Density-graded Foam Research Articles

Impact response of additively manufactured density-graded open-cell foams

Additive manufacturing has made it possible to fabricate materials that were unachievable with traditional methods. This study focuses on understanding the deformation behavior and energy absorption mechanics of additively manufactured cellular materials with gradually varying densities. Foams have unique deformation behavior due to their intricate topology and composition, resulting in excellent energy dissipation capability. Varying the density can significantly influence their deformation response and improve energy absorption and impact resistance. Voronoi tessellation is employed to model the foams, as it effectively captures the cell morphology in foam structures and produces stochastic cellular topologies accurately. Resin-based additive manufacturing techniques are employed to fabricate cellular materials with varying density configurations for low-velocity and high-velocity impact experiments. The study demonstrates that density-graded foams effectively dissipate a broad spectrum of impact energies, surpassing uniform counterparts by transmitting reduced stress, especially at lower energy levels. This characteristic enhances their suitability for advanced energy absorption applications. The results also show that at high impact velocities, the direction of density gradation influences energy dissipation and peak stress transmission.

Effect of core structure on the quasi-static bending behaviors and failure mechanisms of aluminum foam sandwiches at elevated temperatures

In this study, a novel three-step method involving liquid casting, hot-rolling, and foaming was employed to fabricate three types of metallurgical bonded aluminum foam sandwich (AFS): AFS with a uniform foam core (UAFS), AFS with a density-graded foam core (GAFS), and AFS with an interlayer plate (IAFS). The bending behaviors of different AFS structures in four cases were investigated using the digital image correlation (DIC) technique to examine the effect of foam core structure, loading direction, and loading temperature. The results showed that the initial peak load (Fp), plateau load (Fpl) and load oscillation decreased with increasing loading temperature. IAFS demonstrated the low sensitivity to loading temperature, an important reason was the addition of interlayer plate. The deformation mode involved interface separation and foam core detachment occurring in the interface vicinity beneath the indenter at the lower temperatures (≤300 °C) shifted towards well-bonded interface and foam core densification at the higher temperatures (400 °C and 500 °C). Different core structures and loading directions gave rise to four distinct modes of crack initiation and propagation. In addition, as the loading temperature increased, the strain localization effect was diminished, accompanied by hindering in crack formation. The fracture mode of core shear transitioned from brittle to ductile with increasing loading temperature.

Mechanical performance of reverse-engineered resin foam structures developed by image processing on the computed tomography data: A revisit

Using digital design methods, additive manufacturing processes enable us to create novel complex structures. In the current study, 3 and 10 ppi, density-graded, and merged foams (digitally joined 3 and 10 ppi) were reproduced from computed tomography data of the commercially available steel foams using MSLA (masked stereolithography). The mechanical performance of the foams has been characterized by quasi-static compression testing. Density grading increases the slope of the plateau regime and reduces the densification strain. Merged foams at high relative densities (ρrel∼35 %) showed the highest energy absorption capacity, specific strength, and densification strain. 3,10 and density-graded foams deform by bending of struts. In the case of merged foams, the bending-dominated structure has been transformed into a stretch-dominated structure. The power exponent (n = 0.72) delivers the deformation mode of the strut, revealing stretch-dominated behavior. Moreover, additively manufactured resin foams have a lower scattering in mechanical properties than conventionally manufactured metal foams because structures can be remanufactured with the same cell/strut dimensions and imperfections.

Deformation analysis in impact testing of functionally graded foams by the image processing of high-speed camera recordings

We developed an image processing algorithm and applied it on high-speed camera recordings to characterize the deformation response of three-layered density-graded foam structures subjected to drop weight testing. Different densities (30, 40, 50 and 70 kg/m3) of weakly cross-linked polyethylene foam sheets were laminated together to achieve varying density distributions along the thickness, and the effect of layer order on the shock absorption capability was evaluated. Foam structures with a higher density top layer and a negative density gradient showed enhanced energy absorption in the initial stage of deformation, which resulted in lower maximum reaction forces. The positive effect of layer order modification was more dominant at higher impact energies. We provided a detailed explanation of the tendencies by investigating the differences in deformation propagation and the changes in the diameter of the deformation zone. The presented method can be utilized to design sports and packaging foam products.

Quasi-Static Mechanical Response of Density-Graded Polyurea Elastomeric Foams.

Density gradation of foam structures has been investigated and found to be a practical approach to improve the mechanical efficacy of protective padding in several applications based on nature-based evidence of effectiveness. This research aims to disclose a discrete gradation approach without adhesives by relying on the properties of the frothed foam slurry to bond and penetrate through previously cured foam sheets naturally. As confirmed by electron microscopy observations, bilayer- and trilayer-graded elastomeric polyurea foam sheets were fabricated, resulting in seamless interfaces. The mechanical performance of seamless, graded foam samples was compared with monolayer, mono-density benchmark foam, considered the industry standard for impact mitigation. All foam samples were submitted to compressive loading at a quasi-static rate, reporting key performance indicators (KPIs) such as specific energy absorption, efficiency, and ideality. Polyurea foams, irrespective of gradation and interface type, outperformed benchmark foam in several KPIs despite the drastic difference in the effective or average density. The average compressive stress-strain curves were fitted into empirical constitutive models to reveal critical insights into the elastic, plateau, and densification behaviors of the tested foam configuration. The novelty of these outcomes includes (1) a fabrication approach to adhesive-free density-graded foam structures, (2) implementation of a diverse set of KPIs to assess the mechanical efficacy of foams, and (3) elucidation of the superiority of polyurea foam-based lightweight protective paddings. Future research will focus on assessing the dynamic performance of these graded foam structures under impact loading conditions at a wide range of velocities.

Tuning the Mechanical Behavior of Density-Graded Elastomeric Foam Structures via Interlayer Properties.

The concept of density-graded foams has been proposed to simultaneously enhance strain energy dissipation and the load-bearing capacities at a reduced structural weight. From a practical perspective, the fabrication of density-graded foams is often achieved by stacking different foam densities. Under such conditions, the adhesive interlayer significantly affects the mechanical performance and failure modes of the structure. This work investigates the role of different adhesive layers on the mechanical and energy absorption behaviors of graded flexible foams with distinct density layers. Three adhesive candidates with different chemical, physical, and mechanical characteristics are used to assemble density-graded polyurea foam structures. The mechanical load-bearing and energy absorption performances of the structures are evaluated under quasi-static and dynamic loading conditions. Mechanical tests are accompanied by digital image correlation (DIC) analyses to study the local strain fields developed in the vicinity of the interface. Experimental measurements are also supplemented by model predictions that reveal the interplay between the mechanical properties of an adhesive interlayer and the macroscale mechanical performance of the graded foam structures. The results obtained herein demonstrate that the deformation patterns and macroscale properties of graded foam composites can be tuned by selecting different bonding agents. It is also shown that the proper selection of an adhesive can be a practical way to address the strength–energy dissipation dichotomy in graded structures.

Dynamic response of density-graded foam subjected to soft impact

The density-graded foam materials are gaining traction due to their enhanced impact and blast resistance capacities. However, current knowledge in the impact response of density-graded foam is limited to rigid impact, which narrows the design space of target materials. In particular, three main issues remain unclear, i.e., (1) how to quantify soft impact response, (2) what is the reduction of deformation and transferred stress from soft impact as compared to rigid impact, (3) whether density-graded foam can reduce the transferred stress from soft impact. To address these knowledge gaps, an analytical model based on the double shock wave theory is established by using a deformable projectile impinging onto a density-graded foam target. The dynamic stress at the supported end is analyzed for uniform, positive, and negative density gradients. The results indicate that the deformation process due to impact from deformable projectile is vastly different from that of traditional rigid projectile, with the former causing 27.42% smaller deformation and 9.87% stress reduction of the graded foam target, and three separate velocities can be observed throughout the soft impact process. The findings indicate lower mechanical requirements of target materials for soft projectile impact protections, potentially leading to weight and cost savings.

In situ deformation characterization of density-graded foams in quasi-static and impact loading conditions

Digital image correlation is utilized to characterize deformation and strain fields developed within the layers of density-graded multilayered foam structures subjected to uniaxial quasi-static and dynamic compression. Three-layered graded structures fabricated from rigid polyurethane foams with nominal densities of 160, 240, and 320 kg/m3 are subjected to quasi-static and dynamic loading. The quasi-static measurements show that, irrespective of the loading direction, the densification is initiated in the lowest density layer and propagates into other layers later once the first layer is fully densified. The deformation mechanisms are different in the case of dynamic loading conditions than quasi-static loading. In the case of dynamic loading, the deformation mechanism depends on the sample orientation relative to the direction of the applied load. In cases where the higher density layers are impacted, the propagation of the elastic and compaction waves leads to partial deformation of the lowest density layer. Sample deformation continues in all layers upon the reflection of the stress waves from the distal end of the sample. A completely different deformation response is observed in cases where the lowest density layer is oriented towards the impact face. A detailed full-field analysis of strain and stress is performed. The mechanisms associated with the formation and propagation of stress waves from the impact end to the samples' distal end are discussed.

Low-velocity impact of density-graded foam-filled square columns

In this paper, low-velocity impact of square columns filled with density-graded foam (DGF) is investigated experimentally, numerically and analytically. The low-velocity impact experiments are carried out to study the effect of density gradient on the deformation patterns and energy absorption of the DGF-filled columns. Numerical calculations are performed to study the effects of density distribution mode, density difference, average density of DGF and wall thickness of square column on the energy absorption. According to the energy method and basic folding element theory, the instantaneous dynamic crushing force is predicted analytically. The analytical predications are in good agreement with experimental results. It is found that the DGF-filled columns have excellent energy absorption capacity and low initial peak force compared to the uniform-filled columns with the same weight.

Gradient optimization of multi-layered density-graded foam laminates for footwear material design

Several sports-related injuries and orthopedic treatments need the necessity of corrective shoes that can assuage the excessive pressure on sensitive locations of the foot. In the present work, we study the mechanical and energy absorption characteristics of density-graded foams designed for shoe midsoles. The stress-strain responses of polyurea foams with relative densities (nominal density of foam divided by the density of water) of 0.095, 0.23, and 0.35 are obtained experimentally and used as input to a semi-analytical model. Using this model, three-layered foam laminates with various gradients are designed and characterized in terms of their weight, strength, and energy absorption properties. We show that, in comparison with monolithic foams, significant improvement in strength and energy absorption performance can be achieved through density gradation. Our findings also suggest that there is not a single gradient that offers a superior combination of strength, energy absorption, and weight. Rather, an optimal gradient depends on the plantar location and pressure. Depending on the magnitude of the local plantar pressure, density gradients that lead to the highest specific energy absorption are identified for normal walking and running conditions.

Impact response and energy absorption of functionally graded foam under temperature gradient environment

As an effective strategy to enhance the energy absorption and impact resistance capacities of foam materials, density-gradient design has been widely proposed as a viable solution. However, the influence of thermal environment on the impact response and energy absorption of functionally graded foam still remains unclear. In the present paper, an analytical model based on the double shock wave theory is presented to examine the impact performance of density-graded foam rods under temperature gradient environments. A density-graded foam with one end supported and the other end struck by a block of mass is presented to evaluate their impact performances. Both the positive and negative density-gradient models with power-law profiles along the axial direction of the foam rod are considered. The proposed theoretical representation is validated against several previous models, including a finite element (FE) simulation. It is demonstrated that the temperature gradient may lead to transformations in the deformation pattern for the positive and negative density-graded foams. Moreover, the temperature gradient can enlarge the impact resistance property in most cases and can reduce the energy absorption capacity of density-graded foams.

Density graded polyethylene foams: Effect of processing conditions on mechanical properties

Uniform foams (UF) and density graded foams (DGF) were produced by using similar or different temperatures on both sides of a compression molding system. The samples were produced using linear low density polyethylene as the matrix and activated azodicarbonamide as the chemical blowing agent. Morphological properties of the produced samples were analyzed via scanning electron microscopy to relate them to their mechanical properties. In particular, flexural and impact properties are reported for samples produced under a range of temperatures (140–200°C) and blowing agent concentration (0.7–1.0 wt%). The experimental results showed that a significant difference can be obtained in flexural modulus (up to 17%) and impact strength (up to 48%) depending on the side the stress is applied on. In all cases, the DGF showed better mechanical responses than UF of similar relative density for the range of conditions tested.

Fabrication and Characterization of Core–Shell Density-Graded 316L Stainless Steel Porous Structure

In the present work, cylindrical shape 316 L cellular structure with different densities in its core and outer layer (shell) is fabricated by using carbamide as a space holder, via powder metallurgy route and layer-by-layer technique. The arrangement of the created pore is the same as face-centered cubic atomic structure, and different densities are created in two regions by using carbamide particles having two different sizes in the range of 1.7-2 and 2-2.4 mm. The effect of creating a structure with higher porosity (64.5%) in the core and lower porosity (53.8%) in the shell and vice versa and also change in the ratio of the core to the cylinder cross-sectional areas, on the mechanical properties and compaction load bearing of the fabricated foam samples were investigated. In leaching process of the carbamide particles, as an important step of porous structure’s fabrication, it is shown that discontinuous leaching process is more favorable than continuous, by which it would be possible to remove more carbamide particles (around 20%) at the same time. Furthermore, the deformation of the density-graded foam shows the parallel mechanism in the core and shell sections, and the contribution of each part depends on its density and thickness. The energy absorption behavior of the fabricated specimens is evaluated optimally in terms of the energy absorption value associated with the ideal adsorption behavior. The maximum ideal energy absorption efficiency for the samples with more porosity in the shell was approximately equal to 0.91, while for the sample includes the lower amount of porosity in the shell, this value was in the range of 0.85 and 0.89.

Shock loading simulation using density-graded metallic foam projectiles

Density-graded metallic foam projectiles are proposed for shock loading simulation, with special focus placed upon designing pressure pulses having specific shapes. Experiments are performed to explore the potential of density-graded foam projectiles in generating shock loadings of various pulse shapes. Subsequently, three-dimensional Voronoi foam models with varying gradient profiles along the length direction are constructed for finite element (FE) simulations, which are validated against the experimental data. Then, FE simulations of density-graded foam projectiles impacting a stationary rigid wall are conducted to quantify the effect of density gradient on the shape of the pressure pulse generated and explore the physical mechanisms underlying such effect. It is demonstrated that density gradient affects significantly local crushing stress and local density within the shock front when it propagates from the impact end to the other end of the foam projectile. Inspired by the FE simulation results and the classical Taylor impact model, one-dimensional theoretical model for density-graded foam projectiles is developed to predict the contact force between the projectile and the fixed rigid wall. Finally, the theoretical model is employed to determine the geometry, density gradient, and firing velocity of foam projectiles needed to generate shock loadings with prescribed pulse shapes.

Theoretical investigation on impact resistance and energy absorption of foams with nonlinearly varying density

Abstract Compared with traditional uniform foams, the density-graded foam exhibits more excellent impact resistance and energy absorption capacity. In order to exploit its full potential for improved dynamic performance, the density profile should be designed properly. However, the effect of the nonlinear density gradient profile on the impact resistance and energy absorption characteristics is still unclear. The aim of this paper is to study the dynamic response of a nonlinear density-graded foam rod impinged by a mass projectile. The density in the foam rod varies along the longitudinal direction in a power-law exponent form and the coupling effect of density gradient on material properties of foam rods is taken into account. Both the negative and positive density gradients are investigated. The dynamic stress at the impinging and support ends and the energy absorption capacity for different power-law exponents are compared. The present nonlinear gradient model can be degenerated into the previous linear gradient model when the exponent is equal to 1. To validate the theoretical analysis, the finite element simulation is also carried out and a good agreement is achieved. The results indicate that the impact resistance and energy absorption capacity of the foam rod can be improved by using proper nonlinear density-graded profiles.

Protective effect of graded density aluminium foam on RC slab under blast loading – An experimental study

In recent decades, bomb incidents have significantly increased due to various blast accidents and growing terrorist threats. Therefore, the protection of important infrastructures against blast loading has never been more important. Aluminium foam, which is often used as a protective layer to absorb impact energy, has demonstrated its ability to mitigate blast effect in several studies. The outstanding energy absorption capacity of aluminium foam is mainly resulted from its long-lasting plateau-stress region which allows it to only transmit a small stress (which is equal to the plateau stress) to the protected structure while absorbing the rest by self-compaction. For aluminium foam that is manufactured by the same method, the overall energy absorbing capacity per unit volume increases proportionally with mass density; however, the plateau stress also increases with mass density which means a larger stress would be transmitted to the protected structure. Therefore, there is a trade-off between the mass density and the transmitted stress. In order to increase the overall energy absorbing capacity of aluminium foam while keeping the transmitted stress at a reasonably low magnitude, the idea of density-graded foam has been proposed which is simply a foam structure with various densities along its thickness. In this paper, the effectiveness of density-graded foams has been investigated. A number of static compressive tests are conducted on different types of aluminium foams including aluminium foams with uniform density, density-graded aluminium foams with linear gradient as well as density-graded aluminium foams with unordered gradient. In addition, a blast test program is also carried out to investigate the blast mitigation effect of graded density foams on reinforced concrete (RC) slabs.

Production of graded aluminum foams via powder space holder technique

Aluminum open-cell foams with graded cell size and graded density were successfully fabricated by powder-space holder technique using spherical granulated carbamide as space holders. The results revealed that the technique was practically feasible. Compressive properties of the graded foams were studied being compared with their analogous non-graded foams. In both cases graded foams showed no prominence in comparison to their corresponding analogous foams, except for cell size-graded foam (SGF) which demonstrated a wider plateau region in the stress–strain curve, higher densification strain, and higher energy absorption efficiency in respect to those of analogous non-graded foams. Feasibility study to produce density graded foam (DGF) by NaCl spacer was also evaluated, using the same technique. It was shown that carbamide spacer was more feasible than NaCl spacer did in producing density graded foam.

Mechanical properties of a density-graded replicated aluminum foam

The compressive mechanical properties of uniform and density-graded Al-6061 foams, produced by replication of polymer foams, are measured. While the uniform foam shows compressive behavior characteristic of conventional (uniform) metallic foams with a near constant plateau stress, the density-graded foam exhibits a smoothly rising plateau stress. This behavior is modeled using a simple series composite model based on semi-empirical scaling relationships for the compressive behavior of uniform foams.

Uniform and graded chemical milling of aluminum foams

Commercial open-cell aluminum alloy foams are subjected to chemical dissolution to reduce their density. Dissolution rates are measured for various pH, temperature and alloy heat-treatment conditions, and the resulting foam structures and surface conditions are evaluated by microscopy and X-ray microcomputed tomography to identify conditions which minimize corrosive damage. The effect of uniform dissolution on foam compressive mechanical properties is interpreted in terms of these observations. A method for production of density-graded foam samples from uniform-density precursors is also demonstrated.