On the phenomena of deformation and neck formation in LLDPE films subjected to uniaxial and biaxial loading conditions

Heterogeneous deformation in the form of dilatational bands is observed under certain biaxial stress states that closely resembles uniaxial necking in LLDPE blown films. The formation and orientation of dilatational bands is a function of film morphology and stress state. The dilatational bands form, with their lengths aligned with the machine direction (MD) of the film, under equibiaxial stress states and nonequibiaxial stress states when the higher principle stress is coincident with the transverse direction (TD). However, homogeneous deformation is observed if the higher principle stress is coincident with the MD. Similarly, uniaxial specimens show necking when the stress is applied in the TD and affine deformation when the stress is applied in the MD. Neck boundary propagation under uniaxial loading is due primarily to the consumption of undrawn material, while dilatational band boundary propagation under an equibiaxial loading also includes simultaneous continued deformation of the drawn material. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2651–2663, 1999     

Evidences of non-linear short-term stress relaxation in polymers

Back in 1986, investigating the Space Shuttle Challenger disaster, famous physicist Richard Feynman clearly showed how viscoelastic behavior of a polymeric material is of paramount importance in practical engineering. At present day a definitive universal rheological law is not yet available for polymers, as a consequence both theoretical models and experimental investigations of viscoelastic behavior must be necessarily focused independently on each single polymer or, at least, on well-defined classes of polymers. Accurate experimental evidences are needed in order to properly evaluate the mechanical properties of a polymeric material, as a function of its particular applications. In this paper measurements of the stress relaxation behavior of six polymeric materials under uniaxial tension and uniaxial unconfined compression tests, are performed and experimental results are modelled using a stretched exponential function, known as Kohlraush-Williams-Watts time-decay function. In particular the short-term stress relaxation is investigated, as a function of typical environmental temperature range, in order to assess viscoelastic behavior of tested polymeric materials for peculiar industrial and biomedical applications.     

A new characterisation method for rubber

This paper deals with the mechanical characterisation of elastomeric materials. An original method is proposed to identity the material parameters. It consists of performing only one heterogeneous mechanical test, measuring the displacement/strain field using suitable Digital Image Correlation software and applying an inverse method, namely the Virtual Fields Method, to process the resulting displacement/strain maps. For this purpose, a new apparatus was designed to be adapted to a conventional tensile machine. This apparatus enables us to obtain simultaneously uniaxial tension, pure shear and equibiaxial tension, using only one sample. The heterogeneity of the kinematic fields induced by the test is first discussed in relation to two criteria. The main features of the identification method are then presented, and results provided by a test performed on an elastomeric material are discussed in the context of hyperelasticity.     

Prestrained biaxial DMA investigation of viscoelastic nonlinearities in highly filled elastomers

Highly filled elastomers present strong nonlinear mechanical behavior. This study proposes a biaxial dynamic mechanical analysis (DMA) experiment to study the prestrain induced nonlinearity. This phenomenon has already been observed for uniaxial tests, revealing an increase of the amplitude of the dynamic modulus with prestrain. The novelty proposed here is to investigate the problem under biaxial conditions. For this purpose, a specific apparatus and an appropriate specimen have been designed. Strains and stresses have been measured using localization formulae and compared with measurements from digital image correlation and finite element computations. Biaxial DMA tests were performed on a propellant specimen, for different values of biaxial prestrain. The material is a highly filled elastomer with an important influence of the prestrain on the global viscoelastic behavior. The results exhibit increasing amplitude of the complex modulus with increasing prestrain, as in uniaxial experiments. Moreover, the dependence can be characterized using the second invariant of the prestrain, and the viscoelastic behavior is modeled using a closed-form spectrum of relaxation times.     

Measurement of flexural modulus of polymeric foam with improved accuracy using moiré method

The flexural modulus of polymeric foams determined from three-point bending tests is usually inaccurate due to the local deformation undergone by the material during testing. The machine used in the test gives deflection values larger than the actual deflection of the foam specimen due to the deformation of the material at the loading point. This leads to errors in the computation of the modulus value. In this work, the deflection values of a beam made of polymeric foam in a three-point bending test were determined using the moiré method. The change in the moiré pattern at the neutral axis of the foam during loading was recorded and converted into deflection values. The deflection data were used to generate the stress–strain curve from which the flexural modulus of the foam material was determined. The proposed method was verified using aluminum beams, where a high correlation between the deflection data from the machine readings and the moiré method was obtained. The flexural modulus of the foam determined using the moiré method was found to be within 3% of the value published in the material data sheet.     

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.     

Anisotropic mechanical properties of thermoplastic elastomers in situ reinforced with thermotropic liquid‐crystalline polymer fibers revealed by biaxial deformations

The anisotropic mechanical properties of the thermoplastic elastomer (TPE) in situ reinforced with thermotropic liquid‐crystalline polymer (TLCP) fibers were investigated by uniaxial, strip‐biaxial, and equibiaxial tensile measurements. The in situ composite sheets were prepared from an immiscible blend of a TLCP, Rodrun LC3000, and a TPE, styrene‐(ethylene butylene)‐styrene (SEBS) triblock copolymer, by a melt extrusion process. The uniaxial orientation of the TLCP fibers in the TPE matrix generated during processing yielded a significant mechanical anisotropy in the composites. The biaxial tensile measurements clearly demonstrated the anisotropic mechanical properties of the composites: The modulus in the direction parallel to the machine direction (MD) was considerably higher than that in the transverse direction (TD), even at large deformations; in equibiaxial stretching, the yield strain in the MD was smaller than that in the TD; the composite containing 10 wt % of TLCP exhibited the highest mechanical anisotropy among the composites, with 0–30 wt % TLCP. The latter result was in accord with the SEM observation that the composite with 10 wt % of TLCP possessed the best fibrillar morphology and the highest degree of uniaxial orientation of the TLCP fibers. The yield strains in uni‐ and biaxial elongation for the composite containing 10 wt % of TLCP were almost the same as those for the neat styrene‐ethylene butylene‐styrene. The TLCP phase with good fibrillation did not appreciably alter the original yielding characteristics of the elastomer matrix. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 135–144, 2005     

Induced crystallization and orientation of poly(ethylene terephthalate) during uniaxial and biaxial elongation

Stretching PET at a high strain rate above the glass transition temperature has a positive effect on the strength of the material. In a recent paper^[1], we presented the influence of stretch and blow molding parameters on the properties of the final product, especially on the crystallinity induced by stretching. In this paper, we focus on the effects of loading, temperature, elongation and strain rate on macromolecular orientation and crystallization kinetics. We present experimental results from uniaxial and biaxial elongation tests carried out on injected PET specimens. To minimize the effect of quiescent crystallization, specimens are quickly heated with infrared lamps before the test and temperature is regulated during the test. Both uniaxial and biaxial tests are analyzed using a cross correlation technique^[2] that compares a picture used as reference and the picture of the deformed specimen. This technique allows us to determine all strain components at each point of the specimen, even when the strain field is not homogeneous. In a second part, we present measurements of macromolecular orientation and crystallinity ratio performed after each test. The infrared dichroïsm technique is used to determine the orientation of the microscopic morphology of PET before and after the testing. DSC measurements and density measurements are carried out to calculate the crystallinity ratio. Influences of strain rate, temperature and strain path sequence are evaluated in order to build a database for recent models of induced crystallization^[3],[4],[5].     

Biaxial tensile behavior and strength of architectural fabric membranes

The utilization of composite fabric membrane materials for large-span membrane structures has attracted considerable attention in recent decades due to enhanced material properties. Biaxial mechanical properties with respect to real engineering applications are essential and indispensable in comparison with uniaxial ones. This study focuses on true biaxial characteristics of a typical polyvinylidene fluoride (PVDF)-coated polyester membrane material in terms of stress-strain characteristics and breaking criteria.The true stress-strain curves obtained from an experimental study, i.e. seven loading ratios on the basis of symmetry and typical conditions, are investigated with digital image correlation method. The interpolation of these curves in combination of least square method achieves a three-dimensional strain surface as a function of warp and weft strains, which is useful to assess reasonable structural behavior. A new breaking criteria intended for architectural fabric membrane is proposed in analogy to Tsai-Hill, Yeh-Stratton and Norris failure criteria. The basic constants in the criteria are determined using experimental results. A comparative analysis between available uniaxial and biaxial criteria shows that the new criteria can cover all criteria due to the fact that biaxial mechanical properties are larger than uniaxial ones. Furthermore, a similar but glued specimen is employed to compare welded specimens. It is obtained that observations, values and curve tendency are similar, demonstrating the suitability of using new specimens to identify true biaxial properties.     

A new theoretical-experimental model deriving from the contactless measurement of the thickness of bulge-tested elastomeric samples

In this paper, an ultrasound measurement method was applied to bulge test on carbon black-filled SBR specimens, in order to determine their thickness at the top of the dome. This method consists in measuring first the variation in the ultrasonic velocity as a function of the deformation in the uniaxial state and subsequently obtaining the thickness value in the equibiaxial state, assuming the congruence of velocity in uniaxial and equibiaxial stress states, respectively.The comparison between experimental data and the thickness values deriving from the most reliable theoretical criteria for both metallic and rubbers-like materials was shown.A new theoretical approach taking into account the slight compressibility of elastomers to estimate the thickness at the dome apex was proposed. Such an approach provided a general equation to define the thickness of the dome in bulge-tested SBR+20%CB as a function of the Poisson ratio.     

On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for flows of nematic liquid crystals (LCs) has been successfully applied by Rey to study extensional flow-induced, homogeneous phase transitions both for rod-like and disc-like molecular geometry. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the flow-phase diagram (nematic concentration vs. flow rate) for rod-like nematics by analysing all tensor degrees of freedom, i.e. by coupling the three director (eigenvector) degrees of freedom. Here we record and discuss subtleties of the corresponding diagram for discotic LCs in uniaxial extension and uniaxial compression. We focus here on the induced stable orientation configurations. Uniaxial extension (an idealization of fibre flow) yields a low concentration region of unique oblate uniaxial states at every flow rate; a very small finite region of bi-stable oblate and biaxial states; and the predominant region, encompassing all concentrations above the pure I-N transition and all flow rates, where the only stable steady state is a biaxial pattern. Furthermore, whereas uniaxial states are 'unique', all biaxial states occur in a continuous family, corresponding to an arbitrary positioning of the director pair in the plane transverse to the flow axis of symmetry. Uniaxial compression (an idealization of film stretching flow) of discotic LCs exclusively yields stable prolate uniaxial patterns.     

Performance of a parallel viscoelastic-viscoplastic model for a microcellular thermoplastic foam on wide temperature range

This paper is concerned with the experimental testing and the constitutive modelling of a thermoplastic microcellular polyethylene-terephthalate (MC-PET) foam on the temperature range of 21–210 °C in order to investigate the temperature-dependent performance of the applied parallel viscoelastic-viscoplastic material model. By means of carefully designed uniaxial mechanical tests in temperature chamber, the viscous, elastic and yielding behaviours of the investigated material are identified, which are then applied for selecting suitable viscoelastic-viscoplastic constitutive models. The material characterization process is conducted using finite-element-based fitting method, including also the analysis of the applied numerical optimization algorithm. The fitting results are used to analyse the parameter sensitivity and to propose closed-form analytical relations for the temperature dependency of the material parameters. Finally, the utilisation of the analytical temperature functions for speeding up the parameter-fitting process is also demonstrated.     

On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for flows of nematic liquid crystals (LCs) has been successfully applied by Rey to study extensional flow-induced, homogeneous phase transitions both for rod-like and disc-like molecular geometry. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the flow-phase diagram (nematic concentration vs. flow rate) for rod-like nematics by analysing all tensor degrees of freedom, i.e. by coupling the three director (eigenvector) degrees of freedom. Here we record and discuss subtleties of the corresponding diagram for discotic LCs in uniaxial extension and uniaxial compression. We focus here on the induced stable orientation configurations. Uniaxial extension (an idealization of fibre flow) yields a low concentration region of unique oblate uniaxial states at every flow rate; a very small finite region of bi-stable oblate and biaxial states; and the predominant region, encompassing all concentrations above the pure I-N transition and all flow rates, where the only stable steady state is a biaxial pattern. Furthermore, whereas uniaxial states are 'unique', all biaxial states occur in a continuous family, corresponding to an arbitrary positioning of the director pair in the plane transverse to the flow axis of symmetry. Uniaxial compression (an idealization of film stretching flow) of discotic LCs exclusively yields stable prolate uniaxial patterns.     

The heat conductivity of liquid crystal phases of a soft ellipsoid string-fluid evaluated by molecular dynamics simulation

We have applied a nonequilibrium molecular dynamics heat flow algorithm to calculate the heat conductivity of a molecular model system, which forms uniaxial and biaxial nematic liquid crystals. The model system consists of a soft ellipsoid string-fluid where the ellipsoids interact according to a repulsive version of the Gay-Berne potential. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the discotic nematic phase, the heat conductivity has two components, one parallel and one perpendicular to the director, where the last mentioned component is the largest one. This order of magnitudes is reversed in the calamitic nematic phase. In the biaxial nematic phase there are three components of the heat conductivity, one in the direction around which the long axes of the molecules are oriented, this is the largest component, another one in the direction around which the normals of the broadsides of the molecules are oriented, this is the smallest component, and one in the direction perpendicular to these two directions with a magnitude in between those of the first mentioned components. The relative magnitudes of the components of the heat conductivity span a fairly wide interval so it should be possible to use the model to parameterise experimental data.     

The evaluation and implementation of magnetic fields for large strain uniaxial and biaxial cyclic testing of Magnetorheological Elastomers

Magnetorheological Elastomers (MREs) are “smart” materials whose physical properties are altered by the application of magnetic fields. In previous studies the properties of MREs have been evaluated under a variety of conditions, however little attention has been paid to the recording and reporting of the magnetic fields used in these tests [1]. Currently there is no standard accepted method for specifying the magnetic field applied during MRE testing. This study presents a detailed map of a magnetic field applied during MRE tests as well as providing the first comparative results for uniaxial and biaxial testing under high strain fatigue test conditions. Both uniaxial tension tests and equi-biaxial bubble inflation tests were performed on isotropic natural rubber MREs using the same magnetic fields having magnetic flux densities up to 206 mT. The samples were cycled between pre-set strain limits. The magnetic field was switched on for a number of consecutive cycles and off for the same number of following cycles. The resultant change in stress due to the application and removal of the magnetic field was recorded and results are presented.     

The elasticity of nematic networks

Nematic rubbers are composed of crosslinked polymer chains with stiff rods either incorporated into their backbones or pendant as side chains. When nematic effects axe strong, such rubbers exhibit discontinuous stress-strain relationships and spontaneous shape changes. We model such a rubber using Gaussian elasticity theory, including the nematic interaction via a mean field. Results are presented for the cases of uniaxial extension and compression. Under uniaxial extension the rubber can undergo a first order phase transition to a uniaxial nematic phase. Under uniaxial compression first or second order transitions are possible to genuinely biaxial nematic states with biaxial strains. When nematic effects are very small (i.e. T >> T_c where T_c is the nematic-isotropic phase transition temperature of the rubber) we postulate that the model is a good approximation to a conventional, non-nematic elastomer, and fit our model to data from an isoprene rubber.     

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.     

Flow-alignment and viscosity rules for single-phase binary mesomorphic mixtures

A macroscopic model for incompressible homogeneous (single phase) binary nematic mixtures, under isothermal conditions is given. The rheological model is a generalization of the standard Ericksen's nematorheological model for single component uniaxial rod-like nematic liquid crystals. Its special cases include single component orthorhombic biaxial nematics and single component uniaxial nematics. The theory is used to formulate rules for the rotational viscosity and the reactive parameter of nematic mixtures in the presence of weak flows. The predicted mixture rules for the reactive parameter and rotational viscosity are analysed as a function of concentration and rotational viscosity ratio for various monomeric and polymeric mixtures, and for rod-rod, disc-disc, and rod-disc nematic mixtures. The mixture rules are used to compute alignment phase diagrams and alignment transition (orientational instability) thresholds.     

Thermal and mechanical properties of polypropylene in the thermoplastic elastomeric state

One result of the discovery of homogeneous metallocene stereospecific catalysts is the ability to prepare polypropylene in a stereoblock form in which the isotactic stretches give crystallites acting as temporary crosslinks in an elastomeric network structure. The fact that these elastomers are thermoplastic and thus reprocessible increases the importance of establishing their structure-property relationships. In this report, the dependence of their physical properties on isotactic pentad content, molecular weight, and possible strain-induced crystallization are described. Thermal evaluations and mechanical tests of these materials under oscillatory strain, continuous extension and near-equilibrium uniaxial and biaxial elongation showed that they were multiphase, tough elastomeric materials. Their moduli and tensile strengths increased with increase in % isotactic pentad content and with increase in molecular weight. Equilibrium stress-strain measurements showed the occurrence of strain-induced crystallization in uniaxial, but not in biaxial, deformations.     

Landau theory for uniaxial nematic,biaxial nematic,uniaxial smectic-A,and biaxial smectic-A phases

We use the Landau theory of phase transitions to obtain the global phase diagram concerning the uniaxial nematic, biaxial nematic, uniaxial smectic-A and biaxial smectic-A phases. The transition between the biaxial nematic and biaxial smectic is continuous as well as the transition between the nematic phases and the transition between the smectic phases. The transition from uniaxial nematic and uniaxial smectic is continuous with a tricritical point. The tricritical point may be absent and the entire transition becomes continuous. The four phases meet at a tetracritical point.