1998 MRS Spring Meeting & Exhibit

Chairs 

Anthony Evans 
Div of Applied Science 
Harvard Univ 
Cambridge, MA 02138 
617-496-0424

Daniel Schwartz
McDonnell Douglas Aerospace
MC S111-1041
St. Louis, MO 63166-0516
314-232-6835

Donald Shih 
McDonnell Douglas Aerospace 
M/C S111-1041 
St. Louis, MO 63166-0515 
314-232-9202

Haydn Wadley
Dept of MS&E
Univ of Virgina
Charlottesville, VA 22903
804-982-5671

Symposium Support 
*Army Research Office 
*Office of Naval Research 
*NASA Langley Research Center 

* Invited paper

SESSION R1: MECHANICAL BEHAVIOR OF SOLID FOAMS: 
THEORY AND GENERAL OBSERVATIONS 
Chairs: R. Crowe and Anthony G. Evans 
Monday Morning, April 13, 1998 
Nob Hill A

8:30 AM *R1.1 
INFLUENCE OF IMPERFECTIONS ON EFFECTIVE PROPERTIES OF CELLULAR SOLIDS. Joachim L. Grenestedt, Royal Institute of Technology, SWEDEN. 

Closed cell metal foams generally have lower relative stiffness and strength than for example closed cell expanded PVC based polymer foams. We believe that the reason for the poorer performance of the metal foams is due to "imperfections" in the cell geometry. Real cellular solids are far from perfectly ordered structures, and a number of deviations or imperfections can be identified. For example, all cell walls in real foams typically do not have the same thickness. Other imperfections are wavy distortions of the cell walls, and non-uniform size of the cells. In the present paper, a perfectly ordered closed cell structure is first analyzed. Each of the above imperfections are then introduced, and the influence to the different imperfections is quantified. Most of the analyses performed until now regards influence of imperfections on stiffness. However, some results for the influence of imperfections on strength will also be presented. 

9:00 AM R1.2 
MECHANICAL PROPERTIES OF A STRUCTURAL POLYURETHANE FOAM AND THE EFFECT OF PARTICULATE LOADING. S.H. Goods, C.L. Neuschwanger and L.L. Whinnery, Sandia National Laboratories, Livermore, CA. 

The room temperature mechanical properties of a closed-cell, polyurethane encapsulant foam have been measured as a function of foam density. Tests were performed on both unloaded and filler reinforced specimens. Over the range of densities examined, the modulus of the unloaded foam could be described by a power-law relationship with respect to density. This power-law relationship was the same for both tension and compression testing and could be explained in terms of the elastic compliance of the cellular structure of the foam using a simple geometric model put forth by Gibson and Ashby. The collapse stress of the foam was also found to exhibit a power-law relationship with respect to density. Additions of an aluminum powder filler increased the modulus of the foam in a manner that could be explained by the work of Nielson, most often used to describe the influence of a dispersed particulate phase on fully dense materials. 
This work supported by US DOE Contract No. DE-ACO4-94AL85000 

9:15 AM R1.3 
SCALING OF ELASTIC MODULUS IN CELLULAR STRUCTURES. John H. Kinney and Anthony J.C. Ladd, University of Florida, FL. 

Cellular materials are usually modeled as idealized networks, with either open-cell or closed-cell architectures. In three dimensions these models lead to quadratic scaling of the elastic modulus with material density. However, actual cellular foams are often hybrid structures with features of both open and closed cell networks. Experimental measurements on trabecular bone show a range of scaling exponents, from linear to cubic, depending on the geometric structure of the network. A finite element model was used to explore the relationship between trabecular bone density and elastic modulus. Specimens of human trabecular bone were three-dimensionally imaged at a resolution of  with synchrotron microtomography, and incorporated into the finite element model. Density scaling of the modulus was explored by uniformly thinning or thickening the trabecular structure. A power law scaling of the elastic modulus with trabecular bone density was observed, but the scaling exponent varied with specimen and with the orientation of the load axis. Along the primary load axis of the bone the scaling was nearly linear; whereas in other directions the scaling exponent was greater than quadratic. These observations suggest that biological structures may organize their architecture to more efficiently distribute external loads. Even in metallic foams deviations from quadratic scaling were observed; in a comparison study of an aluminum foam, the scaling exponents were invariably greater than 2. We speculate that the failure of idealized models to accurately predict the density dependence of the elastic modulus in metallic foams has its origins in the geometric structure of the joints. X-ray tomographs show a significant taper in the joints and struts; thus during a uniform surface thinning the effective aspect ratio of the struts increases. This may cause an additional softening of the structure, beyond that predicted by idealized models. 

9:30 AM R1.4 
MODELLING OF STRENGTH OF HIGHLY POROUS BUILDING MATERIALS. Thomas Schneider and Peter Greil, University of Erlangen Nuernberg, Department of Materials Science (Glass and Ceramics), Erlangen, GERMANY; Georg Schober, Hebel AG, Materialtechnische Entwicklung, Fuerstenfeldbruck, GERMANY. 

The development of highly porous building materials like aerated autoclaved concrete faces two competitive physical properties: low thermal conductivity and high mechanical strength, which both strongly depend on porosity. While the volume fraction and size of the so called air pores can be controlled in the production process, there is greate interest in optimizing pore size distribution for improved compressive strength of highly porous materials. Finite element calculations were used to investigate the influence of porosity distribution on the compressive strength of aerated autoclaved concrete. Considering the hirarchical pore structure of aerated autoclaved concrete the strength is characterized by the failure probability calculated using FEA and multiaxial Weibull theory. Calculations of failure probability of microstructure with ordered as well as random pore configurations show a dependence of compressive strength on the Weibull modulus of the matrix material and the size and arrangement of pores. The results of the calculations are compared to experimental data of aerated autoclaved concrete. 

10:15 AM R1.5 
FATIGUE OF CELLULAR MATERIALS. Jong-Shin Huang, Jin-Yuan Li, National Cheng Kung University, Department of Civil Engineering, Tainan, TAIWAN. 

Cellular materials are increasingly being used as a load-bearing component in lightweight structures. The fatigue failure of cellular materials might lead to a catastrophic fracture of the lightweight structures. The expression for crack propagation rate of cellular materials with a macro-crack is first derived by using dimensional arguments analysis. In the study, it is assumed that the macro-crack advances one cell size when the first unbroken cell wall ahead of the macro-crack tip ruptures after some cycles of loading. Theoretical modeling of foams for the cases of micro-crack propagation, high cycle fatigue and low cycle fatigue of the first unbroken cell wall is proposed and compared to existing experimental data of phenolic foams; the agreement is good. Results suggest that fatigue of cellular materials with a macro-crack depends on the range of cyclic stress intensity factor, the cell geometry and relative density of cellular materials, and the fatigue parameters of the solid materials from which they are made. Also, the modeling for cellular materials without any macro-crack is presented and compared to experimental data of cementitious foams, giving the dependence of fatigue life on relative density of foams and the fatigue parameters of solid cell wall materials. 

10:30 AM R1.6 
BUCKLING OF METAL FOAM CORE SANDWICH SHELLS. Ming Y. He, Materials Department, University of California, Santa Barbara, CA; J.W. Hutchinson and Anthony G. Evans, Division of Engineering and Applied Sciences, Cambridge, MA. 

A study of cylindrical sandwich shells with foam metal cores is carried out with emphasis on buckling resistance under axial compression. Comparative performance with monocoque and stiffened cylinders is detailed. Earlier work has shown that perfect sandwich shells which buckle in the elastic range can be significantly lighter in weight than their axially stiffened counterparts. The emphasis in this work is on the role of plasticity and imperfections in eroding the buckling strength, and, in particular, on role played by the elastic-plastic properties of the metal foam. Guidelines emerge for foam properties required to give superior performance of the sandwich shells. 

10:45 AM R1.7 
ANALYSIS OF DEFORMATION OF POROUS METALS. Dong Nyung Lee, Kyu Hwan Oh, Division of Materials Science and Engineering and Center for Advanced Materials Research, Seoul National University, Seoul, KOREA; Heung Nam Han, Research Center for Thin Film Fabrication and Crystal Growing of Advanced Materials, Seoul National University, Seoul, KOREA; Hyoung Seop Kim, Department of Materials, Oxford University, Oxford, UNITED KINGDOM. 

Various yield criteria for porous metals hav been reviewd. The elasto-plastic finite element method for the deformation of porous metals was developed using the yield criterion proposed by Lee and Kim. The simple upsetting, indening and ring compression have been analysed by the elasto-plastic finite element method. Changes in geometries and densities of porous metals in simple upsetting, and upsetting loads with upsetting strain have been calculated. The Brinell hardnesses of porous metals with various densities dependent on indenting geometries have been analysed. The changes in geometry of porous metal rings with initial relative density were calculated for various friction coefficient could be determined from the relationship between the change in the inner diameter and height reduction of porous metal rings with various initial relative densities. The thermomechanical elasto-plastic problems in hot forging of the porous metals have been analysed using the thermo-elasto-plastic finite element method. A hardening law of non-porous metal as functions of temperature, plastic strain and strain rate has been proposed. Thermomechanical response and densification behavior of the porous metals during hot forging have been calculated at various initial relative densities, strain rates and temperatures. The results calculated by finite element method were in very good agreement with the measured data. 

11:00 AM R1.8 
CONSTITUTIVE AND INDENTATION BEHAVIOUR OF FOAMED METALS. Ronald E. Miller and John Hutchinson, Harvard University, Division of Engineering and Applied Sciences, Cambridge, MA. 

Metallic foams exhibit a unique combination of mechanical, thermal and acoustic properties. Consequently, there has been considerable recent interest in the development of structural applications for metallic foams. Experimental studies of the plastic deformation of metal foams reveal important differences between their behaviour and that of both fully dense solids and other non-metal foams. These features include a difference between the yield stresses in tension and compression, and a lateral expansion that approaches zero under uniaxial compression. Clearly, any attempt to model the mechanical response of a foamed metal must assess the importance of these effects. In this work, we develop a constitutive model for metal foams within the framework of classical plasticity, and incorporate the aforementioned features that make the plastic flow of foamed metals unique. The model is used in a finite element study of the response of metal foams to indentation. The results provide interpretation of indentation experiments in light of the effects of foamed metal constitutive behaviour. As well, contact will be made with experimental indentation studies to build confidence that the proposed constitutive model is a reliable description of foamed metal plasticity. 

11:15 AM R1.9 
ON THE EFFECTIVE ELASTIC PROPERTIES OF POROUS STRUCTURAL CERAMICS PRODUCED BY PLASMA-SPRAYING. Alexander Wanner, Institut fuer Metallkunde, Universitaet Stuttgart, Stuttgart, GERMANY. 

Plasma-sprayed ceramic materials typically exhibit a porous, laminar microstructure, which is a direct result of the spraying process. Although the porosity of these as-sprayed materials is usually less than 20 vol.%, the effective elastic moduli may be more than one order of magnitude lower than those of corresponding fully dense materials. This pronounced modulus reduction is of key engineering importance but not fully understood. In the present work the amount and orientation dependence of the porosity-induced modulus reduction is investigated in detail. Results of elastic modulus measurements performed on a number of plasma-sprayed bulk ceramics in as-sprayed and in different post-sintered conditions will be presented. These measurements were accomplished using an ultrasonic phase spectroscopy method which is specially suited for tests on samples of porous, highly attenuating materials. The results show that the as-sprayed materials are highly anisotropic, with the lowest modulus parallel to the spraying direction. This can be explained by the preferential alignment of slit-like pores parallel to the substrate on which the material has been deposited. Upon heat treatment, a dramatic modulus increase and a reduction of anisotropy are observed. Microstructural studies as well as theoretical considerations show that this distinct change of elastic properties is primarily caused by the change of pore shape, while the decrease of the total volume content plays only a minor role. The consequences of the results for engineering applications of plasma-sprayed ceramics will be discussed. 

11:30 AM R1.10 
INDENTATION BASED CHARACTERISATION OF SEMI-CLOSED CELL MULLITE FOAMS. Michael Swain, Trevor Bell, CSIRO, Tellecommunications & Industrial Physics, Lindfield, AUSTRALIA, Jean-Marc Tulliani and Laura Montanero, Department of Materials Science and Chemical Engineering, Politechnico di Torino, Turin, ITALY. 

The micro and macro-mechanical properties of two mullite semi-closed cell foams prepared by replication of an elastomeric foam former have been investigted using instrumented indentation techniques. Using either a pointed or small spherical tipped indenter the intrinsic properties of the foam struts have been measured and compared with bulk properties of mullite prepared from the same powder. The macro properties were measured with a large sapphire spherical tipped indenter,   5 mm radius using a novel load partial-unloading technique. The measured average contact pressure at the onset of strut fracture throughout the course of an indentation test was found to be in very good agreement with the crushing strength of the ceramic foam. In a similar manner the measured mean effective modulus of the ceramic foam also agreed well with similar values from crushing or flexural tests of these materials. The results are discussed in terms of simple analytical treatments of the indentation of brittle porous materials. 

11:45 AM R1.11 
Abstract Withdrawn. 

SESSION R2: MECHANICAL PROPERTIES OF METALLIC FOAMS 
Chairs: Lorna J. Gibson and Joachim L. Grenestedt 
Monday Afternoon, April 13, 1998 
Nob Hill A

1:30 PM *R2.1 
MECHANICAL BEHAVIOUR OF ALUMINUM FOAMS. L.J. Gibson, Department of Materials Science and Engineering and A.E. Simone, Department of Civil and Environmental Engineering, MIT, Cambrige, MA. 

The compressive stress-strain responses of two closed-cell aluminum foams were measured. One foam was made by mixing silicon carbide particles in molten aluminum and blowing gas through the melt. The second foam was made by mixing calcium in molten aluminum to increase its viscosity and then adding powdered titanium hydride to the melt; on heating, the hydride decomposes to form hydrogen gas. The mechanical tests indicated that the Young's moduli and compressive strength were substantially less than those expected from existing models. There were a number of microstuctural features which contributed to the reduction in properties: variations in density and anisotropy, curvature in the cell walls and corrugations in the cell walls. Finite element models were developed to estimate the magnitude of the stiffness and strength reduction associated with each feature acting independently. The results of the models are consistent with the reductions in the measured properties. 

2:00 PM R2.2 
COMPRESSIVE, TENSILE AND SHEAR TESTING OF MELT-FOAMED ALUMINIUM. Heiko von Hagen, Wolfgang Bleck, Aachen University of Technology, Institute of Ferrous Metallurgy, Aachen, GERMANY. 

For structural applications, materials have to provide mechanical properties that are reliable for the user. Therefore the most suitable material parameters have to be determined for today's foams by material's testing and evaluation. The overall important influence of the foam density is mostly understood, but for construction purposes it seems to be important to get information about the possible influence of other parameters like the sample thickness on the mechanical properties and the deformation behaviour. Differences in the chemical composition of melt-foamed aluminium material are important for applications because they result in more ductile or more brittle failure mechanisms. The behaviour of aluminium foam samples under compressive, tensile and shear loads can be examined in the special testing methods for sandwich material as described in the German DIN- or the ASTM-standards. The test procedures according to DIN have been established at the Institute of Ferrous Metallurgy for the testing of metal foams and sandwich material (steel facesheets and aluminium foam core). A great number of aluminium foam samples of discontinuously processed melt-foamed material (Shinko-Wire) was tested to get information about the mechanical properties depending on the variation of density (0.2 to 0.43 g/ccm) and thickness (10 to 30 mm). The aim is to provide a complete database of the resulting mechanical properties in compression, tension and shear. Visualizing the results the most reliable and suitable material parameters regarding structural applications can be defined. Additionally samples of continuously melt-foamed material were tested to get information about the differences in mechanical properties and deformation based on the chemical composition and the foaming process. 

2:15 PM R2.3 
THE EFFECTS OF THERMOMECHANICAL PROCESSING ON THE RESULTING MECHANICAL PROPERTIES OF 6061 ALUMINUM FOAM. R.W. Margevicius, P.W. Stanek, and L.A. Jacobson, Los Alamos National Laboratory, Los Alamos, NM. 

The mechanical properties of foamed materials depend not only on such obvious factors as constituent metal or alloy and porosity but also on more subtle factors such as the processing method. Current foaming processes typically produce cellular materials that are approximately 10% of theoretical density, and making a foamed material with a higher density is not straightforward. The aim of the Los Alamos program is ultimately to produce beryllium and beryllium alloy foams that have relative densities higher than 10%. Thermomechanical processing is being evaluated as a potential means to increasing the density of conventionally produced foams. To gain an initial understanding of the effects of compaction of the 10% foams, 6061 aluminum foam was used as a surrogate for beryllium. Foamed alloy was obtained from a commercial vendor in the form of a 100x300x300 mm (4x12x12 inch) cast billet with a pore size of approximately 0.8 mm (20 pores per inch). Increasing the density of the foam was achieved by uni-, bi-, and triaxial compaction (compression, rolling, and HIPing) in the 25-500ƒC temperature range. Metallography and room temperature mechanical testing were performed to characterize both the starting and processed material. Results will be presented which critically compare the processed material to the starting material in terms of their microstructures and mechanical behavior (compression, toughness, and fatigue strength). 
2:30 PM R2.4 
Abstract Withdrawn. 

3:15 PM *R2.5 
COMPRESSIVE DEFORMATION AND YIELDING MECHANISMS IN CELLULAR Al ALLOYS DETERMINED USING X-RAY TOMOGRAPHY AND SURFACE STRAIN MAPPING. Hillary Bart-Smith, Ashraf F. Bastawros, Daniel R. Mumm, Anthony G. Evans, Harvard University, Division of Engineering and Applied Sciences, Cambridge, MA; David J. Sypeck, Haydn N.G. Wadley, University of Virginia, School of Engineering and Applied Science, Charlottesville, VA. 

The mechanisms of compressive deformation that occur in both closed and open cell Al alloys have been established. This has been achieve by using x-ray computed tomography (CT) and surface strain mapping to determine the deformation modes and the cell morphologies that control the onset of yielding. The deformation is found to localize in narrow bands having width of order of a cell diameter. Outside the bands, the material remains elastic. The cells within the bands that experience large permanent strains are primarily elliptical. Conversely, the cells that remain elastic are equiaxed, regardless of their size. The implications for manufacturing materials with superior mechanical properties are discussed. 

3:45 PM R2.6 
SHEAR PROPERTIES ON ALUMINIUM METAL FOAMS PREPARED BY THE MELT ROUTE. Ernesto Saenz, Pedro S. Baranda, UTRC, SPAIN; Jorge Bonhomme, ITMA, SPAIN; Petter Asholt, Hydro Aluminium, NORWAY. 

Tensile shear testing were performed on one alloy of Aluminium metal foam with different densities, supplied by Hydro Aluminium, to determine shear modulus and shear strength. The densities were 0.19 g/cm3 and 0.31 g/cm3. The base material of both alloys contained 15% (vol) of 13um SiC particles. Four panels of each density were tested according to ASTM C 273-61. The specimens were initially bonded on Aluminium plates but due to the plates deformation during the shear test they were bonded to steel plates. The relative displacement of the plates was measured using two extenssometers. Furthermore, with the objective to analyze the possible effect of the cell size distribution on shear properties, cell size and material distribution analyses were done in areas close to the samples. At high densities a fast failure was observed after the maximum shear load while at low densities the failure was progressive. The failures in both materials were located in areas with least number of cells. 

4:00 PM R2.7 
BENDING PROPERTIES OF FOAMED ALUMINUM PANELS AND SANDWICHES. Frantisek Simancik, Jaroslav Kovacik, Natalia Sralliakova, Institute of Materials and Machine Mechanics SAS, Bratislava, SLOVAKIA. 

Panels of aluminum foams are much stiffer than bulk aluminum sheets of the same weight. This is because a more preferable distribution of the metal along the neutral bending axis resulting in a higher cross sectional moment of inertia for the aluminum foam compared to the bulk Al-sheet. Since the foamed panels are usually covered by a dense aluminum skin they can easily be used in various structural applications where high stiffness at a low weight is essential. Experimental samples with a typical density of 0.5-0.8 g/cm³ were prepared from both cast and wrought aluminum alloys via the powder metallurgical route. In this case aluminum alloy powder is mixed with a foaming agent and continuously extruded into a foamable wire-shaped precursor. The precursor is then arranged in a special furnace and heated up to the melting temperature and foamed into panels up to 1000*1000 mm and 5 - 50 mm thick. Sandwiches with a foamed aluminum core were prepared simply by foaming cast aluminum alloy between two aluminum face plates. After the foaming, the face plates are diffusion bonded with the foamed core. This type of bonding enables a formability of the sandwich plate and results in a significant improvement of its mechanical properties and its thermal stability. Bending stiffness of the samples was determined by the four-point bending test. The influence of density, matrix composition, pore size and thickness of the foamed plate on its deflection or fracture was investigated. Up to the maximum possible deflection, limited by the testing tool, only cast alloy based foams have fractured. The samples based on wrought alloys as well as sandwiches have survived this deflection without significant cracks in the structure. It will be shown that the modulus of elasticity of the foam, which depends on its density, cannot be used for the calculation of the bending stiffness of the plates. This is because the apparent density of the plate is influenced by the surface skin on the foam, especially at small thickness. Therefore the cross-sectional moments of inertia were modelled for various square weights of foamed plates. 

4:15 PM R2.8 
HIGH CYCLE FATIGUE PROPERTIES OF ALUMINIUM FOAMS. Bernhard Zettl, Stefanie Stanzl-Tschegg, University of Agriculture, Institute for Meteorology and Physics, Vienna, AUSTRIA; Rudolf Gradinger, LKR-Centre of Competence on Light Metals, Ranshofen, AUSTRIA; H. Peter Degischer, Technical University Vienna, Institute of Material Science, Vienna, AUSTRIA. 

Aluminium foams produced from powder metaluurgical prepared precursor material have a high potential for use in weight sensitive construction parts. The relative density of the foamed Al-Si-Mg wrought alloys and Al-Si casting alloys is in the range of 10 - 30% of the bulk density. Additionally, these materials show excellent energy absorbing properties and therefore are appropriate to be used in vehicle body parts (``light metal construction'', ``crash energy absorber''). The governing parameters for the practical design of a component are based on the strength properties of the construction material. In the present work, the Static mechanical properties and deformation behaviour has been determined by tensile, compression and bend tests. Under compression loading, the stress-strain curves show a pronounced plateau-stress, which is correlated with the initial mass density of the material by a power law dependence. Construction parts in automobile industry, for example, are often subjected to a high nunber of varying stress amplitudes. Therefore the fatigue properties must be known for a reliable use of this cellular material. Since load sequences of typical automotive components may consist of 100 million cycles or more, the fatigue properties in the high cycle fatigue range are of special interest. The fatigue properties of Aluminum foams were investigated using a high frequency fatigue testing method in the present study. Specimens are subjected to a resonance vibration at a frequency of about 20 000 Hz. Fatigue measurements in the range between 10 000 and 1 billion cycles result in a bent SN-curve. The fatigue properties of different Aluminum foams were correlated with the structure of the material described by quantitative image analysis of optical micrographs. The distribution of in the crack initiation area was determined using X-ray computer tomography. Electron microscopical studies served to characterise the crack initiation mechanism. 

4:30 PM R2.9 
STRAIN RATE EFFECTS IN POROUS MATERIALS. James Lankford, Jr. and Kathryn A. Dannemann, Southwest Research Institute, San Antonio, TX. 

Cellular metals are under consideration as potential energy absorbing structural components. The deformation capacity of these lightweight materials allows for significant energy absorption under blast or impact type loading. This paper will provide an assessment of the behavior of metal foams under rapid loading conditions. Dynamic loading experiments have been conducted in our laboratory using a split Hopkinson pressure bar apparatus and a drop weight tester; strain rates ranged from 45 s^-1 to 1000 s^-1. The implications of these experiments on open-cell, porous metals, and closed- and open-cell polymer foams will be presented. It will be shown that there are two contributors to the impact resistance of cellular metals: (i) elastic-plastic resistance of the cellular metal skeleton, and (ii) the buildup of gas pressure within closed-cell structures, or the air pressure generated by airflow within distorted open cells. A theoretical basis for these implications will be discussed. 

4:45 PM R2.10 
THE EFFECT OF PARENT METAL PROPERTIES ON THE PERFORMANCE OF LATTICE BLOCK MATERIAL^TM. Mark L. Renauld, Anthony F. Giamei, Mark S. Thompson, United Technologies Research Center, East Hartford, CT; Jonathan Priluck, JAMCORP, Wilmington, MA. 

Lattice Block Material or LBM is a unique light-weight structure consisting of repeated cells with an internal node connected to 14 ligaments. In its metallic version, this product is available in a variety of castable metals including aluminum alloys, copper alloys, nickel alloys and steels. The relationship between LBM structural performance (strength and stiffness) and parent metal properties is investigated using compression tests in three primary orientations and 3-pt. bend tests.