A Simple Dilatometric Method for Determining Poisson's Ratio of Nearly Incompressible Elastomers

Abstract

A simple apparatus which was developed for measuring the dilatation of specimens tested in uniaxial tension is described. The dilatometer can be used on an Instron testing machine. In spite of its simplicity, this dilatometer enables an accurate determination of Poisson's ratio of nearly incompressible elastomers. We present typical curves showing the effect of strain on Poisson's ratio of filled and unfilled elastomers. We also describe the dilatometric processes observed during straining of granular filled elastomers.     

Properties of Adhesives and their Applications

The stress analysis of an adhesively bonded lap joint requires more information on the mechanical properties of adhesives than it is normally furnished by the manufacturers. For this reason the tests were performed on the three types of adhesives covering a large range of properties. In order to get the true stress-strain curves in tension and compression the change in the Poisson's Ratio with strain was investigated. It was found that the Poisson's Ratio increases almost to the constant volume deformation value until the nonrecoverable deformation sets in. From that point the Poisson's Ratio begins to decrease. Considering only the range of the recoverable deformation, the computer programs developed for the stress analysis of metallic materials can be used for an adhesively bonded lap joint. The recoverable viscoelastic deformation was considered non linear elastic and by applying an effective stress-effective strain relationship the analysis was performed.     

Effect of matrix ductility and interface treatment on mechanical properties of glass fiber mat composites

The influence of matrix properties on randomly oriented glass fiber epoxy composites has been studied. It is shown that an increased ductility (flexibility) of the matrix does not result in greater elongation to failure of the composite under tensile and flexural loads. The tensile (and flexural) strength and the modulus of elasticity are decreased as the ductility of the resin is increased. It is concluded that since the matrix material is subjected to a triaxial state of stress when the composite specimen is subjected to uniaxial loads, the effect of matrix modulus, Poisson's ratio, and yield strength are more important than the matrix ductility measured under uniaxial stress. The effect on mechanical properties of various surface treatments applied to the fibers is also investigated. Finally, scanning electron micrographs are presented showing matrix cracks, fiber debonding, and fiber pull-out.     

The Uniaxial Tensile Response of Porous and Microcracked Ceramic Materials

The uniaxial tensile stress–strain behavior of three porous ceramic materials was determined at ambient conditions. Test specimens in the form of thin beams were obtained from the walls of diesel particulate filter honeycombs and tested using a microtesting system. A digital image correlation technique was used to obtain full‐field 2D in‐plane surface displacement maps during tensile loading, and in turn, the 2D strains obtained from displacement fields were used to determine the Secant modulus, Young's modulus, and initial Poisson's ratio of the three porous ceramic materials. Successive unloading–reloading experiments were performed at different levels of stress to decouple the linear elastic, anelastic, and inelastic response in these materials. It was found that the stress–strain response of these materials was nonlinear and that the degree of nonlinearity is related to the initial microcrack density and evolution of damage in the material.     

Fracture analysis of bonded elastomeric disks subjected to triaxial stress

A theoretical model for the dependence of the modulus of elasticity, M, on the porosity, α, of an elastomeric disk subjected to triaxial stress was developed. An empirical law was proposed for the dependence of the surface energy, Γ, on the porosity, α, of the elastomer. The presented theoretical model is a two-degree-of-freedom model, the parameters of which are determined by fitting with experimental data derived from the elastomer disks. In order to obtain the final mathematical expression for the effective modules of the composite system, a relationship between the strain field within the disk and the porosity was developed. The numerical differentiation of the experimental stress/strain curve from the tested bonded elastomer disks yields the values of the apparent modulus of the elastomer disks as a function of the strain field within the testing specimens. An appropriate combination of the proposed theory and the received experimental data yields the percentage of the growing microvoids within the deformed material. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:1821–1827, 1997     

Coupled mass diffusion and structural deformation of elastomer seals exposed to rapid gas decompression

A sequentially coupled structural–mass diffusion model has been proposed to evaluate the behaviour of elastomer O-rings exposed to rapid gas decompression in the presence of CO₂. The coupling between mass diffusion and the structural deformation of the O-ring was achieved by employing the Peng–Robinson equation of state and two user-subroutines to evaluate the pressure exerted by the rapidly expanding gas. The finite element analysis (FEA) model has been used to evaluate stress and strain distribution inside the O-ring during rapid gas decompression. It was shown that the nominal stresses go through a stress–state change from compression to tension during the decompression cycle, and the strain rate during the stress–state change is dependent upon the decompression rate. The FEA model revealed that the elements in the centre region of the O-ring's cross-section experience high tensile strains and stresses during each decompression cycle.     

Deformation behavior of polystyrene as a function of molecular weight parameters

The mechanical deformation of polystyrene as it relates to molecular weight parameters was investigated. Mechanical testing consisted of uniaxial tension and compression experiments on a variety of polystyrenes. Such quantities as modulus, proportional limit, and various yield stress measurements were determined on polystyrene samples of controlled number-average molecular weight and molecular weight distribution. A basic tool for the mechanical behavior analysis was the use of a power law equation σ = K?ⁿ to examine the initial nonlinear region of each experimentally determined stress–strain curve. Correlations between mechanical deformation and molecular weight parameters were determined using statistical linear regression analysis. It was generally found for uniaxial tension that mechanical parameters in or near the elastic region were independent of M?_n and MWD, while at larger strains correlations were found. For uniaxial compression, stress maxima and the strain where this occurred increased with increasing MWD. Otherwise, mechanical parameter changes in uniaxial compression did not occur with changing M?_n and MWD. Finally, a direct comparison of tension versus compression showed only the initial moduli to be the same. All other mechanical parameters showed significantly differing values, indicating different deformation mechanisms operating in tension verus compression. The analysis of this behavior from both a mechanics and molecular weight viewpoint provides some insight about glassy polymer deformation processes on the microscopic level.     

Poisson's ratio and volume change accompanying deformation of randomly oriented electrospun nanofibrous membranes

ABSTRACT

The present work focuses on the determination of volume change accompanying deformation and Poisson's ratio for electrospun nanofibrous membranes. For this purpose, polyurethane (PU) is considered for the fabrication of electrospun nanofibrous membranes. Three different sample thicknesses are fabricated. Following this, surface morphology analysis and fibre orientation analysis are conducted to investigate the variation of properties between electrospun PU membranes of different thicknesses. Subsequently, PU specimens are subjected to uniaxial extension test where the changes in sample width and thickness are recorded as a function of applied strain. Volume changes are computed while further analysis on the relationship between transverse strains and axial strain provided the values of Poisson's ratio. For all three electrospun PU samples investigated, significant volume changes are observed while the in-plane Poisson's ratio is found to be around 0.55. However, the out-of-plane Poisson's ratio of electrospun PU membranes are not classical and remains undetermined.     

Study on the Viscoelastic Poisson‘s Ratio of Solid Propellants Using Digital Image Correlation Method

Digital image correlation methods were used for further studies of the viscoelastic Poisson's ratio of solid propellants. The Poisson's ratio and the Young's relaxation modulus of solid propellants were separately determined in a single stress relaxation test. In addition, the effects of temperature, longitudinal strain, preload and storage time on the Poisson's ratio of solid propellants were discussed. The Poisson's ratio master curve and the Young's relaxation modulus master curve were constructed based on the time‐temperature equivalence principle. The obtained results showed that the Poisson's ratio of solid propellants is a monotone non‐decreasing function of time, the instantaneous Poisson's ratio increased from 0.3899 to 0.4858 and the time of the equilibrium Poisson's ratio occurred late when the temperature was varied from −30 °C to 70 °C. The Poisson's ratio increased with temperature and longitudinal strain, decreased with preload and storage time, while the amplitude Poisson's ratio increased with preload, decreases with longitudinal strain and storage time. The time of the equilibrium Poisson's ratio occurred in advance with the increase of longitudinal strain, preload and storage time.     

Characterisation of mechanical properties of thin polymer films using a bi-axial tension based on blow-up test

Abstract

Blow-up tests were carried out to evaluate mechanical properties of the thin Nylon film used as bagging films. A new method for calculating bi-axial stress and strain of the thin film in blow-up tests was developed based on the theory of membrane with large strain solutions. The bi-axial tensile elastic modulus, Poisson's ratio, yield strength, fracture stress and bi-axial stress–strain relationship of the thin Nylon film were obtained. Meanwhile, uni-axial tensile tests were conducted and the results were compared with those from blow-up tests. For the Richmond HS-8171 thin Nylon film studied, the bi-axial tensile elastic modulus was slightly more than 2 times greater than the uni-axial tensile elastic modulus. The yield strength was the same for both bi-axial and uni-axial tension. The bi-axial fracture stress was about one-third greater than the uni-axial one, while the bi-axial failure strain was about two-thirds greater than the uni-axial counterpart.     

A new test method to obtain biaxial tensile behaviors of solid propellant at high strain rates

A new test method was proposed and applied for studying the biaxial tensile behaviors of hydroxyl-terminated polybutadiene (HTPB) propellant at high strain rates. The biaxial tensile stress responses of the propellant at room temperature and at different strain rates (0.40–85.71 s^?1) were obtained through the use of biaxial tensile strip samples, a new designed aluminum apparatus and a uniaxial Instron testing machine. A high-speed camera and scanning electron microscop (SEM) were employed to observe the biaxial tensile deformation and the damage of HTPB propellant under the test conditions. The results indicated that strain rate could remarkably influence the biaxial tensile behaviors of HTPB propellant. The effect of strain rate on the characteristics of stress–strain curves, mechanical properties and fracture mechanisms was consistent with that in uniaxial tension. However, the biaxial weakening of HTPB propellant was obvious. The strain at biaxial maximum tensile stress was between 10 and 30 % lower than that at the corresponding uniaxial case. Finally, the correlations between the fracture mechanisms and the mechanical properties of HTPB propellant, stress state and the damage of HTPB propellant were discussed. The damage of the propellant under the biaxial tensile test was less serious than that under uniaxial tension at the same strain rate. In addition, continuously increasing strain rate could change the fracture mechanism of the propellant under the biaxial and uniaxial tensile tests. In this investigation, the dominating fracture mechanism of HTPB propellant changed from the dewetting and matrix tearing at lower strain rate to the particles fracture at higher strain rate.     

Effects of voids on the response of a rubber poker chip sample. III

The effects of voids on the response of a rubber poker chip sample are examined. A theoretical estimation of the diametral contraction of the sample was performed, using the linear theory of stress analysis. Experimental measurements of the lateral contraction at the middle plane of the poker chip elastomer specimen have shown that the testing rubber is not incompressible. By comparing the experimental data with the theoretical predicted equation, the value of the Poisson's ratio v_eff was found to be 0.487, for a given aspect ratio a* of the sample. A theoretical equation for the volume dilatation of the poker chip rubber sample was developed. Using the given aspect ratio, the value of v_eff, and the experimental stress/strain curve of the sample, an estimation of the volume dilatation was formed. The effective Poisson's ratio was also found using the linear stress analysis, by comparing the developed mathematical equations for an incompressible rubber with voids with a compressible one.     

Mechanical Response of Thermoset Polymers under High Compressive Loads, 2

Summary: A nonlinear viscoelastic material model was used to describe the experimental behaviour of thin vinyl ester specimens subjected to compression in thickness direction. The stress‐dependent material functions in the model were found in creep and strain recovery tests on thick cylindrical specimens. The elastic and creep response of thin thermoset polymer specimens subjected to compressive loads was simulated while varying the geometry of the test set samples. The calculated increase in the apparent elastic modulus and decrease of the creep‐strain rate due to reduced thickness‐to‐width ratio is in a good qualitative correlation with experimental results for corresponding geometries. The constraint due to friction and interaction with the material outside the loaded surface area were identified as the cause for high apparent stiffness, which converges with decreasing thickness to an asymptotic value dependent on the modulus and Poisson's ratio of the material.

The shape of a 2 mm‐thick specimen under compression.     

Acoustic emission in bonded elastomer discs subjected to uniform tension. II

The aim of this paper is to evaluate and analyze the growing and tearing mechanisms of existing microvoids within bonded elastomer discs using the acoustic emission (AE) technique. It was shown that the existing microvoids in the deformed disc are responsible for the reduction of the apparent modulus (M) of the elastomer disc, the stress softening, and the hysteresis when the material is subjected to triaxial stress conditions. A series of experiments performed in our laboratory confirmed the existence of microvoids within the deformed bonded unfilled nitrile rubber discs. Valuable information about the size of the deformed voids in the material was obtained using the frequency spectrum of the detected AE signals. More information on the tearing of voids was extracted from the count, event, amplitude, and duration time distribution of the received AE pulses.     

Linear thermoelastic characterization of anisotropic poly(ethylene terephthalate) films

All nine independent elastic constants have been determined for a biaxially stretched poly(ethylene terephthalate) (PET) film using novel mechanical methods. The orthotropic directions and the in‐plane Poisson's ratios were first characterized using vibrational holographic interferometry of tensioned membrane samples. The out‐of‐plane Poisson's ratio was obtained by measuring the change in tension with the change in pressure for constant strain conditions. Pressure–volume–temperature (PVT) equipment was used to measure the bulk compressibility as well as the volumetric thermal expansion coefficient (TEC). The in‐plane Young's moduli were obtained by tensile tests, while the out‐of‐plane modulus was calculated from the compressibility and other elastic constants that describe the in‐plane behavior. The in‐plane TECs in the machine and transverse directions were determined using a thermal mechanical analyzer (TMA). The out‐of‐plane TEC was determined using these values and the volumetric TEC determined via PVT. The resulting compliance matrix satisfies all of the requirements of a positive‐definite energy criterion. The procedure of characterization utilized in this article can be applied to any orthotropic film. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2937–2947, 2002     

Mechanical properties of urea–formaldehyde foam

The mechanical behavior of urea-formaldehyde foam was studied to evaluate its potential for energy absorption applications. The apparent elastic modulus (E_f) as a function of foam density was obtained from force-deformation tests. The values of energy absorption capacity were derived from a numerical integration technique. Poisson's ratio (v) was determined by a method of uniaxial compression of cylindrical samples. An increase in foam density results in an increase in the apparent elastic modulus of the material and therefore in its energy absorption capacity. Poisson's ratio is independent of the foam density. The mechanical properties' values obtained can be incorporated in various analyses for predicting desired characteristics for energy absorption applications.     

Auxetic polypropylene films

Auxetic materials are those exhibiting negative Poisson's ratio (ν) behavior. Polymeric auxetic extruded products in the form of cylinders and fibers have previously been reported. This article reports the successful production of auxetic polypropylene films (～0.15‐mm thick) using a melt extrusion process. Video extensometry and tensile testing techniques have been used to measure the in‐plane Poisson's ratios and Young's moduli of the auxetic film, both on an Instron tensile testing machine and a Deben microtensile testing machine. The film is elastically anisotropic with the Poisson's ratio and Young's modulus along the extrusion (x) direction being ν_xy = ?1.12 ± 0.06 and E_x = 0.34 ± 0.01GPa, respectively, while the Poisson's ratio and Young's modulus in the transverse (y) direction to the extrusion direction are ν_yx = ?0.77 ± 0.01 and E_y = 0.20 ± 0.01GPa, respectively. POLYM. ENG. SCI., 45:517–528, 2005. © 2005 Society of Plastics Engineers     

Nonlinear finite element analysis of the butt-joint elastomer specimen

The practical strength of a butt-joint specimen is of great importance to many industrial applications such as adhesive joints, elastomer mountings, flexible couplings, etc. A butt-joint specimen could fail either cohesively or interfacially, depending on the strength of the materials and the stress distribution in the specimen. In the past, engineering design has been based either on theoretical linear analysis or on empirical rules of thumb. A more realistic analysis based on the nonlinear finite element (FE) method is presented here. The elastomer layer in the butt-joint specimen is modeled by a modified Ogden-Tschoegl strain energy function. The nonlinear axisymmetric FE program is formulated on the total Lagrangian procedure. The nominal strain, the thickness of the rubber layer, the compressibility (or Poisson's ratio), and the strain-hardening (or softening) parameter are taken as the variables in the analysis. The maximum radial and axial stresses are found along the central axis, while the maximum shear stress is near the corner of the bond plane and the free lateral surface. The stiffness as a function of the apparent strains is obtained for various thicknesses, various Poisson's ratios, and various strain-hardening parameters. The lateral contraction and the volume dilatation of the specimen are also calculated and related to the stress distribution in the specimen. A well-defined peak load occurs at a critical strain for thin specimens made of materials with a low strain-hardening parameter and high Poisson's ratio values.     

Viscoelastic-plastic deformation behavior of polypropylene after cyclic preloadings

Stress-relaxation behavior is studied in polypropylene samples subjected to different cyclic preloadings and to simple tension. The relaxation tests are performed under different sets of strain amplitude, number of cycles, and strain rate, using a closed-loop, electrohydraulic, servocontrolled testing machine. The calculated stress-strain curves are determined from a constitutive equation based on an overstress theory in which an equilibrium stress and a viscosity function are treated. The calculated results agree well with the experimental ones. It is concluded that the overstress theory explains the nonlinear viscoelastic-plastic behavior of polypropylene.