Elastic Properties of a Polyethylene Single-Molecule

Analytical closed-form solution of the elastic properties (such as longitudinal stiffness, shear stiffness and Poisson's ratio) of a taut polyethylene single-molecule is developed in this paper in terms of C–C and C–C–C bond parameters. The concepts considered herein include resolution of forces and of displacement, with due application of Hooke's law to determine the longitudinal stiffness and the in-plane Poisson's ratio. Adopting the solid mechanics theory as an analogy, the shear stiffness of a taut polyethylene chain is conveniently obtained. Results reveal unique Poisson's ratio property of a polyethylene single-molecule in comparison to usual bulk materials, thereby suggesting size-dependency of nano-scale materials in terms of the Poisson's ratio. Finally some frequently occurring terms in all three elastic property expressions are grouped to summarize and to reveal some form of uniformity in the analytical solutions.     

A study on correlating reduction in Poisson's ratio with transverse crack and delamination through acoustic emission signals

During the uniaxial loading of fiber reinforced polymer (FRP) composites, Poisson's ratio (ν_xy), which is a constant elastic property for isotropic materials, decreases significantly. Micro-damage created within FRP composites as a result of an applied stress causes this decrease. As the level of micro-damage increases, a greater level of reduction in Poisson's ratio occurs. FRP composites, in general, show three main micro-damage types under uniaxial tensile loading, namely, transverse crack, delamination and fiber rupture. To determine micro-damage types which dominantly affects the relevant reduction in Poisson's ratio, glass fiber reinforced cross-ply laminates with three different off-axis ply content are produced and then tested under a uniaxial tensile loading. The Acoustic Emission (AE) signals are concurrently recorded and grouped into three clusters in accordance with their frequency, which is either associated with transverse crack, delamination or fiber rupture. The frequency based clustering of AE signal facilitates detailed investigation of delamination onset and effect of different micro-damage types on Poisson's ratio. It is proven that stacking sequences with a higher number of transverse cracks and delaminations, quantified based on AE signals, show a greater reduction in Poisson's ratio.     

On the nonlinear evolution of the Poisson's ratio under quasi-static loading for a carbon fabric-reinforced thermoplastic. Part I: Influence of the transverse strain sensor

When observing or describing the damage state in a composite material, often only Young's modulus or residual deformation are considered. Generally, however, the Poisson's ratio is more sensitive to damage than those properties. Rather than observing the Poisson's ratio as a function of crack density, this article studies the evolution of the Poisson's ratio as function of the longitudinal strain, which has a peculiar shape. In Part I, multiple experiments, using strain gauges, optical fibres and an extensometer for transverse strain measurement are discussed to determine whether this behaviour is due to the material or to the sensor used. It can be concluded that the hyperbolic-like shape is entirely caused by material behaviour. A theoretical explanation and validation for this behaviour will be given in part II.The material used for this study is a carbon fabric-reinforced PPS.     

On the nonlinear evolution of the Poisson's ratio under quasi-static loading for a carbon fabric-reinforced thermoplastic. Part II: Analytical explanation

When observing or describing the damage state in a composite material, often only Young's modulus or residual deformation are considered. Generally, however, the Poisson's ratio is more sensitive to damage than those properties. Rather than observing the Poisson's ratio as function of crack density, the evolution of the Poisson's ratio as function of the longitudinal strain was studied in part I of this research, where a peculiar shape of the evolution was observed and proven to be entirely due to the material itself, rather than the sensors used for the strain measurement.In this article, a theoretical explanation for the peculiar evolution of the Poisson's ratio as function of the longitudinal strain is presented. Based on this explanation, extra experiments were conducted for validation purposes.The material used for this study is a carbon fabric-reinforced PPS.     

Displacement measurements using double-exposure speckle photography of small-angle scattered light

Double-exposure speckle patterns created by scattered light were used to study tensile deformation of isotactic polypropylene film. The method makes possible a quantitative investigation of the deformation process (relative magnitude and orientation of the displacement vector, Poisson's ratio μ) by means of a simple optical analysis of stepwise deformations covering the desired range. The displacement vector and Poisson's ratio have been determined with an accuuracy of ± 5% in the range of small deformations (up to 18% relative deformation); and the role of stress relaxation has been examined. Limitations of the method, such as the range of measurable displacements, effect of prestressing, and stability of the system, etc., are discussed. Among advantages of the method are comparative simplicity and accuracy, and the possibility of its application to other systems studied by the small-angle light scattering method.     

Determination of creep compliance,recovery and Poisson's ratio of elastomers by means of digital image correlation (DIC)

This work aims to determine the creep compliance, creep recovery and Poisson's ratio of three common sealing elastomers by means of the digital image correlation (DIC). The tests were conducted by stressing specimens under three different constant stresses during short duration experiments (3 h) to see the prospective of DIC for this application. The strains were measured in x and y axes with time. Thus, the behavior of creep compliance, creep recovery, and the Poisson's ratio of each elastomer were obtained. The creep results exhibited repeatability, as well as, the mean Poisson's ratios estimated were close to reported values for elastomers. Finally, despite of some limitations from the DIC equipment, it was found that this procedure can be implemented as a suitable alternative for the characterization of creep compliance, creep recovery and Poisson's ratio of elastomers. Also, it may be enhanced by following some recommendations given.     

An experimental and numerical study on an innovative metastructure for 3D printed thermoplastic polyurethane with auxetic performance

Metamaterials are specifically designed materials that possess unique properties that cannot be found in naturally occurring substances. These remarkable materials have the capability to bring about a significant transformation across a wide range of industries. Auxetic structures are a recent area of research possess a distinctive characteristic known as a negative Poisson's ratio. Unlike conventional materials that contract when stretched, auxetic structures actually expand in two dimensions. In this study, a new auxetic structure was introduced, and thermoplastic polyurethane samples were 3D printed using a fused filament fabrication method. The samples are then subjected to strains ranging from 5% to 50% and Poisson's ratios are measured both experimentally and numerically using finite element method in Ansys software. By comparing the results of the experimental research and simulation, it is evident that applying strains within this range causes the Poisson's ratio of the samples to change from −0.81 to −0.14 and it showed that the newly introduced structure is auxetic. According to the analysis of root mean square error, the hexagonal mesh with a size of 0.7 mm consistently produced the most accurate results, aligning closely with the experimental sample. Given that this is an entirely novel auxetic structure within the category of arrow-head auxetic structures, there is potential for future research to be conducted in order to further develop and enhance this model.     

Poisson ratios and upper bounds of intrinsic birefringence from brillouin scattering of oriented polymers

To overcome the difficulties in measuring high-frequency shear constants of polymeric materials by ultrasonic or Brillouin scattering technques, we extrapolate results from oriented materials to zero birefringence. Shear constants C₄₄ in the high-frequency limit (GHz) are determined for polyethylene, poly(ethylene terephthalate), poly(vinyl chloride), poly(methyl methacrylate), and polycarbonate using Brillouin scattering. Accurate values of Poisson's ratio are derived. The extrapolation to full orientation using an amended Moseley relation gives upper bounds for the “intrinsic birefringence.” Changes in the character of the orientation process are easily detected by monitoring the mode numbers, which are defined by analogy to Poisson's ratio. Extrapolation of these ratios to their upper bound 0.5 gives an independent check of the maximum intrinsic birefringence. © 1993 John Wiley & Sons, Inc.     

Conversion of low density polyethylene foams into auxetic metamaterials

Cellular polymers, such as polyethylene foams, are commonly used in the packaging industry. These materials have short service life and generate a high volume of waste after use. In order to valorize this waste and produce added-value applications, it is proposed to convert these materials into highly efficient energy absorption structures. This was done by modifying the original cellular morphology of the foams (spheroidal or polygonal) into a re-entrant structure to produce auxetic materials. This work presents an optimized process combining mechanical compression and solvent vapor evaporation-condensation leading to low density foams (77–200 kg/m³) having negative Poisson's ratios (NPR). Three series of recycled low density polyethylene (LDPE) foams with an initial density of 16, 21, and 36 kg/m³ were used to optimize the processing conditions in terms of treatment temperature, time, and pressure. From all the samples prepared, a minimum Poisson's ratio of −3.5 was obtained. To further characterize the samples, the final foam structure was analyzed to relate with mechanical properties and compare with conventional foams having positive Poisson's ratios. The results are discussed using tensile properties and energy dissipation which were shown to be highly improved for auxetic foams. Overall, the resulting foams can be used in several applications such as sport and military protection equipment.     

Anisotropic elastic moduli and Poisson's ratios of a poly(ethylene terephthalate) film

Expressions for the directional dependence of Young's modulus and Poisson's ratio were derived for a general material under plane‐stress conditions. Experiments with a laser extensometer to measure the Young's modulus and Poisson's ratio directly by a tension test are described, and the results are compared with the theoretical expressions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 260–266, 2004     

The quest for a bidirectional auxetic,elastic, and enhanced fracture toughness material: Revisiting the mechanical properties of the BeH2 monolayers

Herein we show a density functional theory-based study performed on two recently predicted polymorphs of the BeH₂ monolayer, α-BeH₂ and β-BeH₂. The α-BeH₂ phase possesses an in-plane negative Poisson's ratio (NPR), introducing it into the unique group of auxetic materials. Our assessment delves into the linear-elastic and finite-strain regimes to understand both polymorphs' structural and mechanical responses to deformation. We find that the in-plane NPR is shown to be only parallel to the bonds in α-BeH₂ and remains along the uniaxial tensile path. Concomitantly, an out-of-plane transition toward auxetic is also revealed in regions exhibiting conventional Poisson's ratios, making α-BeH₂ a bidirectionally auxetic material. While phase transitions in β-BeH₂ are triggered at very short strains, α-BeH₂ displays excellent elasticity against tension, superior to that of most currently known 2D materials.     

Determination of the dynamic complex modulus of viscoelastic materials using a time domain approach

Viscoelastic and poroelastic materials are widely used in multilayer panels for noise control. They are usually used as an inner decoupling layer in double wall systems in order to increase the sound transmission loss of a bare plate. In order to correctly simulate the acoustical behaviour of such systems, it is necessary to measure the elastic parameters of these materials (storage and loss moduli, and Poisson's ratio). Physical properties related to pore morphology also need to be determined for open cell structures. Most of the materials used in trimmed panels can show elastic parameters that vary with frequency, thus a quasi-static measurement technique is not accurate enough to consider such viscoelasticity effects. This paper focuses on the estimation of complex modulus as a function of the frequency of isotropic viscoelastic materials. In particular, the tested material is positioned between two plates, with one of them being excited by an electromagnetic shaker. Using a sine burst as an excitation signal, the accelerometric response in the time domain is measured at the top and bottom plates. The time of flight between the plates and the envelope function of time domain acceleration at the top plate are then found. A transfer matrix model of the experimental setup is used to inversely estimate the complex modulus of the materials once the remaining mechanical and physical properties have been fixed. The results will be presented and discussed for different materials and compared with well-established quasi-static and dynamic techniques.     

Dynamic bulk and shear relaxation in glassy polymers. I. Experimental techniques and results on PMMA

In this paper the authors describe in detail the experimental techniques for the simultaneous measurement of the dynamic Young's modulus and the dynamic Poisson's ratio, from which the dynamic bulk and shear moduli can be calculated. Experimental results are presented on the effects of temperature, frequency, and tensile strain on these properties of poly(methyl methacrylate) (PMMA). The temperature and frequency effects indicate that the β relaxation in PMMA is not a purely internal motion but is coupled to the bulk.     

Mechanical properties of the novel organometallic polymer poly(ferrocenyldimethylsilane)

A study of the mechanical properties of poly(ferrocenyldimethylsilane) [Fe(η‐C₅H₄)₂SiMe₂]_n, 3 , a novel organometallic polymer, has been performed on thin films of this material. The Young's modulus and Poisson's ratio of film samples (15 × 1 × 1 mm) of 3 were measured in quasi‐static tension using a video extensometer. For 3 , the values of the Young's moduli (E) and Poisson's ratios (ν) were similar between axes in the plane and independent of the splicing direction used during sample preparation. The mean and standard deviation of the Young's modulus and Poisson's ratio were 0.78 ± 0.08 GPa and 0.37 ± 0.06 GPa, respectively. Thermomechanical analysis of 3 revealed a steady decrease of E from a room temperature value of approximately 0.70 GPa. Additionally, it was found that at 150 °C, 3 was unable to support even small stresses, consistent with the onset of a melt transition (ca. 135 °C). A mathematical model based on molecular geometry is developed to describe the results. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2280–2288, 2005     

Theoretical prediction of the structural,elastic, electronic,optical and thermal properties of the cubic perovskites CsXF3 (X = Ca,Sr and Hg) under pressure effect

Some physical properties of the cubic perovskites CsXF₃ (X = Ca, Sr and Hg) have been investigated using pseudopotential plane-wave method based on the density functional theory. The calculated lattice parameters within GGA and LDA agree reasonably with the available experimental data. The elastic constants and their pressure derivatives are predicted using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus, Poisson's ratio and Lamé’s constants for ideal polycrystalline aggregates. The analysis of B/G ratio indicates that CsXF₃ (X = Ca, Sr and Hg) are ductile materials. The thermal effect on the volume, bulk modulus, heat capacity and Debye temperature was predicted.     

Uniaxial compression testing of polymeric materials

Two methods for uniaxial compression testing were investigated and compared using polypropylene as a model material. An overview of various parameters affecting compression test results is provided with particular emphasis on friction between the specimen and the compression plate. A procedure for the determination of the compressive modulus is introduced and results are shown. To enable the detection of instability associated with friction and barreling and to calculate true stress-true strain curves, the measurement of transverse expansion of the specimen at large strains is necessary. Nominal and true Poisson's ratio values in the pre- and post-yield regime are presented and the resulting true stress-true strain curves are compared and discussed. While in the post-yield regime nominal stress values misleadingly result in strain hardening, significant strain softening was observed using true stress values representing the intrinsic material behavior.     

Role of PTFE paste fibrillation on Poisson's ratio

Polytetrafluoroethylene (PTFE) flat profiles were extruded using slit dies, which promoted orientation of fibrils in two directions (2-D). Uniaxial tensile experiments were performed on the collected extrudates using the Sentmanat Extensional Rheometer (SER) at different temperatures and Hencky strain rates to determine the mechanical properties of the material. A nonlinear viscoelastic model developed by Matsuoka was found to describe well the transient tensile results using Poisson's ratio as a parameter. Polarized Raman Spectroscopy was also used to gain additional information on the degree of fibril orientation at different locations both along and across the width and length of the extrudates. Results of the Raman spectra were found to be in agreement with the fibril structure/morphology obtained from SEM micrographs. The compressibility of the extrudates upon stretching was studied by measuring the relative density. The results are modeled using a simple equation including the elastic strain recovery coefficient (κ) and Poisson's ratio.     

Assessment of thermal expansion coefficient of methylsilsesquioxane thin film

For the methylsilsesquioxane film whose optical birefringence is almost zero, it was recently reported that its vertical thermal expansion coefficient (CTE) was approximately one order of magnitude larger than the lateral CTE. Though the birefringence is not an absolute predictor of anisotropic behavior, the discrepancy in both the CTEs was so remarkable that it was essential to investigate whether the anisotropy was intrinsic property or not. If the effect of Poisson's ratio is considered in the calculation of the vertical CTE and when elastic modulus measured by surface acoustic wave spectroscopy is used in the assessment of the lateral CTE, both the CTEs are coincident with each other. Therefore, it can be concluded that the discrepancy in the CTEs can be attributed to a higher in‐plane polymer chain orientation but it can also arise from the misleadingly assumed modulus and Poisson's ratio. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3109–3120, 2006     

First-principles study of structural,elastic, electronic and vibrational properties of BiCoO3

We used density functional theory (DFT) to study the structural, elastic, electronic, and lattice dynamical properties of tetragonal BiCoO₃ applying the “norm-conserving” pseudopotentials within the local spin density approximation (LSDA). The calculated equilibrium lattice parameters and atomic displacements are in agreement with the available experimental and theoretical results. Moreover, the structural stability of tetragonal BiCoO₃ were confirmed by the calculated elastic constants. In addition, the elastic properties of polycrystalline aggregates including bulk, shear and Young's moduli, and Poisson's ratio are also determined. The electronic band structure, total and partial density of states (DOS and PDOS) with ferromagnetic spin configuration are obtained. The results show that tetragonal BiCoO₃ has an indirect band gap with both up- and down-spin configurations and its bonding behavior is of covalent nature. We compute Born effective charge (BEC) which is found to be quite anisotropic of Bi, Co and O atoms. The infrared and Raman active phonon mode frequencies at the Г point are found. The phonon dispersion curves exhibit imaginary frequencies which lead from the high-symmetry tetragonal phase to low-symmetry rhombohedral phase in BiCoO₃. The six independent elastic constants, including bulk, shear and Young's moduli, and Poisson's ratio, complete BEC tensor and phonon dispersion relations in tetragonal BiCoO₃ are predicted for the first time. Results of the calculations are compared with the existing experimental and theoretical data.     

Comparing the mechanical response of di‐, tri‐, and tetra‐functional resin epoxies with reactive molecular dynamics

The influence of monomer functionality on the mechanical properties of epoxies is studied using molecular dynamics (MD) with the Reax Force Field (ReaxFF). From deformation simulations, the Young's modulus, yield point, and Poisson's ratio are calculated and analyzed. Comparison between the network structures of distinct epoxies is further advanced by the monomeric degree index (MDI). Experimental validation demonstrates the MD results correctly predict the relationship in Young's moduli. Therefore, ReaxFF is confirmed to be a useful tool for studying the mechanical behavior of epoxies. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 255–264