Mechanical characterization of the role of defects in sintered FeCrAlY 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 cost- effective 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 (FeCrAlY) 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 throughout 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 open-cell foam. The project supported by the US Office of Naval Research (N000140210117), the National Basic Research Program of China (2006CB601202), the National Natural Science Foundation of China (10328203, 10572111, 10632060), and the National 111 Project of China (B06024).     

Three-dimensional modeling of the mechanical property of linearly elastic open cell foams

Three-dimensional Voronoi models are developed to investigate the mechanical behavior of linearly elastic open cell foams. Dependence of the Young’s modulus, Poisson’s ratio and bulk modulus of the foams on the relative density is evaluated through finite element analysis. Obtained results show that in the low density regime the Young’s modulus and bulk modulus of random Voronoi foams can be well represented by those of Kelvin foams, and are sensitive to the geometric imperfections inherent in the microstructure of foams. In contrast, the compressive plateau stress of the foams is less sensitive to the imperfections. Failure surface of the foams subject to multi-axial compression is determined and is found to comply with the maximum compressive principal stress criterion, consistent with available experimental observations on polymer foams. Numerical results also show that elastic buckling of cell edges at microscopic level is the dominant mechanism responsible for the compressive failure of elastic open cell foams.     

Modeling and prediction of bulk properties of open-cell carbon foam

The emerging ultralightweight material, carbon foam, was modeled with three-dimensional microstructures to develop a basic understanding in correlating microstructural configuration with bulk performance of open-cell foam materials. Because of the randomness and complexity of the microstructure of the carbon foam, representative cell ligaments were first characterized in detail at the microstructural level. The salient microstructural characteristics (or properties) were then correlated with the bulk properties through the present model. In order to implement the varying anisotropic nature of material properties in the foam ligaments, we made an attempt to use a finite element method to implement such variation along the ligaments as well as at a nodal point where the ligaments meet. The model was expected to provide a basis for establishing a process-property relationship and optimizing foam properties.The present model yielded a fairly reasonable prediction of the effective bulk properties of the foams. We observed that the effective elastic properties of the foams were dominated by the bending mode associated with shear deformation. The effective Young's modulus of the foam was strongly influenced by the ligament moduli, but was not influenced by the ligament Poisson's ratio. The effective Poisson's ratio of the foam was practically independent of the ligament Young's modulus, but dependent on the ligament Poisson's ratio. The effective Young's modulus of the carbon foam was dependent more on the transverse Young's modulus and the shear moduli of the foam ligaments, but less significantly on the ligament longitudinal Young's modulus. A parametric study indicated that the effective Young's modulus was significantly improved by increasing the solid modulus in the middle of the foam ligaments, but nearly invariant with that at the nodal point where the ligaments meet. Therefore, appropriate processing schemes toward improving the transverse and shear properties of the foam ligaments in the middle section of the ligaments rather than at the nodal points are highly desirable for enhancing the bulk moduli of the carbon foam.     

Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength.     

Simulations of flow through open cell metal foams using an idealized periodic cell structure

A new approach to modeling the flow through a porous medium with a well defined structure is presented. This approach entailed modeling an idealized open cell metal foam based on a fundamental periodic unit of eight cells and solving the flow through the three-dimensional cellular unit. To model an infinitely large matrix, periodic boundary conditions were set on the walls parallel to the flow direction, while a pseudo-periodic boundary condition with a prescribed volumetric flow rate was set over the inlet–outlet pair of the unit cell. The pressure drop data of the flow through the cellular unit were then compared on a length-normalized basis against experimental data. The pressure drop values predicted by the simulations were consistently 25% lower than the values obtained in the experiments on a similar foam and under identical flow conditions. One explanation for the discrepancy between the two sets of data is the lack of pressure drop increasing wall effects in the simulations. The increase in the pressure drop from wall effects in the simulation was quantified.     

泡沫铝率相关性能的有限元模拟

构建了三维随机分布球形泡孔模型,模拟开、闭孔混合结构泡沫铝材料的微细观结构,并通过有限元方法计算了10~104 s-1应变率范围内、孔隙率35%~65%泡沫铝材料的率相关性以及应变率和相对密度变化对泡沫铝动态压缩力学性能的影响。研究表明:中、低应变率下,泡沫铝材料率相关性能主要取决于基体材料的应变率敏感性;高应变率下,泡沫铝材料率相关性能受基体材料的应变率敏感性以及微结构惯性联合作用,且相对密度较低泡沫铝材料的微结构惯性效应更显著。     

The role of plastic deformation on the impact behaviour of high aspect ratio aluminium foam-filled sections

The main objective of this work is to investigate the role of the plastic deformation of metal foams on the dynamic behaviour of aluminium foam-filled columns with respect to their energy absorbing capabilities. The influence of the cross-section shape as well as other parameters is thoroughly studied. A comparison with correspondent hollow-sections is performed concerning the dissipation of kinetic energy and the obtained deformed profiles. For this particular purpose, three-dimensional finite element modelling dynamic analyses are carried out using ABAQUS/Explicit in order to achieve an in-depth study of the structural crash behaviour, during which energy needs to be absorbed in a controlled manner. A comprehensive numerical study of the crush behaviour of aluminium foam-filled sections undergoing axial compressive loading is performed. The results obtained are also analysed with respect to the reduction in the length of the structural element and impact time, the effect of friction between the foam and the outer skin, the energy decomposition, the role of plastic deformation, the influence of the skin material and impact velocity, and the influence of the shape of the cross-section on the impact behaviour. A comparison with existing analytical expressions is made in order to corroborate the numerical results.     

Compressive response of a sandwich plate containing a cracked diamond-celled lattice

The compressive strength is determined for a sandwich plate containing a centre-cracked core made from an elastic–brittle, diamond-celled lattice. It is assumed that the lattice fails when the major component of principal stress anywhere in the lattice attains the compressive or tensile strength of the solid, or when local buckling intervenes. First, analytical and numerical predictions are given for the unnotched strength of the core and for the compressive fracture toughness of the lattice K_IC. Second, finite element simulations and analytical models are reported for the fracture response of the sandwich plate with cracked core. The active failure mechanism in the cracked core is sensitive to core height, crack length, lattice geometry and material choice; this is illustrated by means of material-property charts.     

Constitutive modeling of aluminum foam including fracture and statistical variation of density

An existing constitutive model applicable for aluminum foam was evaluated. The model was implemented in LS-DYNA, and several test cases were analyzed and compared to experimental data. The numerical analyses consisted of foam subjected to both simple and more complex loading conditions where fracture was of varying importance. Therefore, simple fracture criteria were added to the model. Additionally, the inhomogeneities in the foam were modeled by incorporating the possibility of statistical variation of the foam density. The implemented model is efficient and robust, and gives satisfactory results compared with the experimental results.     

Attenuation of shock waves propagating in polyurethane foams

Shock wave attenuation in polyurethane foams is investigated experimentally and numerically. This study is a part of research project regarding shock propagation in polyurethane foams with high-porosities = 0.951 ~ 0.977 and low densities of ρc = 27.6 ~55.8 kg/m³. Sixty Millimeter long cylindrical foams with various cell numbers and foam insertion condition were installed in a horizontal shock tube of 50 mm i.d. and 5.4 mm in length. Results of pressure measurements in air/foam combination are compared with CFD simulation solving the one-dimensional Euler equations. In the case of a foam B fixed on shock tube wall, pressures at the shock tube end wall increases relatively slowly comparing to non-fixed foam, free to move and a foam A fixed on shock tube wall. This implies that elastic inertia hardly contributes to pressure build up. Pressures behind a foam C fixed on shock tube wall decrease indicating that shock wave is degenerated into compression wave. Dimensionless impulse and attenuation factor decrease as the initial cell number increases. The momentum loss varies depending on cell structure and cell number.     

The effects of micro-defects and crack on the mechanical properties of metal fiber sintered sheets

The effects of three types of defect (i.e., two micro defects—broken fibers and separation of fiber joints and one macro defect—crack) on the mechanical properties of porous metal fiber sintered sheets (MFSSs) are investigated by a combination of numerical simulation, analytical modeling, and experimental test. All simulations are based upon the previously developed micromechanics random beam model (Jin et al., 2013). Broken fibers are realized by removing cell edges (i.e., fibers between two joints) in an otherwise perfect model. Their induced decreases in the elastic moduli and strengths are found to be much lower than those of two dimensional (2D) foams and Kagome grids. For the defect in the form of separation of fiber joints, both analytical and numerical models are developed. The predicted linear decreases in the moduli and strengths (except for the compressive strength) with increasing number of separated fiber joints indicate that MFSSs be insensitive to the defect of joint separation. To explore the effect of crack, fracture toughness of MFSSs is measured and is found to be significantly higher than that of metal foams of the same relative density (i.e., volume fraction of the constituent solid material). The underlying ductile mechanism of MFSSs is further investigated by numerical simulations, showing that plastic deformation spreads all over the fibers in ligament rather than concentrates around crack tip. This study shows that MFSSs are superior in view of their resistance to the considered micro-defects and crack.     

基于同步辐射原位CT的聚氨酯泡沫微观变形机理研究

为揭示聚氨酯泡沫的微观结构性能关系,本文依靠自主研发的微型材料试验机,在美国APS光源2BM线站上搭建了原位CT系统,对闭孔硬质聚氨酯泡沫在准静态压缩加载下的变形损伤行为进行了三维实时表征,分辨率可达0.87μm。通过原位CT试验获取了硬质聚氨酯泡沫的应力应变关系,以及三个变形阶段(弹性、平台、压实)的三维结构演化过程。三维图像显示,在平台段会观察到局部压缩带从样品两端向中间传播的过程,且压缩带传播速度会超过压头速度。同时,利用数字体图像相关技术精确计算了聚氨酯泡沫的三维变形场,表明压缩变形主要集中在变形带内部。通过追踪胞元变形过程并利用表面曲率场来量化胞壁变形,发现胞元坍塌主要源于包壁屈曲形成的褶皱。     

On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations

A recently proposed reduced enhanced solid-shell (RESS) element [Alves de Sousa, R.J., Cardoso, R.P.R., Fontes Valente, R.A., Yoon, J.W., Grácio, J.J., Natal Jorge, R.M., 2005. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part I – Geometrically Linear Applications. International Journal for Numerical Methods in Engineering 62, 952–977; Alves de Sousa, R.J., Cardoso, R.P.R., Fontes Valente, R.A., Yoon, J.W., Grácio, J.J., Natal Jorge, R.M., 2006. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part II – Nonlinear Applications. International Journal for Numerical Methods in Engineering, 67, 160–188.] is based on the enhanced assumed strain (EAS) method with a one-point quadrature numerical integration scheme. In this work, the RESS element is applied to large-deformation elasto-plastic thin-shell applications, including contact and plastic anisotropy. One of the main advantages of the RESS is its minimum number of enhancing parameters (only one), which when associated with an in-plane reduced integration scheme, circumvents efficiently well-known locking phenomena, leading to a computationally efficient performance when compared to conventional 3D solid elements. It is also worth noting that the element accounts for an arbitrary number of integration points through thickness direction within a single element layer. This capability has proven to be efficient, for instance, for accurately describing springback phenomenon in sheet forming simulations. A physical stabilization procedure is employed in order to correct the element’s rank deficiency. A general elasto-plastic model is also incorporated for the constitutive modelling of sheet forming operations with plastic anisotropy. Several examples including contact, anisotropic plasticity and springback effects are carried out and the results are compared with experimental data.     

泡沫铝泡孔动态变形特性研究

在SHPB实验中采用应变冻结法将试件冻结于设定的压缩应变,然后观察内部泡孔的变形情况并讨论其变形机理。分别对同一相对密度(40%)、不同基体材料的两种泡沫铝以及两种相对密度(19%和8%)、相同基体材料的泡沫铝进行实验,讨论了基体材料的本构关系、泡沫的相对密度对变形模式的影响。利用ANSYS/LS DYNA软件对泡沫铝在动态压缩时泡孔的变形进行数值模拟计算,进一步说明泡沫铝泡孔变形的模式与基体材料本构关系及相对密度的关系。     

Modeling of dielectric viscoelastomers with application to electromechanical instabilities

Soft dielectrics are electrically-insulating elastomeric materials, which are capable of large deformation and electrical polarization, and are used as smart transducers for converting between mechanical and electrical energy. While much theoretical and computational modeling effort has gone into describing the ideal, time-independent behavior of these materials, viscoelasticity is a crucial component of the observed mechanical response and hence has a significant effect on electromechanical actuation. In this paper, we report on a constitutive theory and numerical modeling capability for dielectric viscoelastomers, able to describe electromechanical coupling, large-deformations, large-stretch chain-locking, and a time-dependent mechanical response. Our approach is calibrated to the widely-used soft dielectric VHB 4910, and the finite-element implementation of the model is used to study the role of viscoelasticity in instabilities in soft dielectrics, namely (1) the pull-in instability, (2) electrocreasing, (3) electrocavitation, and (4) wrinkling of a pretensioned three-dimensional diaphragm actuator. Our results show that viscoelastic effects delay the onset of instability under monotonic electrical loading and can even suppress instabilities under cyclic loading. Furthermore, quantitative agreement is obtained between experimentally measured and numerically simulated instability thresholds. Our finite-element implementation will be useful as a modeling platform for further study of electromechanical instabilities and for harnessing them in design and is provided as online supplemental material to aid other researchers in the field.     

Damage growth by debonding in a single fibre metal matrix composite: Elastoplasticity and strain energy density criterion

A displacement-based finite element-based numerical approach has been employed to study the damage growth in a unidirectional SiC/Al composite containing a pre-existing crack along the fibre/matrix interface. The composite is modeled as a two-material cylinder subjected to uniform displacement. A detailed analysis is made for the stress field in the vicinity of the debond crack tip. This approach incorporates an elastic-plastic analysis combined with a strain energy density criterion to predict debonded crack growth direction, extended stable growth and final termination. The influence of contact taking place between the debonded surfaces is also considered. It is shown that such surface contact leads to reduced stress and strain fields around the crack tip, while the extent of reduction is increased with debonding length. By combining the reduced stress field with the strain energy density criterion, a limiting value for the debonding extension can be calculated for the critical applied displacement that led to fibre fracture.     

Modeling the dynamic response of visco-elastic open-cell foams

This article introduces a mesoscopic formulation for modeling the dynamic response of visco-elastic, open-cell solid foams. The effective material response is obtained by enforcing on a representative 3D unit cell the principle of minimum action for dissipative systems. The resulting model accounts explicitly for the foam topology, the elastic and viscous properties of the cell wall, and the inertial effects arising from non-affine motion within the cells. The microinertial effects become significant in retarding the foam collapse during exceedingly high strain-rate loading. As an application example, a heterogenous case of compressive deformation at high strain rate is simulated utilizing the present model as a constitutive update in a non-linear finite element analysis code. This FEM simulation shows the ability of the model to capture the progressive foam collapse during the dynamic compression as observed in experimental studies. Using the microscopic model, the inertial and viscous strain-rate effects are investigated through the foam density, viscosity, and relative density. Based on the physics incorporated into the local cell model, we provide insight into the physical mechanisms responsible for the experimentally observed strain-rate effects on the behavior of dynamically loaded foam materials.     

Evaluation of the residual stresses due to the sintering process of diamond–metal matrix hot-pressed tools

The sintering process of diamond–metal matrix hot-pressed tools, usually used for cutting hard materials (e.g., stone cutting) originates residual stresses, which should be taken into account in the performance of the tool. The work concerns the use of finite element simulation for modelling of thermal residual stresses generated during the sintering process of metal matrix diamond tools normally employed by the industry. Stress distribution fields were determined for two different diamond shapes (modelled with 2D axisymmetric elements, with the sphere shape generated from the revolution of one circle and the octahedron shape generated from the revolution of one octagon, respectively) using an 8-node biquadratic axisymmetric quadrilateral, reduced integration element type CAX8. The thermal residual stress field in the nearby region of a diamond particle with the shape generated from the octagon is examined by using three different matrix materials, each one sintered at different temperatures. The analyses have demonstrated how much the residual stresses are sensitive to the stress–strain behaviour of the metal matrices.     

Modeling of anisotropic wound healing

Biological soft tissues exhibit non-linear complex properties, the quantification of which presents a challenge. Nevertheless, these properties, such as skin anisotropy, highly influence different processes that occur in soft tissues, for instance wound healing, and thus its correct identification and quantification is crucial to understand them. Experimental and computational works are required in order to find the most precise model to replicate the tissues' properties. In this work, we present a wound healing model focused on the proliferative stage that includes angiogenesis and wound contraction in three dimensions and which relies on the accurate representation of the mechanical behavior of the skin. Thus, an anisotropic hyperelastic model has been considered to analyze the effect of collagen fibers on the healing evolution of an ellipsoidal wound. The implemented model accounts for the contribution of the ground matrix and two mechanically equivalent families of fibers. Simulation results show the evolution of the cellular and chemical species in the wound and the wound volume evolution. Moreover, the local strain directions depend on the relative wound orientation with respect to the fibers.     

Self-lubricated transport of aqueous foams in horizontal conduits

The flow characteristics of aqueous foams were studied in a thin flow channel and a round pipe instrumented for pressure gradient and flow rate measurements. The quality of the foam was varied by controlling the volumetric flow rate of liquid and gas, and different flow types were identified and charted. Uniform foams move as a rigid body lubricated by water generated by breaking foam at the wall. A lubrication model leading to a formula for the thickness of the lubricating layer is presented. The formula predicts a layer thickness of 6–8 μm in the channel and 10–12 μm in the pipe. The thickness depends weakly on foam quality. An overall correlation for the friction factor as a function of Reynolds number which applies to both channel and pipe is derived. This correlation is consistent with a model in which a rigid core of foam is lubricated by laminar flow of a water layer in the range of measured thickness.