微孔结构对PMI泡沫准静态压缩性能的影响

基于BBC点集建立了聚甲基丙烯酰亚胺(PMI)闭孔泡沫的Kelvin十四面体模型和Laguerre模型,并采用有限元方法研究了其在准静态载荷作用下的压缩性能。分析了孔径大小、泡孔体积离散系数对压缩弹性模量、初始峰值应力和能量吸收能力的影响。结果表明:Kelvin十四面体模型可以较好地预测PMI泡沫的压缩弹性模量和峰值应力;在相同相对密度条件下,小孔径泡沫的初始峰值应力和能量吸收能力均高于大孔径泡沫,而压缩弹性模量则低于大孔径泡沫;随着泡孔体积离散系数的增大,闭孔PMI泡沫压缩弹性模量、初始峰值应力和能量吸收能力均减小。     

Effective conductive properties of open-cell foams

The work is devoted to the problem of simulation of the effective electro and thermoconductive properties of open-cell foam materials with slim highly conductive ligaments. The solution of this problem depends on two small parameters: the ratio of the typical length and the cross-section size of the ligaments, and the ratio of the conductivities of the host medium and the ligaments. The principal terms of the asymptotic solutions (with respect to these parameters) for the fields inside the ligaments are obtained and used in the framework of a finite element method for the numerical simulation of the fields inside the representative volume element (RVE) of the foam material. The Laguerre tessellation procedure is applied for simulation of foam microstructures with various distributions of cell-sizes inside the RVE. Effective conductivity constants of the foams are obtained by averaging the detailed fields over the RVE. The number of cells inside the RVE for reliable calculations of the effective conductivities is indicated. Dependences of the effective conductive properties of the foams on the shapes of the ligaments and the distribution law of the cell-sizes are obtained and analyzed.     

Formulation optimization of unreinforced and lignin nanoparticle-reinforced phenolic foams using an analysis of variance approach

Formulations of unreinforced and lignin nanoparticle-reinforced phenolic foams were optimized using an analysis of variance approach. The variables studied in the formulation of phenolic foams were stirring speed (650–850 rpm) and blowing agent amount (1.5–3.5 wt.%). For lignin nanoparticle-reinforced phenolic foams, the variables were lignin nanoparticle weight fraction (1.5–8.5 wt.%) and blowing agent amount (1.5–3.5 wt.%). The responses measured for both foams were density, compressive modulus, and compressive strength. In addition, the morphology of the foams was observed using scanning electron microscopy (SEM) to determine cell size distributions. The results showed that the variables studied exhibited a strong influence on the responses and the cell size distribution of the foams. Statistical models allowed for prediction of the properties of the foams and for comparison of the properties of unreinforced and lignin nanoparticle-reinforced phenolic foams. The incorporation of lignin nanoparticles in phenolic foams results in a compressive modulus and compressive strength that has up to 128% and 174%, respectively, of the values for unreinforced foams. The amount of blowing agent saved to produce a reinforced foam was up to 31% of the amount necessary to produce an unreinforced foam of the same density.     

The mechanical response of Rohacell foams at different length scales

The quasi-static mechanical response of polymethacrylimide (PMI) foams of density ranging from 50 to 200 kg m⁻³ is investigated in order to provide experimental data to inspire and validate numerical constitutive models for the response of polymer foams. The macroscopic mechanical response is characterised by conducting quasi-static compression, tension, shear and indentation experiments, whereas microscopic deformation mechanisms are identified by conducting in situ SEM observations during static compression and tension tests; it is shown that foams of low density collapse by cell wall buckling while foams of high density undergo plastic cell-wall bending. As a result, both the elastic and plastic macroscopic response of the foam display a tension/compression asymmetry.     

Nonlinear material behaviour and failure of closed-cell polymer foams

Classical strength criteria, like the von Mises criterion, are used to postulate the failure of ductile materials like steel or brass. It is known that for the application of foams in modern lightweight structures extended criteria are required, since foams are sensitive to hydrostatic stress. This observation on the macroscale can be explained by the deformation mechanisms of one single foam cell. Under hydrostatic stress, the deformation of the cell causes a non-uniform stress state of the cell walls. To understand the mechanism on the microlevel, a finite element model on the basis of a tetrakaidecahedron as unit cell was implemented. Utilising a strain energy-based homogenisation concept, the effective properties of the foam can be obtained. To adapt the geometric properties of the model to the real microstructure of the foam, results of a computer tomography image analysis were used by considering several imperfections in the cell geometry. For the analysis of the stress state on the microlevel, different load cases were applied to the unit cell. By means of these simulations, the geometrically nonlinear stress–strain curves on the macrolevel were deduced. Furthermore, the analysis of the finite element model provides an insight into the deformation mechanism on the microscale and allows the prediction of failure as well. Finally, the predicted failure points are represented in the Burzyński plane and compared with experimental results. The current paper focuses on the hard foam ROHACELL\({^{\circledR}}\) IG-series (industrial grade), which is a closed-cell PMI foam produced by Evonik Industries AG, Germany.     

纳米纤维增强闭孔泡沫材料的力学性能

为研究纳米纤维增强闭孔泡沫材料的力学性能,采用Voronoi随机泡沫模型对闭孔泡沫材料的细观几何结构进行模拟,并将纳米纤维随机分布在泡沫材料的胞壁中,利用改进的自动搜索耦合（ASC）技术将纤维单元与基体单元进行耦合,建立了能够反映纳米纤维增强闭孔泡沫材料细观结构的数值模型。在此基础上,进一步研究了泡沫模型随机度、相对密度以及纳米纤维长径比和质量分数对纳米纤维增强闭孔泡沫材料弹性模量与屈服强度的影响规律。结果表明:由所建立的数值模型得到的纳米纤维增强闭孔泡沫材料的弹性模量和屈服强度与实验值吻合较好;提高泡沫模型的随机度会使复合泡沫材料的弹性模量和屈服强度增加,而当随机度达到0.450以后,材料的弹性模量和屈服强度几乎不再发生变化;当相对密度在0.05~0.30范围内变化时,复合泡沫材料的弹性模量与屈服强度几乎随相对密度的增加呈线性增长;提高纳米纤维长径比和质量分数也会使材料的弹性模量和屈服强度得到提高,但当纤维长径比达到500以后,纤维长径比的增强作用逐渐减弱。所得结论对纳米纤维增强闭孔泡沫材料的制备具有重要意义。      

Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores

The present study investigates the influences of representative volume element RVE mesh and material parameters, here cell wall elastic moduli, on the effective stiffness properties of three dimensional orthotropic honeycomb cores through strain driven computational homogenization in the finite element framework. For this purpose, case studies were carried out, for which hexagonal cellular RVEs were generated, meshed with eight node linear brick finite elements of varying numbers. Periodic boundary conditions were then implemented on the RVE boundaries by using one-to-one nodal match for the corresponding corners, edges and surfaces for the imposed macroscopic strains. As a novelty, orthotropic material properties were assigned for each cell wall by means of the transformation matrices following the cell wall orientations. Thereafter, simulations were conducted and volume averaged macroscopic stresses were obtained. Eventually, effective stiffness properties were obtained, through which RVE sensitivity analysis was carried out. The investigations indicate that there is a strong relation between number of finite elements and most of the effective stiffness parameters. In addition to this, cell wall elastic moduli also play critical role on the effective properties of the investigated materials.     

考虑界面影响的混凝土弹性模量的数值预测

提出了一种考虑界面过渡层影响的混凝土弹性模量的数值预测方法。将球形骨料与包裹它的界面过渡层作为二相复合球结构的等效颗粒,由广义自洽方法计算不同粒径骨料与界面过渡层组成复合球的有效模量。然后由等效颗粒生成的随机骨料模型建立体积表征单元,施加均匀位移边界条件,通过数值方法计算该体积表征单元中的应力和应变场,由细观力学数值均匀化方法预测体积表征单元的有效弹性模量。计算结果表明:对于不同骨料含量的混凝土,有效弹性模量的预测值与试验值非常接近,界面过渡层的厚度对混凝土的整体弹性性质有较大影响。     

Prediction of compressive properties of closed-cell aluminum foam using artificial neural network

The design of artificial neural network (ANN) is motivated by analogy of highly complex, non-linear and parallel computing power of the brain. Once a neural network is significantly trained it can predict the output results in the same knowledge domain. In the present work, ANN models are developed for the simulation of compressive properties of closed-cell aluminum foam: plateau stress, Young’s modulus and energy absorption capacity. The input variables for these models are relative density, average pore diameter and cell anisotropy ratio. Database of these properties are the results of the compression tests carried out on aluminum foams at a constant strain rate of 1 × 10⁻³ s⁻¹. The prediction accuracy of all the three models is found to be satisfactory. This work has shown the excellent capability of artificial neural network approach for the simulation of the compressive properties of closed-cell aluminum foam.     

纤维丝束带复合材料的有效性能预测与实验测试

依据纤维丝束带复合材料的相关几何结构参数值和所确定的纤维丝束带特征体积单元（RVE）模型几何结构尺寸,以有限元软件MSC.Patran/Nastran为平台建立纤维丝束带复合材料RVE有限元模型并在模型中置入相应的制备缺陷。各类制备缺陷的置入均采用删除网格单元的方法,置入裂纹型制备缺陷时偏移裂纹两侧单元相对面以获得当前裂纹宽度,置入孔洞型制备缺陷时尽量模拟其真实形貌。根据复合材料力学关于材料各性能参数的定义和细观力学基本理论推导了有限元计算细观力学（FECM）方法预测复合材料有效弹性性能和有效热膨胀性能的过程。根据FECM方法预测了不含制备缺陷、含单一制备缺陷和含各类制备缺陷时的弹性常数和有效热膨胀系数。结果表明:各类制备缺陷的存在均会使弹性模量和剪切模量减小,泊松比和热膨胀系数可能增大也可能减小。通过与实验测试结果对比分析可知,数值预测结果普遍比实验测试结果偏大,但总体效果较为理想,最大相对误差为6.04%。      

Cell structure and compressive behavior of an aluminum foam

The plastic collapse strength, energy absorption and elastic modulus of a closed cell aluminum foam are studied in relation to cell structures. The density, node size and the cell wall thickness of the aluminum foams decrease with increasing cell size. The failure of the foam cells under compressive load progresses successively from the top or/and bottom to the mid-layer of the compression specimens, and no initial rupture of the foam cells is observed in the mid-height of the foam samples. When foam density increases from 0.11 to 0.22 g/cm ³, the plastic collapse strength rises from 0.20 to 1.29 MPa, while the elastic modulus of the closed cell aluminum foam increases from 0.70 to 1.17 GPa. In contrast, the energy absorption of the foams decreases rapidly with increasing cell size. When cell size increases from 4.7 to 10.1 mm, the energy absorption drops from over unity to 0.3 J/cm ³. The normalized Yong’s modulus of the closed cell aluminum foam is E^*/E_s = 0.208 (ρ^*/ρ_s), while the normalized strength of the foams, σ */σ_s is expressed by σ */σ_s = c ⋅ ρ */ρ_s where c is a density-dependent parameter. Furthermore, the plastic collapse strength and energy absorption ability of the closed cell aluminum foams are significantly improved by reducing cell size of the aluminum foams having the same density.     

Elastic behavior of multi-scale,open-cell foams

The mechanical properties of cellular materials are still subject to numerous theoretical and experimental investigations. In particular, the impact of cell size on the foam’s elastic response has not been studied systematically mainly due to the lack of experimental techniques with which the cell size and relative density of materials can be varied independently. This paper presents the results of a study of the elastic behavior of open-cell foams as a function of relative density and the size of the interconnected, spherical pores. First, the chemical procedure allowed us to produce polystyrene open-cell foams in which the relative density and the average cell diameters were varied independently. The results of compression tests performed on these foams showed an unexpected influence of the cell diameter (at constant relative density) on the elastic response. The analysis of the microstructure of the foam revealed the presence of a complex nanostructure in the edge of the cells that appeared during the synthesis procedure. An analytical model (an extension of the Gibson–Ashby model) is presented, which takes into account the complex multi-scale structure of the foam and accurately describes the observed dependence of the measured Young’s moduli on cell size. This approach was confirmed further by a finite element numerical simulation. We concluded that the observed dependence of elastic modulus on cell size was due to the heterogeneous nature of the material that constitutes the walls of the cells.     

支柱弯曲对开孔泡沫铝力学性能影响的理论分析与数值模拟

首先根据实际泡沫材料中存在不少弯曲支柱,且形状接近于弧线,在假设全部支柱为弯曲支柱的情况下,利用理论方法分析了支柱弯曲对开孔泡沫材料刚度和强度性能的影响规律,得到了理论预测含弯曲支柱开孔泡沫材料杨氏模量和屈服强度的公式。然后,通过有限元模拟方法验证了上述理论预测模型的有效性。最后,利用有限元模型研究了不同比例的弯曲支柱、不同弧度的弯曲支柱和不同各向异性比对泡沫铝压缩力学行为的影响。结果表明,弯曲支柱对弹性模量的影响比对塑性坍塌强度的影响大;而弯曲支柱对泡沫铝压缩力学行为的影响则与支柱的弧度、支柱含量和胞体结构的各向异性比有关。     

Laguerre tessellations for elastic stiffness simulations of closed foams with strongly varying cell sizes

The dependency of the elastic stiffness, i.e., Young’s modulus, of isotropic closed-cell foams on the cell size variation is studied by microstructural simulation. For this purpose, we use random Laguerre tessellations which, unlike classical Voronoi models, allow to generate model foams with strongly varying cell sizes. The elastic stiffness of the model realizations is computed by micro finite element analysis using shell elements. The main result is a moderate decrease of the effective elastic stiffness for increasing cell size variations if the solid volume fraction is assumed to be constant.     

Polymeric foams and sandwich composites: Material properties,environmental effects,and shear-lag modeling

Marine composite sandwich structural materials, comprising of low density PVC foam core and carbon fiber reinforced vinyl ester based resin composite facings, are studied for associated degradation in mechanical behavior caused by sea water. This paper presents experimental and analytical results concerning the properties and response of closed cell polymeric foams (PVC H100) and their sandwich composites. Data regarding the elastic properties of foam (shear and Young’s modulus) are collected by means of novel custom made devices and interpreted by means of displacement based analytical models. Emphasis is placed on environmental effects and a novel approach of using expansional strain analogy to study the effects of both sea water and temperature are proposed.     

二维二轴1×1编织复合材料细观结构模型及力学性能有限元分析

考虑纤维束相互挤压及横截面形状变化, 采用纤维束截面六边形假设, 建立了二维二轴1×1编织复合材料的参数化单胞结构模型。通过引入周期性位移边界条件, 基于细观有限元方法, 对编织材料的弹性性能进行预测, 讨论了编织角及纤维体积含量对面内弹性常数的影响, 并分析了典型载荷下单胞细观应力场分布。研究表明: 单胞结构模型有效反映了纤维束的空间构型和交织特征, 实现了不同编织工艺参数下模型的快速建立; 基于单胞有限元模型的弹性性能预测结果与试验结果较为吻合; 模型给出了单胞合理的应力场分布, 为二维编织复合材料的结构优化和损伤预测奠定基础。      

Effective elastic properties of foam-filled honeycomb cores of sandwich panels

Filling with foams of honeycomb structures has been proposed as some enhancement of honeycomb-cored sandwich material systems. The present study considers aluminum honeycomb cores filled with polyvinyl chloride foams with the aim to predict their material elastic properties. The displacement-based homogeneous technique using 3D finite element analysis is applied to evaluate the effective elastic properties of foam-filled honeycomb cores. The special attention is paid to stress predictions at the skin/core interface and the stress distributions within the honeycomb cell walls. The influence of the foam filler on distribution of local stresses within the cell is examined. The FE modelling is performed with the commercial available software ABAQUS. The structural benefits of the foam-filled honeycomb cores are also discussed.     

Preparation of polybenzoxazine foam and its transformation to carbon foam

An organic foam derived from a new type of phenolic resin, namely polybenzoxazine, was successfully prepared with a noncomplex and economical foaming method by using azodicarbonamide (AZD) as a foaming agent. The influence of foam density on the physical and mechanical properties of the foams was studied. All resulting polybenzoxazine foams and carbon foams exhibit a tailorable uniform microstructure. Polybenzoxazine foams showed a density in the range of 273–407 kg/m³, and a compressive strength and a compressive modulus in the range of 5.2–12.4 MPa and 268–681 MPa, respectively. The foam density not only affects the physical and mechanical properties, but also affects the deformation response of the foam. In addition, the polybenzoxazine foam was further transformed into carbon foam by carbonization at 800 °C under an inert atmosphere, and its properties were examined.     

Mechanical Properties of Open Cell Foams: Simulations by Laguerre Tesselation Procedure

The Laguerre tessellation procedure is used for simulation of microstructures of open-cell foams. In contrast with the conventional Voronoii tessellation, the Laguerre one permits to simulate the foam microstructures with a given law of distribution of cell diameters. An original finite element method is developed for calculating the elastic properties: the ligaments are modelled as Timoshenko beams and each ligament is treated as one finite element. The size of the representative volume element for reliable calculations of the effective elastic properties is evaluated by computational experiments. Dependence of the properties on the cell size distributions and ligament shapes are analyzed.     

不同单体配比聚甲基丙烯酰亚胺泡沫的制备与性能

以甲基丙烯酸(MAA)和丙烯腈(AN)为单体,通过加热结合超声的方法引发反应,快速制备了不同单体配比的聚甲基丙烯酰亚胺(PMI)泡沫。通过傅里叶变换红外光谱、热重分析、动态力学热分析、垂直燃烧、极限氧指数(LOI)和扫描电镜对PMI泡沫结构、热性能、燃烧性能和形貌进行表征,同时对PMI泡沫的力学强度进行分析。结果表明,高温下氰基与羧基通过重排异构化反应生成酰胺键,制备的PMI泡沫具有良好的成炭性能和较高的玻璃化转变温度,LOI随AN含量的增加而提高,泡沫呈蜂窝状结构,孔径在0.1~0.3 mm之间。力学性能分析表明,PMI泡沫具有较高的力学强度,50.1 kg/m 3的PMI泡沫的拉伸强度、弯曲强度和压缩强度分别为1.85 MPa、2.71 MPa和3.74 MPa。