Gradient Foam Research Articles

Density gradient structure foams prepared by novel two-step foaming strategy: Performance, simulation and optimization

Functional gradient foam materials play a crucial role in meeting the diverse performance and functionality requirements of modern engineering. Density gradients enable the distribution of mechanical, dielectric, and optical properties within materials, exhibiting a gradient representation. However, creating density gradients within foams poses a significant challenge, especially for semi-crystalline polymers. The paper proposed a novel two-step foaming method for preparing polypropylene (PP) foams with density gradient structure (DGS). Initially, a pre-foaming process was conducted to prepare PP pre-foams with uniform structure (US) at low temperatures, followed by a secondary foaming process on partially saturated PP pre-foams to fabricate PP DGS foams. By adjusting the duration of partial saturation time, PP foams with various DGS can be achieved. Compared with the commonly used one-step foaming method and uniform foaming method in the literature, the DGS foams prepared by the two-step foaming method exhibit not only a significant enhancement in mechanical property but also achieve the lowest thermal conductivity, while maintaining comparable and outstanding sound insulation performance. Finally, a comprehensive evaluation model using COMSOL Multiphysics was developed for the DGS foams, providing insights for optimizing foam performance through process enhancements.

Performance investigation of a thermoelectric generator for vehicle exhaust recovery using graded pore density foam metal

Improving the efficiency of thermoelectric generators (TEGs) used to harness residual heat from automobile exhausts is crucial for their widespread adoption. To enhance fluid heat transfer, the Kelvin tetrahedron model is employed for metal foam, and a multiphysical field model of the thermoelectric generator based on metal foam is established. The effects of inserting metal foam with uniform and gradient pore densities into the heat exchanger on the performance of the TEG are investigated. Experimental verification is conducted by constructing a test bench with dimensions identical to those of the model The findings suggest that inserting foam metal significantly enhances the output performance of the TEG, resulting in increases in both output power and efficiency as pore density rises. At Ta = 573 K and ma = 30 g/s, the output power of the TEG with inserted 20 PPI foam metal is enhanced by 140.46 %, while the efficiency experiences a remarkable increase of 197.50 % compared to a smooth pipe. Compared to the performance metrics of uniform foam metal, the positive gradient foam metal exhibits a maximum power increase of 7.89 % and a maximum efficiency increase of 34.46 %, along with an average pressure drop reduction of 27.29 %.

The role of Voronoi catalytic porous foam in reactive flow for hydrogen production through steam methane reforming (SMR): A pore-scale investigation

Complex pore structures in catalysts can significantly impact flow, heat transfer, and ultimately, reaction efficiency. In steam methane reforming (SMR) for hydrogen production, replacing simple catalyst geometries with intricate, interconnected structures can enhance heat transfer and optimize the SMR process. Reactive flow in Voronoi catalytic foams (VCFs) with conjugate heat transfer is investigated using OpenFOAM for pore-scale simulations. The study examines the impact of porosity, pore density (PPI), PPI distribution (uniform vs. gradient), flow direction, inlet velocity, and temperature on hydrogen production rates within a selected representative elementary volume (REV). The results show that reducing the porosity of the simple foam from 0.8 to 0.6 has led to a 25% increase in the hydrogen production mass flow rate. Additionally, replacing the simple foam with a porosity of 0.6 with a gradient foam with the same porosity can improve the hydrogen production rate by 17%. Also, it is observed that the inlet velocity has a more significant effect on the hydrogen production rather than the inlet temperature, such that increasing the inlet velocity from 0.5 to 2 m/s results in a remarkable 75% increase in the hydrogen production rate.

Lightweight thermoplastic polyurethane/multi-wall carbon nanotube foams with a continuous gradient cell structure for electromagnetic interference shielding

With the rapid development of portable microelectronic devices, materials with tunable electromagnetic shielding (EMI) performance and comfort of use have become urgently necessary. A lightweight, conductive thermoplastic polyurethane/multi-walled carbon nanotube (TPU/MWCNT) composite foam with a continuous gradient cell structure has been developed to impede electromagnetic wave reflection induced by excessive impedance mismatch. The continuous gradient distribution of cell structure and conductivity provides the TPU/MWCNT composite foams with distinct shielding effects of electromagnetic waves in both front and back gradient directions. The maximum front absorption coefficient (A) reached 0.93, which is higher than any foam with a uniform cell size within the cell size range of the gradient composite foams. At the same time, the gradient composite foams possess the characteristics of lightweight, high elasticity, and extensibility. The weight was decreased by 67.27–85.45 %, the elastic recovery ratio of compression reached 95 %, and the toughness was also excellent. Numerical simulation of the gradient foam model was conducted using CST Microwave Studio to uncover the gradient asymptotic dissipation mechanisms. The lightweight and stretchable continuous gradient foams show great promises for the next-generation portable electronic devices that generate no radiation pollution.

A breathable and sweat-absorbing pressure sensor based on PDMS gradient foam to achieve high sensitivity and wide detection range

Various designs of porous structures have been introduced to enhance the sensitivity of resistive pressure sensors. However, this method often comes at the cost of narrowing down the measurement range, limiting its use to low-pressure detection. This study proposes a soft pressure sensor with two-layer gradient foam structure. By finely adjusting the porosity and cross-linking degree of the PDMS, we aim to enhance the sensitivity without compromising the range of the sensor. Testing results demonstrate that the sensitivity of the gradient foam increases with a higher porosity, and the measurement range expands with a higher cross-linking degree. The soft sensor with the PDMS gradient stiffness foam (PGSF) achieves a sensitivity of 0.202 kPa−1 in the range of 0–40 kPa, 0.067 kPa−1 in the range of 40–210 kPa and 0.020 kPa−1 in the range of 210–850 kPa. Furthermore, the sensor exhibits a minimum detection limit of 50 Pa and demonstrates excellent stability (withstanding over 8000 testing cycles), breathability and sweat absorption. Additionally, we conducted motion detection, health monitoring and pressure mapping tests to showcase the potential applications of our proposed soft sensor in these fields.

Functionally Gradient Macroporous Polymers: Emulsion Templating Offers Control over Density, Pore Morphology, and Composition.

Gradient macroporous polymers were produced by polymerization of emulsion templates comprising a continuous monomer phase and an internal aqueous template phase. To produce macroporous polymers with gradient composition, pore size, and foam density, we varied the template formulation, droplet size, and internal phase ratio of emulsion templates continuously and stacked those prior to polymerization. Using the outlined approach, it is possible to vary one property along the resulting macroporous polymer while retaining the other properties. The elastic moduli and crush strengths change along the gradient of the macroporous polymers; their mechanical properties are dominated by those of the weakest layers in the gradient. Macroporous polymers with gradient chemical composition and thus stiffness provide both high impact load and energy adsorption, rendering the gradient foam suitable for impact protective applications. We show that dual-dispensing and simultaneous blending of two different emulsion formulations in various ratios results in a fine, bidirectional change of the template composition, enabling the production of true gradient macroporous polymers with a high degree of design freedom.

Anisotropic compression response of functionally gradient syntactic foam comprising of fly ash cenosphere and polyurethane

A novel functionally gradient (FG) syntactic foam with hierarchical cell structure was prepared by incorporating fly ash cenosphere of different size distribution into rigid polyurethane foam (PUR). The mechanical anisotropic behavior was experimentally studied by axial and traverse compression, and the influence of density gradient on failure mechanism was discussed through digital image correlation (DIC) technique. Results shown that the density graded (GD) syntactic foam produced stepwise stress strain response under axial compression, but failed by global shear pattern under traverse compression. The plateau stress of layered density (LD) syntactic foam gradually increased under both compression modes. The mechanical anisotropic property of FG syntactic foam was much smaller than that of functionally gradient aluminum foam. Failure mechanism of FG syntactic foam under axial compression was mainly controlled by the compression strain band generated in low density layers, and the deformation band successively extended to high density region. Under traverse compression, the material interfaces in LD foam significantly affected the propagation of shear deformation bands generated in high density layers, producing more short-range interpenetrating shear bands. The layered density gradation shown great potential in decreasing the anisotropic characteristics of syntactic foams. These findings can provide a valuable guide for designing and optimizing the impact resistance of functionally gradient foams.

Effect of density value and gradient distribution on the deformation mechanism of foamed concrete

Foamed concrete is an essential material in engineering that can be categorized into two types based on density distribution, namely uniform foamed concrete (UFC) and gradient foamed concrete (GFC). However, there exists a research gap concerning the mesoscopic deformation mechanism of UFC and GFC. The objective of this research is to bridge this gap by examining the quasi-static compression characteristics of UFCs with three distinct densities and GFCs with different density sequences. The results reveal that the strength of pore walls significantly influences the failure mechanism of UFCs with varying densities. Specifically, UFCs with low density exhibit weak pore-wall strength, leading to stress concentration at the pore-wall junction. During compression, these weak pore walls are widely dispersed within the specimen, resulting in a powdering failure mode. Conversely, UFCs with high density possess stronger pore walls, which prevent the powdering failure mode by maintaining adequate pore-wall strength. Nevertheless, the existence of a dominant crack within the specimen results in a splitting failure mode. In the context of GFCs, deformation occurs in a sequence from low to high density, with each layer exhibiting a failure mode corresponding to its density. Note that the last-deforming layer in this brittle gradient foam cannot attain the strength of the corresponding uniform foam. This is due to the failure of the second layer, which results in uneven contact surfaces and prompts the third layer to crack simultaneously. Finally, a statistical model is developed to forecast the compressive Stress–strain curve of foamed concrete, demonstrating remarkable agreement with experimental data.

Failure modes and energy absorption mechanism of CFRP thin-walled square tubes filled with gradient foam aluminum under axial compression

Carbon Fiber Reinforced Plastic (CFRP) thin-walled square tube filled with gradient foam aluminum represents a novel component known for its exceptional energy absorption capabilities. This paper investigates the failure modes and energy absorption mechanisms of CFRP thin-walled square tubes filled with gradient foam aluminum using a combination of numerical simulations and quasi-static axial compression tests. The influences of some factors, including lay-up angles, lay-up sequences, and lay-up thicknesses have been analyzed. Additionally, the impact of the gradient foam aluminum filler on the crashworthiness characteristics has been scrutinized. The results reveal that the samples with lay-up angles below 45° showed a failure mode characterized by layer bundle buckling during axial compression. Conversely, the samples with lay-up angles exceeding 45° exhibited lateral shear failure during axial compression, with the latter demonstrating notably higher energy absorption efficiency. Increasing the proportion of circumferential angle and setting the circumferential angle on both the inner and outer sides of the axial lay-up, the energy-absorption capacity of the filled CFRP tubes under axial compression can be improved. This study demonstrates the potential of CFRP tubes filled with gradient foam aluminum to be used as energy absorbers.

Electromagnetic interference shielding composites and the foams with gradient structure obtained by selective distribution of MWCNTs into hard domains of thermoplastic polyurethane

In this paper, multilayer thermoplastic polyurethane (TPU)/multiwalled carbon nanotubes (MWCNTs) electromagnetic interference shielding composite foams with gradient structure was prepared. The gradient distribution of effective concentration of filler and cell size were realized by selective distribution of MWCNTs into hard domains of TPU, which improved interlayer interface polarization of electromagnetic waves and impedance matching between the material and the air. The average electromagnetic interference shielding efficiency (EMI SE) of TPU/MWCNTs composites with gradient structure is 1.2 times larger than that of homogeneous composites. After foaming, the average EMI SE of the gradient foams was higher than that of the homogeneous foams, with maximum average EMI SE of 35.4 dB. This work is the first time to correlate the interaction of fillers with the soft domains and hard domains of TPU and EMI shielding performance, providing a feasible method for designing lightweight composites with low filler and better EMI shielding performance.

A new microcellular foaming strategy to develop structure-gradient thermoplastic polyurethane foams with enhanced elasticity

Functionally graded polymer foams are advanced materials that exhibit great potential for applications in energy absorption, electromagnetic interference shielding, and high-elasticity due to the graded cellular structure for mechanical performance and functional properties enhancements. However, producing polymer foams with tailored gradient structures remains a significant challenge. Herein, a new microcellular foaming strategy with two-step adsorptions was developed to prepare thermoplastic polyurethane (TPU) foams with gradient cellular structures. The TPU samples were saturated with low-pressure CO2 in the first sorption stage and partially saturated with high-pressure CO2 in the second sorption stage. By regulating CO2 pressure in the first stage and adsorption duration in the second stage, TPU samples with gradient CO2 concentrations were achieved, thereby leading to structure-gradient TPU foams. Finally, a prospective microcellular-macrocellular gradient foam with a cell size range of 30 μm to 400 μm was successfully prepared. The energy loss coefficient of structure-gradient TPU foam can be reduced by 21.5% compared to that of the foam with uniform cellular structure. Structure-gradient TPU foams show significantly enhanced mechanical performance and elasticity, and the underlying mechanism was clarified. The super-elastic TPU foams with tailored gradient structures hold significant promise for broaden applications requiring lightweight, flexibility, and elasticity.

Low-velocity impact of square conical gradient aluminium foam-filled automobile energy-absorbing boxes

In this paper, the low-velocity impact and lightweight design of the square conical gradient aluminium foam-filled automobile energy-absorbing boxes (EABes) is numerically studied. Firstly, the validity of the finite element calculation model is verified by comparing with the experimental results. Then, the influences of the conical bottom angle, tube-wall thickness, the number, position, height and depth of induction grooves, and the parameters of gradient foam on the energy absorption properties of the EABes under axial low-velocity impact are studied. After that, the mitigation and energy absorption of square conical gradient aluminium foam-filled automobile EAB are optimised. The results indicate that the aluminium tube-wall thickness has no obvious effect on improving the energy absorption properties of the EAB, and other factors have good effects on improving the energy absorption properties of the EAB. Compared with the constant cross-section EAB before optimisation, the peak impact force (F max) of the finally optimised square conical gradient aluminium foam-filled automobile EAB reduces by 22.4%, and the specific energy absorption (SEA) increases by 59.8%. The investigation is helpful for the design of the square conical gradient aluminium foam-filled automobile EAB.

Melting of phase change materials inside metal foams with uniform/graded porosity: Pore-scale simulation

Latent heat thermal storage system has the potential for industrial applications to reduce excessive consumption of fossil fuels. However, the commonly employed phase change materials (PCMs) have the drawback of poor heat transfer capability, causing slow charging/discharging rates for thermal storage systems. To enhance the melting rate of PCM, metal foams (MFs) with good thermal conductivity were exploited, focusing on the contribution of porosity gradients in foam structures to the melting characteristics. Based on tetradecahedron cells, geometric models of MFs with uniform porosity or porosity gradients were created, including negative gradient foam (NGF), homogeneous foam (HF), and positive gradient foam (PGF). Pore-scale numerical simulations (PNS) based on the tetradecahedron cells with porosity gradients were carried out. Results of PNS demonstrated that the complete melting time for the NGF, the HF and the PGF were 92 s, 92 s and 132 s, respectively. However, the NGF had the fastest integrated average temperature response rate (IATRR). Specifically, compared with the HF, the IATRR of NGF increased by 15.4%, while that of the PGF decreased by 36.1%. In addition, natural convection enhanced the heat transfer efficiency between the PCM and the metallic skeletons of the MF. The impact of natural convection on the phase transition process was analyzed from the microscopic pores. Under the influence of natural convection, the top PCM melted faster than the bottom PCM in the z-direction.

Fabrication of one-step shape memory gradient sound absorber with wrinkled inner wall and closed-pore structure

Plastic foam sound-absorbing material is of great significance to improve indoor sound environment. However, since the preparation of foamed material is fundamentally induced to form a homogeneous pore structure, the sound absorption frequency range is relatively narrow, limiting the sound absorption performance to a great extent. In order to improve the sound absorption performance in a wide frequency range, this work designed the combination of macro-porous gradient foam (MGF) and closed-pore resonator, introduced part of polyimide (PI) components based on the one-step free foaming method of polyurethane foam (PUF), and proposed a straightforward route to prepare basic polymer gradient foam. Through the arrangement and combination of different bubble holes, the sharp hole structure and the Helmholtz resonance structure were constructed by analogy. Importantly, the internal structure of the foam system was reorganized under the action of surface tension due to the inward collapse of the viscous bubbles during the process of bursting, resulting in the formation of wrinkled structures and small bubbles, which enhanced the resonant sound absorption at lower frequencies. In 200–6400 Hz, the MGF1 sample had the highest sound absorption capacity, with a cavity size range of 8.27–4.14 mm and the ability to absorb 90% of the acoustic wave above 1100 Hz. In addition, MGF samples also exhibited heat insulation behavior (0.047–0.061 W/(m·K)), shape memory, and energy absorption capacity. This gradient compound resonance structure satisfies the convenience of process manufacturing and high-efficiency sound absorption performance, which is essential for the wide application of plastic foam sound-absorbing materials.

Axial Crushing Behaviors of Metal Density Gradient Foam-Filled Square Taper Tubes: Analytical Model and Numerical Calculation

Abstract Metal tube is a traditional energy-absorbing structure, and metal foam is a lightweight material with advantages, i.e., high energy absorption and high specific strength. The foam-filled square tube can improve crashworthiness and has better energy absorption, which is higher than the sum of the energy absorption of the tube and foam. Axial crushing behaviors of metal density gradient foam (DGF) filled square taper tubes are studied analytically and numerically in this paper. An analytical model is presented to study the crushing behavior of DGF-filled square taper metal tube under axial loading, in which the interaction between square taper tube and DGF is considered. The numerical calculation is conducted, and the deformation mode is obtained. The analytical predictions are well consistent with the experimental and numerical results. The influences of taper angle, foam strength, maximum relative density, and minimum relative density of gradient foam on the compressive behavior of metal DGF-filled square taper tubes under axial loading are considered. It is demonstrated that when the taper angle is less than 85 deg, the average crushing force increases as the minimum density of the DGF increases. However, when the taper angle is greater than 85 deg, the average crushing force decreases with the increase of the minimum density of the gradient. This proposed analytical model can effectively predict the axial crushing behaviors of metal DGF-filled square taper tubes.

Research on plastic structural wave behavior and crashworthiness of continuous gradient mesoscopic foam structures under high speed impact

Under high speed impact, the macro and mesoscopic mechanical behavior, the stress wave propagation mechanism, and the relationship between density gradient and crashworthiness of continuous density gradient foam are the key issues to improve and optimize the protection capability of support structures. The numerical simulation of various density gradient foams is carried out, and the meso-discontinuity of foams is overcome by using the local gradient tensor method of least square error, and the plastic structure wavefronts with clear interfaces are obtained. The plastic structure wave propagation mechanism of foam with different density configurations was analyzed and the relationship between density gradient and crashworthiness was further revealed. The results show that inertia effect is the dominant factor of collapse in the early stage of impact. In the middle and late stage of impact, the dominant factor of collapse changes to the microscopic density of foam. The distribution of continuous density gradient significantly affects the impact resistance. Compared with low-high density configuration foam (LH), high-low density configuration gradient foam (HL) has a 140% increase in impact end force, a 24% decrease in support end force, a 3% decrease in maximum compression, and a 41% longer response time.

Aerodynamic vs. frictional damping in primary flight feathers of the pigeon Columba livia

During flight, vibrations potentially cause aerodynamic instability and noise. Besides muscle control, the intrinsic damping in bird feathers helps to reduce vibrations. The vanes of the feathers play a key role in flight, and they support feathers’ aerodynamic function through their interlocked barbules. However, the exact mechanisms that determine the damping properties of the vanes remain elusive. Our aim was to understand how the structure of the vanes on a microscopic level influences their damping properties. For this purpose, scanning electron microscopy (SEM) was used to explore the vane’s microstructure. High-speed videography (HSV) was used to record and analyze vibrations of feathers with zipped and unzipped vanes upon step deflections parallel or perpendicular to the vane plane. The results indicate that the zipped vanes have higher damping ratios. The planar surface of the barbs in zipped vanes is responsible for aerodynamic damping, contributing 20%–50% to the whole damping in a feather. To investigate other than aerodynamic damping mechanisms, the structural and material damping, experiments in vacuum were performed. High damping ratios were observed in the zipped vanes, even in vacuum, because of the structural damping. The following structural properties might be responsible for high damping in feathers: (i) the intact planar surface, (ii) the interlocking of barbules, and (iii) the foamy inner material of the barb’s medulla. Structural damping is another factor demonstrating 3.3 times (at vertical deflection) and 2.3 times (at horizontal deflection) difference in damping ratio between zipped and unzipped feathers in vacuum. The shaft and barbs filled with gradient foam are thought to increase the damping in the feather further.

Study on protective performance and gradient optimization of helmet foam liner under bullet impact.

Protective equipment in war plays a vital role in the safety of soldiers, the threat to soldiers from brain damage caused by deformation at the back of the helmet cannot be ignored, so research on reduce blunt post-cranial injury has great significance and value. This study first conducted gunshot experiments, used rifle bullets impact bulletproof plate and different density liner foam to record the incident process and internal response of craniocerebral model. After verifying the accuracy of finite element model through experimental data, optimization model is established based on response surface method to optimize the structure of gradient foam, analyze the cranial strain and energy absorption to select the best density and thickness distribution of each foam layer. Optimization results show that liner foam which designed to have lower density and thicker thickness for impact and brace layers, higher density and thinner thickness for middle layer can significantly improve the energy absorption efficiency. Compared to the 40.65 J of energy absorption before optimization, the optimized gradient foam can absorb 109.3 J of energy, with a 169% increase in the absorption ratio. The skull strain in the craniocerebral model was reduced from 1.260 × 10–2 to 1.034 × 10–2, with a reduction of about 22%. This study provides references for the design and development of protective equipment and plays an important role in ensuring the safety of soldiers in the battlefield environment.

Switching Frontal Polymerization Mechanisms: FROMP and FRaP

Two frontal polymerization (FP) mechanisms, frontal ring-opening metathesis polymerization (FROMP) of dicyclopentadiene and frontal radical polymerization (FRaP) of benzyl acrylate and hexanediol diacrylate, were combined for rapid manufacturing of welded thermoset materials. Leveraging the immiscibility of the two different FP resins, welded thermosets and gradient foams of varying composition were achieved by switching of FP mechanisms. The adhesion strength of the welded thermoset materials differed depending on the originating mechanism. Finally, welded thermoset foams of varying porosity and homogeneity were generated through initiation from the bottom of the two resins.

Effect of stepwise gradient on dynamic failure of composite sandwich beams with metal foam core subject to low-velocity impact

Dynamic failure behaviors of fully clamped and simply supported composite sandwich beams with stepwise gradient foam cores subject to low-velocity impact have been investigated experimentally. The sandwich beams with uniform foam core, positive-gradient foam core and negative-gradient foam core are designed and manufactured. The experimental results show that the mass distributions of cores have significant effect on the failure modes. The low-density foam layer at the impact end would lead to local failure mode of indentation or face fracture, while the high-density foam layer at the impact end would bring about global failure mode of combined core shear and debonding. The simply supported graded sandwich beam exhibits softening post-failure behavior, while the fully clamped graded sandwich beam displays hardening post-failure behavior. The initial strengths of fully clamped and simply supported sandwich beams with negative-gradient foam core are the highest, while the subsequent strength of the fully clamped sandwich beams with positive-gradient foam core is the highest. Among all gradient distributions of foam cores, the impact resistance of the fully clamped composite sandwich beams with negative-gradient foam cores design is the highest.