The effects of relative density of metal foams on the stresses and deformation of beam under bending

The exact analytic solution of the pure bending beam of metallic foams is given. The effects of relative density of the material on stresses and deformation are revealed with the Triantafillou and Gibson constitutive law （TG model） taken as the analysis basis. Several examples for individual foams are discussed, showing the importance of compressibility of the cellular materials. One of the objects of this study is to generalize Hill＇s solution for incompressible plasticity to the case of compressible plasticity, and a kinematics parameter is brought into the analysis so that the velocity field can be determined.

Experimental Study on Heat Storage Properties Comparison of Paraffin/Metal Foams Phase Change Material Composites

Heat storage properties of phase change materials(PCMs) are essential characteristics that perform a key role in thermal heat energy storage systems.The thermal properties of PCMs can be improved by developing metal foam/PCM composites.The addition of metal foam in PCMs has a significant effect on the thermal characteristics of PCMs.In this paper,the heat storage properties of two different metal foam/PCM composites were experimentally examined.The behavior of paraffin in metal foam(copper and iron-nickel)/paraffin composites concerning pure paraffin at a constant heat flux of 1000 W/m^(2) in three directions simultaneously(x,y,and z) was studied.Paraffin was infiltrated into copper and iron-nickel foams to develop composite materials which resulted in enhancing the thermal conductivity of the paraffin.A comparative analysis is made on the heat storage properties of paraffin in copper and iron-nickel foams/paraffin composites.Inner temperature distribution during the phase transition process is experimentally evaluated.This comparison indicates that temperature uniformity in copper foam/paraffin composite is better than in iron-nickel foam/paraffin composite and pure paraffin at the same heat flux.Experimental results show that at heat flux of 1000 W/m^(2),the heat storage time for copper foam/paraffin composite is 20.63% of that of iron-nickel foam/paraffin composite.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Compression properties of cost-efficient porous expanded clay reinforced AA7075 syntactic foams fabricated by industrial-oriented die casting technology

In today’s manufacturing industries,hard competition between rival firms makes it compulsory for researchers to design lighter and cheaper machine components due to the megatrends of cost-effectiveness and anti-pollution.At this point,aluminum syntactic foams(ASFs)are new-generation engineering composites and come into the upfront as a problem-solver.Owing to their features like low density,sufficient elongation,and perfect energy absorption ability,these advanced foams have been considerably seductive for many industrial sectors nowadays.In this study,an industrial-oriented automatic die casting technology was used for the first time to manufacture the combination of AA7075/porous expanded clay(PEC).Micro evaluations(optical and FESEM)reveal that there is a homogenous particle distribution in the foam samples,and inspections are compatible with the other ASF studies.Additionally,T6 aging heat treatment was operated on one half of the produced foams to explore the probable impact of aging on the compressive responses.Attained results show that PEC particles can be an alternative to expensive hollow spheres used in the previous works.Besides,a favorable relationship is ascertained between the aging treatment and mechanical properties such as compression strength and plateau strength.

Study on the melting process of phase change materials in metal foams using lattice Boltzmann method

A thermal lattice Boltzmann model is developed for the melting process of phase change material (PCM) embedded in open-cell metal foams. Natural convection in the melt PCM is considered. Under the condition of local thermal non-equilibrium between the metal matrix and PCM, two evolution equations of temperature distribution function are pre-sented through selecting an equilibrium distribution function and a nonlinear source term properly. The enthalpy-based method is employed to copy with phase change problem. Melting process in a cavity of the metal foams is simulated using the present model. The melting front locations and the temperature distributions in the metal foams filled with PCM are obtained by the lattice Boltzmann method. The effects of the porosity and pore size on the melting are also investigated and discussed. The re-sults indicate that the effects of foam porosity play important roles in the overall heat transfer. For the lower porosity foams, the melting rate is comparatively greater than the higher porosity foams, due to greater heat conduction from metal foam with high heat conductivity. The foam pore size has a limited effect on the melting rate due to two counteracting effects between conduction and convection heat transfer.

Bestow metal foams with nanostructured surfaces via a convenient electrochemical method for improved device performance

Metal foams have been intensively studied as three-dimensional （3-D） bulk mass-support for various applications because of their high conductivities and attractive mechanical properties. However, the relatively low surface area of conventional metal foams largely limits their performance in applications such as charge storage. Here, we present a convenient electrochemical method for addressing this problem using Cu foams as an example. High surface area Cu foams are fabricated in a one-pot one-step manner by repetitive electrodeposition and dealloying treatments. The obtained Cu foams exhibit greatly improved performance for different applications like surface enhanced Raman spectroscopy （SERS） substrates and 3-D bulk supercapacitor electrodes.

Theoretical and experimental advances on heat transfer and flow characteristics of metal foams

Open cell metal foam can be applied to greatly improve thermal performance of heat sink and heat exchanger,so that it has been widely used in the fields of thermal(or heat)control system of aerospace vehicle and energy utilization system and become a very important topic for research in the aerospace thermophysics field,and more and more attentions have been attracted.The optimal design of metal foam heat transfer devices is based on the understanding the flow and heat transfer characteristics in metal foam.This article reviews some recent progresses of theoretical and experimental researches on heat transfer enhancement and flow characteristics of metal foam.We found that the pore cell simplification models of metal foams generally fall into four categories,among which the most commonly used cell model is Kelivin model.Some exploratory works performed by the current authors are also introduced,such as the effect of boundary conditions on the heat transfer enhancement;the theoretical modelling of interfacial convective heat transfer taking into account heat conduction between foam ligaments;and the flow characteristics under relatively high velocity.The analytical results show that the flow characteristics of metal foam at relatively high speed are completely different from those at low speed,a further thorough study of the heat transfer and flow characteristics of metal foam is necessarily required.In this paper,two types of partial filling techniques are discussed.The heat transfer performance of partially filled tubes was evaluated by both the performance evaluation criteria and the performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving.The results show that the filling type of metal foam have a significant impact on its heat transfer enhancement performance.Therefore,the filling method of metal foam should be further studied,in order to optimize the thermophysical properties of heat transfer devices.

Compression behavior of metal foams with real pore structures through CT scan images

Based on the real pore structure obtained from computed tomography(CT)scan images,a three-dimensional(3D)model of the metal foam sample with specified porosity is established,and the model is compressed and simulated by finite element method with the simulation results compared with the experimental test results for validation.At the same time,based on the spatial distribution characteristics of cells extracted from 3D model construction,a widely used metal foam model with Voronoi pore structure or spherical pore structure was established and simulated under compression.The two compression simulation results with regular pore structure models were also compared with the experimental results and CT model results to study the influence of cell wall morphology on the compression performance of metal foams.The simulation results show that CT model agrees well with the experimental results and is more accurate than Voronoi pore or spherical pore model,which can provide a more reasonable option for investigation of metal foams.

Elasto-plastic analysis of crack in metallic foams

To determine the solutions of the well-known problem of a finite width strip with single edge crack,some results on elasto-plastic fracture analysis for metallic foams are reported.Meanwhile,in order to discuss and put an insight into the nonlinear fracture analysis,the Dugdale model for plastic deformation of this configuration for metallic foams is recommended and solved.Combining the asymptotic solution with the Dugdale model and elastic solution,the stress field in the plastic zone and the size of the plastic zone are expressed as analytical forms.Based on Williams expansion method,the estimate of the scale factor is also completed and analyzed.In view of these analytical solutions,the results show the scale factor is a useful parameter for the fracture theory of metallic foams.

ULTRALIGHT POROUS METALS:FROM FUNDAMENTALS TO APPLICATIONS

Over the past few years a number of low cost metallic foams have been produced and used as the core of sandwich panels and net shaped parts.The main aim is to develop lightweight structures which are stiff,strong,able to absorb large amount of energy and cheap for application in the transport and construction industries.For example,the firewall between the engine and passenger compartment of an automobile must have adequate mechanical strength,good energy and sound absorbing properties,and adequate fire retardance.Metal foams provide all of these features,and are under serious consideration for this applications by a number of au- tomobile manufacturers(e.g.,BMW and Audi).Additional specialized applications for foam-cored sandwich panels range from heat sinks for electronic devices to crash barriers for automobiles,from the construction panels in lifts on aircraft carriers to the luggage containers of aircraft,from sound proofing walls along railway tracks and highways to acoustic absorbers in lean premixed combustion chambers.But there is a problem.Before metallic foams can find a widespread application,their basic properties must be measured,and ideally modeled as a function of microstructural details,in order to be included in a design.This work aims at reviewing the recent progress and presenting some new results on fundamental research regarding the mi- cromechanical origins of the mechanical,thermal,and acoustic properties of metallic foams.

Performance Evaluation of Electromagnetic Shield Constructed from Open-Cell Metal Foam Based on Sphere Functions

This study evaluates the performance of a model of open-cell metal foams generated by sphere functions.To this end,an electromagnetic shield constructed from the model was inserted between two horn antennas in an electromagnetic wave propagation simulation.The foam-hole diameter in the electromagnetic shield model was varied as d=2.5 and 5.0 mm,and the frequency of the electromagnetic waves was varied from 3 to 13 GHz.In the numerical experiments of shield effectiveness,the shields with foam holes of both diameters attenuated the electromagnetic waves across the studied frequency range.The shield effectiveness was enhanced at low frequencies and in the shield with smaller hole diameter.

Exact Solution of a Cylinder Tube Made of Metallic Foam Under Inner Pressure

Exact solution of the stress and velocity fields of a cylinder tube of metallic foams under inner pressure is given in which the Triantafillou and Gibson constitutive law （TG model） for the material is taken as a basis of the calculation. The nonlinear equation is turned linear equation by introducing a kinematics parameter. The differences between the full condensed materials and the effect of the relative density are also discussed.

Mechanical characterization of the role of defects in sintered FeCrAIY foams

Open celled metal foams fabricated through metal sintering are a new class of material that offers novel mechanical and acoustic properties. Previously, polymer foams have been widely used as a means of absorbing acoustic energy. However, the structural applications of these foams are limited. The metal sintering approach offers a costeffective means for the mass-production of open-cell foams from a range of materials, including high-temperature steel alloys. In this first part of two-paper series, the mechanical properties of open-celled steel alloy （FeCrA1Y） foams were characterized under uniaxial compression and shear loading. Compared to predictions from established models, a significant knockdown in material properties was observed. This knockdown was attributed to the presence of defects throu- ghout the microstructure that result from the unique fabrication process. Further in situ tests were carried out in a SEM （scanning electronic microscope） in order to investigate the effects of defects on the properties of the foams. Typically, the onset of plastic yielding was observed to occur at defect locations within the microstructure. At lower relative densities, ligament bending dominates, with the deformation initializing at defects. At higher relative densities, an additional deformation mechanism associated with membrane elements was observed. In the follow-up of this paper, a finite element model will be constructed to quantify the effects of defects on the mechanical performance of the opencell foam.

Modeling of the role of defects in sintered FeCrAlY foams

The metal sintering approach offers a costeffective means for the mass-production of open-cell foams from a range of materials, including high-temperature steel alloys, which offer novel mechanical and acoustic properties. In a separate experimental study, the mechanical properties of open-celled steel alloy （FeCrA1Y） foams have been characterized under uniaxial compression and shear loading. Compared to predictions from established models, a significant knockdown in material properties was observed. This knockdown was attributed to the presence of defects throughout the microstructure that result from the unique fabrication process. In the present paper, the microstructure of sintered FeCrA1Y foams was modeled by using a finite element （FE） model. In particular, microstructural variations were introduced to a base lattice, and the effects on the strength and stiffness calculated. A range of defects identified under scanning electronic microscope （SEM） imaging were considered including broken ligaments, thickness variations, and pore blockages, which are the three primary imperfections observed in sintered foams. The corresponding levels of defect present in the material were subsequently input into the FE model, with the resulting predictions correlating well with experimental data.

A plastic indentation model for sandwich beams with metallic foam cores

Light weight high performance sandwich composite structures have been used extensively in various load bearing applications.Experiments have shown that the indentation significantly reduces the load bearing capacity of sandwiched beams.In this paper,the indentation behavior of foam core sandwich beams without considering the globally axial and flexural deformation was analyzed using the principle of virtual velocities.A concisely theoretical solution of loading capacity and denting profile was presented.The denting load was found to be proportional to the square root of the denting depth.A finite element model was established to verify the prediction of the model.The load-indentation curves and the profiles of the dented zone predicted by theoretical model and numerical simulation are in good agreement.

Development in applications of porous metals

Applications of porous metal materials are reviewed so far. These applications deal with filtration and separation, energy absorption, electrode matrix, fluid distribution and control, heat exchangers, reaction materials, constructional materials, electromagnetic shielding, biomaterials and so on. All these are expected to promote the improvement of the property and structure for porous metals.

Mechanical Property of Foamed Metal

A comprehensive study on the mechanical behavior of foamed metals was demonstrated.The relationship among their mechanical properties,preparation method,porosity and the structure was briefly studied as well.

Properties and corrosion behavior of Al based nanocomposite foams produced by the sintering-dissolution process

The properties orAl based nanocomposite metal foams and their corrosion behaviors were investigated in this study. For this, the composite metal foams with different relative densities （porosity） reinforced with alumina nanoparticles were prepared using a powder me- tallurgy-based sintering-dissolution process （SDP） and NaC1 particles were used as space holders. Then, the effect of nanoparticle rein- forcement and different amounts of NaC1 space holders （corresponding porosity） on the microstructure, morphology, density, hardness, and electrochemical specifications of the samples were investigated. It was found that as the relative density increased from 60% to 70%, the wall thickness increased from about 200 to 300 pro, which led to a decrease in pore size. Also, the addition of nanoparticle reinforcement and the increased relative density result in increasing metal foam hardness. Moreover, electrochemical test results indicated that increasing the A1203 content reduced the corrosion rate, but increasing the porosity enhanced it.

Low-velocity impact of rectangular foam-filled fiber metal laminate tubes

Through theoretical analysis and finite element simulation,the low-velocity impact of rectangular foam-filled fiber metal laminate(FML)tubes is studied in this paper.According to the rigid-plastic material approximation with modifications,simple analytical solutions are obtained for the dynamic response of rectangular foam-filled FML tubes.The numerical calculations for low-velocity impact of rectangular foam-filled FML tubes are conducted.The accuracy of analytical solutions and numerical results is verified by each other.Finally,the effects of the metal volume fraction of FMLs,the number of the metal layers in FMLs,and the foam strength on the dynamic response of foam-filled tubes are discussed through the analytical model in details.It is shown that the force increases with the increase in the metal volume fraction in FMLs,the number of the metal layers in FML,and the foam strength for the given deflection.

Thermal Modeling and Analysis of Metal Foam Heat Sink with Thermal Equilibrium and Non-Equilibrium Models

In the present study,the thermal performance of metal foam heat sink was numerically investigated by adopting the local thermal non-equilibrium(LTNE)model and local thermal equilibrium(LTE)model.Temperature field distributions and temperature difference field distributions of solid and fluid phases were presented.Detailed thermal performance comparisons based on the LTE and LTNE models were evaluated by considering the effects of the relevant metal foam morphological and channel geometrical parameters.Results indicate that a distinct temperature difference exists between the solid and fluid phases when the LTNE effect is pronounced.The average Nusselt numbers predicted by both the LTE and LTNE models are approaching with the increase of porosity,pore density,Reynolds number,large thermal conductivity ratio,and large aspect ratio.This is attributed to the significant reduction of the interstitial convective thermal resistance between the solid and fluid phases,as a result,the LTE model can replace the LTNE model for thermal modeling in these conditions.In addition,the overall thermal performance assessment of metal foam heat sink is compared with the non-porous heat sink,and it shows that the thermal performance factor of metal foam heat sink is approximately two times of the non-porous heat sink.