, defects present in the cell structure, such as cell wall curvature and cell shape irregularities, can cause significant reduction in mechanical properties [19,151]. Indeed, recent finite element analyses simulating the deformation of a closed cell tetrakaidecahedral unit cell with curved cell walls indicated that such defects may be responsible for reductions in modulus and strength up to 70% relative to the values for cells with planar cell walls [150]. Unfortunately, strength-limiting defects are not taken into account in traditional models, and their effects are not well understood. This chapter describes how foam defects affect the compression strength of steel foam, and how strength depends on strain rate. The role of defects in foam deformation is explored through measurements of cell wall curvature, which are then related to compressive strength. Experiments are also performed to determine the effects of strain rate on yield strength and energy absorption of steel foams. Strain rate sensitivity is an important issue for cellular materials, as they are ofien intended to absorb impact energy. In the case of polymeric foams, yield strength generally increases linearly with strain rate, while stiffness is strain-rate independent [21]. For metallic foams, strain rate sensitivity is largely unexplored, although this is a subject of considerable importance because of potential energy absorbing applications. Experiments performed to determine 144 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the effect of different strain rates are described in chapter 5.4.3 and 5.4.4, and morphological defects are described in chapter 5.4.5. 5.4.2 Experiments Experiments were performed on a closed-cell steel foam fabricated by a powder metallurgical (P/M) process [136, 152]. Using this process, iron and carbon powders (Fe- 2.5 wt% C) were mixed with 0.2 wt% of a granular foaming agent (MgCCh). The powder mix was compacted by uniaxial cold-pressing, yielding compacts that were virtually pore-free. The compacts were subsequently melted in a box furnace at 1330°C to effect foam expansion. The heating rate was 30°C per min and the total time above Tm was ~ 5 min. Compression test samples were cut to approximately 20x18x17 mm using a low-speed diamond saw. Cut samples were annealed for 1 hour at 950°C in air prior to compression testing. Compression tests were performed at strain rates ranging from 4.5xl0's to 1.6x10* sec'1 . The experimental strain rates were calculated on the basis of initial specimen height and crosshead displacement Total strains were typically 0.6-0.7. Resulting yield strengths (compression strengths) were compared with predictions of current theoretical models. All compression tests were conducted with the load applied parallel to the foam growth direction. Finally, effects of structural defects on mechanical behavior of foam samples were investigated by microstructural analysis prior to compression testing. Cell wall I4S Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. curvatures were measured for individual foam samples, and cell wall undulations were determined from metallographic sections. 5.43 Yield strength with strain rate Steel foam samples showed a characteristic stress-strain behavior when loaded in compression (figure 5.21). The stress-strain curves typically exhibited a distinct knee at a yield stress where the slope of the stress-strain curve changed from a high value to near zero. A long deformation plateau of almost constant stress ensued, during which the cell walls buckled and collapsed (region II). The yield stress, which marked the end of linear elastic deformation (region I) and the beginning of foam collapse, was approximately equal to the compression strength, as determined from the stress plateau The duration of the plateau depended on the density of the foam sample, while the stress level o f the plateau was affected by foam structure, heat treatment, and orientation [136, 152]. Finally, the plateau ended and the stress began to rise sharply (region III), as the cell walls were completely collapsed and impinged. The strain rate dependence of the yield strength (a*) is shown in figure 5.22. The dependence is bilinear, showing a marked change in slope at a strain rate o f-3.3 x 10'2 sec*1 . For lower strain rates (< 3.3xl0*2 sec*1 ), the yield strength shows a weak dependence on strain rate, while at higher strain rates, the dependence is stronger. For closed-cell foams of low density, the yield strength should show a linear dependence on the relative density [19,21,159,160], given by 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 700 600 ■ ----- steel Foam (Relative Density=0.45) 500 "a ^ 400- 1 1 1 / ¥ £ 300 - (0 200 - I n 100 - 60(Y.S) 0 - 0.0 0.2 0.4 0.6 0.8 Strain Figure 5.21 Stress-strain curve of steel foam and A1 foam. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where o* is the yield strength of the foam 0 y s is the yield strength of the cell wall material p* is the density of the foamed material p, is the density of the cell wall material, and a i and a 2 are constants. These equations are developed assuming uniform thickness within the cell walls and cell wall junctions. The controlling deformation mechanism in closed-cell foam is membrane stretching, while beam bending is the primary deformation mechanism for open-cell foam deformation [21,161]. However, the compression test results show that the yield strength is smaller than the values predicted by equation (48). This discrepancy is mainly due to morphological defects, discussed in chapter S.4.S, such as curves and kinks that make the process of cell buckling easier. [ 159] The relationship between the foam yield strength and strain rate is given by [21] f • > (49) where (<r^ y represents the yield strength of the metal at OK A and ea are cell wall material properties Tm is the melting point of the metal, and 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. s is the strain rate From equation (48), the yield strength of foam (o^*) is directly proportional to the yield strength of the bulk metal that comprises the cell walls. Therefore, ays* should increase linearly with the log of the strain rate ( e ). However, the results shown in figure 5.22 indicate that the relationship between yield strength and strain rate is bilinear, with a transition at a strain rate of 3.3xl0*2 sec'1 . From this observation, it can be assumed that the deformation mechanism(s) in steel foam is strain rate dependent. The results presented in figure 5.22 can be understood in terms of the operative deformation mechanisms and the associated strain rate dependence. During compression loading, deformation occurs by buckling of cell walls and stretching of faces [21]. However, because of the presence of weak cells, strain tends to be localized. The collapse of a weak cell is followed by collapse of cells in close proximity in coordinated fashion, leading to the formation of discrete bands of deformation. Deformation proceeds by the successive formation of such bands, as reported previously [136]. Clearly, the local strain rate within deformation bands is larger than the nominal or global strain rate. According to Klintworth and Stronge, at sufficiently high strain rates, buckling of cell walls is resisted by inertia, leading to a phenomenon known as micro inertial hardening [162]. The phenomon derives from the geometry of the deformation mode, in which cell walls rotate about plastic hinges. Microinerdal hardening reportedly tends to diffuse strain localization, causing the yield strength to increase at higher strain rates. Their theory was supported by experiments on aluminum 149 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 90 - £ 80 - s t 70 ■ c 1 60 - (0 ■o $ 50 - 40 • 30 - 1e-5 1e-4 1a-3 1e-2 1e-1 1e+0 1e+1 Strain Rate (sec1 ) Figure 5.22 Yield strength (a*) with different strain rates (sec'1 ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. honeycomb. In the present experiments on steel foam, cell wall buckling is also the primary mechanism of deformation. Thus, the stronger dependence of yield strength on strain rate evident at higher strain rates (figure 5.22) is attributed to microinertial hardening [162]. S.4.4 Variation of energy absorption capacity with strain rate One of the critical performance metrics for metallic foams is the energy absorption capacity and its dependence on strain rate. The energy absorption capacity is defined as the energy necessary to deform a given specimen to specific strains, and is used to compare foams of different density. The energy absorption per unit volume, W, is given by the area under the stress-strain curve, or simply by [26] W = [ D a(e)de (50) where the upper limit of integration, sD , is the densification strain, which marks the end of the stress plateau. Typical values eD for steel foam are -50%. Figure 5.23 shows the variation of energy absorption (IV) with the strain rate (s ) during deformation of steel foam samples with a relative density o f0.53-0.54. The energy absorption was measured up to a compression strain of 50%. The graph indicates that energy absorption increases linearly with increasing strain rate throughout the range of strain rates selected. This behavior contrasts with the strain rate dependence of yield strength shown in figure 5.22, which is distinctly bilinear. The difference in the relationships stems from strain 1S1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1 0 100 n E -» 2 c o Q. w O 5 < >* S » o c UJ 1e- 2 1e+ 0 1e+ 1 1e-5 1e-3 Strain Rate Figure 5.23 Energy absorbed (W) by various strain rates (sec'1 ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. localization during deformation, which may contribute to the uniform increase in energy absorption. Local effects, such as localized heterogeneity and stress concentrations, have a significant effect on the yield strength, which depends on the weakest cross-section of the sample. However, the entire sample absorbs energy throughout the deformation process. Thus, the energy absorption dependence on strain rate at higher strain rates is less than that of the yield strength. The majority of the energy during deformation is irreversibly converted into plastic deformation energy [26]. This occurs primarily in the broad stress plateau and imparts a large capacity for energy absorption. During the stress plateau, cell walls absorb energy by buckling and collapsing. When this mechanism is exhausted, the stress begins to rise, and the material undergoes densification. The magnitude (height) of the stress plateau is strongly affected by the intrinsic yield strength of the metal, while the duration (length) increases with decreasing relative density. Meanwhile, the energy absorbed generally increases substantially with increasing foam density [134,145]. 5.4.5 Morphological defects A simple cubic cell model proposed by Ashby and Gibson predicts the equation (46) that shows relationship between the foam yield strength and the relative density. Here, the parameter 4 is defined as a distribution constant representing the fraction of solid material contained in the cell edges. The distribution constant is bounded by the equation (47). One limiting case is when 4=1, which corresponds to an open-cell foam. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For closed-cell foams, 4 is less than 1, and smaller values of ^ correspond to foams with thinner cell edges. Equation (46) and equation (48) assume an "ideal" cell structure comprised of straight cell walls and edges of uniform thickness. However, most metal foam structures exhibit morphological defects that diminish the yield strength [19,151, 163,164]. Consequently, yield strength is not always accurately represented by these equations. The primary defects responsible for the disparity between theoretical predictions and measured yield strengths are curved and corrugated cell walls, thin or missing walls, and high relative density domains [154, 165]. Recent theoretical modeling has attempted to elucidate the effects of morphological defects in foams [19,151,159], and two important effects of structural defects have emerged. First, as cell walls are uniformly thinned and material is relocated to the nodes, the strength does not decrease until the walls become very thin relative to the cell diameter (negligible wall thickness). The relative insensitivity of the strength to the distribution of material within the cellular structure is attributed to resistance of cell nodes (edges) to bending effects. However, curved or corrugated cell walls can markedly reduce the yield strength, and this is the second effect [137, 165]. If closed-cell foams have straight walls and nodes with uniform thickness then the yield strength approaches the theoretical value that is calculated by equation (48). However, elliptical cells typically have nodes with large entrained angles, as explained below. Such nodes are subject to appreciable bending moments. The inference is that cell ellipticity results in bending effects that reduce the yield strength [20,151]. 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The task of measuring cell wall curvature in steel foam requires a framework to define the geometric parameters of interest. Assuming a constant radius-of curvature, figure 5.24 shows that cell wall curvature can be defined by an enclosed angle 0, given where 0= enclosed angle A = triangle area L = base of triangle Simon and Gibson suggested that the enclosed angle, 0, is related to the normalized curvature parameter L/2R by [19] where the R is the radius of curvature. Thus, in a spherical cell, 0 would be 45°, and LflR would be 0.414. These relations provide a basis for quantifying simple structural defects in foam. Cell wall curvatures within steel foam samples had a significant effect on the measured yield strengths in the present study. Two steel foam samples (A and B) were prepared with different cell wall curvatures and equivalent density (3.77 g/cm3 ). Figures 5.25 and 5.26 show histograms of the enclosed angles for cells in samples A and B, respectively. Sample A has relatively low curvatures, such that -77% of the cells exhibit enclosed angles of less than 50°. In contrast, figure 5.26 shows that sample B exhibits by [167] (51) (52) ISS Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.24 Method for measuring cell wall curvature 156 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 d >* u c o 3 v S 18 - I 16 14 12 ■ 10 ■ 8 - 6 ■ 4 2 0 20 40 60 80 Curvature Distribution (Degree) 100 Figure 5.25 Curvature distribution for steel foam sample A Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 20 - d § 3 < x 9 15 - 10 5 - 20 40 60 80 Curvature Distribution (Degree) 1 0 0 Figure 5.26 Curvature distribution for steel foam sample B Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. higher curvatures, such that only -40% of the cells have enclosed angles of less than 50°. The yield strength of both samples was determined from compression tests, and the relative yield strength versus relative density is plotted in figure 5.27. The yield strength of sample A was -50% higher than that of sample B, a fact attributed to the greater number of high-curvature cells, noted above. Also plotted on the graph are the theoretical predictions of Gibson and Ashby’s model for closed cell foam. From equation (46), the yield strength for closed-cell foam was calculated using $=0.8 (previous measurements indicated $=0.77) [136]. Comparison of samples A and B indicates that the yield strength of sample A is closer to the value of closed-cell foam predicted from Equation (46). Irregularities in the cell wall topography constitute a second important morphological defect that causes yield strength reduction. Differences in cell wall configuration were associated with the methods used to mix the powders and foaming agent [152], as shown in figure 5.28. Type I foam (produced from powders blended by drill mixing) exhibited smooth cell walls with few surface irregularities (figure 5.28(a)). Type II foam (ball milling) showed a much different cell structure in which most of the cells showed cell wall irregularities, as shown in figure 5.28(b). Finally, in type III foam (cryomilling), nearly all of the cells showed irregular (non-spherical and non-ellipsoidal) configurations with "corrugated” cell walls (figure 5.28(c)). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Relative strength ( c tV c j ) 0.1 Sample A # Sample B ■ 0.05 0.02 0.5 0.4 R elative d e n sity (p’/p#) Figure 5.27 Relative strength versus relative density for steel foam sample A and B (density = 3.78 g/cm3 ). The solid line represents the prediction of closed cell with $=0.8. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.28 Three samples with different cell wiggles: (a) Type I (drill mixing) (b) Type II (Ball-milling) (c) Type ID (Cryomilling) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Compression tests performed on the three types of foam revealed markedly different density dependence, as shown in figure 5.29. Types II and III showed similar yield strengths, both of which were considerably lower than those of type I. The noted similarity is attributed to the presence of corrugated cell walls in both types o f foam. Nearly all o f the cell walls in type III foam were corrugated, resulting in the lowest yield strength of the three types. Type I foam appeared to show the strongest density dependence, presumably because the morphological defects present in types II and III facilitated cell wall collapse at lower stress levels, masking the density dependence. 5.4.6 Conclusion In the present work, steel foams fabricated by a P/M route showed a bilinear dependence of yield strength on strain rate. The bilinear response was directly related to the geometry of the mode of deformation, which was characterized by cell wall resistance to rotation. Microinertial resistance to rotation caused steep increases in yield strength at high strain rates. This is particularly significant because energy absorption is a key characteristic of steel foam for the envisioned applications. Because of the increased energy absorption at high strain rates, steel foam may provide effective protection against impact In particular, the energy absorption efficiency could be employed in automotive structures (e.g., side impact bars) to improve crash energy absorption while simultaneously reducing noise and vibration. 162 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Strength (MPa) 10U - • Type 1 (Drill mixing) 160 - ■ Type I I (Ballmilling) • 140 - a Type I I I (Cryomilling) e 120 - e 100 - e e a 80 • e 60 - e 40 - * 20 - e 0 ■ « i « ' ■ 2 3 4 5 6 Density (g/cm3 ) Figure 5.29 The yield strengths for three samples: type I (•), type II (■), and type III (▲) 163 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The effects of morphological defects, such as cell wall curvature and kinks, on the yield strength of steel foam was also investigated. The compressive yield strength was roughly an order of magnitude lower than those predicted by the Gibson-Ashby model [21]. The discrepancy between prediction and observation implies that the presence of curvature and kinks in the cell walls may be partly or largely responsible for lower-than- expected yield strengths. Morphological defects create localized heterogeneity and stress concentrations. These local effects degrade the yield strength, which depends on the strength of the weakest cross-section of the foam. Presumably, considerable improvements in mechanical properties can be achieved by removal of such the morphological defects. Future efforts should concentrate on elimination of defects through improved process control. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6. GASAR POROUS Mg 6.1 Introduction Recently, porous metals and ceramics have been made by a GASAR process that is a novel solid-gas eutectic solidification process. The GASAR process was developed by Shapovalov at the Dnepropetrovsk Metallurgical Institute (DMI) in the Ukraine [10]. A liquid metal saturated with hydrogen in a metal-hydrogen system is cooled through the eutectic point. The solidification of the metal and nucleation of pores occur simultaneously at the eutectic point, and pores develop from the diffusion of gaseous hydrogen out of the melt as it freezes. [10] The purpose of the present work was to investigate the microstructure o f GASAR Mg and AZ31 Mg alloy. The intent was to explore the microstructural features in the vicinity of pores to gain better understanding of the mechanisms involved in pore formation, which in turn would suggest improvements in processing methods. 6.2 Experiments GASAR Mg and AZ31 Mg alloy specimens were supplied by NRL (Naval Research Lab). Cylindrical specimens 8 cm long by 2cm were sectioned longitudinally and transversely. First, each sample was cut 2.5 cm from the “chill end” of the mold (sample #1). The chill end of the mold was the first to contact the cooling sink. The solidification front originated at this end and moved through the sample along its length. Following the first cut, a second cut was made 3.5 cm from the cooled end (sample #2), 165 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. then 5 cm from the cooled (sample #3), and finally 6 cm from the cooled end (sample #4). Figure 6.1 shows the sectioning of sample. A total of four cuts were made using a low-speed diamond saw, resulting in five pieces. Afterwards, sample edges were beveled to remove rough edges and facilitate polishing. Glycol was used exclusively to disperse the diamond polishing abrasives. After each samples were cleaned ultrasonically in ethanol for 5 min. Samples were examined by conventional metallography and TEM. TEM samples were prepared by ion milling. Cold End 1 f p 2.5cm ^ c n T " 1.5cm" ^cm* Sample Number ► 1 2 3 4 Figure 6.1 Sectioning of samples 166 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.3 Porosity and pore size distribution Mg and AZ31 Mg alloy exhibited different pore structures and sizes. In each material, porosity and pore size varied with distance from the chill end (sample number). Mg exhibited more uniform porosity than AZ31. Figures 6.2 shows the pore distributions in Mg. 63.1 Porous Mg Near the chill end, the pore distribution is fairly uniform except in the peripheral region, where the sample is almost pore-free (figure 6.2(a)). The distribution of pore sizes is shown in the accompanying histogram, which shows that most of the pores are under 200 pm. The pores are roughly cylindrical and extend up to 2.5 cm along the cylinder axis. As the distance from the chill end increases, the pore distribution becomes less uniform. Figure 6.2(b) shows sample #2 (3.5 cm from the chill end). The peripheral region (1mm thick) is virtually pore-free, while the core region exhibits a few large spherical pores over 500 pm in diameter. The distribution of pore sizes is similar to sample #1, although there are more large pores (over 200 pm). Sample #3 confirms the trend, as shown in figure 6.2(c). The pore distribution is highly non-uniform, and the pore-free annul us is -2.5 mm thick. Numerous micropores (>10 pm) were observed, although the 16 large pores accounted for much of the pore volume and were distributed throughout the cross-section. 167 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The shape of the pores varied with the radical position. Near the center, pores were cylindrical less than 1.5 cm in length, while beyond the mid-radius, the pores ranged from spherical to radially elongated. Finally, at 6 cm from the shill end, the pore distribution was dominated by large radial elliptical pores in peripheral regions, accompanied by micropores (>10pm), shown in figure 6.2(d). The core region showed cylindrical pores, although much shorter in length than in previous samples. 6.3.2 Porous AZ31 The pore distribution in AZ31 was coarser than in pure Mg, as shown in figure 6.3, taken 2.5cm from the chill end. The pore sizes ranged from 10pm to 2 mm in diameter, although most were in the range of 0.1-0.5 mm in diameter. The largest pores were cylindrical and less than 1 cm in length, while the small pores tended to exhibit irregular shapes. With increasing distance from the chill end, the pore distribution became less uniform and more bimodal, with few large pores, and numerous much smaller pores. Irregular pore shapes can result from exposure of grown-out dendrites. [168] Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 35 g * s 28 5 20 I* £ 10 . 5 MO S O - 100- 180- 200- 280- 300- 360- 100 180 200 280 300 . 300 480 Dlomotois (mJcrooMter) (a) Figure 6.2(a) Picture of transverse section and fraction of pore diameters: sample number 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4° r 38 • 3? 30 g a 5 20 • 5 ■ 040 S O - 100- 180- 200- 280- 300- 380- 100 180 200 280 300 .360 480 Diamatofi (micro motor) Figure 6.2(b) Picture of transverse section and fraction of pore diameters: sample number 2 0 (b) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 a s .5 0 040 S O - 100- 190- 200- 290- 300- 300- 100 1 » 200 290 300 300 460 OlaiMtora (micranwtar) (c) Figure 6.2(c) Picture of transverse section and fraction of pore diameters: sample number 3 1 7 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MO 50- 100- 150- 200- 250- 300- 350- 100 150 200 290 300 350 480 DUmu t u r u (mierom tCr) (d) Figure 6.2(d) Picture of transverse section and fraction of pore diameters: sample number 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 63(a) Pictures of transverse section of AZ31 Mg alloy: sample 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (b) Figure 63(b) Pictures of transverse section of AZ31 Mg alloy: sample 2 174 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (C) Figure 63(c) Pictures of transverse section of AZ31 Mg alloy: sample 3 175 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.4 Microstructure 6.4.1 Porous Mg The micrographs of porous Mg specimens are shown in figure 6.4(a). The transverse sections of the porous specimens reveal that several pores are contained within each grain and that the grain boundaries run from one pore to the next. Simone showed similar micrographs (e.g., sample 4), which appear both intragranularly and along grain boundaries, as shown in figure 6.4(b) [19]. 6.4.2 Porous AZ31 Optical micrographs reveal the metallurgical structure of AZ31. Figure 6.4(c) shows a dendritic structure typical of sand-cast or gravity-die-cast Mg alloys such as AZ91 or AZ80 [168,169]. The dendrites are a-Mg with intergranular P-Mgi7Ali2. In the cast state, the P-phase MgpAlu appears in alloys containing more than 2 % aluminum [169]. The grain size is fairly large in comparison with the coarse grains in die castings. However, the microstructure close to the pores shows much smaller grain sizes (less than SO pm), also confirmed by TEM observations, as discussed below. TEM analysis was performed on AZ31 porous samples, and attention was focused on two areas - the dense annular peripheral area and regions immediately adjacent to pores. The peripheral region exhibited extensive deformation and twinning, as shown in figure 6.5 (a). [170, 171] From electron diffraction pattern and x-ray spectral analysis, this phase is MgnAlu. However, the microstructures are different near the pores. The 176 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 6.4(a) Micrographs showing pores in porous Mg Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (b) Figure 6.4(b) Micrographs showing micropores in porous Mg 178 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (C) Figure 6.4(c) Micrographs showing porous AZ31 Mg alloy 179 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. grain size is smaller and twinning is absent, as shown in figure 6.5(b). The small grain size is attributed to the pressure near the pores, which is relatively higher in the core region than in peripheral regions. Two interesting results should be noted. First, apparent cracks, possibly “gas tracks”, exist near the pores. The features are ~800 pm long by 10 pm across. Some areas show a rather large crack, and the grain size in the adjoining material is small (figure 6.6(a)). Other areas, such as figure 6.6 (b), exhibit a vein-like network of fine parallel cracks, with fine grain sizes (less than 5 pm). The boundary between coarse- and fine- grain regions is shown in figure 6.7(a). EDS spectral analysis shows substantial oxygen content in the fine-grain area. Electron diffraction and EDS analysis led to identification of the coarse- and fine-grain phase as MgpAlu. The typical SAD ring pattern is shown in figure 6.7 (b) and 6.7(c), where the spottiness of the rings arises from the small grain size [171]. Secondly, there exist two ternary intermetallic phases within the alloy, identified by diffraction and EDS as Mg3 2((Zn,AL)4 9 ) and Mg$Zn2Al2. Figure 6.8 shows a region of both ternary intermetallic phases. The small dark area is Mg3 2((Zn,Al)4 9), while the large grain is Mg$Zn2Al2 phase, the MgnAlu phase, and liquid at 393° C. The M gsZ^Ah phase crystallizes directly from liquid within a relatively narrow range of compositions [172]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) Figure 6.5(a) TEM pictures: peripheral region 1 8 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (b) Figure 6.5(b) TEM pictures: Near the pores 182 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100/MI (a) Figure 6.6(a) TEM pictures: large gas track 183 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (b) Figure 6.6(b) TEM pictures: Vein-like network of fine gas track 184 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) (b) (c) Figure 6.7 TEM picture: (a) The boundary between coarse- and fine-grain regions (b) SAD ring pattern for coarse-grain regions (c) SAD ring pattern for fine-grain regions I8S Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 6.8 The ternary intermetallic phases Mgi2 ((Zn,Al)4 9 ) and MgsZ^Ah 186 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.5 Conclusion Microscopic studies of GASAR process Mg ingots have demonstrated the presence of different pore size ranges. The pore distribution depends on the distance from the cold end of ingots. Porous Mg shows more uniform pore size distribution than the porous AZ31 Mg alloy. TEM observations revealed different microstructures in the predominantly solid area and the regions near the pores. Also, TEM revealed two interesting facts: one is the crack lines (gas marks) near the pores and the other is the ternary phases in the sample. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7. Summary and conclusion Steel foams with relative densities of <0.5 were synthesized by a PM process. Both the mixing process and the heating procedure (particularly the time at temperature above Tm ) had major effects on foam density, although the compaction pressure did not The pore size distribution within the foam was somewhat coarse, and clearly greater process control will be needed to achieve more uniform pore structures. Despite the coarse and irregular pore structures of the foams, the compression stress-strain curves showed the distinctive stress plateaus characteristic of metallic foams with more uniform pore structures. The stress-strain response was strongly affected by annealing, which reduced carbon content and replaced much of the pearlitic structure with ferrite. This appeared to enhance the ductility of the cell walls and altered the mechanism of cell wall collapse, thereby greatly increasing the energy absorption during compression loading. The response during compression loading indicated that substantial energy absorption capacity was possible in metallic foams, even with thick cell walls. Further substantial improvements in energy absorption behavior should be possible by reducing the cell wall thickness and density of the foam, and improving the pore size uniformity. Steel foam synthesis requires careful control of process parameters to prevent pore coalescence during foam expansion. In the present work, two of these parameters were investigated and optimized, and a novel method for constraining pore growth during foam expansion was implemented. One of the critical processing challenges is preventing pore coalescence and collapse during the expansion. This can be accomplished by 188 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. increasing the melt viscosity, extracting heat (freezing) more quickly, and/or limiting the coalescence of pores through barriers or constraints, such as the interlayer membranes. In spite of the relatively coarse pore structures of the steel foams produced in this work, the resulting foams showed characteristic foam-type mechanical response to compressive loading, with a long stress plateau during which cell walls underwent buckling. This indicates that considerable improvements in mechanical properties are possible with greater uniformity of the pore structure. Steel foams fabricated by a P/M route show distinct anisotropy when subjected to uniaxial compressive loading. The foams are ~3x stronger in the transverse direction than in the longitudinal direction, and exhibit a more pronounced yield point drop. The anisotropic response is directly related to the foam structure, which is characterized by ellipsoidal cells with thick walls extending transverse to the foaming direction. In both orientations, behavior is described by a power-Iaw with a similar stress exponent (n = 1.8). The distinctly different structure of steel foam, with its thick cell walls and irregular cell geometry, will require a different model based on a more realistic relation between microstructure, deformation mechanisms, and plastic response. Plastic deformation of steel foam is characterized by strain localization and occurs in a characteristic sequence. The first step is elastic deflection of the cell elements, followed by localized deformation in a few cells. Collapse and densification of cells leads to the initiation of a deformation band, which gradually spreads across the sample. The deformation mechanism proceeds in a sequential manner with repeating cycles of yield, collapse and densification of cells. 189 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Steel foams showed a bilinear dependence of yield strength on strain rate. The bilinear response was directly related to the geometry of the mode of deformation, which was characterized by cell wall resistance to rotation. Microinertial resistance to rotation caused steep increases in yield strength at high strain rates. This is particularly significant because energy absorption is a key characteristic of steel foam for the envisioned applications. Because of the increased energy absorption at high strain rates, steel foam may provide effective protection against impact. In particular, the energy absorption efficiency could be employed in automotive structures (e.g., side impact bars) to improve crash energy absorption while simultaneously reducing noise and vibration. The effects of morphological defects, such as cell wall curvature and kinks, on the yield strength of steel foam was also investigated. The compressive yield strength was roughly an order of magnitude lower than those predicted by the Gibson-Ashby model [9]. The discrepancy between prediction and observation implies that the presence of curvature and kinks in the cell walls may be partly or largely responsible for lower-than- expected yield strengths. Morphological defects create localized heterogeneity and stress concentrations. These local effects degrade the yield strength, which depends on the strength of the weakest cross-section of the foam. Presumably, considerable improvements in mechanical properties can be achieved by removal of such the morphological defects. Future efforts should concentrate on elimination of defects through improved process control. The anisotropic character of steel foam might one day provide design engineers greater freedom than possible with isotropic foams. For example, mechanical anisotropy 190 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. should make it possible to soften structures selectively, thus forcing loads away from highly stressed areas. Similarly, strain localization might make certain manufacturing operations more tractable, such as repairs, joining, and machining. For example, strain localization might make it feasible to selectively density certain locations within a component, which could then be machined or welded more readily. In any event, both anisotropy and strain localization must be well understood to effectively implement steel foam into future engineering applications. The most likely applications are ones in which weight savings translate into significant performance gains, and those in which energy absorption is important. Foreseeable applications in the automotive industry include engine valves, camshafts, wheel rims, and door intrusion beams. Finally, the method employed for making steel foam is simple and is potentially affordable for small-to-midsize parts, provided process controls can be implemented without adding too much additional cost. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. REFERENCES [1]. H.G. Allen, “Analysis and Design of Structural Sandwich Panels”, Pergamon Press (1969) Oxford. [2]. M.F. Ashby, Met. Trans. 14A (1983) 1755. [3]. J.D. Currey, “Mechanical Adaptations of Bones”, Princeton University Press (1984) Princeton, NJ. [4]. L.J. Gibson, M at Sci. Eng. A110 (1989) 1. [5]. G.C. Kiessling, Modern Packaging, 35(3A) (1961) 287. [6]. J.D. LeMay, R.W. Hopper, L.W. Hrubesh and R.W. Pekala, M at Res. Soc. Bull. 15 (12)(1990)19. [7]. R.E. Mark, “Cell Wall Mechanics of Tracheids”, Yale University Press (1967) New Haven, CT. [8]. S. Semerdjiev, “Introduction of Structural Foams”, Society of Plastics Engineers (1982) Brookfield Center, CT. [9]. D.W. Shaefer, Mat. Res. Soc. Bull. 19(4) (1994) 14. [10]. V. Shapovalov, Mat. Res. Soc. Bull. 19(4) (1994) 24. [11]. F.A. Shutov, Advances in Polymer Science, 51 (1986) 155. [12]. K. Sieradzki, D.J. Green and L.J. Gibson, Mat. Res. Soc. Sym. Proc. 207 (1991). [13]. B.C. Wendle, “Engineering Guide to Structural Foams”, Technomic Publishing Co. (1976) Westport, CT. [14]. L.J. Gibson, M.F. Ashby, Cellular Solids, Oxford (1988). [15]. B.C. Allen, US-Patent 3,087,807 (1963). [16]. J. Baumeister, German Patent DE 41 01 630 (1991). 192 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [17]. C.J. Yu, H.H. Eifert, M. Knuewer, M. Weber, J. 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Park, Chanman
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Development of steel foam processing methods and characterization of metal foam
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