Example Application We envision a plate made of steel foam, simply supported at all four edges and loaded in-plane in pure compression, and calculate the elastic buckling and crushing loads that result as the plate is considered to be made of steel foam with different relative densities. The thickness of the plate is adjusted to keep the total plate mass constant as the relative density of the foam is lowered. Assuming that the elastic modulus and yield stress of the foam vary with the relative density as described by Gibson and Ashby [6], the surface describing the minimum of the elastic buckling and crushing loads is defined by the following equations and figures. In general, for slender plates, reducing the relative density of the foam results in increasing elastic buckling capacity until the crushing load, which is reduced by increasing the relative density, becomes dominant.

Introduction Foam and cellular materials have been produced from base materials that include polymers, ceramics, and metals such as titanium, aluminum, and copper, and such foams have been applied to solve engineering problems primarily in the aerospace, automotive, and process control domains. Steel is one of the most widely used engineering materials, yet today no foam using steel as the base material is commercially available. Perhaps because of the lack of commercial availability of steel foam, no applications have been developed or widely implemented.

Research conducted over the last 10-15 years has shown that it is possible to fabricate steel foams at the laboratory scale and that these foams can be made to have potentially desirable mechanical properties. To date, the only experimental investigations of the potential use of steel foam in structural applications, as opposed to material characterization tests, have been to test some one foot long steel foam filled tubes [9] and some 40mm long steel foam beams [4] to failure.

The dual purposes of our research project are: (1) to experimentally characterize steel foams with respect to their cyclic, tensile, and shear response, properties that are critical to structural performance but are essentially unknown for steel foams; (2) to develop and computationally test candidate applications of steel foam that will improve the performance of civil structures by, for example, improving energy dissipation or mitigating local structural instabilities.

Reconfiguring Steel Structures: Energy Dissipation and Buckling Mitigation Through the Use of Steel Foams PIs: SR Arwade (UMass), JF Hajjar (Northeastern), BW Schafer (Johns Hopkins)

CMMI-1000334, 1000167, 0970059 Abstract

Steel foam is a material that can now be produced at the laboratory scale using a variety of different processes that create materials with a variety of different morphologies. Steel foam has not, however, been adopted in structural applications. Here we review some of the methods available for processing steel foams and the material properties that result from those processes, and demonstrate a possible application of steel foam in mitigating instability in structural members susceptible to local instability.

Acknowledgements This work was supported by the National Science Foundation through grants CMMI-1000334, 1000167, 0970059. Graduate students M Moradi, B Smith, and postdoc S Szyniszewski performed much of the work shown in this poster.

References [1] Adler J, Standke G, and Stephani G (2004). “Sintered open-celled metal foams made by replication method - manufacturing and properties on example of 316L stainless steel foams.” Proceedings of the Symposium on Cellular Metals and Polymers (CMaP). Deutsche Forschungsgemeinschaft (DFG), 12-14 October 2004, Fürth, Germany, p.89-92. [3] Angel S, Bleck W, and Scholz P-F (2004). “SlipReactionFoamSintering (SRFS) - process: production, parameters, characterisation.” Proceedings of the Symposium on Cellular Metals and Polymers (CMaP). Deutsche Forschungsgemeinschaft (DFG), 12-14 October 2004, Fürth, Germany. [3] Ashby M, Evans A, Fleck N, Gibson L, Hutchinson J, Wadley H. (2000) Metal Foams: A Design Guide. Butterworth-Heinemann. [4] Brown JA, Vendra LJ, and Rabiei A (2010). “Bending properties of Al-steel and steel-steel composite metal foams.” Metallurgical and Materials Transactions A. Online:1 July 2010. [5] Friedl O, Motz C, Peterlik H, Puchegger S, Reger N, and Pippan R (2007). “Experimental investigation of mechanical properties of metallic hollow sphere structures.” Metallurgical and Materials Transactions B. 39(1):135-146. [6] Gibson L, Ashby M. (1999) Cellular solids: Structure and properties-second edition. Cambridge University Press. [7] Gong L, Kyriakides S, Jang W-Y. (2005). “Compressive response of open-cell foams. Part I. Morphology and elastic properties.” International Journal of Solids & Structures 42, 1355–1379. [8] Kremer K, Liszkiewicz A, Adkins J. (2004) “Development of steel foam materials and structures.” Tech. rep., Fraunhofer USA Delaware Center for Manufacturing and Advanced Materials, 9 Innovation Way Newark, DE 19711, US. [9] Muriel J, Sanchez Roa A, Barona Mercado W, and Sanchez Sthepa H (2009). “Steel and gray iron foam by powder metallurgical synthesis.” Suplemento de la Revista Latinoamericana de Metalurgia y Materiales. 2009. S1(4):1435-1440. [10] Neville BP and Rabiei A (2008). “Composite metal foams processed through powder metallurgy.” Materials and Design 29:388-396. [11] Park C and Nutt SR (2000). “PM synthesis and properties of steel foams.” Materials Science and Engineering A. A288:111-118. [12] Park C and Nutt SR (2001). “Anisotropy and strain localization in steel foam.” Materials Science and Engineering A. A299:68-74. [13] Park C and Nutt SR (2002). “Strain rate sensitivity and defects in steel foam.” Materials Science and Engineering A. A323:358-366. [14] Tuchinsky L (2005). “Novel fabrication technology for metal foams.” Journal of Advanced Materials. 37(3):60-65. [15] Rabiei A and Vendra L J (2009). “A comparison of composite metal foam's properties and other comparable metal foams.” Materials Letters 63:533-536. [16] Verdooren A, Chan HM, Grenestedt JL, Harmer MP, and Caram HS (2005). “Fabrication of low density ferrous metallic foams by reduction of ceramic foam precursors.” Journal of the Materials Science. 40:4333-4339. [17] Verdooren A, Chan HM, Grenestedt JL, Harmer MP, and Caram HS (2005). “Fabrication of low density ferrous metallic foams by reduction of chemically bonded ceramic foams.” Journal of the American Ceramic Society. 89(10):3101-3106. [18] Weise J, Beltrame Derner Silva G, and Salk N (2010). “Production and properties of syntactic steel and iron foams with micro glass bubbles.” In Proceedings of MetFoam 2009, Bratislava, Slovakia

Manufacturing and Processing Investigators have succeeded in fabricating steel foams with various cell morphologies with relative densities that range from 0.04 to 0.95. Metal foams that use aluminum, titanium, or copper as a base metals have relative densities of 0.05 to 0.20, and have typically been used in applications demanding high ratios of the stiffness to weight or compressive energy absorption to weight. Such low density foams have very low material strength relative to the base metal, with yield stress as low as 1% of the base material yield stress [7]. In structural applications we expect reasonable material strength to be critical to the satisfactory performance of the material, and therefore call particular attention to the ability to achieve foams with relative density greater than 0.40 using the powder metallurgy and composite hollow sphere methods. Although high relative density is also achievable using injection molding with glass balls or the working and sintering of bimaterial rods, these materials are either expensive or not suitable for structural applications. Finally, although the sintering of hollow steel spheres can produce materials with relative density only up to 0.20, it is likely the closest to commercialization. We therefore intend to focus our investigations on materials produced by powder metallurgy, sintering of hollow steel spheres, or composite powder metallurgy / hollow steel sphere processes.

Material Properties Foam materials have typically been employed in mechanical or aerospace applications in which they were asked to undergo large compressive deformations at relatively low stress, or provide substantial stiffness at extremely low weight. For that reason, characterization of steel foam material properties has focused exclusively on compression testing of small rectilinear prisms of material providing the elastic modulus and compressive yield stress of the material.

In all published material characterizations, the number of experiments reported is small, usually in the single digits. This reflects the substantial challenges and costs still associated with the production of steel foam. The table below lists published material properties for some steel foams. Values of the elastic modulus and compressive yield stress are reported for most materials. Several of the papers also report material hardness, which is of little consequence for civil engineering design, and there exists only one published report of the tensile capacity of a steel foam, which states tensile yield stresses on the order of 1-10 MPa. We could find no published reports on the cyclic or shear response of steel foams, and both cyclic and shear loading commonly arise in civil structural applications. Steel foams with low relative density have yield stresses on the order or 1% of typical yield stress values for bulk steel, whereas when the relative density is closer to 0.50, steel foam yield stress of up to roughly 50% of steel yield stress are achievable. These findings highlight the potentially critical role that high density foams might play in civil engineering design. Steel foam elastic moduli vary from less than 1% of the bulk property to as much as 5% of the bulk property. These are low material stiffnesses, and point out that maintaining sufficient stiffness in structural applications of steel foam will be a critical and challenging objective. The table clarifies the nearly complete lack of material property characterization beyond compressive properties, and provides strong motivation for our efforts at cyclic, tensile, and shear measurements.

ρ = relative density b = plate width

ts = plate thickness Pcrf = buckling load Pyf = crushing load Pcry = min(Pcrf,Pyf)

Table 1: Manufacturing processes, cell morphology, and relative density of steel foams

Figure 1: Plate response for variable steel foam density and plate width. Dashed line divides buckling from crushing regimes, solid line shows how response of a particular plate with fixed geometry changes with decreasing foam relative density. Surface defined by

equations above. (a) variable foam density and plate width; (b) variable foam density and plate thickness

Table 2: Steel foam mechanical properties

(a) (b)