Technical Report A comparison among FE models to simulate metallic foams forming – An experimental validation F. Gagliardi, L. De Napoli, L. Filice, D. Umbrello * Department of Mechanical Engineering, University of Calabria, 87036 Rende, Italy article info Article history: Received 30 April 2008 Accepted 21 June 2008 Available online 2 July 2008 abstract Metallic foams are new materials mainly produced by expansion in a proper chamber and mainly char- acterized by internal voids: a material characterized by a very low density is obtained in this way. A lot of foamed components are commonly produced, directly by injecting a gas or foaming agent into molten metal inside a closed die. However, secondary operations on these materials can play an important role in order to enhance the foam production flexibility. From the above considerations, the deformation behaviour of an aluminium foam was investigated by compression tests. The study compares three dif- ferent numerical analyses highlighting their points of strength and weakness in order to verify their applicability in process design. More in detail, two models based on the implicit formulation were inves- tigated; in one case, the billet material was set as porous object with the material density which was cal- culated and updated as part of the simulation. The second implicit analysis, instead, was built using the plastic material formulation; the porosity, in this case, was physically created introducing voids within the workpiece. The latter simulation class was carried out through an explicit investigation; an efficient model con- struction was proposed introducing spherical surfaces connected each other with plans. Experimental data were used to validate the calculated results and a discussion concerning the three different numer- ical analyses was finally reported. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction The interest in metallic foams has grown quickly bringing to excellent results in innovative parts where, for example, low weight, high stiffness and high energy absorption are strict design parameters [1,2]. A lot of foamed components are commonly made by injecting gas or foaming agents into molten metal inside a prop- er closed die as reported in a literature review [3]. The behaviour of metallic foams during forming has to be taken into account to have good components, even, through secondary operations [4–7]. In this way, manufacturing cost could be signifi- cantly reduced. In fact, it is sometimes more convenient to produce standard- ized parts which are subsequently worked to approach a desired geometry. In the past years, several researches were focused on the deformation behaviour of metal foams utilizing the finite ele- ment methods. However, most of them simply utilized built-in porous material modelling when the metallic foams were studied. In detail, Reyes et al. [8] evaluated an existing constitutive model applicable for aluminium foam through LS-Dyna code; a lot of dif- ferent test cases were analyzed and compared to experimental data. The same explicit, non linear, code was utilized during differ- ent studies carried out, fore example, by Lopatnikov et al. [9] and Hanssen et al. [10]. A similar numerical investigation was conducted by Chen [11]. He used a rigid-plastic finite element software investigating the relative density distribution, the void closure behaviour, the defor- mation mechanisms and the stress–strain distribution around the internal voids for various rolling conditions using the commercial FE code Deform Ò [12]. Some of the authors of the paper here pro- posed, used this approach in previous researches [13–15]; basi- cally, aforementioned works were focused on the secondary processing of foam materials where shapes of simple billets have to be bent or modelled into complex sculptured parts. Meguid et al. [16] developed a modified unit cell model which was replaced more times before creating the final one. The multi- ple cell FE model, in fact, used 125 units with a total of 11,500 shell elements. The explicit LS-DYNA code was used for the proposed analysis and obtained results were compared with experimental investigation. Czekanski et al. [17], instead, proposed a new closed unit cell formed by use of ellipsoids which are interconnected through a truncated pyramid. In this case, mostly spherical cells are firstly created, followed by small ellipsoidal cells, which fill the remaining space. A new way to build the complex foam micro- structure was proposed by Shen et al. [18,19]; they developed a 0261-3069/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2008.06.051 * Corresponding author. Tel.: +39 0984494820; fax: +39 0984494673. E-mail addresses: f.gagliardi@unical.it (F. Gagliardi), ldenapoli@unical.it (L. De Napoli), l.filice@unical.it (L. Filice), d.umbrello@unical.it (D. Umbrello). URL: http://www.unical.it (D. Umbrello). Materials and Design 30 (2009) 1282–1287 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes