Polypropylene foam behaviour under dynamic loadings: Strain rate,density and microstructure effects

Expanded polypropylene foams (EPP) can be used to absorb shock energy. The performance of these foams has to be studied as a function of several parameters such as density, microstructure and also the strain rate imposed during dynamic loading. The compressive stress–strain behaviour of these foams has been investigated over a wide range of engineering strain rates from 0.01 to 1500 s⁻¹ in order to demonstrate the effects of foam density and strain rate on the initial collapse stress and the hardening modulus in the post-yield plateau region. A flywheel apparatus has been used for intermediate strain rates of about 200 s⁻¹ and higher strain rate compression tests were performed using a viscoelastic Split Hopkinson Pressure Bar apparatus (SHPB), with nylon bars, at strain rates around 1500 s⁻¹ EPP foams of various densities from 34 to 150 kg m⁻³ were considered and microstructural aspects were examined using two particular foams. Finally, in order to assess the contribution of the gas trapped in the closed cells of the foams, compression tests in a fluid chamber at quasi-static and dynamic loading velocities were performed.     

Compressive behavior of closed-cell aluminum alloy foams at medium strain rates

Compressive behavior of closed-cell aluminum alloy foams at strain rates of 10⁻³-450 s⁻¹ has been studied experimentally. The fully stress-strain curves of specimens at medium strain rates were obtained using the High Rate Instron Test System, which can maintain a constant loading rate. The experimental results show that plateau stress and energy absorption capacity are remarkable dependent on strain rate, while the densification strain has a negligible dependence.     

Effect of strain rate and density on dynamic behaviour of syntactic foam

The final objective of this study is to improve the mechanical behaviour of composite sandwich structures under dynamic loading (impact or crash). Cellular materials are often used as core in sandwich structures and their behaviour has a significant influence on the response of the sandwich under impact. Syntactic foams are widely used in many impact-absorbing applications and can be employed as sandwich core. To optimize their mechanical performance requires the characterisation of the foam behaviour at high strain rates and identification of the underlying mechanisms.Mechanical tests were conducted on syntactic foams under quasi-static and high strain rate compression loading. The material behaviour has been determined as a function of two parameters, density and strain rate. These tests were complemented by experiments on a new device installed on a flywheel. This device was designed in order to achieve compression tests on foam at intermediate strain rates. With these test machines, the dynamic compressive behaviour has been evaluated in the strain rate range up [6.7 · 10⁻⁴ s⁻¹, 100 s⁻¹].Impact tests were conducted on syntactic foam plates with varying volume fractions of microspheres and impact conditions. A Design of Experiment tool was employed to identify the influence of the three parameters (microsphere volume fraction, projectile mass and height of fall) on the energy response. Microtomography was employed to visualize in 3D the deformation of the structure of hollow spheres to obtain a better understanding of the micromechanisms involved in energy absorption.     

Polymeric foam behavior under dynamic compressive loading

Polymeric foams are commonly used in many impact-absorbing applications and thermal-acoustic insulated devices. To improve their mechanical performances, these structures have to be modeled. Constitutive equations (for their macroscopic behavior) have to be identified and then determined by appropriate tests.Tests were carried out on polypropylene foams under high strain rate compression. In this work, the material behaviour has been determined as a function of two parameters, density and strain rate. Foams (at several densities) were tested on a uniaxial compression for initial strain rates equal to 0.34 s⁻¹ and on a new device installed on a flywheel for higher strain rates. This apparatus was designed in order to do stopped dynamic compression tests on foam. With this testing equipment, the dynamic compressive behaviour of the polymeric foam has been identified in the strain rate range [6.7.10⁻⁴s⁻¹, 100s⁻¹].Furthermore, the sample compression was filmed with a high speed camera monitored by the fly wheel software. To complete this work, picture-analysis techniques were used to obtain displacement and strain fields of the sample during its compression. Comparisons between these results and stress-strain responses of polypropylene foam allow a better understanding of its behaviour. The multiscale damage mechanism, by buckling of the foam structure, was emphasised from the image analysis.     

The effects of strain rate,density, and temperature on the mechanical properties of polymethylene diisocyanate (PMDI)-based rigid polyurethane foams during compression

Compressive experiments on three types of rigid polyurethane foams were conducted by employing modified split Hopkinson pressure bars (SHPBs). The foam materials, which were based on polymethylene diisocyanate (PMDI), varied only in density (0.31 × 10³, 0.41 × 10³, and 0.55 × 10³ kg/m³) and were compressed at strain rates as high as 3 × 10³ s⁻¹. Dynamic experiments were also performed on these three foam materials at temperatures ranging from 219 to 347 K, while maintaining a fixed high strain rate of ~3 × 10³ s⁻¹. In addition, an MTS materials testing frame was used to characterize the low-strain-rate compressive response of these three foam materials at room temperature (295 K). Our study determined the effects of density, strain rate, and temperature on the compressive response of the foam materials, resulting in a compressive stress–strain curve for each material.     

Effect of hollow sphere size and size distribution on the quasi-static and high strain rate compressive properties of Al-A380–Al2O3 syntactic foams

Metal matrix syntactic foams are promising materials for energy absorption; however, few studies have examined the effects of hollow sphere dimensions and foam microstructure on the quasi-static and high strain rate properties of the resulting foam. Aluminum alloy A380 syntactic foams containing Al₂O₃ hollow spheres sorted by size and size range were synthesized by a sub-atmospheric pressure infiltration technique. The resulting samples were tested in compression at strain rates ranging from 10^?3 s^?1 using a conventional load frame to 1720 s^?1 using a Split Hopkinson Pressure-bar test apparatus. It is shown that the quasi-static compressive stress–strain curves exhibit distinct deformation events corresponding to initial failure of the foam at the critical resolved shear stress and subsequent failures and densification events until the foam is deformed to full density. The peak strength, plateau strength, and toughness of the foam increases with increasing hollow sphere wall thickness to diameter (t/D) ratio. Since t/D was found to increase with decreasing hollow sphere diameter, the foams produced with smaller spheres showed improved performance. The compressive properties did not show measurable strain rate dependence.     

软质聚氨酯泡沫的冲击力学性能

采用岛津试验机与改进的分离式霍普金森压杆(SHPB)试验装置,得到了两种分别用作汽车坐垫和靠垫材料的软质聚氨酯泡沫在不同应变率下的应力应变曲线。实验结果表明,材料强度对密度和应变率敏感。动态条件下,泡沫密实后,横向惯性效应导致泡沫被拉坏。而准静态变形达到80%时,卸载后变形仍能回复。评价两种泡沫的吸能特性时,发现两种密度的海绵动态吸能性能比静态时要差。最后对坐垫泡沫的厚度进行了优化设计。     

Cell structure and compressive behavior of an aluminum foam

The plastic collapse strength, energy absorption and elastic modulus of a closed cell aluminum foam are studied in relation to cell structures. The density, node size and the cell wall thickness of the aluminum foams decrease with increasing cell size. The failure of the foam cells under compressive load progresses successively from the top or/and bottom to the mid-layer of the compression specimens, and no initial rupture of the foam cells is observed in the mid-height of the foam samples. When foam density increases from 0.11 to 0.22 g/cm ³, the plastic collapse strength rises from 0.20 to 1.29 MPa, while the elastic modulus of the closed cell aluminum foam increases from 0.70 to 1.17 GPa. In contrast, the energy absorption of the foams decreases rapidly with increasing cell size. When cell size increases from 4.7 to 10.1 mm, the energy absorption drops from over unity to 0.3 J/cm ³. The normalized Yong’s modulus of the closed cell aluminum foam is E^*/E_s = 0.208 (ρ^*/ρ_s), while the normalized strength of the foams, σ */σ_s is expressed by σ */σ_s = c ⋅ ρ */ρ_s where c is a density-dependent parameter. Furthermore, the plastic collapse strength and energy absorption ability of the closed cell aluminum foams are significantly improved by reducing cell size of the aluminum foams having the same density.     

Quasi-static and dynamic crushing of empty and foam-filled tubes

Metallic foam-filled tubes and their empty counterparts have been tested at quasi-static and dynamic strain rates in order to determine their energy absorption capabilities. Data from the Split-Hopkinson Pressure Bar have been used to generate force vs. displacement curves that are somewhat analogous to pseudo-engineering stress-strain curves. Force balance calculations have also been made. These results indicate that, on an equal weight basis, foam-filled tubes offer greater energy absorption capability than empty tubes at quasi-static strain rates. However, the benefit of foam filling does not appear to be extended to strain rates of the order of 200–500 s^–1. Force balance calculations are shown to have potential as a method for monitoring the crushing of metallic foams at high strain rate.     

Effect of a high energy electrical pulse on the dynamic stress-strain behavior of a copper alloy

Electromagnetic launchers (EML) dispatch projectiles at extreme velocities (Mach 7-8), using copper/copper alloy rails which are subjected to high rates of loading under a high energy electrical pulse. Results from Split Hopkinson Pressure Bar (SHPB) testing of a copper alloy at high strain rates in the order of 10³ s^− 1 with simultaneous application of a high energy electrical pulse show that the plastic deformation of the copper alloy is increased and a higher degree of work hardening is observed under these conditions.     

Split Hopkinson pressure bar multiple reloading and modeling of a 316 L stainless steel metallic hollow sphere structure

The high strain rate (600 s⁻¹) compression deformation of a 316 L metallic hollow sphere (MHS) structure (density: 500 kg m⁻³; average outer hollow sphere diameter: 2 mm and wall thickness: 45 μm) was determined both numerically and experimentally. The experimental compressive stress–strain behavior at high strain rates until about large strains was obtained with multiple reloading tests using a large-diameter compression type aluminum Split Hopkinson Pressure Bar (SHPB) test apparatus. The multiple reloading of MHS samples in SHPB was analyzed with a 3D finite element model using the commercial explicit finite element code LS-DYNA. The tested MHS samples showed increased crushing stress values, when the strain rate increased from quasi-static (0.8 × 10⁻⁴ s⁻¹) to high strain rate (600 s⁻¹). Experimentally and numerically deformed sections of MHS samples tested showed very similar crushing characteristics; plastic hinge formation, the indentation of the spheres at the contact regions and sphere wall buckling at intermediate strains. The extent of micro-inertial effects was further predicted with the strain rate insensitive cell wall material model and with the strain rate sensitive behavior of MHS structure similar to that of the cell wall material. Based on the predictions, the strain rate sensitivity of the studied 316 L MHS sample was attributed to the strain rate sensitivity of the cell wall material and the micro-inertia.     

Compressive behaviour of closed-cell aluminium foams at high strain rates

It has been well established that ALPORAS® foams is a strain rate sensitive material. However, the strain rate effect is not well quantified as it is not unusual for strain rate to vary during high speed compression. Moreover, according to previous research, aluminium foams, especially ALPORAS® foams, behave differently at low and high strain rates. Therefore, different plastic deformation mechanisms are expected for low and high strain rate loadings as a result of micro-inertia of cell walls. In this paper, the strain rate effect on the energy dissipation capacity of ALPORAS® foam was investigated experimentally by using a High Rate Instron Test System, with cross-head speed up to 10 m/s. The compressive tests were conducted over strain rates in the range of 1 × 10^?3 to 2.2 × 10² s^?1, with each test being at a fairly constant strain rate. An energy efficiency method was adopted to obtain the densification strain and plateau stress. The effect of strain rate and the foam density was well presented by empirical constitutive models. The experimental data were also discussed with reference to the recent results by other researchers but with different range of strain rates. An attempt has been made to qualitatively explain the observed decrease of densification strain with strain rate.     

Dynamic compression of cellular cores: temperature and strain rate effects

Cross-linked polyvinyl chloride closed-cell foams were examined under quasi-static and high strain rate compression loading using a servo-hydraulic testing machine and a modified split Hopkinson pressure bar apparatus consisting of polycarbonate bars for strain rates up to 1900 s⁻¹. Three foam densities were examined viz. 75, 130, and 300 kg/m³. Each core density has been subjected to compressive loading at room and elevated temperatures. A reverse trend in failure modes was observed when moving from room to elevated temperatures at high strain loading, which was not found in quasi-static testing at elevated temperatures. Accordingly, post-impact tests were conducted to evaluate the residual strength of the foam cores subject to elevated temperatures and HSR. Results of the post-impact test revealed that the foam cores are still capable of taking some loading. The residual strength of cores was fairly constant regardless of temperature therefore recovery of volume does not signify an increase in residual strength of cores.     

Fracture energy of concrete at high loading rates in tension

The effect of high loading rates in tension on the failure energy and strength of concrete is reported in this paper. High loading rates exceeding 5000 GPa/s corresponding to strain rates higher than ∼120 s⁻¹ can be applied by use of Hopkinson bar set-up designed to produce spall. Tension tests were performed on cylindrical specimens made of micro-concrete. At high loading rates, or strain rates, the failure energy of micro-concrete, as well as the strength, was found to substantially increase.     

Effects of density and strain rate on properties of syntactic foams

Syntactic foams are characterized for high strain rate compressive properties using Split-Hopkinson Pressure Bar (SHPB) technique in this study. The results at high strain rates are compared to quasi-static strain rate compressive properties of the same material. Four different types of syntactic foams are fabricated with the same matrix resin system but different size microballoons for testing purpose. The microballoons have the same outer radius. However, their internal radius is different leading to a difference in their density and strength. The volume fraction of the microballoons in syntactic foams is maintained at 0.65. Such an approach is helpful in isolating and identifying the contribution of matrix and microballoons to the dynamic compressive properties of syntactic foams. Results demonstrate considerable increase in peak strength of syntactic foams for higher strain rates and increasing density. It is also observed that the elastic modulus increases with increasing strain rate and density. Scanning electron microscopy is carried out to understand the fracture modes of these materials and the density effect on high strain rate properties of syntactic foam.     

Mechanical properties of Epon 826/DEA epoxy

Polymers are becoming increasingly used in aerospace structural applications, where they experience complex, non-static loads. Correspondingly, the mechanical properties at high strain rates are of increasing importance in these applications. This paper investigates the compressive properties of Epon 826 epoxy resin cured with diethynolamine (DEA) across strain rates from 10⁻³ to 10⁴ s⁻¹. Specimens were tested using an Instron mechanical testing machine for static loading, traditional split Hopkinson pressure bars (SHPBs) for high strain rates, and a miniaturized SHPB for ultra-high strain rates. Additionally, the material was tested using dynamic mechanical analysis to determine the effects of time and temperature equivalences on the strain rate behavior of the samples. The experimental data is used to fit the Mulliken-Boyce model, modified for one-dimension, which is able to capture the compressive mechanical properties over a range of strain rates.     

Compressive strength of ice at impact strain rates

The compressive strength of ice was measured at high strain rates of 10³ s⁻¹ order of magnitude. Since ice compressive strength is known to be strongly dependent on strain rate, properties corresponding to high strain rates are needed for engineering predictions of the behavior of ice under dynamic crushing scenarios. The split Hopkinson pressure bar (SHPB) apparatus was used to successfully measure compressive strength over a strain rate range of 400–2,600 s⁻¹. Strain rate variation was achieved by adjusting the specimen length and the velocity of the SHPB striker bar; increased velocity and reduced specimen length produced higher strain rates. Since the compressive strength was found to be nearly uniform over the measured strain rate range, an average value of 19.7 MPa is reported. However, when comparing the present results with data in the existing literature spanning several orders of magnitude in strain rate, a trend of continuously increasing strength for strain rates beyond 10¹ s⁻¹ can be observed.     

Volume fraction effect on high strain rate properties of syntactic foam composites

The volume fraction effect on the high strain rate compressive properties of syntactic foams is characterized using a pulse-shaped Split-Hopkinson Pressure Bar (SHPB) technique. Eighteen different types of syntactic foams are fabricated with the same matrix resin system but six different microballoon volume fractions and three different size microballoons. The volume fractions of the microballoons in the syntactic foams are maintained at 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6. The microballoons have the same mean outer radius of 40 μm, but different internal radii leading to a difference in their density. Analysis is carried out on the effect of microballoon volume fractions on the high strain rate properties for each type of syntactic foam. This approach is helpful in understanding the effect of microballoon reinforcement at different volume fractions on the dynamic compressive properties of syntactic foams. The results at high strain rates are compared to quasi-static strain rate compressive properties of the same material. The results show that there is a decrease in both compressive strength and modulus as the microballoon volume fraction increases for the same type of syntactic foam at all strain rates. However, at strain rates of quasi-static and 450/s, the decrease tends to be gradual across all volume fractions, while for strain rates of 800/s, there is a dramatic decrease from 10 to 20% followed by a gradual decline for most specimens. The fracture mode plays a major role in the dynamic behavior of syntactic foams.     

Fabrication of ferrous metallic foams by reduction of ceramic foam precursors

A process has been developed for obtaining closed cell metallic foams using a ceramic foam precursor. In the present study, the major constituent of the ceramic foam precursor was iron oxide (Fe₂O₃), which was mixed with various foaming/setting additives. The mixture set rapidly at room temperature, stabilizing the foam generated by hydrogen release. The oxide foam was then reduced by annealing at 1240^∘C in a non-flammable hydrogen/inert gas mixture to obtain a metallic foam with a relative density of 0.23 ± 0.017, and an average cell diameter of 1.32 ± 0.32 mm. The iron foams were tested in compression and yielded an average compressive strength of 29 ± 7 MPa. The compressive stress-strain curves obtained were typical of cellular metals. The normalized strengths of the metal foams obtained in the present study compare favorably with those of steel foams produced by other techniques.     

An experimental assessment of friction effects in the split Hopkinson pressure bar using the ring compression test

The potential error due to friction in compression split Hopkinson pressure bar (SHPB) tests is assessed and conditions for minimising this error are investigated. Theoretical friction factors are inferred from ring compression tests. Experimental results are reported for mild steel, copper and aluminium ring specimens tested quasi-statically (∼10⁻² s⁻¹), using a servo-hydraulic test machine, and at high strain rates (∼10³ s⁻¹) on a SHPB. Specimens were tested dry, or lubricated using a molybdenum disulphide grease. The influence of surface finish and strain rate on the friction effect is discussed. The inferred friction factors are in the range m=0.08–0.14 (equivalent to Coulomb friction coefficients between μ=0.05 and 0.08). These results imply that the friction error in routine compression SHPB tests of metals lies between 2% and 3%.