The mechanical properties of cellular solids, or solid foams, is affected by “imperfections” such as wavy distortions of cell walls, variations in cell wall thickness, non-uniform cell shape, etc. The present paper is focused mainly on elastic stiffnesses of closed cell cellular solids. A “perfect” model is first discussed and shown to predict the behavior of PVC foams well. However, this model over-estimates the stiffnesses of aluminum foams. The relatively poor properties of the aluminum foam are believed to be caused by imperfections in the cells. The main body of the paper focuses on modeling different kinds of imperfections, and analyzing their impact on foam properties.

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 unfilled 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 could be explained in terms of the elastic compliance of the cellular structure of the foam using a simple geometric model found in the literature. 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 relative to the unfilled foam.

Highly porous building materials like aerated autoclaved concrete are characterized by low thermal conductivity and high mechanical strength, which both strongly depend on porosity. The influence of porosity distribution on the compressive strength of aerated autoclaved concrete was investigated by using finite element analysis and multiaxial Weibull theory. Calculations of failure probability of microstructures 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.

Dimensional arguments are used to analyze the fatigue of cellular materials. A modeling describing the fatigue of foams with or without macrocrack is derived and compared to the existing experimental data of cementitious foams and phenolic foams; agreement is good.

The elasto-plastic finite element method using a yield criterion advanced by Lee and Kim was employed to analyze the effect of indenting geometry on the Brinell hardness of sintered porous copper specimens with various densities. The changes in geometry of porous iron rings with various initial relative densities were also calculated for various friction coefficients between the metal rings and compression platens. The calculated hardness values were in very good agreement with the measured data. The 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.

A yield surface is proposed that can be fit to the plastic flow properties of a broad class of solids which exhibit plastic compressibility and different yield points in tension and compression. The yield surface is proposed to describe cellular solids, including foamed metals, and designed to be fit to three simple experimental results: (1) the compressive stress-strain response (including densification), (2) the difference between the tensile and compressive yield points and (3) the degree of compressibility of the foam, as measured by the lateral expansion during a uniaxial compression test. The model is implemented using finite elements and used to study the effects of plastic compressibility on two problems: the compression of a doubly notched specimen and indentation by a spherical indenter.

This study focuses on the relationship between porosity and elastic stiffness of structural ceramic materials produced by plasma-spraying. Mg-AI-spinel was chosen as a model material and studied in as-sprayed condition as well as upon annealing to increasingly higher temperatures up to 1650°C. The detailed analysis of the stiffness and mass density evolution offers a deep insight into the initial microstructural state of the material and into the morphological changes that occur upon heat treatment.

Measurements of the Young's modulus and compressive strength of several closedcell aluminum foams indicate that they are lower than expected from models for foam behaviour. Microstructural characterization has revealed that there are a number of defects in the cell structure which may contribute to the reduction in mechanical properties. These include: cell wall curvature, cell wall corrugations, density variations and non-equiaxed cell shape. Finite element analysis of a closed-cell tetrakaidecahedral unit cell with idealized curved or corrugated cell walls indicates that these two types of defects can reduce the Young's modulus and compressive strength by up to 70%. In this paper we report the results of measurements of the curvature of the cell walls and of the amplitude and frequency of corrugations in the cell walls and use simple bounds to estimate the reduction in modulus that they are responsible for.

For construction purposes it is utterly important to get detailed information on the possible influence of the foam thickness on the mechanical properties and on the deformation behaviour of metallic foams. The effect of compressive, tensile and shear loads on aluminium foam samples has been examined with the testing methods for sandwich material as described in German and ASTM-standards. The aim is to provide more data on these mechanical properties varying the sample density and thickness. Regarding the results the most reliable material parameters as well as steps towards a relationship between the different strength parameters can be obtained.

High porosity aluminum was fabricated in a number of ways. The starting material was a cast 6101 aluminum that had a relative density of 9.8%. The cast aluminum block was compressed by uniaxial, biaxial, and triaxial densification. Uniaxial compression was done at room temperature and 200°C. Biaxial compression was achieved by unidirectional rolling at room temperature and 200°C. Triaxial compression was done by cold isostatic pressing at 3.4, 6.7, and 34 MPa (0.5, 1.0, and 5.0 ksi). Metallography and mechanical test specimens were machined from the processed bars. The mechanical properties showed that the relative yield strength depended both on relative density and processing temperature.

The mechanisms of compressive deformation that occur in closed cell Al alloys have been established. This has been achieved 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. A group of cells work collectively to allow large localized deformation. Size does not appear to be the initiator of the deformation bands. Equiaxed cells remain elastic. The implications for manufacturing materials with superior mechanical properties are discussed. Visualization of internal deformation of a closed cell Al alloy core, as part of a sandwich panel construction, is also possible using x-ray tomography. Preliminary results for a punch indentation test are presented.

The shear modulus and shear strength of AISi7Mg aluminum foam with 15% (vol) of 13tm SiC particles were determined through shear testing. A foam slab with a density of 0.31 g/cm3 was supplied by Hydro Aluminium.

Four samples were tested according to ASTM C 273–61. The specimens were bonded to steel load plates. The relative displacement of the plates was measured using two extensometers. In order to evaluate the effect of the cell size distribution on shear properties, cell size and material distribution analyses were carried out for the metal foam slab in areas close to those from which the shear specimens were extracted.

A fast failure was observed after the maximum shear load. The failure in the samples were located in the central section of the slab mainly because the lower density was located there.

The foamed panels and sandwiches were prepared by powder metallurgical route using various matrix alloys. The effect of the apparent density, geometry and structure of the foam on its bending stiffhess was studied with respect to the results of the four-point-bending. It has been shown that the modulus of elasticity of the foam cannot be related only to its apparent density, because the distribution of the cell-wall material along the thickness of the foamed panel is not uniform. Therefore the real moment of inertia of the foam's cross-section should be used for the calculation of bending stiffness. This moment can be determined from the square weight of the foamed sample.

Fatigue lifetime measurements have been performed on foamed Al-Mg-Si wrought alloys and Al-Si cast alloys in the high cycle range using an ultrasonic resonance testing method. The porous structure of the material is described by quantitative image analysis of optical micrographs and non destructively by X-ray computer tomography. The static mechanical properties as determined by tensile, compression and bending tests in earlier studies are used for material characterisation in this paper. The evaluation of the stress strain curves is specified for porous structures to obtain the stiffness and the plateau strength. The influence of the surface skin on the mechanical properties as well as on oscillation behaviour during lifetime measurements was studied.

The behavior of metal foams under rapid loading conditions is assessed. Dynamic loading experiments were conducted in our laboratory using a split Hopkinson pressure bar apparatus and a drop weight tester; strain rates ranged from 45 s−1 to 1200 s−1. The implications of these experiments on open-cell, porous metals, and closed- and open-cell polymer foams are described. It is shown that there are two possible strain-rate dependent contributors to the impact resistance of cellular metals: (i) elastic-plastic resistance of the cellular metal “skeleton,” and (ii) the gas pressure generated by gas flow within distorted open cells. A theoretical basis for these implications is presented.

Lattice Block MaterialTM, or LBMTM is a unique lightweight structure consisting of repeated cells with an internal node connected to, in the most common configuration, 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 LBMTM structural performance (strength and stiffness) and parent metal properties is investigated using compression tests in three primary orientations and 3-pt. bend tests. Analytical assessment of the LBMTM via finite element analysis shows reasonable agreement with experimental findings and provides predictions for LBMTM capabilities with different materials, unit cell sizes and ligament geometries.

The possibilities for making metallic foams or similar porous metal structures are reviewed. The various processes are classified according to the state of the starting metal - liquid, powdered, ionised. Liquid metal can be foamed directly by injecting gas, gas-releasing foaming agents or by producing supersaturated metal-gas solutions. Indirect methods include investment casting and usage of filler materials. Metal powders can also be used as starting materials for metallic foams: mixtures of such powders with foaming agents are compacted to foamable precursor materials that can be foamed in a second step. Instead of foaming agents inert gas can be directly entrapped in the precursor. Metal foams can also be made from metal powder slurries or by using polymer/powder mixtures. Finally, galvanic electro-deposition also allows to make highly porous metallic structures with open pores.

The production of foamed aluminum has long been considered difficult to realize because of such problems as the low foamability of molten metal, the varying size of cellular structures, solidification shrinkage and so on. Recently these problems have been solved by a number of researches and some manufacturers produce foamed aluminum by their own methods. We have been employing a batch casting process and manufacturing foamed aluminum under the tradename ALPORAS® since 1986. This paper presents the manufacturing process, physical properties and some typical applications of ALPORAS.

Melt routes to metallic foam production offer attractions of low cost and the potential for good microstructural control. In situ gas generation may be preferable to external gas injection in terms of the important objective of generating a fine and uniform cell structure. The main difficulty with this approach has been that of ensuring that the gas-generating powder is suitably dispersed throughout the melt before the gas is released and the cells are formed.

In the present paper, procedures are outlined for preparation of powders for use in aluminium melts, where gas will be released only after a suitable delay, allowing the powders to first become well-dispersed in the melt and solidification to start. Pre-treatment of the foaming agent also facilitates a flexible production of castings with various porosity at the same processing conditions simply by varying the thickness of a diffusion barrier layer on the gas-releasing agent. The role of the melt viscosity history, as a function of a heat extraction rate from the solidifying melt and an alloy composition, on the final porosity of the castings is also briefly discussed.

During earlier investigations conducted at the Fraunhofer Institute for Applied Materials Research (IFAM), concentrating on the metal foaming technology using the powder metallurgy process, it was shown that some steel alloys are foamable with Fraunhofer's patented powder technology approach. To further investigate the foamability of steel alloys, suitable foaming agents need to be identified and characterized. This article reports the finding of two metallic compounds used for steel foaming. The foaming behaviors of the selected foaming agents in the steel powder compacts are also evaluated in terms of different alloying elements.