Characterization of irregular open-cell cellular structure with silicone pore filler

The paper presents the results of studying the influence of silicone polymer pore filler on the macroscopic quasi-static and dynamic compressive behaviour of aluminium foam with irregular open-cell structure. The study is based on a mechanical experimental testing programme, where the deformation mechanism and mechanical energy absorption capacity of aluminium foam with silicone pore filler have been observed for the first time. As plastic yielding is accompanied by significant heat energy dissipation, this study was additionally supported by thermal imaging, which enables visualization of plastification to better understand the deformation process of observed specimens. The influence of specimen size on the behaviour of aluminium foam specimens has also been investigated. The results show that introduction of silicone pore filler considerably increases the energy absorption capacity at almost unchanged densification strain under both quasi-static and dynamic loading conditions. The silicone pore filler also significantly influences the deformation behaviour of aluminium foam specimens, which is manifested in a different stress distribution and a significant transverse deformation with conical plastification front. However, only a minor difference in response of different size specimens has been observed.     

Anisotropic compressive behavior of rigid PVC foam at strain rates up to 200 s−1

The elevated strain rate compressive response of closed-cell polyvinyl chloride (PVC) foam at various densities is investigated. Two loading directions, (i.e., parallel and perpendicular to foam rise direction) were considered to investigate structural anisotropy. The elevated strain rates tests (up to 200 s⁻¹) were performed using a customized drop tower device. Engineering stress/strain behavior, energy dissipation, and maximum stress capacity were obtained for each density and compared against each other. Except for the lowest density of 45 kg/m³, strain rate effects were clearly observed through increased compressive strength and plateau stress when loading in the foam rise direction. The strain rate effect is more evident at higher densities. However, no significant strain rate effect was observed when loading perpendicular to the foam rise direction. Scanning electron microscopy (SEM) analysis showed that plastic hinges are the primary deformation mechanism for PVC foam cells. An analytical model has been calibrated using the experimental results and successfully predicted the mechanical response of the foam. Shape anisotropy has been measured employing the SEM images. The analytical approach was also able to predict the foam's anisotropic mechanical response.     

Characterizing the constitutive response and energy absorption of rigid polymeric foams subjected to intermediate-velocity impact

As an optimum energy-absorbing material system, polymeric foams are needed to dissipate the kinetic energy of an impact, while maintaining the impact force transferred to the protected object at a low level. Therefore, it is crucial to accurately characterize the load bearing and energy dissipation performance of foams at high strain rate loading conditions. There are certain challenges faced in the accurate measurement of the deformation response of foams due to their low mechanical impedance. In the present work, a non-parametric method is successfully implemented to enable the accurate assessment of the compressive constitutive response of rigid polymeric foams subjected to impact loading conditions. The method is based on stereovision high speed photography in conjunction with 3D digital image correlation, and allows for accurate evaluation of inertia stresses developed within the specimen during deformation time. Full-field distributions of stress, strain and strain rate are used to extract the local constitutive response of the material at any given location along the specimen axis. In addition, the effective energy absorbed by the material is calculated. Finally, results obtained from the proposed non-parametric analysis are compared with data obtained from conventional test procedures.     

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.     

Influence of relative humidity and loading frequency on the PA6.6 thermomechanical cyclic behavior: Part II. Energy aspects

In this study, we investigated the influence of relative humidity (RH) and loading rate on the energy response of PA6.6 matrix specimens. The latter were subjected to oligocyclic tensile-tensile tests at 3 different RH and 2 loading rates. Infrared thermography was used to obtain a direct estimate of heat sources using the heat diffusion equation. Using the mechanical and thermal responses discussed in the first part of this work, complete energy rate balances were drawn up. In particular, the time courses of deformation, and dissipated and stored energy rates are discussed. The strong influence of the loading frequency and RH on the energy storage mechanisms is also highlighted.     

Compressive response of composite ceramic particle-reinforced polyurethane foam

Quasi-static and dynamic compressive tests are undertaken on the polyurethane (PU) foam and fumed silica reinforced polyurethane (PU/SiO₂) foam experimentally. The ceramic microspheres with varying mass fractions are adopted to mix with the PU/SiO₂ foam to fabricate the composite particle-reinforced foams. The effects of strain rate and particle mass fraction are discussed to identify and quantify the compressive response, energy-absorbing characteristic, and the associated mechanisms of the composite foams. The results show the initial collapse strength and plateau stress of the foams are improved significantly by reinforcing with the ceramic microsphere within 60 wt% at quasi-static compression. The rate sensitivity is observed on all the foams, but in different patterns due to the influence of ceramic microsphere. The compressive response affected by ceramic microsphere can be attributed to the particle cluster effect and stress wave propagation. Together with the deformation, the compressive characteristic experiences non-monotonic change from the low to high strain rates. The specific energy absorption (SEA) of the foam with 41 wt% ceramic microsphere show the largest magnitude at quasi-static compression. With the increasing strain rate, the ceramic reinforced foam exhibits superior energy absorption efficiency at high strain rates to that of the pure foams.     

Ballistic Impact Behaviour of Glass/Epoxy Composite Laminates Embedded with Shape Memory Alloy (SMA) Wires

This paper aims to estimate the enhancement in the energy absorption characteristics of the glass fiber reinforced composites (GFRP) by embedding prestrained pseudo-elastic shape memory alloy (SMA) that was used as a secondary reinforcement. The pseudo-elastic SMA (PE-SMA) embedded were in the form of wires and have an equiatomic composition (i.e., 50%–50%) of nickel (Ni) and titanium (Ti). These specimens are fabricated using a vacuum-assisted resin infusion process. The estimation is done for the GFRP and SMA/GFRP specimens at four different impact velocities (65, 75, 85, and 103 m/s) using a gas-gun impact set-up. At all different impact velocities, the failure modes change as we switch from GFRP to SMA/GFRP specimen. In the SMA/GFRP specimen, the failure mode changed from delamination in the primary region to SMA-pull out and SMA deformation. This leads to an increase in the ballistic limit. It is observed that energy absorbed by SMA/GFRP specimens is higher than the GFRP specimens subjected to the same levels of impact energy. To understand the damping capabilities of SMA embedment, vibration signals are captured, and the damping ratio is calculated. SMA dampens the vibrations imparted by the projectile to the specimen. The damping ratio of the SMA/GFRP specimens is higher than the GFRP specimens. The damping effect is more prominent below the ballistic limit when the projectile got rebounded (65 m/s).     

Experimental and numerical investigations of the anisotropic deformation behavior of low-density polymeric foams

Low-density porous materials and foams have been widely used for a variety of applications, such as light structural components, impact energy absorption, thermal insulation and sound absorption. The macroscopic deformation of such materials is strongly dependent on their inherent micro-cellular structure. This study investigated the compressive anisotropic deformation behavior of low-density polymeric foam by using X-ray computed tomography (CT) and the finite element method (FEM) in order to understand both the microscopic and macroscopic deformation behavior. The foams used in this study have a closed cell structure, with pores that are elliptical in shape. Three different types of expansion ratios were employed. The porosities of these materials were 93.5, 95, and 96%. From the observations using the X-ray CT method, the averaged pore heights were 1 mm and the aspect ratios were 2, 2.5, and 2.25, respectively. The foam demonstrated anisotropic deformation, dependent on the uni-axial compression direction. It was found that the deformation rigidity in the longitudinal direction was larger than that in the transverse direction. By using the X-ray CT method in situ, the microscopic deformation behavior when subjected to compressive loading was observed. Deformation and collapse of pores was observed for both directions during the loading. In conjunction with this, FEM computations were carried out to elucidate how such pore geometry undergoes elastoplastic deformation and leads to macroscopic deformation behavior. The FEM-created three-dimensional spatial structures were based on elongated rhombic dodecahedrons. It is revealed that the FEM computation shows relatively good agreement with the experimental results. Thus, our experimental and computational models may be useful for microstructural design using anisotropic cellular materials.     

Impact behaviour of Dyneema® fabric-reinforced composites with different resin matrices

This paper presents an experimental study on the impact behaviour of composite laminates made of a Dyneema^® woven fabric and four different resin matrices. Three thicknesses of each kind of resin laminate were subjected to impact by a spherical steel projectile in a velocity regime ranging from 100 to 200 m/s. The results revealed that the laminates having flexible matrices performed much better in perforation resistance and energy absorption, but had a greater extent of deformation and damage than the counterparts with rigid matrices. It was found that the matrix rigidity played a crucial role in controlling the propagation of transverse deformation, and thereby the local strain and perforation resistance of laminates. The more rigid matrix restrained the laminate's transverse deformation to a smaller area at a given time, which led to higher local strain and lower perforation resistance. Fibre failure in tension was identified as the dominant failure mechanism for the tested laminates.     

Mechanical response of three semi crystalline polymers under different stress states: Experimental investigation and modelling

The mechanical responses of high‐density polyethylene (HDPE), polypropylene (PP) and polyamide 6 (PA 6) were experimentally investigated for a wide range of stress states and strain rates. This was accomplished by testing numerous specimens with different geometries. The uniaxial compression of cylindrical unnotched specimens and the uniaxial tensile behaviour of dumbbell specimens at different strain rates, was determined. A series of biaxial loading tests (combined shear and tension/compression, pure shear, pure tension/compression) using a designed Arcan testing apparatus were also performed. Flat and cylindrical notched specimens with different curvature radii were additionally tested in order to explore a wider range of stress states. The Drucker‐Prager yield criterion was calibrated with a set of experimental data, for which analytical formulae for stresses are available, and then applied to predict the deformation behaviour under different stress states, prior to strain localization. The results of the numerical simulations show that the Drucker‐Prager model can capture the initial elastic range and the post‐elastic response very satisfactorily. For triaxial and biaxial stress states there is a good agreement, however some load‐displacement responses are only satisfactorily described. Deviations observed in the predicted and experimental results are very likely attributed to the third invariant stress tensor, which was not explored in the model calibration. The evolution of stress triaxiality and Lode angle parameters with equivalent plastic strain were extracted and analysed for several specimens. The results show a plastic yielding behaviour sensitive to the stress state, which can be attributed to different combinations of stress triaxialities and Lode angle parameters.     

Plastic deformation of glassy polymethylene: Computer-aided molecular-dynamic simulation

Molecular-dynamic simulation of low-temperature plastic deformation (T _def = 50 K, T _def/T _g ≤ 0.3) is studied for glassy polymethylene under the regime of active uniaxial compression and tension for a cell composed of 64 chains containing 100 -CH₂ groups in each (as united atoms) and with periodic boundary conditions. Thirty-two such cells are created, and, in each cell, polymethylene chains in the statistical coil conformation are independently constructed. The cells are subjected to isothermal uniaxial compression at T _def = 50 K by ɛ = 30% and by ɛ = 70% under uniaxial tension. In the course of loading, a σ-ɛ diagram is recorded, while the mechanical work spent on deformation, the changes in the overall potential energy of the system, and the contributions from various potential interactions (noncovalent van der Waals bonds, chemical links, valence and torsional angles) are estimated. The results are averaged over all 32 cells. The relaxation of stored potential energy and residual strain after complete unloading of the deformed sample is studied. The relaxation of stored energy and residual strain is shown to be incomplete. Most of this energy and strain is stored in the sample at the deformation temperature for long period. The conformational composition of chains and the average density of polymer glass during loading are analyzed. Simulation results show that inelastic deformations commence not with the conformational unfolding of coils but with the nucleation of strain-bearing defects of a nonconformational nature. The main contribution to the energy of these defects is provided by van der Waals interactions. Strain-bearing defects are nucleated in a polymer glass during tension and compression primarily as short-scale positive volume fluctuations in the sample. During tension, the average density of the glass decreases; during compression, this parameter slightly increases to ɛ ≈ 8% and then decreases. An initial increase in the density indicates that, during compression and at ɛ < 8%, coils undergo compactization via an increase in chain packing. During compression, the concentration of trans conformers remains unchanged below ɛ ≈ 8% and then decreases. During compression, it means that in a glass, coils do not increase their sizes at strains below ɛ ≈ 8%. During tensile drawing, coils remain unfolded below ɛ ≈ 35%; at higher strains, coils become enriched with trans conformers or unfold. At this stage, the concentration of trans conformers linearly increases. The development of a strain-induced excess volume (strain-bearing defects) entails an increase in the potential energy of the sample. Under the given conditions of deformation, nucleation of strain-bearing defects and an increase in their concentration are found to be the only processes occurring at the initial stage of loading of glassy polymethylene. The results of computer-aided simulation are compared with the experimental data reported in the literature.     

FEM simulation of polymeric foam with random pore structure: Uniaxial compression with loading rate effect

This study establishes FEM modeling for compressive deformation behavior of polymeric foams with different loading rates. The polymeric foam used in this study was made from polypropylene (the base matrix of the polymer) with porosity of about 95%. The pore size and shape were randomly distributed in the foam. The X-ray CT method was first conducted to observe the microstructure, the geometric feature of which was reproduced in the FEM model. Uniaxial compression tests with different loading speeds were carried out to investigate an effect of loading rate (strain rate) dependency on the deformation behavior. By using the X-ray CT method, in situ observation of microscopic deformation was carried out. Furthermore, FEM computations were carried out to simulate macroscopic and microscopic deformation behaviors. The random porous structure was modeled using Surface Evolver. The elastoplastic property with strain rate dependency was used in this model. The established FEM framework may be useful for a porous polymer with a random pore structure and for deformation modeling with strain rate effect.     

Impact testing of polymeric foam using Hopkinson bars and digital image analysis

The present investigation aims at testing polymeric foam under impact loading using large diameter nylon Hopkinson bars and optical field measurements. Accurate average stress-strain relations can be obtained when soft large diameter polymeric pressure bars and the appropriate data processing are used. However, as there are generally no homogeneous strain and stress fields for polymeric foams, an optical field observation is needed. In contrast to quasi-static tests where the digital image correlation (DIC) measurement is commonly used, technical difficulties still remain for the reliable use of DIC under impact conditions. In this paper, an accurate synchronization method based on the displacement measurement of the end of pressure bars (calculated by a robust DIC algorithm) is preferred to conventional MCDL box time synchronization. Also, the bar end displacement measurement offers a complementary calibration method for the tension/strain conversion coefficient. Strain fields are obtained for tests on foam sample at impact velocities up to 20 m/s. The localized strain fields permit better understanding of the observed stress plateau from SHPB results. The relevance of the present method for establishing mechanical response of polymeric foam is then demonstrated.     

Fading memory of deformation history in carbon black-filled thermoplastic elastomers

Observations are reported on a carbon black–reinforced thermoplastic elastomer in multistep uniaxial tensile cyclic tests with a mixed deformation program (oscillations between maximum elongation ratios k_max and various minimum stresses σ_min with k_max monotonically increasing with number of cycles n). Fading memory of deformation history is demonstrated: when specimens are subjected to two loading programs that differ along the first n −1 cycles of deformation and coincide afterwards, their stress–strain diagrams become identical starting from the nth cycle. A constitutive model is developed in cyclic viscoplasticity with finite deformations, and its adjustable parameters are found by fitting the observations. Ability of the stress–strain relations to describe the fading memory phenomenon and to predict the mechanical response of polymer composites in multi-step cyclic tests with large strains is confirmed by numerical simulation.     

Determination of reliable fatigue life predictors for magnetorheological elastomers under dynamic equi-biaxial loading

Fatigue life prediction is of great significance in ensuring magnetorheological elastomer (MRE) based rubber components exhibit reliability and do not compromise safety under complex loading, and this necessitates the development of plausible fatigue life predictors for MREs. In this research, silicone rubber based MREs were fabricated by incorporating soft carbonyl iron magnetic particles. Equi-biaxial fatigue behaviour of the fabricated MREs was investigated by using the bubble inflation method. The relationship between fatigue life and maximum engineering stress, maximum strain and strain energy density were studied. The results showed that maximum engineering stress and stored energy density can be used as reliable fatigue life predictors for SR based MREs when they are subjected to dynamic equi-biaxial loading. General equations based on maximum engineering stress and strain energy density were developed for fatigue life prediction of MREs.     

Dynamic behavior of interfaces: Modeling with nonequilibrium thermodynamics

In multiphase systems the transfer of mass, heat, and momentum, both along and across phase interfaces, has an important impact on the overall dynamics of the system. Familiar examples are the effects of surface diffusion on foam drainage (Marangoni effect), or the effect of surface elasticities on the deformation of vesicles or red blood cells in an arterial flow. In this paper we will review recent work on modeling transfer processes associated with interfaces in the context of nonequilibrium thermodynamics (NET). The focus will be on NET frameworks employing the Gibbs dividing surface model, in which the interface is modeled as a two-dimensional plane. This plane has excess variables associated with it, such as a surface mass density, a surface momentum density, a surface energy density, and a surface entropy density. We will review a number of NET frameworks which can be used to derive balance equations and constitutive models for the time rate of change of these excess variables, as a result of in-plane (tangential) transfer processes, and exchange with the adjoining bulk phases. These balance equations must be solved together with mass, momentum, and energy balances for the bulk phases, and a set of boundary conditions coupling the set of bulk and interface equations. This entire set of equations constitutes a comprehensive continuum model for a multiphase system, and allows us to examine the role of the interfacial dynamics on the overall dynamics of the system. With respect to the constitutive equations we will focus primarily on equations for the surface extra stress tensor.     

An investigation of the yield and postyield behavior and corresponding structure of poly(methyl methacrylate)

The mechanical behavior of glassy polymers is time and temperature dependent as evidenced by their viscoelastic and viscoplastic response to loading. The behavior is also known to depend strongly on the prior history of the material, changing with time and temperature without chemical intervention. In this investigation, we examine the effects of this process of physical aging on the yield and postyield behavior and corresponding evolution in the structural state of glassy polymers. This has been achieved through a systematic program of uniaxial, isothermal, constant strain–rate tests on poly(methyl methacrylate) (PMMA) specimens of different thermal histories and by performing positron annihilation lifetime spectroscopy (PALS) measurements prior to and after mechanical deformation. PALS is an indicator of the free volume content, probing size and density of free volume sites and can be considered to be a measurement of structural state. The results of the mechanical tests show that aging acts to increase both the initial yield stress and the amount of strain softening which occurs subsequent to yield. Moreover, the amount of strain softening was found to be independent of strain rate indicating that softening is related to an evolution in structure as opposed to deformation kinetics. Furthermore, after sufficient inelastic straining, the initial thermal history is completely erased as evidenced by identical values of flow stress following strain softening, for both annealed and quenched polymer. Strong confirmation of the structural state or free volume related nature of the strain softening process is obtained by our companion PALS measurements. PALS detects an increase in the size of free volume sites following inelastic deformation and finds the initially annealed and quenched specimens to posses the same post-deformation distribution. The size of sites is found to evolve steadily with inelastic strain until it attains a steady-state value. This evolution of free volume with strain follows the observed softening of the flow stress to a steady-state value. These results provide experimental evidence that an increase in free volume with inelastic straining accompanies the strain softening phenomenon in glassy polymers and that strain softening is indeed a de-aging process. Based on our experimental results a mechanistically based constitutive model has been formulated to describe the effects of thermal history on the yield and postyield deformation behavior of glassy polymers up to moderate strains. The model is found to successfully capture the effects of physical aging, strain softening, strain rate, and temperature on the inelastic behavior of glassy polymers when compared with experimental results. © 1993 John Wiley & Sons, Inc.     

单壁碳纳米管拉伸变形的原子尺度模拟

The molecular dynamics method was adopted to investigate the tension deformation for SWCNTs with different chiralities and radius. The results show that nanotubes have an extremely large breaking strain. Carbon nanotubes are completely ductile before their structural defects appear. Through tracing the evolution of the spacial configuration of a micro structural cell of SWCNTs, it is found that the torsion deformation results in the change of structural symmetry. Thus the load is no longer well distributed. The structural defects will occur with further loading. The systematic energy change of SWCNTs is observed. It can be seen that there is a structural transformation around the initial vacancy defects when the axial tension strain reaches a certain value. The two adjacent hexagons change to one pentagon and one heptagon (also called the Stone Wales transformation). The 5 7 configuration makes strain energy release, and the systematic energy falls. This configuration is more preferable from the viewpoint of the energy. The results also show that fewer defects have weak influence on the mechanical properties of SWCNTs under the present initial vacancy defect condition.     

Atomic origin of hysteresis during cyclic loading of Si due to bond rearrangements at the crack surfaces

The atomistic origin of fatigue failure in micron-sized silicon devices is not fully understood. Two series of density-functional theory calculations on cubic diamond Si explore the effect of surface bond formation on crack healing in systems which exhibit strong surface reconstruction. Both series introduce a separation between Si(100) layers (i.e., the crack) and allow the ions to relax to their minimum-energy configuration. The initial surface ionic positions are either bulk terminated or 2 x 1 reconstructed. A plot of the energy versus the introduced separation reveals that once the surfaces reconstruct, the crack is no longer able to return to the equilibrium configuration. Rather, the healed crack interface contains defects which places the flawed energy minimum at a finite strain of 3% and an increased energy of 1.13 Jm2 relative to the equilibrium configuration. The irreversible plastic deformation supports the mechanism proposed by Kahn et al. [Science 298 1215 (2002)] that invokes mechanically induced subcritical cracking to explain the delayed onset of failure.     

Damage resistance of carbon fibre reinforced epoxy laminates subjected to low velocity impact: Effects of laminate thickness and ply-stacking sequence

A major concern affecting the efficient use of composite laminates is the effect of low velocity impact damage on the structural integrity [1–3]. The aim of this study is to characterize and assess the effect of laminate thickness, ply-stacking sequence and scaling technique on the damage resistance of CFRP laminates subjected to low velocity impact. Drop-weight impact tests are carried out to determine impact response. Ultrasonic C-scanning and cross-sectional micrographs are examined to assess failure mechanisms of the different configurations.It is observed that damage resistance decreases as impact energy increases. In addition, thicker laminates show lower absorbed energy but, conversely, a more extensive delamination due to higher bending stiffness. Thinner laminates show higher failure depth. Furthermore, quasi-isotropic laminates show better performance in terms of damage resistance. Finally, the results obtained demonstrate that introducing ply clustering had a negative effect on the damage resistance and on the delamination area.