Deformation mechanisms and the yield surface of low-density,closed-cell polymer foams

The geometry of low-density, closed-cell, polyethylene and polystyrene foams was modelled with a Kelvin foam having uniform-thickness cell faces; finite element analysis (FEA) considered interactions between cell pressures and face deformation. Periodic boundary conditions were applied to a small representative volume element. In uniaxial, biaxial and triaxial tensile stress states, the dominant high-strain deformation mechanism was predicted to be tensile yield across nearly flat faces. In uniaxial and biaxial compression stress states, pairs of parallel plastic hinges were predicted to form across some faces, allowing them to concertina. In hydrostatic compression, face bowing was predicted. The rate of post-yield hardening changed if new deformation mechanisms became active as the foam strain increased. The effects of foam density and polymer type on the foam yield surface were investigated. Improvements were suggested for foam material models in the FEA package ABAQUS.     

Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model

Dynamic crushing responses of three-dimensional cellular foams are investigated using the Voronoi tessellation technique and the finite element (FE) method. FE models are constructed for such closed-cell foam structures based on Voronoi diagrams. The plateau stress and the densification strain energy are determined using the FE models. The effects of the cell shape irregularity, impact loading, relative density and strain hardening on the deformation mode and the plateau stress are studied. The results indicate that both the plateau stress and the densification strain energy can be improved by increasing the degree of cell shape irregularity. It is also found that the plastic deformation bands appear firstly in the middle of the model based on tetrakaidecahedron at low impact velocities. However, the crushing bands are seen to be randomly distributed in the model based on Voronoi tessellation. At high impact velocities, the “I” shaped deformation mode is clearly observed in all foam structures. Finally, the capacity of foams absorbing energy can be improved by increasing appropriately the degree of cell shape irregularity.     

Characterization of close-celled cellular aluminum alloys

The deformation behaviour of two different types of aluminium alloy foam are studied under tension, compression, shear and hydrostatic pressure. Foams having closed cells are processed via batch casting, whereas foams with semi-open cells are processed by negative pressure infiltration. The influence of relative foam density, cell structure and cell orientation on the stiffness and strength of foams is studied; the deformation mechanisms are analysed by using video imaging and SEM (scanning electronic microscope). The measured dependence of stiffness and strength upon relative foam density are compared with analytical predictions. The measured stress versus strain curves along different loading paths are compared with predictions from a phenomenological constitutive model. It is found that the deformations of both types of foams are dominated by cell wall bending, attributed to various process induced imperfections in the cellualr structure. The closed cell foam is found to be isotropic, whereas the semi-open cell foam shows strong anisotropy.     

FE modeling of the compressive behavior of porous copper-matrix nanocomposites

Compressive mechanical test and numerical simulation via finite element modeling have been employed on closed-cell copper-matrix nanocomposite foams reinforced by alumina particles. The FE analysis' purpose was to model the foam deformation behavior under compressive loading and to investigate the correlation between material characteristics and the compressive mechanical behavior. Exploring this, several foam samples with different conditions were manufactured and compression test was carried out on the samples. Scanning electron microscopy and image analysis have been performed on the foam samples to obtain the required data for the numerical simulation. The stress–strain curves exhibited plateau stress between 18 and 112.5 MPa and energy absorption in the range of 20.03–51.20 MJ/m³ for the foams with different relative densities. The foams exhibited enhanced mechanical properties to an optimum value, as a consequence of increasing the reinforcing nanoparticles, through both experimental tests and numerical simulation data. Also, the validated model of copper-matrix nanocomposite foams has been used to probe stress distribution in the foams. In addition, the results obtained by numerical simulation via ABAQUS CAE finite element modeling provided support for experimental test results. This confirmed that FEM is a favorable technique for predicting mechanical properties of nanocomposite copper foams.     

Pseudo-elastic description of polymeric foams at finite deformation with stress softening and residual strain effects

Polymeric foams are typical materials for energy absorber in such areas as aircraft, car industry and in the field of electronic packaging. Besides the typical hyperelastic behaviour, non-linear stress–strain behaviour in large elastic deformation, polymeric foams may also exhibit some inelastic effects, like stress softening and residual strain. In this paper we first describe some experiment results that illustrate the stress softening in compressible expanded polypropylene (EPP) foams together with associated residual strain effects. Then, based on Ogden and Dorfmann’s results, a pseudo-elastic model is introduced to capture the stress softening and residual strain effects by including of two variables in the energy function. Numerical simulations of uniaxial-compression tests of two types of EPP foam are used to determine the material parameters of Ogden’s model, stress softening and residual strain effects. The numerical simulations indicate that the pseudo-elastic model provides reasonably accurate predictions of the inelastic behaviour of polymeric foam.     

Micromechanics based modelling of deformation behaviour of grain refined rheocast Al–7Si–0.3Mg alloy

Microscale deformation behaviour, plastic strain localisation and plastic instability of grain refined rheocast Al–7Si–0.3Mg alloy have been studied here, following micromechanical approach. Micromechanics based simulations have been performed by means of the two-dimensional representative volume element of the actual microstructure, using the popular finite element (FE) package ABAQUS. The molten alloy has been rheocast after grain refiner addition, using cooling slope, and comparison has been made with its conventional cast counterpart. Effect of grain size, shape and its orientation on microlevel stress/strain state of the material, before the final failure, has been predicted in the present study. Increasing uniformity in stress and strain distribution at the microscale has been evidenced with the increasing sphericity and volume fraction of the primary Al phase.     

Experimental and numerical study of the elastic properties of PMI foams

The elastic properties of polymethacrylimide (PMI) foams were investigated experimentally and numerically. Standard tests were carried to measure the mechanical properties of ROHACELL^? WF and RIST grades foams. The tetrakaidekahedral unit cell was adopted to generate a 3D representative volume element (RVE) for the microstructure of PMI foams. It is assumed that the RVE represents the foam within the framework of elasticity. The RVE models thus created were analyzed with periodic boundary conditions to obtain the elastic properties of PMI foams by using finite element analysis (FEA). The numerical results were compared with the experimental data and the prediction of existing theoretical models, and the proposed model was found to give the best prediction for the effective modulus of PMI foams. Parameter studies were also carried out using the RVE models to investigate the effect of the foam cell size and cell thickness on the effective modulus of PMI foams.     

The mechanical behaviour of aluminium foam structures in different loading conditions

The use of foam has the potential for energy absorption enhancement. Many types of materials can be produced in the form of foams, including metals and polymers. Of the metallic based foams, aluminium based are among the most advanced. Aluminium foams couple good specific mechanical properties with high thermal stability. Among the various aspects still to be investigated regarding their mechanical behaviour is the influence of a hydrostatic state of stress on yield strength. Unlike metals, the hydrostatic component affects yields. Therefore, different loading conditions have to be considered to fully identify the material behaviour. Another important issue in foam structure design is the analysis of composite structures. The mechanical behaviour of an aluminium foam has been examined. The foam was subjected to uniaxial, hydrostatic stress, pure deviatoric stress, and combinations thereof. Results obtained will be presented as quasi-static and dynamic uniaxial compression and quasi-static bending and shear loading. Moreover, composite structures were made by assembling the foam into aluminium cold extruded closed section 6060 aluminium tubes. The results show that the energy absorption capability of the composite structures is much greater than the sum of the energy absorbed by the two components, the foam and the tube.     

梯度泡沫金属的冲击吸能特性

基于闭孔泡沫铝的显微CT扫描信息,考虑胞孔的不规则形貌及胞孔分布的不均匀性,以及胞孔尺寸和壁厚沿泡沫高度的梯度分布,建立了梯度泡沫金属材料的二维细观有限元模型,分析了梯度泡沫金属材料在动态压缩过程中的变形、塑性波的传播和能量变化特征。对于平均相对密度0.3、平均梯度系数0.4的梯度泡沫铝,低速（10 m/s）加载时,梯度泡沫金属在变形的整个过程中吸收的总能量均低于均匀泡沫金属;高速加载时,梯度泡沫金属沿负梯度方向压缩的早期吸能比均匀泡沫金属有优势,而且速度越高,优势越明显。     

硬质聚氨酯泡沫塑料压缩力学性能

研究了三种密度不同的聚氨酯泡沫塑料的低速压缩力学性能，用ＳＥＭ分析了初始胞体结构，确定了胞体尺寸及结构特性。     

塑性大变形有限元静水压力的改进算法

本文针对塑性大变形有限元中静水压力计算精度低的问题,研究了三维八节点等参元的偏应力导数佳点,提出了一种改进的静水压力间接积分算法。将该算法应用于金属塑性成型过程的有限元模拟,较好地解决了大步长情况下应力计算精度低的问题。     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

Cell nucleation in solid-state polymeric foams: evidence of a triaxial tensile failure mechanism

The mechanism for nucleation phenomenon in solid-state microcellular foams is identified as a solid-state failure process. This process originates at internal flaws within the gas-polymer matrix, where it is induced by the presence of a state of hydrostatic tensile stress within the polymer matrix. The hydrostatic tensile stress is caused by the presence of the saturating gas within the polymer. The nucleation phenomenon is thermally activated at the effective glass transition temperature of the gas-polymer mixture. At this critical temperature, the hydrostatic tensile stress within the gas-polymer mixture is sufficient to cause the polymer matrix to fail, thereby creating a foam cell nucleus. In general, the nucleation sites are observed to be flat, approximately circular, fracture sites. After the appearance of the initial fracture, gas diffuses from the gas-polymer matrix into the fracture. The fracture seam inflates during the growth process, in which growth begins with the appearance of a disk shaped fracture and concludes with an approximately spherical cell. The results and conclusions presented herein suggest a new avenue to explain the cell nucleation phenomena observed in this process.     

基于Johnson-cook本构模型的EPE包装跌落冲击模拟

目的将聚乙烯泡沫塑料在动态压缩试验下得到的力学性能引入有限元中,创建材料模型,并应用于跌落冲击仿真分析,以提高仿真的精确度。方法通过聚乙烯泡沫塑料在不同速率下的压缩试验,得到真实的应力-应变曲线,并基于Johnson-cook本构模型在有限元中建立EPE的材料模型。最后用AnsysWorkbench中的LS-DYNA模块对聚乙烯泡沫缓冲包装的跌落过程进行仿真分析,用LS-PREPOST软件进行后处理。在此基础上,对比分析仿真结果和实验结果。结果仿真结果的误差分别为0.85%,1.6%,2.97%,与实验结果基本一致。结论基于Johnson-cook本构模型构建的聚乙烯泡沫塑料有限元材料模型能有效提高低速冲击的仿真精度,为非线性材料和应变率敏感材料的有限元动态冲击分析提供了参考。     

Geometrically nonlinear stress–strain behavior of hyperelastic solid foams

The present study is concerned with an effective stress analysis of cellular solids in the finite strain regime. The homogenization of the microstructure is performed by means of a strain energy based RVE-procedure which assumes macroscopic equivalence of a representative volume element for the given microstructure and a similar volume element consisting of the effective medium, if the average strain energy density in both volume elements is equal provided that the deformation gradient with respect to both elements is equal in a volume average sense. Disordered microstructures are considered by means of a randomized periodic model in conjunction with a stochastic approach. The model is applied to an analysis of the effective stress–strain behavior of two-dimensional model foams with periodic and disordered microstructure. Special interest is directed to effects of the geometric nonlinearity.     

Numerical and experimental studies of polyurethane foam under impact loading

Proper predictions of the behaviour of shock absorber materials are of utmost importance in safety assessments for licensing casks for transport and storage of highly active waste. After having identified significant discrepancies between numerical results and the actual response of polyurethane foam limiters subjected to accidental scenarios, a new research project ENREA was established by BAM. A major objective is to enhance and to develop advanced material models intended to simulate limiters under impact loading. They should account for all major factors influencing the load–deformation relationship like temperature, strain rate and specific stress state. The corresponding test program, applicable plasticity models, the overall parameter identification strategy based on local and global optimization techniques as well as experimental and numerical results are presented here in particular for closed cell foams.     

A micromechanical analysis to predict the cord-rubber composite properties

Both three- and two-dimensional generalized plane strain finite element analyses based on a micromechanics approach were carried out to investigate the linear and nonlinear effective composite properties as well as the stress fields. A unit cell model of cord-rubber composite subjected to different loadings was studied to predict the effective composite properties. The numerical results of effective composite properties obtained from 2D and 3D finite element analyses were compared with experimental data and other finite element results available in the literature. The effects of rubber material nonlinearity and large deformation on the effective composite properties and interface stress distributions are presented and discussed.