Closed-cell Polymer Foams Research Articles

Low density polyethylene, expanded polystyrene and expanded polypropylene: Strain rate and size effects on mechanical properties

Polymeric foam materials may be used as energy absorbing materials for protection in impact scenarios, and design with these materials requires the mechanical properties of foams across a range of deformation rates, where high deformation rate testing often requires small samples for testing. Owing to their cellular macrostructure, and the large deformations that occur during loading of foams, the measured stress-strain response of a foam material may be influenced by the sample size. In this study, the mechanical properties of three closed-cell polymeric foams (Low Density Polyethylene, Expanded Polystyrene and Expanded Polypropylene) at two different densities were investigated over a range of deformation rates from 0.01 s−1 to 100 s−1. For each foam material, three different nominal sample sizes (10 mm, 17 mm and 35 mm) were tested. On average, the polymeric foam materials exhibited increasing stress with increasing deformation rate, for a given amount of strain.Density variation was identified at the sample level, with smaller samples often exhibiting lower density. Expanded Polystyrene demonstrated the highest variability in sample density and corresponding variability in mechanical response, qualitatively supported by observed variations in the macrostructure of the foam. Expanded Polypropylene exhibited variability in density with sample size, and observable variability in the material macrostructure; however, the dependence of the measured mechanical properties on sample size was modest. Low Density Polyethylene was found to have a relatively consistent cell size at the macrostructure level, and the material density did not vary significantly with sample size. In a similar manner, the dependence of measured mechanical properties on sample size was modest. The effect of sample size was identified to be material specific, and it is recommended that this be assessed using sample-specific density measurements and considering different sized samples when testing foam materials.

Application of a microstrain continuum to size effects in bending and torsion of foams

Classical theories of bending and torsion predict that the stiffness of a specimens scales with the square of the cross sectional area. However, many experiments have shown that this relation does not hold if the dimensions of the cross section become comparable to relevant length scales of the microstructure. In particular, such size effects are significant for foam materials which are nowadays extensively used in lightweight applications, since the cell size as relevant microstructural length may often be in the range of the structural component. In a number of studies, Cosserat theory was used phenomenologically to capture size effects of foam materials. However, this theory cannot describe all observed size effects and the determination of the increased number of parameters is not trivial. Recently, a model for foam materials was derived from a strict homogenisation within the microstrain framework.The scope of the present study is to investigate whether this microstrain model is suitable to describe the size effects of foams. For this purpose, the analytical solutions for elastic torsion and bending are derived for the microstrain theory. A comparison with experimental data from literature demonstrates that the model can adequately describe the size effects in bending and torsion of closed-cell polymeric foams. Only for very high porosities the size effects are overestimated.

Investigation of the dynamic stress–strain response of compressible polymeric foam using a non-parametric analysis

Dynamic stress–strain response of rigid closed-cell polymeric foams is investigated in this work by subjecting high toughness polyurethane foam specimens to direct impact with different projectile velocities and quantifying their deformation response with high speed stereo-photography together with 3D digital image correlation. The measured transient displacement field developed in the specimens during high stain rate loading is used to calculate the transient axial acceleration field throughout the specimen. A simple mathematical formulation based on conservation of mass is also proposed to determine the local change of density in the specimen during deformation. By obtaining the full-field acceleration and density distributions, the inertia stresses at each point in the specimen are determined through a non-parametric analysis and superimposed on the stress magnitudes measured at specimen ends to obtain the full-field stress distribution. The process outlined above overcomes a major challenge in high strain rate experiments with low impedance polymeric foam specimens, i.e. the delayed equilibrium conditions can be quantified.

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 Burzynski 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.

Evaluation of temperature effects on low velocity impact damage in composite sandwich panels with polymeric foam cores

In this study we investigate the response of closed cell polymeric foam core sandwich panels with woven carbon/epoxy laminate facesheets under low velocity impacts. Two levels of energy, 10J and 50J simulating barely visible and visible impact damage categories are examined under cold, room and high temperature conditions. A finite element modeling framework is proposed for the sandwich composite comprising continuum damage, cohesive layers and crushable foam model with isotropic hardening for the core. The model shows how progressive damage in the facesheets, interlaminar damage between the layers and the crushable foam can be used to model low velocity impact and temperature effects. Ultrasonic testing and high speed cameras are used to determine the damage and delamination characteristics. The higher exposure temperatures result in larger damage zones for both the low and high impact energies. The elevated temperature enhanced the penetration rate and indentation depth showing degradations in the out of plane properties. The visible damage test results in significant damage in the core and facesheets dependent on the temperature ranges tested. In the barely visible damage category, the composite facesheet layers attached to the foam experience a tension failure under low energy impact despite surface indications showing no fiber fracture.

Effect of the skin layer on the overall behavior of closed-cell polyethylene foam sheets

This article presents an experimental investigation of the effect of the skin layer on the mechanical behavior of a closed-cell polymeric foam material. The skin layer is a thin layer with increased density due to the manufacturing processes, which results in inhomogeneity. The skin-layer effect is investigated by comparing the stretch-stress characteristics of specimens with and without this skin layer on a particular closed-cell polyethylene foam sheet. The characteristics were recorded via uniaxial tension and compression tests, respectively, in all principal manufacturing directions. Thus, the skin-layer effect can be obtained by analyzing the recorded data points, which are also presented. The skin-layer-free specimens are prepared with a particularly designed assembly in accordance with the ASTM standards.

Effects of cell size and cell wall thickness variations on the stiffness of closed-cell foams

This paper concerns with the micromechanical modelling of closed-cell polymeric foams (M130) using Laguerre tessellation models incorporated with realistic foam cell size and cell wall thickness distributions. The cell size and cell wall thickness distributions of the foam were measured from microscope images. The Young’s modulus of cell wall material of the foam was characterised by nanoindentation tests. It is found that when the cell size and cell wall thickness are assumed to be uniform in the models, the Kelvin, Weaire–Phelan and Laguerre models overpredict the stiffness of the foam. However, the Young’s modulus and shear modulus predicted by the Laguerre models incorporating measured foam cell size and cell wall thickness distributions agree well with the experimental data. This emphasizes the fact that the integration of realistic cell wall and cell size variations is vital for foam modelling. Subsequently the effects of cell size and cell wall thickness variations on the stiffness of closed-cell foams were investigated using Laguerre models. It is found that the Young’s modulus and shear modulus decrease with increasing cell size and cell wall thickness variations. The degree of stiffness variation of closed-cell foams resulting from the cell size dispersion and cell wall thickness dispersion are comparable. There is little interaction between the cell size variation and cell wall thickness variation as far as their effects on foam moduli are concerned. Based on the simulation results, expressions incorporating cell size and cell wall thickness variations were formulated for predicting the stiffness of closed-cell foams. Lastly, a simple spring system model was proposed to explain the effects of cell size and cell wall thickness variations on the stiffness of cellular structures.

Shock Hugoniot measurements in foam

The present study outlines a new approach to collecting shock Hugoniot data in foams using photonic Doppler velocimetry to perform mid-plane measurements of the foam deformation. Plate impact experiments were carried out to investigate wave propagation in a closed-cell polymeric foam and an open-cell aluminum foam. Dual-wave structures were observed in both materials with the leading precursor wave determined to be an elastic wave. The discussion of the results focuses on the nature of foam compression under high-rate loading, particularly the difference between the strain history in a foam undergoing uniform stress compaction and uniaxial strain compression. These results are discussed in reference to the current interpretations of Taylor-Hopkinson bar experiments on similar metallic foams. The importance of gas-filtration driven flows in the wave dynamics of open-cell foams is discussed in relation to the nature of the precursor waves.

New laws for the tension/compression properties of Voronoi closed-cell polymer foams in relation to their microstructure

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.

Finite Element Modelling of Polymeric Foam-Filled Aluminium 2024-T4 Alloy Tube under Dynamic Axial Loading

The paper presents the numerical studies of two different tubes under axial impact loading structures. The cylindrical tubes filled with closed-cell polymeric foam. The deformation and failure mechanism of this new structure were observed and analyzed numerically using the finite element method. It is revealed that the stress distribution and fracture of the foam-filled tube structure are different from those of foam-filled tube. In comparison with double cell foam-filled tubes, the load-carrying capacity of this new structure is much steadier, the collapse behavior resistance is enhanced, and the weight efficiency of energy absorption is higher. Parameters affecting the performance of the foam-filled tube structures are also studied. Comparison were carried out with load versus displacement curve and also dynamic mean load as well as dynamic absorbed energy versus deformation of tubular collapse modeling failure mode using finite element analysis.

In situ analysis of fatigue crack propagation in polymer foams

This paper presents an in situ SEM experimental study on cyclic crack propagation in closed-cell polymer foams. The microscopic failure mechanisms in precracked PVC and PES specimens of 60 and 90kg/m3 densities were examined under low-cycle fatigue loading. In the PVC foam, crack propagation occurred incrementally by successive failure of cell boundaries in front of the crack tip. The crack occasionally jumped to cell boundaries above or below the main crack resulting in non-self similar growth. Crack propagation in the PES foam occurred incrementally by extensive plastic tearing and subsequent tensile failure of the cell edge in front of the crack tip. Crack advance sometimes occurred by coalescence of the main crack with a secondary crack above or below the main crack. Such crack bridging involved extensive shear deformation of the cells bridging the two adjacent cracks. Overall, crack growth in the PES foams occurred through the center of the cells. At a given cycle load level, more loading cycles were required to extend the crack in the PES foam than for the PVC foam as a result of the higher ductility of the PES polymer.

In situ analysis of crack propagation in polymer foams

This article presents an experimental study on the microscopic mechanisms associated with crack propagation in closed cell polymer foams. A brittle, slightly cross-linked polyvinyl chloride (PVC) foam of density 60 kg/m3 and a ductile thermoplastic polyether sulfone (PES) foam of density 90 kg/m3 were examined. The PVC and PES foams have similar cell size (≈0.7 mm) but the cell edges of the PES foam were much thicker than those in the PVC foam. Overall, it was observed that the elements of both foams fractured in an extensional mode. Crack propagation in the PVC foam was inter-cellular, where agglomerates of very small cells formed a region of weakness. Damaged cell walls were observed on both sides of the crack plane. For the PES foam, craze-like deformation bands were observed in the highly stretched region ahead of the blunted crack tip. Further ahead of the crack tip, highly stretched cells were observed. Fracture occurred predominantly through the center of the cells in the PES foam.

Crashworthiness design of transport aircraft subfloor using polymer foams

An innovative crashworthiness subfloor design concept was developed for middle or larger transport aircrafts. Closed-cell Rohacell-31 polymer foam blocks were introduced into the aircraft subfloor to enhance the energy absorption capability and mitigate peak acceleration during crash. Eight different configurations of foam blocks’ longitudinal distribution were considered. To provide a cost-effective method for assessing fuselage crashworthiness, compelling finite element models of an aircraft fuselage for these configurations were developed and vertical drops of the fuselage models were then simulated using the non-linear finite element code LS-DYNA. Impact responses, including failure behaviour, energy absorption and acceleration characteristics, were obtained and detailed effects of different foam block configurations on the crashworthiness was discussed. The analysis of the results showed that the optimal foam block length is 100–126 mm in our studied cases. The fuselage failure mode appeared to be symmetric, energy absorption by foam blocks became more efficient, peak acceleration transmitted to the occupants showed a remarkable reduction and the secondary impact was prevented.

Advanced material modelling in numerical simulation of primary acetabular press-fit cup stability

Primary stability of artificial acetabular cups, used for total hip arthroplasty, is required for the subsequent osteointegration and good long-term clinical results of the implant. Although closed-cell polymer foams represent an adequate bone substitute in experimental studies investigating primary stability, correct numerical modelling of this material depends on the parameter selection. Material parameters necessary for crushable foam plasticity behaviour were originated from numerical simulations matched with experimental tests of the polymethacrylimide raw material. Experimental primary stability tests of acetabular press-fit cups consisting of static shell assembly with consecutively pull-out and lever-out testing were subsequently simulated using finite element analysis. Identified and optimised parameters allowed the accurate numerical reproduction of the raw material tests. Correlation between experimental tests and the numerical simulation of primary implant stability depended on the value of interference fit. However, the validated material model provides the opportunity for subsequent parametric numerical studies.

Homogeneous phase and multi-phase approaches for modeling radiative transfer in foams

The aim of the present study is to investigate the suitability of two different continuum-based approaches for the modeling of the radiative transfer in two types of foams lying in the geometric optic regime: open cell metal foams and closed cell polymer foams. The two approaches are the commonly used Homogeneous Phase Approach (HPA) and the Multi-Phase Approach (MPA) which is rather new in the field of radiative transfer. For both approaches, the radiative properties involved in their respective frameworks are determined using newly developed Ray-Tracing methods applied to 3-D meshes representing the porous structures of open cell or closed cell foams. The 3-D meshes have been obtained from X-Ray Tomography applied to real metal and polymer foams. The radiative properties determined are used to compute the transmittances and reflectances of one-dimensional slabs of foams by the two approaches. They are compared with the results of a baseline Monte Carlo simulation in order to evaluate, for the two types of foams, the suitability of each method. It appears that both approaches are globally appropriate for predicting the radiative transfer in open cell metal foams although they are not able to match exactly the directional distribution of the transmittances and reflectances. For polymer foams, the accuracy of the HPA is demonstrated whereas the MPA provides significant differences with the reference MC simulations.

An experimental and theoretical investigation of the compressive properties of multi-walled carbon nanotube/poly(methyl methacrylate) nanocomposite foams

Polymer nanocomposite foams are promising low density substitutes for nanocomposites. Carbon nanotube/polymer nanocomposite foams possess high strength, low density, and can be made conductive. Good control of foam properties is of great importance in the application of such materials. In the current study, multi-walled carbon nanotubes (MWNTs) with controlled aspect ratio were used to alter the foam morphology in MWNT/poly(methyl methacrylate) (PMMA) nanocomposite foams produced by a supercritical carbon dioxide (CO 2) foaming process. It was found that with the addition of one weight percent of MWNTs, the Young’s modulus of polymer foams increased by as much as 82%, and the collapse strength increased by as much as 104%. The influence of MWNT aspect ratio on the compressive properties of nanocomposite foams was investigated. The addition of MWNTs influenced the foam properties in two ways: improving the compressive properties of the solid matrix, and reducing the bubble size of the nanocomposite foams. A modified constitutive model for predicting the compressive properties of high density closed-cell polymer foams was developed. The influence of the bubble size on the mechanical properties of polymer foams was discussed based on the new model.

Microcellular and nanocellular solid-state polyetherimide (PEI) foams using sub-critical carbon dioxide II. Tensile and impact properties

Microcellular foams, closed-cell polymer foams with cells of order 10 μm, have been studied for over two decades. These foams have shown significant improvements in mechanical properties, such as strength-to-weight ratio, over conventional foams with cells on the order of 1 mm. Will an additional 100-fold reduction in cell size yield further improvement in properties? Here we answer this question in the solid-state PEI–CO 2 system, a unique gas–polymer system in which cellular structures can be created throughout the polymer volume at either micro or nano scales. The tensile and impact behaviors of microcellular (cells in 2–5 μm range) and nanocellular (cells in the 50–100 nm range) structures are experimentally compared for foams with relative densities, to that of the starting solid, in the range of 0.75–0.90. We found that nanofoams show a significantly higher strain to failure, resulting in an improvement in the modulus of toughness by up to 350% compared to microcellular foams. Falling weight impact tests show evidence of a brittle-to-ductile transition in nanofoams resulting in impact energies that are up to 600% higher compared to microcellular foams. These results point to the promise of nanofoams as an important new class of materials.

Inverse Analysis of Material Parameters of Multiple Foam Layers Based on Artificial Neural Network

Closed cell polymeric foams are widely used in sport and medical equipments. In this study, an artificial neural network (ANN) based inverse finite element (FE) program has been developed and used to predict the nonlinear material properties of EVA foams with multiple layers. A 2-D parametric FE model was developed and validated against experimental data. Systematic data from FE simulations was used to train and validate the ANN model. The accuracy and validity of the ANN method were assessed based on both blind tests and experimental data. Results showed that the proposed artificial neural network model is robust and efficient in predicating the nonlinear parameters of foam materials.

Emerging Trends in Failures Involving EPS-Block Geofoam Fills

Expanded polystyrene (EPS) is a closed-cell polymeric (“plastic”) foam that, in its generic block-molded form, has seen increasing use worldwide as a cellular geosynthetic in the geofoam category. This growth is due to the fact that block-molded EPS is unique among geofoam products for the large and diverse variety of functional applications for which it is technically well suited and relatively economical as well as for its proven long-term in-ground durability. However, as often happens when there is rapid growth in a technology based on a generic commodity product such as block-molded EPS, its use outstrips the acquisition of critically important technical knowledge by end users. This can result in inefficient and even incorrect use that can lead to failures in project applications. There is evidence that this cause and effect is currently occurring in the United States at least for some widely used EPS-block geofoam functional applications such as lightweight fill for road construction. This paper con...

Deformation mechanisms and the yield surface of low-density, closed-cell polymer foams

The geometry of low-density, closed-cell, polyethylene and polystyrene foams was modelled with a Kelvin foam having uniform-thickness cell faces; finite element analysis (FEA) considered interactions between cell pressures and face deformation. Periodic boundary conditions were applied to a small representative volume element. In uniaxial, biaxial and triaxial tensile stress states, the dominant high-strain deformation mechanism was predicted to be tensile yield across nearly flat faces. In uniaxial and biaxial compression stress states, pairs of parallel plastic hinges were predicted to form across some faces, allowing them to concertina. In hydrostatic compression, face bowing was predicted. The rate of post-yield hardening changed if new deformation mechanisms became active as the foam strain increased. The effects of foam density and polymer type on the foam yield surface were investigated. Improvements were suggested for foam material models in the FEA package ABAQUS.