Relative Density Of Foam Research Articles

Dynamic Crushing of All-Metallic Corrugated Panels Filled With Close-Celled Aluminum Foams

Under quasi-static uniaxial compression, inserting aluminum foams into the interstices of a metallic sandwich panel with corrugated core increased significantly both its peak crushing strength and energy absorption per unit mass. This beneficial effect diminished however if the foam relative density was relatively low or the compression velocity became sufficiently high. To provide insight into the varying role of aluminum foam filler with increasing compression velocity, the crushing response and collapse modes of all metallic corrugate-cored sandwich panels filled with close-celled aluminum foams were studied using the method of finite elements (FEs). The constraint that sandwich panels with and without foam filling had the same total weight was enforced. The effects of plastic hardening and strain rate sensitivity of the strut material as well as foam/strut interfacial debonding were quantified. Three collapse modes (quasi-static, transition, and shock modes) were identified, corresponding to different ranges of compression velocity. Strengthening due to foam insertion and inertial stabilization both acted to provide support for the struts against buckling. At relatively low compression velocities, the struts were mainly strengthened by the surrounding foam; at high compression velocities, inertia stabilization played a more dominant role than foam filling.

Investigation into stress wave propagation in metal foams

The aim of this study is to investigate stress wave propagation in metal foams under high-speed impact loading. Three-dimensional Voronoi model is established to represent real closed-cell foam. Based on the one-dimensional stress wave theory and Voronoi model, a numerical model is developed to calculate the velocity of elastic wave and shock wave in metal foam. The effects of impact velocity and relative density of metal foam on the stress wave propagation in metal foams are explored respectively. The results show that both elastic wave and shock wave propagate faster in metal foams with larger relative density; with increasing the impact velocity, the shock wave propagation velocity increase, but the elastic wave propagation is not sensitive to the impact velocity.

Spherical indentation of closed-cell aluminum foams: An empirical force–depth relation

The plastic indentation behavior of closed-cell aluminum foams with a spherical indenter was investigated experimentally. Dimensional analysis was introduced to present a simple scaling relation between the indentation force and the indentation depth. Indentation tests were carried out on closed-cell aluminum foams with different relative densities to examine the dependency of plastic indentation responses of aluminum foams on the densification strain. Uniaxial compression and indentation of closed-cell aluminum foams at different temperatures were carried out experimentally. The onset strain of densification was found to be temperature independent. Effects of temperature on the spherical indentation responses of aluminum foams were studied. An empirical formula for the indentation force incorporating the effects of temperature, relative density of foam and dimensionless indentation depth was presented.

Prediction of Creep Properties of Fiber-Reinforced Closed-Cell Metallic Foams

The anti-creep capability of metallic foams is important to structural applications at elevated temperatures. Currently, available creep models for opened-cell foam materials are usually derived by rather simplified meso-structural models. Here, we try to predict the creep properties of new fiber-reinforced closed-cell foams with more realistic 3D meso-structures. In the study, three-dimensional Voronoi structures are constructed to describe the inner structure of closed-cell foams, and reinforcing fibers are modeled by line segments penetrating through cell walls. Based on the recommended model, not only the steady creep strain rates of both the unreinforced and the reinforced foam materials are well predicted with considering the effects of temperature, stress, and relative density, but also the creep evolution features of metal foam are revealed from the meso-deformation behaviors. It is found that, at moderate temperature and stress, the creep rate of the fiber-reinforced metallic foam can also be well described by a power law with respect to the foam relative density. The influence of addition of fibers on the creep properties is parametrically studied and it is shown that addition of fibers has a positive effect on restricting the creep rate. It is observed that during creep, the stresses of cell walls are redistributed and become more homogeneous with time. When the creep rate of metallic foam reaches steady state depends on when the stresses of cell walls become homogeneous.

Asymmetric microcellular composites: Morphological properties

Asymmetric microcellular composites were prepared by injection molding to study the effects of temperature gradient inside the mold (0 to 60℃) as well as blowing agent (0 to 1%) and natural fibers (0 to 30%) contents. High-density polyethylene, flax fiber, and azodicarbonamide were used as the matrix, reinforcement, and chemical blowing agent, respectively. From the samples produced, a complete morphological characterization was performed. As expected, cell size, cell density, and skin and core thicknesses were affected by blowing agent and natural fiber contents and mold temperatures. It was found that a better microcellular asymmetric structure was obtained with higher fiber and blowing agent contents and higher average mold temperature. From the data obtained, a simple mathematical model was used to fit the relative density of asymmetric foams to include skin, core, and transition zone thicknesses.

THE RANDOM POROUS STRUCTURE AND MECHANICAL RESPONSE OF LIGHTWEIGHT ALUMINUM FOAMS

ABSTRACTLightweight porous foams have been of particular interest in recent years, since they have a very unique set of properties which can be significantly different from their solid parent materials. These properties arise from their random porous structure which is generated through specialized processing techniques. Their unique structure gives these materials interesting properties which allow them to be used in diverse applications. In particular, highly porous Al foams have been used in aircraft components and sound insulation; however due to the difficulty in processing and the random nature of the foams, they are not well understood and thus have not yet been utilized to their full potential. The objective of this study was to integrate experiments and simulations to determine whether a relationship exists between the relative density (porous density/bulk density) and the mechanical properties of open-cell Al foams. Compression experiments were performed using an Instron Universal Testing Machine (IUTM) on ERG Duocel open-cell Al foams with 5.8% relative density, with compressive loads ranging from 0-6 MPa. Foam models were generated using a combination of an open source code, Voro++, and MATLAB. A Finite Element Method (FEM)-based software, COMSOL Multiphysics 4.3, was used to simulate the mechanical behavior of Al foam structures under compressive loads ranging from 0-2 MPa. From these simulated structures, the maximum von Mises stress, volumetric strain, and other properties were calculated. These simulation results were compared against data from compression experiments. CES EduPack software, a materials design program, was also used to estimate the mechanical properties of open-cell foams for values not available experimentally, and for comparison purposes. This program allowed for accurate prediction of the mechanical properties for a given percent density foam, and also provided a baseline for the Al foam samples tested via the IUTM method. Predicted results from CES EduPack indicate that a 5.8% relative density foam will have a Young’s Modulus of 0.02-0.92 GPa while its compressive strength will be 0.34-3.37 MPa. Overall results revealed a relationship between pores per inch and selected mechanical properties of Al foams. The methods developed in this study can be used to efficiently generate open-cell foam models, and to combine experiments and simulations to calculate structure-property relationships and predict yielding and failure, which may help in the pursuit of simulation-based design of metallic foams. This study can help to improve the current methods of characterizing foams and porous materials, and enhance knowledge about theirproperties for novel applications.

Bulk Density Reduction of Injection Molded Thermoplastic Foams via a Mold Design Approach

This study investigates the inter-relationships amongst processing parameters and mold design and their effects on relative density of injection molded foams. The limitation in lowering the overall bulk density of polymeric foams is one of the main drawbacks in injection foaming process. A sheet mold with a rectangular cavity was designed and manufactured which, includes an overflow channel connected with the main cavity via a secondary gate, the size of which was varied in this research. The effects of three parameters including chemical blowing agent weight percentage, gate width, and part thickness on reduction of relative density were investigated. Full factorial test experiments were applied in this research work. The results were used to determine the optimum conditions in terms of low foam bulk density and high cell density. The results showed that enhanced cell structure can be achieved at a larger part thickness and adjusting the secondary gate to an optimum thickness. The conclusions revealed that part thickness and secondary gate width were the most influential factors on reduction of relative density and part weight.

Effect of loading rate on the compressive properties of open-cell metal foams

Based on the three-dimensional tetrakaidecahedron model, the dynamic compressive properties of the open-cell aluminum foam was investigated using the finite element (FE) method. Qualitatively analyzing the effects of the impact velocity and the relative density on the deformation modes, plateau stress, densification strain and energy absorption of the open-cell foam, it is found that the different impact velocity causes different failure modes and patterns: the foam follows the kind of bending–buckling deformation pattern under the low impact velocities while follow the kind of buckling–bending–buckling one under high impact velocities. Two types of the deformation mechanisms have been observed by the macroscopic stress–strain responses, and it transpires that the crushing deformation of metallic foams tends to the type I response under the lower impact velocity; while it tends to the type II response under the higher impact velocity. The results also indicate that both the plateau stress and the densification strain energy are not dependent on crushing velocity for the low relative density, but loading-rate sensitivity for the high relative density foam. Moreover, both of them can be improved by increasing the foam relative density. The relative density has little effect on the densification strain, while the impact velocity has greater influence on the densification strain but with no simple monotonous change

Compressive properties of aluminum foam produced by powder-Carbamide spacer route

Effects of cell shape and size, and relative density of aluminum foam on its compressive behavior have been investigated. Aluminum foams were produced via aluminum powder-Carbamide spacer route. The results show that angular cells significantly reduce mechanical properties of the foam. They also indicate that compressive properties of the foams, including plateau stress (σpl), densification strain (εD), and energy absorption, increase by cell size and relative density of the foams. Experimental results were compared with theoretical predictions; they were fairly corresponded to theoretical conceptions; this arises from near-ideal architecture of the foams with almost spherical cells, in this study. Constant values of C, n and α in theoretical modulus and densification strain equations wear calculated as 1.22, 2.09 and 0.95, respectively. The values indicate compressive behavior approaches to ideal morphology foam via employing spherical space holder.

Microstructure and Properties of Microcellular Poly (phenylene sulfide) Foams by Mucell Injection Molding

A series of microcellular poly (phenylene sulfide) (PPS) foams were prepared by Mucell injection molding. The cell structure, mechanical properties, crystallization behavior and dielectric property of microcellular PPS foams were systemically investigated. The results showed that the longer the length of flow passage of injection mold, the larger cell size of microcellular PPS foams. The injection parameter of shot size played an important role in relative density of microcellular PPS foams. When the relative density of microcellular PPS foam reached to 0.658, the tensile strength, flexural strength and impact strength of PPS foam materials achieved 10.82 MPa, 52.99 MPa and 0.305 J/cm2, respectively. Meanwhile, with the relative density decreasing, the dielectric constant of PPS foam materials reduced, while the volume resistivity of its uprated.

Nano-deposition on 3-D open-cell aluminum foam materials for improved energy absorption capacity

Open cell aluminum (Al) foams have been used as energy absorbers for decades. Their energy absorption capacity can be enhanced by thickening the foam struts, or increasing the foam's relative density. However, the enhancement is compromised by the inherent characteristics of its stress–strain property relationship, whereby upon homogeneous strut thickening, an increase in the plateau stress without a reduction in densification strain cannot be achieved. In this work, to overcome this inherent barrier, nano-crystalline copper (Cu) was deposited onto the Al foam and novel 3-D Cu/Al, heterogeneously thickened, composite foam structured materials were fabricated and tested for the first time. A non-cyanide nano-crystalline copper electro-deposition system was setup for the coating of open-cell Al foam, and, the energy absorption capacity as a function of foam pore size and Cu coating thickness was investigated. A variety of characterization methods confirmed the nano-crystalline structure of the Cu deposition (38nm). The energy absorption capacity of Al foams (with average strut thickness of 192μm) reinforced with a 60μm Cu coating was 3 times greater than that of plain foams. The compressive stress–strain response of the composite samples showed no significant reduction of the densification strain compared to the uncoated foams due to the small change in the foam strut thickness and pore size. A comparison between thin Cu-coated and uncoated Al foam samples with the same overall strut thickness (i.e., same effective volume density and porosity) showed that the nano-reinforced foams had superior energy absorption capacity over plain foams with the same overall thickness, (∼2 times greater).

Simulation on Shock Wave Propagation in Metallic Foams Subjected to Impact Loading

A discretization elastic-plastic material model was used for simulating the shock waves transmission within metallic foams. The density heterogeneity of metallic foams was considered. Several types of aluminum foams are studied on the transmission of displacement and stresses wave under impact loading. The results reveal the characteristics of compressive wave propagation within the metal foams. Under low impact pulses, considerable energy is dissipated during the progressive collapse of foam cells, and then reduces the crush of the objects. When the pulse is high sufficiently, on the fixed end of foam, stress enhancement may take place, where high peak stresses usually occur. The magnitude of the peak stress depends on the relative density of foams, the pulse loading intensity, the pulse loading duration as well as the density homogeneity of foam materials. This research offers valuable insight into the reliability of the metal foams used as vehicles and protective structure.

NUMERICAL MODELING OF THE FRACTURE BEHAVIOR OF OPEN CELL FOAMS

The objective of this work is to numerically study the individual and mixed mode fracture behavior of open-cell foams. Three-dimensional tetrakaidecahedron model is adopted and finite element method is employed in analysis. The overall elastic properties of open-cell foams are numerically obtained. Then, modes I, II, III and mixed mode I–II fracture behavior of open-cell foams are numerically predicted respectively, in which both solid/hollow and square/circular strut cross-sections are considered. It is seen that the relationship between the overall critical stress intensity factor and the relative density of foam obeys power law for individual crack problems. Effects of the shape and the topology of strut cross-section are discussed in detail. For mixed mode I–II crack problem, the relationship between KI/KICand KII/KIICis obtained and the effect of the shape of strut cross-section is discussed.

Multiaxial creep of low density open-cell foams

► A more reasonable modified foam creep expression is presented. ► A phenomenological constitutive model for multiaxial foam creep is deduced. ► FE results by random cell models are well captured by theoretical models. ► Foam creep deformation show high sensitivity to foam relative density. Open-cell foams have wide applications in structural components, energy adsorption, heat transfer, sound insulation, and so on. When their in-service temperature is high, time dependent creep may become significant. To investigate the secondary creep of low density foams under multiaxial loading, three-dimensional (3D) finite element (FE) Voronoi models are developed. The effects of relative density, temperature, cell irregularity, and stress state on the uniaxial creep are explored. By taking the mass at strut nodes into account, the creep foam model by Gibson and Ashby (Cellular Solids: Structure and Properties, 2nd ed., Cambridge University Press, Cambridge, UK, 1997) is modified. Obtained results show that the uniaxial secondary foam creep rate predicted by the FE simulations can be well captured by the modified creep model. For multiaxial secondary creep, a phenomenological elastoplastic constitutive model is extended to include the rate effect into the creep response of 3D Voronoi foams. Again, the model predictions agree well with the FE results.

The potential of wood fibers as reinforcement in cellular biopolymers

Wood fiber-reinforced polylactic acid composite foams have been successfully produced using supercritical carbon dioxide. The addition of fibers had a strong effect on microstructure of the foams. An increase in wood fiber content implied smaller average cell size and higher average cell wall thickness as estimated from image analysis of scanning electron microscopy micrographs. Addition of 10 wt% wood fibers seemed to be a limit to obtain foams, with the used processing conditions. The stiffness properties of the foams in compression improved upon addition of wood fibers. A significant increase of specific stiffness was achieved by adding 5–10 wt% wood fibers. It was shown that the stiffness was about 50% higher in the transverse direction for reinforced foams. The strength in the transverse direction increased for foams with unmodified wood fibers but decreased for foams with two types of treated wood fibers as compared with the strength of the pure polylactic acid foam of similar density. A butyl tetracarboxylic acid treatment followed by an additional surfactant treatment results in reduced wood fiber network-forming ability and reduced fiber–matrix adhesion. This contributes to the inferior observed strength properties in this study. The experimental stiffness was comparable with a superposed micromechanical model for a three-phase fiber-reinforced foam. The model shows that increasing the relative density, that is, the ratio of the density of the foam to the density of the composite material, by adding wood fibers results in a noteworthy increase in the transverse compression stiffness of the foams but only at relative density values above 0.2 for the used processing conditions in this study. The key factor for reinforcement is the relation between foam relative density and fiber volume fraction in the preform. The foaming conditions have to be adapted for each wood fiber content to obtain foams with the desired relative density.

Structural and mechanical properties of flexible polyurethane foams cured under pressure

Flexible two-component polyurethane foam was synthesized under various extents of overpressure up to 2 bar. The influence of the pressure conditions on shrinkage and basic foam properties such as the relative density, microstructure, and ratio of open to closed pores as well as the elastic mechanical properties were investigated. The relationship between the relative foam density and the applied overpressure is shown to be rather linear. An abrupt change of the mainly open pore structure to essentially closed-cell foam was found in the narrow range between 50% and 60% relative density. A way to control the shrinkage properties of closed-cell foam via the extent and duration of overpressure applied during the foam synthesis was found and a hypothetic qualitative model describing the basic underlying mechanisms is given. Closed-cell flexible foam showing no effective shrinkage was produced this way. The achieved foam properties display an interesting potential for the application as e.g. gasket material.

Effect of wheat bran on the mechanical properties of extruded starchy foams

Incorporation of wheat bran has a significant effect on the texture of extruded starchy products. This can be explained by changes in the mechanical parameters of the products. The stress at rupture and elastic modulus of wheat flour-based solid foams, obtained at different extrusion conditions and bran concentration, were measured using a three-point bending test. Both parameters were positively correlated with the foam relative density according to the Gibson–Ashby model. At same relative densities and bran concentration, finer structures with higher density of small cells led to a higher mechanical strength of the foams. The stress at rupture of the unexpanded material was decreased when increasing the bran concentration. Nevertheless, expanded foams with added bran at an intermediate level showed increased mechanical strength. This was attributed to the finer cellular structures obtained. The effect of increasing the bran to a higher concentration on the mechanical properties was depending on the cell wall thickness and bran particle dimensions. At high relative density, the strength of the foams was further increased due to the even finer structures obtained. At low relative density, even though finer structures were also obtained, the stress at rupture of the foams was decreased. This may be explained by the lower cell wall thicknesses and low adhesion properties between bran and starch favoring rupture of the cell walls.

Manufacturing of Al/SiCp composite foams using calcium carbonate as foaming agent

The aluminium composite foams reinforced by different volume fractions of SiC particles were manufactured with the direct foaming route of melt using different contents of CaCO3 foaming agent. The density of produced foams changed from 0·43 to 0·76 g cm−3. The microstructural features and compressive properties of the Al/SiCp composite foams were investigated. Compressive stress–strain curve of Al/SiCp composite foams is not smooth and exhibits some serrations. At the same relative density of composite foams, the plateau stress of the composite foams increases with increasing volume fraction of SiCp and decreasing weight percentage of CaCO3. The relation between plateau stress, relative density, weight percentage of CaCO3 and SiCp volume fraction of Al/SiCp composite foams with a given particle size was investigated.

Numerical Study on the Large Deformation of Silicone Rubber Foams Based on Random Cell Models

Two-dimensional (2D) random cell models composed of circular cells with different sizes are developed to simulate the microstructure of silicone rubber foams. The two-parameter Mooney-Rivlin strain energy potential model is employed to characterize the hyperelasticity of the solid of which the foams are made. Finite element method is used to simulate the large deformation of the foams. Predicted uniaxial compressive stress-strain curves exhibit universally three deformation regions: an initial linear-elastic response, an extended plateau region, and a final densification stage as cell collapsing. It is also found that with the foam relative density increasing, the initial linear-elastic region is found to extended, the buckling plateau section becomes indistinctive, and final densification stage is hastened.

Micromechanical prediction of the effective electromechanical properties of cellular ferroelectrets

Cellular space-charge foams, which have very sensitive transducer properties and are called cellular ferroelectrets, emerged as a kind of novel electromechanical transducer materials. In recent years, the understanding of charging is advanced significantly. However, some fundamental theoretical aspects, as to the relation between the electromechanical behavior and their mesostructures, are still far from clear. As is well known, the transducer coefficients in the thickness direction strongly depend on the relative density of foam, which is essentially relevant to the mesostructure, such as void shape, void fraction, etc. In this article, a theoretical model based on micromechanics is proposed to estimate the overall electromechanical moduli of cellular ferroelectrets. From the viewpoint of composites, in this model, the voids with surplus charge are deemed as heterogeneous inclusions, which show piezoelectriclike effect under deformation. The matrix is the nonpolar polymer. Within the micromechanical framework for piezoelectric composites, the generalized Eshelby tensor is obtained for both isotropic and anisotropic matrix. The equivalent inclusion method is employed to treat inhomogeneities. Similar to the classical differential scheme for pure elasticity, the differential equation for the effective electromechanical moduli is derived, from which the overall behavior of cellular space-charge foam can be numerically solved. Detailed analysis is presented with respect to material parameters and geometrical variables of void. Finally, this model is used to simulate the inflation experiments of cellular ferroelectret film published in literature. Results show this model is capable of predicting the extremum of the effective electromechanical moduli. In the meantime, quantitative comparison indicates that theoretical simulation is in good consistency with experiment data.