Impact of material processing and deformation on cell morphology and mechanical behavior of polyurethane and nickel foams

The cell morphology and mechanical behavior of open-cell polyurethane and nickel foams are investigated by means of combined 3D X-ray micro-tomography and large scale finite element simulations. Our quantitative 3D image analysis and finite element simulations demonstrate that the strongly anisotropic tensile behavior of nickel foams is due to the cell anisotropy induced by the deformation of PU precursor during the electroplating and heat treatment stages of nickel foam processing. In situ tensile tests on PU foams reveal that the initial main elongation axis of the cells evolves from the foam sheet normal direction to the rolling direction of the coils. Finite element simulations of the hyperelastic behavior of PU foams based on real cell morphology confirm the observation that cell struts do not experience significant elongation after 0.15 tensile straining, thus pointing out alternative deformation mechanisms like complex strut junctions deformation. The plastic behavior and the anisotropy of nickel foams are then satisfactorily retrieved from finite element simulations on a volume element containing eight cells with a detailed mesh of all the hollow struts and junctions. The experimental and computational strategy is considered as a first step toward optimization of process parameters to tailor anisotropy of cell shape and mechanical behavior for applications in batteries or Diesel particulate filtering.     

数字图像相关方法在闭孔泡沫铝压缩试验中的应用

为了了解相对密度与胞孔结构对闭孔泡沫铝力学性能的影响,本文采用放大成像及数字图像相关技术对两种不同密度的泡沫纯铝试样进行了实验研究.利用数字图像相关方法对泡沫纯铝变形前后的图像进行相关计算,获得了弹性范围内静态压缩情况下闭孔泡沫铝材料表面的全场变形及局部孔结构的变形,同时根据试验结果计算了试件的名义弹性模量.实验结果表明泡沫铝整体孔结构的变形与泡沫金属材料相对密度有关,而单个孔结构的变形主要与孔壁面光滑程度和皱褶有关.实验结果还表明图像相关方法能够有效地应用于闭孔泡沫金属的力学性测量和评估的研究.     

复合泡沫塑料力学行为的研究综述

复合泡沫塑料是一种重要的防护材料,它在国防工业和民用工业各部门均有许多重要的应用,对这类材料的力学行为进行研究具有重要的学术价值和应用前景.本文对复合泡沫塑料力学行为的研究文献进行了综述.首先,对复合泡沫塑料力学行为研究的早期工作进行了简介.然后,重点介绍了复合泡沫塑料力学行为研究的最新进展,其中也包括作者近期在该领域开展的一些工作;对复合泡沫塑料进行了静、动态压缩实验和细观加载实验,研究了材料的宏观变形规律和细观失效机制;在理论研究方面,探讨了复合泡沫塑料的能量吸收和缓冲特性,从宏、细观力学分析出发研究了复合泡沫塑料有关力学性能的理论预测问题;还利用计算机和通用软件对高密度复合泡沫塑料进行了有限元分析,研究了高密度复合泡沫塑料的失效行为.最后,给出对该领域研究工作的一些展望.      

Simulation of the densification of real open-celled foam microstructures

Ubiquitous in nature and finding applications in engineering systems, cellular solids are an increasingly important class of materials. Foams are an important subclass of cellular solids with applications as packing materials and energy absorbers due to their unique properties. A better understanding of foam mechanical properties and their dependence on microstructural details would facilitate manufacture of tailored materials and development of constitutive models for their bulk response. Numerical simulation of these materials, while offering great promise toward furthering understanding, has also served to convincingly demonstrate the inherent complexity and associated modeling challenges.The large range of deformations which foams are subjected to in routine engineering applications is a fundamental source of complication in modeling the details of foam deformation on the scale of foam struts. It requires accurate handling of large material deformations and complex contact mechanics, both well established numerical challenges. A further complication is the replication of complex foam microstructure geometry in numerical simulations. Here various advantages of certain particle methods, in particular their compatibility with the determination of three-dimensional geometry via X-ray microtomography, are exploited to simulate the compression of “real” foam microstructures into densification. With attention paid to representative volume element size, predictions are made regarding bulk response, dynamic effects, and deformed microstructural character, for real polymeric, open-cell foams. These predictions include a negative Poisson's ratio in the stress plateau, and increased difficulty in removing residual porosity during densification.     

Multiscale mass-spring models of carbon nanotube foams

This article is concerned with the mechanical properties of dense, vertically aligned CNT foams subject to one-dimensional compressive loading. We develop a discrete model directly inspired by the micromechanical response reported experimentally for CNT foams, where infinitesimal portions of the tubes are represented by collections of uniform bi-stable springs. Under cyclic loading, the given model predicts an initial elastic deformation, a non-homogeneous buckling regime, and a densification response, accompanied by a hysteretic unloading path. We compute the dynamic dissipation of such a model through an analytic approach. The continuum limit of the microscopic spring chain defines a mesoscopic dissipative element (micro-meso transition) which represents a finite portion of the foam thickness. An upper-scale model formed by a chain of non-uniform mesoscopic springs is employed to describe the entire CNT foam. A numerical approximation illustrates the main features of the proposed multiscale approach. Available experimental results on the compressive response of CNT foams are fitted with excellent agreement.     

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.     

Compressive response of open-cell foams. Part I: Morphology and elastic properties

This study is concerned with the understanding and modeling of the compressive response of open cell foams. The response starts with a nearly linear elastic regime which terminates into a limit load followed by an extensive load plateau. The plateau, which is responsible for the excellent energy absorption capacity of foams, is followed by a second stiff branch. Results from polyester urethane open cell foams with relative densities of about 0.025 are used to illustrate this behavior using experiments coupled with several levels of modeling. The experiments include characterization of the microstructure and the properties of the base material and measurement of the compressive response of the foams of various cell sizes.A sequence of models for predicting the complete response of such foam is developed. The foam is idealized to be periodic using the space-filling Kelvin cell assigned the major geometric characteristics found in the foams tested. The cells are elongated in the rise direction, the ligaments are assumed to be straight, to have Plateau border cross-sections and nonuniform cross-sectional area distribution. The ligaments are modeled as shear-deformable extensional beams and the base material is assumed to be linearly elastic. Prediction of the initial elastic moduli are addressed in Part I. Closed form expressions for the material constants are presented as well as results using a FE model of the characteristic cell. Comparison between measurements and predictions is very favorable. The paper finishes with results from a limited parametric study of the elastic moduli. The results demonstrate that inclusion of the geometric complexities mentioned above is essential for successful prediction of the moduli of such foams. The nonlinear parts of the response including the foam crushing behavior are addressed in Part II.     

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。     

On the microstructure of open-cell foams and its effect on elastic properties

Synthetic open-cell foams have a complex microstructure consisting of an interconnected network of cells resulting from the foaming process. The cells are irregular polyhedra with anywhere from 9 to 17 faces in nearly monodisperse foams. The material is concentrated in the nearly straight ligaments and in the nodes where they intersect. The mechanical properties of such foams are governed by their microstructure and by the properties of the base material. In this study micro-computed X-ray tomography is used to develop 3D images of the morphology of polyester urethane and Duocel aluminum foams with different average cell sizes. The images are used to establish statistically the cell size and ligament length distributions, material distributions along the ligaments, the geometry of the nodes and cell anisotropy. The measurements are then used to build finite element foam models of increasing complexity that are used to estimate the elastic moduli. In the most idealized model the microstructure is represented as a regular Kelvin cell. The most realistic models are based on Surface Evolver simulations of random soap froth with N³ cells in spatially periodic domains. In all models the cells are elongated in one direction, the ligaments are straight but have a nonuniform cross sectional area distribution and are modeled as shear deformable beams. With this input both the Kelvin cell models and the larger random foam models are shown to predict the elastic moduli with good accuracy but the random foams are 5–10% stiffer.     

基于分形的泡沫金属细观结构与尺寸效应研究

提出采用分形理论对泡沫金属的细观结构及尺寸效应进行研究的方法. 针对一系列具有不同相对密度和细观结构的泡沫铝,证明了其细观结构在一定尺度内符合分形特征,比较了小岛分维、计盒分维和信息分维等算法对泡沫金属分形表征的适用性,分析了细观结构特征对分维的影响. 结合推广的Sierpinski垫片模型研究了泡沫铝的屈服强度与分维的联系,建立了泡沫铝屈服强度的尺寸效应模型. 研究结果表明,由于引入了表征细观结构特征的分形维数,该模型除能表征屈服强度随试样尺寸的变化规律外,还在一定程度上直接反映了泡沫金属细观结构特征对力学性能的影响.      

On the dynamic mechanical properties of open-cell metal foams – A re-assessment of the ‘simple-shock theory’

Metal foams are increasingly used for energy absorption especially in lightweight structures and to resist blast and impact loads. This requires an understanding of the dynamic response of these materials for modelling purposes. As a supplement to Tan et al., 2005a, Tan et al., 2005b, hereinafter referred to as T–L for brevity, this paper provides experimental data for the dynamic mechanical properties of open-cell Duocel® foams having a three-dimensional (3D) distribution of cells. These confirm significant enhancement of the foam’s compressive strength, accompanied by changes in their deformation pattern in certain loading régimes, particularly what has come to be described as the ‘shock’ régime by Zheng et al. (2012). This paper examines experimentally, in a similar fashion as T–L, how the structural response of the individual cell walls is affected by cell-shape anisotropy at the cell (meso)-scale and how this, in turn, alters the pattern of cell crushing and the dynamic, mechanical properties. The distinctive role of cell microinertia and ‘shock’ formation are discussed in relation to the mechanical properties measured for these 3D cylindrical specimens. For consistency the same procedures described in T–L are used. The features identified are shown to be consistent with those observed in finite-element simulations of two-dimensional (2D) honeycombs as estimated by the one-dimensional (1D) steady-shock theory summarised in T–L. The different deformation patterns that develop in the various loading régimes are categorised according to the compression rate/impact speed. Critical values of impact velocity, corresponding to the transition from one pattern to the other, are quantified and predictive formulae for the compressive uniaxial strengths in the directions of two of the principal axes of the material in each loading régime are derived and discussed. The accuracy of the predictive formula in T–L is shown to critically depend on the ‘densification strain’ of the foam specimens. This parameter and the discussion that follows could assist the formulation and validation of alternative theoretical/computational models on the dynamic deformation of such materials.     

泡沫材料的应变率效应

对泡沫材料的应变率敏感性进行了系统深入的讨论,认定这种材料是应变率敏感材料,这种敏感性主要是由于泡孔的变形特性产生的。泡沫材料变形的局部化、微观惯性和致密性导致压垮应力明显提高,基体的应变率效应及泡孔的形状大小并不能对泡沫材料应变率敏感性起主导作用。     

基于三维细观力学模型的开孔泡沫弹性性能预测

泡沫材料的宏观力学性能主要取决于基体材料的力学特性及其微细观结构特征,基于细观力学模型的分析方法是泡沫材料力学性能研究的重要途径。文中基于Matlab语言和Abaqus软件构建了描述中等孔隙率开孔弹性泡沫材料微结构特征的三维随机分布球形泡孔模型,并采用有限元方法对弹性泡沫压缩变形进行了模拟,并计算给出了不同孔隙率弹性泡沫材料弹性模量、剪切模量、体积模量以及泊松比的分布,建立了相应的唯象表达式。与理论模型及测试结果的比较表明,本文基于三维随机泡孔模型模拟结果构建的唯象表达式能够对弹性泡沫材料的弹性力学性能给出很好的预测。     

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。     

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).     

宽γ辐照剂量范围内硅泡沫本构模型研究

基于实验和理论建模研究了白炭黑增强硅泡沫材料在γ辐照剂量范围为0~1000kGy作用后的单轴压缩力学行为。实验结果表明辐照导致硅泡沫出现明显硬化现象,初始杨氏模量和固定应变下应力幅值均随γ辐照剂量近似线性增加。辐照后硅泡沫泡孔结构完整,硅橡胶基体中高分子交联反应占主导,且交联密度随辐照剂量线性增大。基于实验分析结果,实现了Ogden Hyperfoam超弹本构模型参数与辐照剂量的关联。结果表明初始剪切模量参数与辐照剂量成线性关系,硬化指数和泊松比参数与辐照剂量无关。基于应力应变实验数据拟合得到模型参数,并与未参与拟合的实验数据对比,验证了模型的准确性,表明该模型能够表征宽辐照剂量范围内硅泡沫的压缩力学行为。     

宽γ辐照剂量范围内硅泡沫本构模型研究

基于实验和理论建模研究了白炭黑增强硅泡沫材料在γ辐照剂量范围为0~1000kGy作用后的单轴压缩力学行为。实验结果表明辐照导致硅泡沫出现明显硬化现象，初始杨氏模量和固定应变下应力幅值均随γ辐照剂量近似线性增加。辐照后硅泡沫泡孔结构完整，硅橡胶基体中高分子交联反应占主导，且交联密度随辐照剂量线性增大。基于实验分析结果，实现了Ogden Hyperfoam超弹本构模型参数与辐照剂量的关联。结果表明初始剪切模量参数与辐照剂量成线性关系，硬化指数和泊松比参数与辐照剂量无关。基于应力应变实验数据拟合得到模型参数，并与未参与拟合的实验数据对比，验证了模型的准确性，表明该模型能够表征宽辐照剂量范围内硅泡沫的压缩力学行为。     

On the compressive strength of open-cell metal foams with Kelvin and random cell structures

Two families of finite element models of anisotropic, aluminum alloy, open-cell foams are developed and their predictions of elastic properties and compressive strength are evaluated by direct comparison to experimental results. In the first family of models, the foams are idealized as anisotropic Kelvin cells loaded in the <100> direction and in the second family more realistic models, based on Surface Evolver simulations of random soap froth with N³ cells are constructed. In both cases the ligaments are straight but have nonuniform cross sectional area distributions that resemble those of the foams tested. The ligaments are modeled as shear deformable beams with elasto-plastic material behavior. The calculated compressive response starts with a linearly elastic regime. At higher stress levels, inelastic action causes a gradual reduction of the stiffness that eventually leads to a stress maximum, which represents the strength of the material. The periodicity of the Kelvin cell enables calculation of the compressive response up to the limit stress with just a single fully periodic characteristic cell. Beyond the limit stress, deformation localizes along the principal diagonals of the microstructure. Consequently beyond the limit stress the response is evaluated using finite size 3-D domains that allow the localization to develop. The random models consist of 3-D domains of 216, 512 or 1000 cells with periodicity conditions on the compressed ends but free on the sides. The compressive response is also characterized by a limit load instability but now the localization is disorganized resembling that observed in experiments. The foam elastic moduli and strengths obtained from both families of models are generally in very good agreement with the corresponding measurements. The random foam models yield 5–10% stiffer elastic moduli and slightly higher strengths than the Kelvin cell models. Necessary requirements for this high performance of the models are accurate representation of the material distribution in the ligaments and correct modeling of the nonlinear stress–strain response of the aluminum base material.