Large strain compressive response of 2-D periodic representative volume element for random foam microstructures (original) (raw)
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Effects of cell irregularity on the high strain compression of open-cell foams
Acta Materialia, 2002
The high strain compression of low-density open-cell polymer foams has been modelled by finite element analysis. We used a Voronoi method to generate periodic structures with different degrees of randomness of the cell size and shape, then to investigate the influence of this randomness on the response of Voronoi open-cell foams to high strain compression. It is found that, although the reduced compressive stress-strain relationship and the Poisson's ratio vary in different directions for individual samples, the models are, on average, isotropic. A highly irregular foam has a larger tangential modulus at very low strains and a lower effective stress at high compressive strains than a more regular foam. The geometrical properties were investigated and used to predict the compressive stress-strain relationships for random open-cell foams with different degrees of cell regularity. For irregular low density foams, strut bending and twisting (the "springs-in-parallel" model) dominate the mechanical response at low strains and strut buckling (the "springs-in-series" model) becomes the main deformation mechanism at large compressive strains.
Size effects in foams: Experiments and modeling
Progress in Materials Science, 2011
Mechanical properties of cellular solids depend on the ratio of the sample size to the cell size at length scales where the two are of the same order of magnitude. Considering that the cell size of many cellular solids used in engineering applications is between 1 and 10 mm, it is not uncommon to have components with dimensions of only a few cell sizes. Therefore, both for mechanical testing and for design, it is important to understand the link between the cellular morphology and size effects, which is the aim of this study. In order to represent random foams, two-dimensional (2D) Voronoi tessellations are used, and four representative boundary value problems -compression, shear, indentation, and bending -are solved by the finite element (FE) method. Effective elastic and plastic mechanical properties of Voronoi samples are calculated as a function of the sample size, and deformation mechanisms triggering the size effects are traced through strain maps. The modeling results are systematically compared with experimental results from the literature. As a rule, with decreasing sample size, the effective macroscopic stiffness and strength of Voronoi samples decrease under compression and bending, and increase under shear and indentation. The physical mechanisms responsible for these trends are identified.
Modelling of the Mechanical Properties of Low-Density Foams
Foamed materials are applied in many products, because of the special combination of mechanical properties and low density. The mechanical properties of foams are determined by the properties of the solid material inside the foam and the topology of the foam structure. This makes it possible to model the mechanical behaviour of foams with the help of a Finite Element Method. In this thesis, FE analyses are performed on various types of foams and the effects of various geometrical features of the foam geometry are studied. The majority of the existing models is based on regular structures consisting of struts and walls associated with the structural elements in foams. The main advantage of the presented random model in comparison with already existed ones is the use of a geometry very close to the real foam geometry. This allows to understand the dominant deformation mechanisms in foams and, therefore, to predict the behaviour of foams. The FE analysis results were compared to the results of experiments from which the mechanical properties were obtained. The experimental investigations of foams also comprised a microscopic analysis of the geometrical features of the foam. Various types of foams were studied in this way: polyurethane, polystyrene, polymethacrylimide, glass and aluminium foams. First, an open-cell random foam model has been created with the help of the 3D Voronoi technique. The deformation behaviour of regular foams is dominated by bending of struts. This has already been recognized by several other scientists. However, it has been shown in this thesis that the behaviour of random foams is different. Axial deformations in random foams play an important role even in the initial stage of the deformations. This is opposed to the regular models often used in practice. The FE analyses showed that the stiffness of a random foam model is higher than that of corresponding regular models due to the “coincidental” percolations of chains of randomly oriented struts. These chains bear a significant axial load. The random open-cell model showed that axial deformation becomes dominant in all foams under large tensile strains. Geometrical anisotropy of open-cell foam is also modelled. It is described by the introduction of two kinds of anisotropy. This technique allows to reach a close correspondence between the geometrical features of real foams and those of the model. Consequently, the behaviour of foam can be modelled and predicted. Similar to the open-cell foams, also a closed-cell random foam model is created. It has been shown that the geometry of a model is important for the prediction of the mechanical properties of foams. The distribution of the solid material between struts and walls in foam is very important, and foams with all material inside the walls (struts are not pronounced) exhibit the highest mechanical properties. Moreover, not all walls are closed in closed-cell foams. Some of them are ruptured during or after processing. This is also one of the geometrical features which influence the foam behaviour considerably. Comparison of regular and random foam models showed that simple fcc- and bcc-based foam models can be used to predict the Young's modulus of isotropic foam, if the main part of the material in the modelled foam is concentrated in walls. Otherwise, if the fraction of solid in struts is considerable, regular models give inaccurate results and the use of the random model is advisable. Furthermore, the anisotropy in closed-cell foam is described analogous to that in the open-cell foam model. The predicted Young's modulus in real foam is much more accurate than previously described (literature) models. Finally, a complete random anisotropic closed-cell foam model is created and successfully used to predict both linear and nonlinear mechanical behaviour of a real anisotropic closed-cell foam.
A simple method to predict high strain rates mechanical behavior of low interconnected cell foams
Polymer Testing - POLYM TEST, 2007
A method to model high strain rate compressive properties of PU foams was investigated. The nonlinear mechanical response of the foam was split into three independent contributions: foam morphology, time-dependent polymer response, gas entrapped in the cells.The foam morphology contribution was estimated by a simple uniaxial compression test at very low strain rate. The time (temperature)-dependent behavior of the polymeric foam was evaluated by stress relaxation tests. Due to the low degree of cell interconnections of the studied foam, at low strain rates the gas contribution was predicted by using a gas flow model derived from Darcy's law. Starting from 2s−1 compressive strain rate, the foam exhibited a transition and the gas contribution was evaluated by a scaled closed cell model.The proposed method is able to predict the mechanical response of foams at high strain rates using data obtained by few low strain rates mechanical tests.
Foam mechanics: nonlinear response of an elastic 3D-periodic microstructure
International Journal of Solids and Structures, 2002
The compressive response of a 3D open-cell foam with periodic tetrakaidecahedral cells is studied through combined theoretical and numerical efforts. Under compressive loading the response is characterized by an extended load plateau following the relatively sharp rise to a maximum load. Several processes of loading have been simulated numerically using appropriately nonlinear kinematics. The onset of failure under macroscopic loading conditions is shown to be the reason of the load plateau. A failure surface is defined in macroscopic stress space by the onset of the first buckling-type instability encountered along proportional load paths. The analysis is carried out through two methods. The first one consists in increasing specimen size with periodic boundary conditions leading to the termed microfailure surface. The second one consists in considering both periodic and nonperiodic displacements variations on a minimum unit cell. The resulting failure surfaces are shown to coincide. Moreover, the postbuckling analysis has been carried out for two particular loadings: the uniaxial compression and the uniaxial deformation. Ó
Effect of density, microstructure, and strain rate on compression behavior of polymeric foams
Materials Science and Engineering: A, 2005
In this paper two types of polymeric foams, namely, cross-linked poly-vinyl chloride (PVC) and polyurethane (PUR) were examined under compression loading at different strain rates. Quasi-static compression tests were performed using a servo-hydraulic material testing system (MTS) at strain rate of 0.001, 0.01, and 0.1 s −1 . Higher strain rate compression tests were performed using a split Hopkinson pressure bar (SHPB) apparatus with polycarbonate bars at strain rate ranging from 130 to 1750 s −1 . PVC foams with three densities and two microstructures, and PUR foams with two densities were considered. All foam specimens were tested in the thickness (rise) direction and the stress-strain responses at different strain rate were established to determine the peak stress and energy absorption. Both peak stress and energy absorption were found to be dependent on foam density, foam microstructure, and strain rate. A power law relationship between the peak stress and foam density revealed that the constants were different at different strain rate. Microstructural examinations of the failed specimens showed that PUR foams disintegrated completely around 1600 s −1 whereas PVC foams densified completely like a solid material.
2014
Closed-cell polymer foams are well-known for their thermal capabilities, but works on the mechanical behavior of these materials are scarce, especially concerning the influence of the foam's microstructure. The objective of this study is to investigate the influence of the relative density and irregularity of Voronoi closed-cell foam structures on their elastic characteristics (such as the Young's modulus and the Poisson's ratio) and plastic characteristics (such as elastic limits and collapse stresses). New laws are proposed in order to approximate the macroscopic mechanical behavior of Voronoi closed-cell foams under uniaxial tension and compression.
Materialia, 2018
Polymer foams have many industrial applications because of their good mechanical properties combined with low material density. However, their study and the prediction of their behavior is challenging due to the massive influence of their complex microstructure. This paper focused on a polyurethane foam containing 70 vol% of porosity and aims at determining its behavior when submitted to large deformations under dynamic compressive loads. A model based on the material point method was set to study the whole stress-strain relationship of representative realistic foam sample, obtained from CT-scans. The dynamic model was validated to compression results from Split Hopkinson Pressure Bar experiments allowing the study of a shock due to a container fall. Direct influence of the microstructure was then evaluated. We first added virtual realistic manufacturing defects on the geometry and then studied the foam behavior of fully computer-designed microstructures. Recent developments in additive fabrication make the manufacturing of such structures possible and would widen the possibilities of virtually optimizing material designs.
Influence of Microstructure on the Dynamic Behaviour of Polyurethane Foam with Various Densities
Journal of Basic & Applied Sciences, 2023
Polyurethane foam is reinforced with varying proportions of metal loads and other components to increase shock absorption and mechanical impact. The main objective is to develop high-performance polymeric materials based on polyurethane foam developed with different compositions and specific densities. We monitor the growth distances and temperatures of the polyurethane foam in time to reach the optimum formulations. We conduct static compression tests and investigate the effect of drop weight on the deformation of polyurethane foam structures by dropping a weight from a specified height. Dynamic collisions cause deformations of the polyurethane foam structure. After investigating the low weight, we found that polyurethane foams have a good absorption coefficient at certain frequencies. Dynamic stress-strain response curves are used to characterize different stress rates. High-stress levels and similar strains indicate a high resistance to shock. We follow the evolution of microstructure structures by scanning electron microscopy (SEM) to observe deformation and fracture behavior with reversibility and recovery.