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.     

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.     

Prediction of compressive properties of closed-cell aluminum foam using artificial neural network

The design of artificial neural network (ANN) is motivated by analogy of highly complex, non-linear and parallel computing power of the brain. Once a neural network is significantly trained it can predict the output results in the same knowledge domain. In the present work, ANN models are developed for the simulation of compressive properties of closed-cell aluminum foam: plateau stress, Young’s modulus and energy absorption capacity. The input variables for these models are relative density, average pore diameter and cell anisotropy ratio. Database of these properties are the results of the compression tests carried out on aluminum foams at a constant strain rate of 1 × 10⁻³ s⁻¹. The prediction accuracy of all the three models is found to be satisfactory. This work has shown the excellent capability of artificial neural network approach for the simulation of the compressive properties of closed-cell aluminum foam.     

Characterisation of aluminium matrix syntactic foams under drop weight impact

It is a challenging task to develop a lightweight, and at the same time, strong material with high energy absorption for applications in military vehicles, which are able to withstand impact and blast with minimum injury to occupants. This paper presents a study on aluminium matrix syntactic foams as a possible core material for a protection system on military vehicles. Experimental work was first carried out which covers sample preparation through pressure infiltration and impact tests on aluminium matrix syntactic foams manufactured. Numerical models were then developed using commercial finite element code ABAQUS/Explicit to simulate the dynamic behaviour of the foam. The effect of strain rate on their compressive behaviour was investigated as these properties are vital in terms of the applications of these materials. Characterisation of the foam behaviour under low velocity impact loading and an identification of the underlying failure mechanisms were also carried out to evaluate the effective mechanical performance. It was found that samples subjected to drop weight impact offered a 20–30% higher plateau stresses than those of the samples subjected to quasi-static compression loading. The degree of correlation between the numerical simulations and the experimental results has been shown to be reasonably good.     

Constitutive equations to predict high temperature flow stress in a Ti-modified austenitic stainless steel

The experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1523 K) and strain rates (10⁻³–10² s⁻¹), were employed to develop constitutive equations in a Ti-modified austenitic stainless steel. The effects of temperature and strain rate on deformation behaviors were represented by Zener-Holloman parameter in an exponent type equation. The influence of strain was incorporated in the constitutive analysis by considering the effect of strain on material constants. The constitutive equation (considering the compensation of strain) could precisely predict the flow stress only at 0.1 and 1 s⁻¹ strain rates. A modified constitutive equation (incorporating both the strain and strain rate compensation), on the other hand, could predict the flow stress throughout the entire temperatures and strain rates range except at 1123 K in 10 and 100 s⁻¹. The breakdown of the constitutive equation at these processing conditions is possibly due to adiabatic temperature rise during high strain rate deformation.     

An investigation on the dynamic response of polymeric,metallic, and biomaterial foams

Mechanical characterization of foams at varying strain rates is indispensable for the selection of foam as core material for the proficient sandwich structure design at dynamic loading application. Both servo-hydraulically controlled Material Testing System (MTS) and Instron machines are generally considered for quasi-static testing at strain rates on the order of 10⁻³ s⁻¹. Split Hopkinson pressure bar (SHPB) with steel bars is typically utilized for characterizing metallic foams at high strain rates, however modified SHPB with polycarbonate or soft martial bars are used for characterizing polymeric and biomaterial foams at high strain rates on the order of 10³ s⁻¹ for impedance match between the foam specimens and bars. This paper reviews the effect of strain rate of loading, density, environmental temperature, and microstructure on compressive strength and energy absorption capacity of various closed-cell polymeric, metallic, and biomaterial foams. Compressive strength and energy absorption capacity increase with the increase in both strain rate of loading and density of foams, but decrease with the increase in surrounding temperature. Foams of same density can have different strength and can absorb unequal amount of energy at the same strain rate of loading due to the variation of microstructure.     

FE modeling of the compressive behavior of porous copper-matrix nanocomposites

Compressive mechanical test and numerical simulation via finite element modeling have been employed on closed-cell copper-matrix nanocomposite foams reinforced by alumina particles. The FE analysis' purpose was to model the foam deformation behavior under compressive loading and to investigate the correlation between material characteristics and the compressive mechanical behavior. Exploring this, several foam samples with different conditions were manufactured and compression test was carried out on the samples. Scanning electron microscopy and image analysis have been performed on the foam samples to obtain the required data for the numerical simulation. The stress–strain curves exhibited plateau stress between 18 and 112.5 MPa and energy absorption in the range of 20.03–51.20 MJ/m³ for the foams with different relative densities. The foams exhibited enhanced mechanical properties to an optimum value, as a consequence of increasing the reinforcing nanoparticles, through both experimental tests and numerical simulation data. Also, the validated model of copper-matrix nanocomposite foams has been used to probe stress distribution in the foams. In addition, the results obtained by numerical simulation via ABAQUS CAE finite element modeling provided support for experimental test results. This confirmed that FEM is a favorable technique for predicting mechanical properties of nanocomposite copper foams.     

High temperature deformation behavior of a near alpha Ti600 titanium alloy

The high temperature deformation behavior of a near alpha Ti600 titanium alloy was investigated with isothermal compression tests at temperatures ranging from 800 to 1000 °C and strain rates ranging from 0.001 to 10.0 s⁻¹. The apparent activation energy of deformation was calculated to be 620.0 kJ mol⁻¹, and constitutive equation that described the flow stress as a function of the strain rate and deformation temperature was proposed for high temperature deformation of Ti600 titanium alloy in the α + β phase region. The processing map was calculated to evaluate the efficiency of the forging process in the temperatures and strain rates investigated and to recognize the instability regimes. High efficiency values of power dissipation over 55% obtained under the conditions of strain rate lower than 0.01 s⁻¹ and temperature about 920 °C was identified to represent superplastic deformation in this region. Plasticity instability was expected in the regime of strain rate higher than 1 s⁻¹ and the entire temperature range investigated.     

Constitutive analysis to predict high-temperature flow stress in modified 9Cr–1Mo (P91) steel

Constitutive analysis for hot working of modified 9Cr–1Mo (P91) ferritic steel was carried out employing experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1373 K), strains (0.1–0.5) and strain rates (10⁻³–10² s⁻¹). The effects of temperature and strain rate on deformation behaviour were represented by Zener–Hollomon parameter in an exponent-type equation. The influence of strain was incorporated in the constitutive equation by considering the effect of strain on different material constants. Activation energy was found to vary with strain in the range 369–391 kJ mol⁻¹. The developed constitutive equation (considering the compensation of strain) could predict flow stress of modified 9Cr–1Mo steel over the specified hot working domain with very good correlation and generalization.     

A multiphase mechanical model for Ti–6Al–4V: Application to the modeling of laser assisted processing

A multiphase model for Ti–6Al–4V is proposed. This material is widely used in industrial applications and so needs accurate behaviour modeling. Tests have been performed in the temperature range from 25 °C to 1020 °C and at strain rates between 10⁻³ s⁻¹ and 1 s⁻¹. This allowed the identification of a multiphase mechanical model coupled with a metallurgical model. The behaviour of each phase is calibrated by solving an inverse problem including a phase transformation model and a mechanical model to simulate tests under thermomechanical loadings. A scale transition rule (β-rule) is proposed in order to represent the redistribution of local stresses linked to the heterogeneity of plastic strain. Finally this model is applied to two laser assisted processes: direct laser fabrication and laser welding.     

Development of rubberized syntactic foam

This study explored a novel hybrid syntactic foam for composite sandwich structures. A unique microstructure was designed and realized. The hybrid foam was fabricated by dispersing styrene–butadiene rubber latex coated glass microballoons into a nanoclay and milled glass fiber reinforced epoxy matrix. The manufacturing process for developing this unique microstructure was developed. A total of seven groups of beam specimens with varying compositions were prepared. Each group contained 12 identical specimens with dimensions 304.8 mm × 50.8 mm × 15.2 mm. The total number of specimens was 84. Among them, 42 beams were pure foam core specimens and the remaining 42 beams were sandwich specimens with each foam core wrapped by two layers of E-glass plain woven fabric reinforced epoxy skin. Both low velocity impact tests and four-point bending tests were conducted on the foam cores and sandwich beams. Compared with the control specimens, the test results showed that the rubberized syntactic foams were able to absorb a considerably higher amount of impact energy with an insignificant sacrifice in strength. This multi-phase material contained structures bridging over several length-scales. SEM pictures showed that several mechanisms were activated to collaboratively absorb impact energy, including microballoon crushing, interfacial debonding, matrix microcracking, and fiber pull-out; the rubber layer and the microfibers prevented the microcracks from propagating into macroscopic damage by means of rubber pinning and fiber bridge-over mechanisms. The micro-length scale damage insured that the sandwich beams retained the majority of their strength after the impact.     

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.     

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.     

Quasistatic and dynamic crushability of polymeric foams in rigid confinement

An approach was developed for investigating the crushability behavior of epoxy-based, low-density structural polymeric foam (initial bulk density 0.81 g/cm³ was used for test illustration) under quasistatic and high strain rate conditions in rigid confinement. Quasistatic crushability tests were conducted in a steel confinement cell using an MTS material testing system and the high strain rate (dynamic) crushability behavior was investigated by placing a foam specimen in a steel confinement tube and then loading the specimen using two different split Hopkinson pressure bar systems, namely, a magnesium bar and steel bar. The dynamic deformation characteristics were obtained using a multi-step incremental loading procedure. It was found that these foams exhibited large uniform inelastic deformation during the confined loading. It is verified that multi-step incremental loading can be used to construct the complete stress–strain response curve for the specimens under both quasistatic and dynamic loading conditions. A phenomenological constitutive model was then applied to parametrically describe the crushability response and to determine the rate sensitivity of the foams. The rate sensitivity of yield stress was found to be around three under rigid confinement.     

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.     

Comprehensive analyses of syntactic foam behaviour in deepwater environment

Over the past 10 years, numerous studies were performed to better understand the behaviour of the glass syntactic foams used as thermal insulation of pipes for deepwater production. The obtained results outlined some specific behaviour of polymeric syntactic foams reinforced by glass microballoons in service conditions: both water uptake and mechanical stress have a key impact on thermal properties. This article focuses first on the wet behaviour of glass syntactic foams. The effect of water is investigated to better model the nature of water diffusing in syntactic foams with and without a topcoat protection. Secondly, the effect of hydrostatic pressure on coated structure is addressed by using a confined compression test. As polymer material is bonded to the steel surface, it is not submitted to pure hydrostatic loading but to non-spherical loading in the vicinity of the pipe. The confined compression test is then chosen to represent these non-spherical loadings of material. The rupture of glass microballoons is monitored by acoustic emission for different matrices and attempts are made to quantify the resulting acoustic emission signals by comparison with prior tomography results. These experimental analyses provide a better understanding of the main factors affecting the functional properties of syntactic foams.     

High Strain Rate Response of Sandwich Composites with Nanophased Cores

Polyurethane foam materials have been used as core materials in a sandwich construction with S2-Glass/SC-15 facings. The foam material has been manufactured from liquid polymer precursors of polyurethane. The precursors are made of two components; part-A (diphenylmethane diisocyanate) and part-B (polyol). In one set of experiments, part-A was mixed with part-B to manufacture the foam. In another set, TiO₂ nanoparticles have been dispersed in part-A through ultrasonic cavitation technique. The loading of nanoparticles was 3% by weight of the total polymer precursor. The TiO₂ nanoparticles were spherical in shape, and were about 29 nm in diameter. Sonic cavitation was carried out with a vibrasound liquid processor at 20 kHz frequency with a power intensity of about 100 kW/m². The two categories of foams manufactured in this manner were termed as neat and nanophased. Sandwich composites were then fabricated using these two categories of core materials using a co-injection resin transfer molding (CIRTM) technique. Test samples extracted from the panel were subjected to quasi-static as well as high strain rate loadings. Rate of loading varied from 0.002 s^–1 to around 1300 s^–1. It has been observed that infusion of nanoparticles had a direct correlation with the cell geometry. The cell dimensions increased by about 46% with particle infusion suggesting that nanoparticles might have worked as catalysts during the foaming process. Correspondingly, enhancement in thermal properties was also noticed especially in the TGA experiments. There was also a significant improvement in mechanical properties due to nanoparticle infusion. Average increase in sandwich strength and energy absorption with nanophased cores was between 40–60% over their neat counterparts. Details of manufacturing and analyses of thermal and mechanical tests are presented in this paper.     

Effects of strain on the workability of a high strength low alloy steel in hot compression

Based on the experimental results from the hot compression tests of 42CrMo steel, the efficiencies of power dissipation and instability parameter were evaluated. The effects of strain on the efficiency of power dissipation and instability parameter of 42CrMo steel have been discussed in detail. Processing maps were constructed by superimposition of the instability map over the power dissipation map. The dynamic recrystallization domains and instable zones were identified in the processing map. The effects of strain on microstructural evolutions were correlated with the processing maps. According to the 3D processing maps, the optimum domain of hot deformation is in the temperature range of 1050–1150 °C and strain rate range of 0.01–3 s⁻¹, with its peak efficiency of 32% at about 1140 °C and 0.23 s⁻¹, which are the optimum hot working parameters.     

Dynamic fracture of bovine bone

True clinical fracture of bones in bovine, race horses or humans occur predominantly during impact loading (e.g. car accidents, falls or physical violence). Although static fracture tests provide an estimate of fracture toughness or R-curve behavior in bones, the static toughness values may be ill suited for predicting failure under dynamic loading conditions due to the visco-elastic response of bone (i.e. strain rate dependent properties). Despite decades of the study on deformation rate dependency of bone properties such as compression and fracture toughness, high-quality dynamic fracture data remain limited. Preliminary tests (compression and fracture toughness) have been conducted on dry and wet bovine bone under both static and dynamic loading conditions. While compression tests have been conducted with loading direction parallel and perpendicular to the bone axis (longitudinal and transverse, respectively), fracture tests were performed only in the transverse direction. The strain rate in compression tests varied between 10^− 3 and 10³ s^− 1, and the stress intensity rate varied between ∼10^− 3 and 10⁵ MPa√m/s. While low strain rate tests were conducted on conventional mechanical testing machines, high strain rate experiments were conducted on a split-Hopkinson bar under compression and a novel three-point bend configuration. The fracture morphology and the extent of damage of bone in each case were characterized using SEM, and an attempt is made to relate these to the rate dependent fracture toughness of the bone. It is believed that such understanding is crucial for mechanistic interpretation of bone fracture phenomenon and eventually for predicting bone failure reliably.     

Energy absorption during projectile perforation of thin steel plates and the kinetic energy of ejected fragments

This paper concerns energy absorption in thin (0.4 mm) steel plates during perforation by spherical projectiles of hardened steel, at impact velocities between 200 and 600 m s⁻¹. Absorbed energies have been obtained from measured incident and emergent projectile velocities. These tests were simulated using ABAQUS/Explicit, using the Johnson and Cook plasticity model. A strain rate-dependent, critical plastic strain fracture criterion was employed to model fracture. Good agreement is obtained between simulations and experiment and the model successfully captures the transitions in failure mode as projectile velocity increases. At velocities close to the ballistic limit, the plates fail by dishing and discing. As the incident velocity is increased, there are two transitions in failure mode, firstly to shear plugging and secondly to fragmentation and petalling. The simulations also show that, during the latter mode of failure, the kinetic energy of ejected debris is significant, and failure to include this contribution in the energy balance leads to a substantial over-estimate of the energy absorbed within the sheet. Information is also presented relating to the strain rates at which plastic deformation occurs within the sample under different conditions. These range up to about 10⁵ s⁻¹, with the corresponding strain rate hardening effect being quite substantial (factor of 2–3 increase in stress).