On the polymeric foams: modeling and properties

Polymeric foams are now widely used and researched. The physical properties of polymeric foam can be related to a set of independent structural parameters or variables of the foam. Study of these variables and correlation with commercial FE packages is essential for reliable and faster product development. Some aspects of foam behavior are widely studied while some are little less, like correlation of physical unloading behavior. For example, a lot of work in the area of phenomenological constitutive modeling of uniaxial loading was done, though research in areas of unloading–reloading and their correlation still demands more attention. Increasing number of OEMs and suppliers are moving to computer simulations in the design phase to assess their future products. Hence, different parameters within FE packages play a significant role and also affect the results. Appropriate use of these parameters will narrow down error band and automatically reduce the cycle time and development cost. This brief review is expected to set the perspective for major research work done so far in terms of FE modeling correlation and constitutive modeling of polymeric foam vis-a-vis to its properties.     

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.     

Experiments and simulations of liquid imbibition in aqueous foams under microgravity

We describe the capillary motion of liquid into aqueous foams under microgravity. Experiments in which a constant input of liquid is added to a foam under a variety of controlled experimental conditions (bubble size, cell geometry, bubble interfacial properties) have been performed in parabolic flights and in the MAXUS 6 sounding rocket. For comparison, we also performed numerical simulations, based on the foam drainage equations in which the gravitational contributions are removed. The agreement between these simulations and the experimental data is good, and the quantitative adjustment between them enables us to estimate foam permeabilities and surface shear viscosities.     

Continuum modeling of strain localization phenomena in metallic foams

Aluminium foams obtained by injecting a gas into the liquid metal are prone to localization of strain and damage. Under compression, crushing bands form, multiply and propagate through the whole sample. A continuum model based on a compressible plasticity framework is presented that is suitable for the simulation of such strain localization bands. The importance of accounting for strain localization phenomena in structural computations is illustrated by finite element simulations of the compression of cube and tapered specimens, and of an indentation test. A regularization procedure is proposed to obtain mesh–independent results.     

Microstructural characterization of metal foams: An examination of the applicability of the theoretical models for modeling foams

Establishing the geometry of foam cells is useful in developing microstructure-based acoustic and structural models. Since experimental data on the geometry of the foam cells are limited, most modeling efforts use an idealized three-dimensional, space-filling Kelvin tetrakaidecahedron. The validity of this assumption is investigated in the present paper. Several FeCrAlY foams with relative densities varying between 3 and 15% and cells per mm (c.p.mm.) varying between 0.2 and 3.9 c.p.mm. were microstructurally evaluated. The number of edges per face for each foam specimen was counted by approximating the cell faces by regular polygons, where the number of cell faces measured varied between 207 and 745. The present observations revealed that 50-57% of the cell faces were pentagonal while 24-28% were quadrilateral and 15-22% were hexagonal. The present measurements are shown to be in excellent agreement with literature data. It is demonstrated that the Kelvin model, as well as other proposed theoretical models, cannot accurately describe the FeCrAlY foam cell structure. Instead, it is suggested that the ideal foam cell geometry consists of 11 faces with 3 quadrilateral, 6 pentagonal faces and 2 hexagonal faces consistent with the 3-6-2 Matzke cell.     

Hypervelocity impact on honeycomb target structures: Experiments and modeling

This paper reviews some experimental and modeling works carried out at the CEG on hypervelocity ballistic properties of honeycomb structures representative of satellites structural bodies. Honeycomb structural panels were considered for HVI experiments using CEG's Persephone two-stage light gas gun in order to provide reference data to assess the Ouranos simulation software that was then used intensively during the second phase of the study. A ballistic limit equation (BLE) derived from Christiansen's equation was fitted for projectile velocities ranging from 2 to 10 km/s under normal and oblique impacts. In case of perforation, when the projectile diameter is greater than the critical perforation diameter, particle clouds orientation and amplitude in the plane of impact have been characterised and modeled analytically for inclusion within a global vulnerability software.     

High density polyethylene (HDPE): Experiments and modeling

The uniaxial tension (loading and unloading), creep and relaxation experiments on high density polyethylene (HDPE) have been carried out at room temperature. The stress–strain behavior of HDPE under different strain rates, creep (relaxation) behavior at different stress (strain) levels have been investigated. These experimental results are used to compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183–2201, 2000). It is observed that elasto-viscoplasticity model by Boyce et al. (Polymer 41:2183–2201, 2000) is not good enough to simulate stress–strain, creep and relaxation behaviors of HDPE. However, the aforementioned behaviors can be modeled quantitatively by using VBO model.     

Analysis of the polypropylene mechanical behaviour response: Experiments and numerical modeling

The security requirements in the industrial world incite an ever deeper understanding of the behaviour and the fracture of polymeric materials used as structural parts of the passenger compartment. We are looking at a polypropylene commonly used in this field in order to identify the physical processes responsible for their mechanical properties. The mechanical characterization of the response of the polymer under simple and complex strain relies on a unique method of combining performing numerical analysis techniques. The behaviour of polypropylene with large deformations dissipative involves several processes. Its consequences on the mechanical properties of materials are significant. The analysis of these results to emphasis that the plasticity of the polymer involves addition mechanical properties. Taken together, these observations can lay the groundwork for a thermodynamic modeling of the behaviour law to this class of polymer. The contribution of this approach was demonstrated by experimental and numerical modeling of the polypropylene mechanical behaviour.     

Biaxial cyclic deformation of an epoxy resin: Experiments and constitutive modeling

Biaxial (proportional and non-proportional) cyclic tests were conducted on thin-walled tubular specimens to investigate deformation behavior of an epoxy resin, Epon 826/Epi-Cure Curing Agent 9551. The focus was placed on the biaxial stress-strain response and their dependency on the load control mode, stress or strain range and loading path. Experimental results indicated that under strain-controlled equi-biaxial (proportional) cyclic loading, mean stress relaxation occurred in both axial and hoop directions, whereas under stress-controlled equi-biaxial cyclic loading, ratcheting strains accumulated in both principal directions. Under strain- or stress-controlled non-proportional cyclic loading, anisotropy in stress-strain responses was induced in both axial and hoop directions, and the axial and hoop hysteresis loops rotated in opposite directions. This was particularly evident at high stress or strain levels. The experimental results were further used to evaluate the predictive capabilities of a nonlinear viscoelastic constitutive model. Qualitative and quantitative comparison with the test data indicated a good agreement in predicting the complex stress-strain response under biaxial cyclic loading with various loading paths, applied stress or strain ranges and loading control modes.     

Relationship between pore structure and compressive strength of concrete: Experiments and statistical modeling

Properties of concrete are strongly dependent on its pore structure features, porosity being an important one among them. This study deals with developing an understanding of the pore structure-compressive strength relationship in concrete. Several concrete mixtures with different pore structures are proportioned and subjected to static compressive tests. The pore structure features such as porosity, pore size distribution are extracted using mercury intrusion porosimetry technique. A statistical model is developed to relate the compressive strength to relevant pore structure features.     

Experiments and modeling of edge fracture for an AHSS sheet

With the emergence of advanced high strength steels (AHSSs) and other light–weight materials, edge fracture has been one of the important issues evading reliable prediction using CAE tools. To study edge fracture behavior of AHSS, a comprehensive hole expansion test (HET) program has been carried out on a DP780 sheet. Specimen with three different edge conditions (milled edge, water jet cut edge and punched edge) are manufactured and tested. Results reveal that the hole expansion ratio (HER) of the present DP780 sheet is around 38 % for milled specimen and water jet cut specimen, and about 14 % for punched specimen. A novel method of a central hole specimen tension is also introduced for edge fracture study, showing a similar trend as found in HET. The paper briefly presents a procedure and the results for a full calibration of the DP780 sheet for plasticity and fracture, where a hybrid testing/simulation method is used to obtain parameters for Hill 48 plasticity model and modified Mohr–Coulomb fracture model. The finite element simulation gives an accurate prediction of HER, as well as the load displacement response and specimen deflection distribution in the hole expansion tests on uncracked material. The correlation between simulation and tests on central hole specimen also turns out to be very good. The paper also presents a very interesting insight of the initiation and propagation of cracks from the hole edge during a hole expansion test by numerical simulation in comparison with testing observation. The number of final cracks are accurately predicted. Other new aspects of the present paper include an improved 3D DIC measurement technique and a simplified analytical solution, from which a rapid estimation of displacement and hoop strain field can be made (see “Appendix 2”).     

Size effects in double-layer metallic films

An analysis is made of the electrical conductivity of double-layer, continouos, metallic films using the free-electron Boltzmann equation with elastic and isotropic bulk scattering. The electron-surface scattering is assumed to be specular. The analysis shows that a size effect can be expected when the thickness of the double-layer is of the same order of magnitude as the mean free path of the conduction electrons in the better conductor. The theoretical results are compared with the results obtained using the Fuchs-Sondheimer formalism and assuming diffuse electron-boundary scattering. The theoretical results are also related to published experimental results with superimposed metallic films.     

Size effects in superfluid field emission

A detailed experimental investigation has been made of the influence of chamber dimensions on field emission characteristics in liquid He.⁴ The current was found to be a strong function of the emitter-collector separation, in satisfactory quantitative agreement with the predictions of a simple theory     

Size effects in single grain fragmentation

Size effects on the compressive strength of cylinders and spheres are considered using Weibull statistical flaw size distribution. It is shown that failure is almost surely initiated from the bulk of the particle for large sizes, rather than from the vicinity of the loading contact points. Experiments performed on plaster on cylinders support our theoretical prediction, for the scaling of the particle strength with its size, using the experimentally determined Weibull modulus.     

Size effects in nanostructured ferroelectric films

The dependence of the effective dielectric permittivity of a nanostructured ferroelectric film on the grain size and the thickness of a dead (nonferroelectric) surface layer in inhomogeneous grains has been theoretically studied.