Full-field characterization of mechanical behavior of polyurethane foams

The foam material of interest in this investigation is a rigid closed-cell polyurethane foam PMDI with a nominal density of 20 pcf (320 kg/m³). Three separate types of compression experiments were conducted on foam specimens. The heterogeneous deformation of foam specimens and strain concentration at the foam–steel interface were obtained using the 3-dimensional digital image correlation (3D-DIC) technique. These experiments demonstrated that the 3D-DIC technique is able to obtain accurate and full-field large deformation of foam specimens, including strain concentrations. The experiments also showed the effects of loading configurations on deformation and strain concentration in foam specimens. These DIC results provided experimental data to validate the previously developed viscoplastic foam model (VFM). In the first experiment, cubic foam specimens were compressed uniaxially up to 60%. The full-field surface displacement and strain distributions obtained using the 3D-DIC technique provided detailed information about the inhomogeneous deformation over the area of interest during compression. In the second experiment, compression tests were conducted for cubic foam specimens with a steel cylinder inclusion, which imitate the deformation of foam components in a package under crush conditions. The strain concentration at the interface between the steel cylinder and the foam specimen was studied in detail. In the third experiment, the foam specimens were loaded by a steel cylinder passing through the center of the specimens rather than from its end surface, which created a loading condition of the foam components similar to a package that has been dropped. To study the effects of confinement, the strain concentration and displacement distribution over the defined sections were compared for cases with and without a confinement fixture.     

High-velocity deformation properties of polyurethane foams

This paper presents the results of dynamic uniaxial-stress tests performed on polymer-foam material. A water-blown ester polyurethane foam designated as rigid and a castor-oil-base polyurethane foam designated as semirigid were tested in tension and compression at rates of loading from 10^?3 in./in./sec to 10³ in./in./sec at room temperature. A gas-operated medium-strain-rate machine was used for rates of loading from 10^?3 to about 10² in./in./sec. Tests at higher rates were performed on a split Hopkinson-bar device. Highspeed photographic techniques were used to study dynamic fracture.     

Modeling morphology evolution and mechanical behavior during thermo-mechanical processing of semi-crystalline polymers

A new model is proposed that combines statistical mechanics and thermodynamic aspects to characterize orientation development, nucleation and growth of crystallites, and chain entanglement slippage with interdependent relationships necessary to accurately correlate and in some cases predict the morphology and mechanical behavior of semi-crystalline polymers during various thermo-mechanical processes in the rubbery state, close to the glass transition temperature. Internal state variables (ISVs) that directly represent the underlying microstructure state are used to characterize polymer morphology and the resulting properties throughout deformation. The model uses fundamental thermodynamic coefficients for polyethylene terephthalate (PET) and is correlated to experimental data at various strain rates and temperatures just above the glass transition temperature. Experimental data are used that measure the stress, amorphous orientation, and crystallinity during uniaxial deformation of PET. The model is found to correlate well to these experimental data.     

Micromorphic continuum modelling of the deformation and fracture behaviour of nickel foams

An anisotropic compressible plasticity model is incorporated into the framework of the micromorphic continuum theory in order to describe some size effects observed in ductile nickel foams. This continuum model reproduces the fact that the presence of a machined hole in a foam plate does not affect its mechanical response when the hole size becomes comparable to the cell size of the material. Finite element simulations are compared to strain field measurements in nickel foam plates with a machined hole for different hole sizes, in order to identify the characteristic length of the model. Based on a simple ductile damage law, the model is then shown to be able to account for the strong anisotropy of the initiation of crack propagation in central crack panels made of nickel foams under mode I loading conditions.     

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。     

Analytical models for the mechanical behavior of closed and open-cell Al foams

Two 3D analytical models are proposed for the determination of mechanical properties of Al closed and open-cell foams under compression load. The first model, referring to closed cell foams, is symmetrical, considering ellipsoid cells equally arranged in a rectangular plate, whereas the second one, related to open-cell foams, consists of a simple unit parallelepiped cell.The closed cell model produces much higher values of the plateau stress than comparable experimental results, mainly due to the associated conditions of symmetry, contrary to the open-cell model which yields values close to experimental and theoretical results of other investigators. Additionally, in the latter case, a unit cubic cell is also considered for comparison reasons. Both models are solved by the finite element method using a commercial program. The open-cell model is simple, time sparing and easy to use. Finally, a fracture analysis of the model is conducted based on the energy density concept and results are given for distortion and dilatational effects.     

多晶体变形、应力的不均匀性及宏观响应

从单晶滑移变形分析的角度探讨多晶体塑性变形和应力的不均匀性及宏观力学响应：建议了 一种当前构形下以应力为基本变量的单晶黏塑性增量迭代计算方法；用Voronoi晶粒集合体 模型研究多晶体由于晶粒几何及取向的随机性造成的变形和应力的不均匀性, 进行了多晶集 合体的宏观响应和晶粒位向演化数值分析. 结果表明：(1)多晶体内等效塑性应变和应力分量在统计上呈现高斯分布，在应变硬化过程中, 随着塑性变形增加多晶体微观应力的统计变异系数会越来越大；(2)用Voronoi模型计算可得到沿最大剪应力方向的滑移变形带；(3)多晶体内最高三轴拉应力一般出现在晶界特别是三晶交界处；(4)Voronoi模型能用于织构分析.     

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.     

泡沫金属材料的孔径效应

在分离式霍普金森压杆(SHPB)和MTS810材料试验机上分别对泡沫纯铝材料和铝硅合金泡沫材料进行了动态与准静态压缩实验研究。实验结果表明:孔径的大小对泡沫铝的弹性变形包括弹性模量没有影响,但对泡沫铝的屈服强度和塑性硬化模量有影响,且这种影响主要取决于泡沫铝基体材料的韧脆特性,泡沫铝的相对密度也会影响这种孔径效应。     

Effect of structural and mechanical characteristics of the composite material on the deformation of a reflector antenna

This is a study of the effect of structural and mechanical characteristics of a composite material on the stress–strain state of a reflector antenna shaped as a composite thin shell of revolution subjected to gravity, wind, and temperature loads. The boundaryvalue problem for the system of partial differential equations governing the behavior of this structure is reduced to a sequence of boundaryvalue problems for inhomogeneous systems of ordinary differential equations with variable coefficients. The resulting stiff systems of equations are solved by Godunov's method of discrete orthogonalization.     

Simultaneous measurement of viscoelastic changes and cell opening during processing of flexible polyurethane foam

A parallel-plate rheomete was constructed and used to study the development of dynamic shear modulus and cell opening under forced adiabatic conditions for a series of flexible slabstock polyurethane foams. Typical industrial formulations were used. The plates were heated to follow the adiabatic temperature profile of a real foam bun during foaming. The rheometer overcomes difficulties encountered in other methods such as heat loss and bubble damage caused by the probe.A four-stage modulus development profile was observed: initial bubble growth, bubble network, polymer stiffening and final curing. Chemical structure development was also studied under forced adiabatic conditions, using Fourier transform infrared spectroscopy. Polymer stiffening coincided with bidentate (hydrogen-bonded) urea formation.The normal force exerted by the expanding foam on the plates was found to be a function of the rate of foam expansion and the foam modulus. A sudden drop in the normal force typically coincides with the visually observed blow-off in the reacting foam bun, thus the normal force profile is a new and accurate indicator of cell opening. The normal force profile clearly shows that cell opening occurs just after the onset of polymer stiffening, thus illustrating the role of polymer rheology in the cell opening mechanism.Dedicated to the memory of Professor Tasos C. PapanastasiouPortions presented at the SPI Polyurethanes Technical/Marketing Conference, October 9–12, 1994, Boston, massachusetts, USA (Best paper award) and at the XIIth International Congress on Rheology, August 18–23, 1996, Québec City, Québec, Canada.     

Impact of mixing procedure on phase morphology and fracture mechanical properties of carbon black-filled NR/SBR blends

Based on a viscoelastic model, the filler distribution and the amount of interphase of carbon black-filled blends of natural rubber (NR) with styrene-butadiene rubber (SBR) are evaluated. Hereby, the total dissipated energy \(G''\) during dynamical straining is decomposed into the contributions of the different polymer phases and the interphase. For the NR/SBR blends, we find a higher filling of the SBR phase and the interphase and a lower filling of the NR phase. The filler distribution itself depends not only on the affinity of the polymer to the filler but also on the mixing procedure. This is investigated by studying NR/SBR blends prepared by two different mixing procedures. In the standard mixing procedure, the polymers are mixed first, and then, the filler is added. In the batch mixing procedure, the filler is previously mixed in the NR only and then blended with SBR. Batch mixing is resulting in an increase in the filling of the interphase due to filler transfer from NR to SBR. The results for the filler distribution are compared to fatigue crack propagation rates under pulsed excitation. The crack propagation is accelerated when substituting NR with SBR. The batched samples show higher crack propagation rates at higher tearing energies due to a worse dispersion of the carbon black and/or higher filler loading of the interphase.     

Experimental studies on the yield behavior of ductile and brittle aluminum foams

Specimen size effects are a major cause of the unreliability of foam models in finite element codes. Here, the modified Arcan apparatus is used to investigate the biaxial yielding of ductile and brittle Al foams. This apparatus subjects a central section of a “butterfly-shaped” specimen to a uniform state of plane stress. The stresses have local maxima at the central section, thus ensuring that yielding occurs there. A yield envelope, which directly relates to the crushing process, can then be determined. Size effects are introduced when using conventional methods such as tri-axial or plate-shear tests. In such tests, averages of stress and strain are measured. These measures do not represent the actual yield event, because foam's internal structure is inhomogeneous and so is the deformation field. Strain localization and failure can occur at any weak layer of cells in the bulk. In this study, we have performed a series of biaxial tests on isotropic Alporas and anisotropic Hydro closed-cell Al foams of approximately equal densities. Alporas failed locally by a ductile phenomenon of progressive crushing of cells. It also possessed uniaxial strength asymmetry. Hydro specimens parallel and perpendicular to ‘foam rise’ were investigated. The Hydro foam developed a local, characteristic brittle crack at loads in the vicinity of the yield point. Phenomenological yield surfaces, which incorporate these features are obtained for the foams, and show dependence on both the deviatoric and hydrostatic stresses. We also provide expressions for the shear and hydrostatic strengths in terms of the uniaxial strengths. Finally, the size-independence of the yield surface is verified using the uniaxial compression of tapered specimens.     

Assessment of material uncertainties in solid foams based on local homogenization procedures

The present study is concerned with a numerical prediction and assessment of uncertainties in the macroscopic material properties of solid foams. The material properties are determined by means of a homogenization analysis considering a large scale representative volume element. The microstructure for the representative volume element is determined randomly using a Voronoï tesselation in Laguerre geometry with prescribed cell size distribution. For assessment of the scatter in the effective material response, the homogenization scheme is applied to subsets of the large scale representative volume element. By this means, an interrelation between the local microstructural characteristics and the local mesoscopic material response is established. In a first approach, the individual cells of the foam microstructure are employed as testing volume elements. As an alternative, a moving window technique is applied. The sets of homogenization results obtained by both approaches are evaluated by stochastic methods. For the local effective properties, a distinct scatter is observed. The results in both cases reveal that the local porosity is the most important influence parameter. For the microstructures investigated, only weak local correlations of the effective stiffnesses with a rapid spatial decay of the correlation is observed.     

非均匀泡沫金属材料在冲击载荷下的变形模拟

提出一种二维非线性弹塑性质量-弹簧-连杆模型,该模型将泡沫金属材料离散成许多质量块,质量块在受载方向由非线性弹塑性弹簧连接,垂直于受载方向由可延伸的弹性连杆铰接。采用该模型模拟并分析了层非均匀泡沫金属材料及局部不均匀泡沫金属材料在冲击载荷下的变形特性,说明了非均匀性对泡沫金属材料冲击变形的影响。     

The kinetic nature of material deformation and fracture

Some physical mechanisms of deformation and fracture of solids are considered on the basis of state-transition kinetics. The effect of stress state on the energy barriers of state transition is studied for the process of deformation and fracture. Evolution equations are derived with and without consideration of the damage effect on the evolution of deformation and fracture. Some relations between various theories of deformation and fracture are found.     

Influence of thermal aging on tensile and creep behavior of thermoplastic polyurethane

Changes in mechanical and physical properties of polyurethane thermoplastic during aging at 70 °C and 90 °C were investigated. The loss weight response was analyzed by gravimetric measurements under these temperatures. Changes in appearance and morphology of TPU after thermal aging were revealed by optical microscopy. The prolongation of the thermal exposure time, up to 270 days, leads to a progressive increase in tensile strength. In fact, elastic modulus and stress at 200% of strain were increased with thermal exposure time. These results can be explained by the increase of thermal stability due to the increase of material rigidity and the decrease in chain mobility. The evolution of the mechanical properties from tensile tests seems to be well correlated to the creep behavior. Finally, Scanning Electron Microscopy (SEM) revealed the modification of TPU morphology fracture surface after thermal aging.