Uniaxial Elongation Research Articles

Rheology of Bead‐NonLinear Spring Chain Macromolecules

The finitely extensible nonlinear spring chain model for polymer molecules in dilute solution is considered under the Peterlin approximation. A time‐dependent normal modes analysis is performed, and the equation governing the distribution of internal configurations is separated and solved. Both the integral and differential forms of the constitutive equation for the solution are obtained; they are expressed in terms of a set of eigenvalues that depend on the kinematic history of the material. The differential constitutive equation is similar to a multimode White‐Metzner equation. Material functions for steady shear, the inception of steady shear, steady uniaxial elongation, and the inception of uniaxial elongation, are calculated by solving a set of moment equations numerically. The results in the limits of very slow shear and very fast elongation agree quantitatively with results that are obtained without the Peterlin approximation.

Non-linear stress relaxation in polymer melts subject to shear or uniaxial elongation

Non-linear stress relaxation in melts of monodisperse polymers subject to shear or uniaxial elongation has been analysed on the basis of a constitutive equation derived previously. The theoretical approach developed describes known and predicts new features of stress relaxation in linear polymers of high molar mass.

Structure development in melt spinning and drawing poly ether ether ketone (peek) fibers.

A study of the development of crystallinity and orientation in the melt spinning and drawing of poly ether ether ketone fibers is presented. Melt spun fibers are characterized by differential scanning calorimetry, birefringence, and wide angle x-ray diffraction. These fibers were subsequently drawn at 160°, 180°, and 230°C. The drawn fibers were characterized by the same techniques as the melt spun fibers. Uniaxial stress-strain behavior, tensile strength, and elongation to break characteristics have been determined and correlated with fiber structure. Particularly important results are that drawdown ratios and spinline stresses can induce significant crystallization in the spinline. Correlations of fiber mechanical properties are developed with spinline stress and birefringence.

Rheological behaviour of non-cured elastomer under uniaxial elongation

Polybutadiene of narrow molecular weight distribution, filled with acetylenne carbon black of high activity, was investigated under conditions of uniaxial elongation. The behaviour of the composite resembled that of plastic dispersed systems. The deformation and ultimate characteristics are closely related to the polymer viscoelasticity and its variation, brought about by thixotropic destruction of the original structure, and to the appearance of flow-induced high elasticity.

Mechanical behaviour of linear low density polyethylene fibres

The mechanical behaviour of linear low density polyethylene fibres has been investigated by means of uniaxial elongation tests and thermomechanical measurements. A mechanical model initially introduced by Grubb for HDPE fibres is proposed to account for the experimental results. This model is built on the basis of a high modulus Takayanagi-type model in which the crystalline continuity is interrupted by adjunction of a small fraction of amorphous phase in series with the mechanically active crystals. This fraction is determined by means of an original theoretical treatment of the stress-strain curves of the fibres. Correlations have been set up between this additional parameter and the mechanical properties of the fibres.

Non-linear rheo-optics of concentrated polymer solutions and melts

A molecular kinetic theory of birefringence in concentrated solutions and melts of linear polymers subject to steady-state or non-steady-state flow has been developed for an arbitrary geometry of flow. A rheo-optical equation of state containing a non-affine convective derivatives has been derived from the non-linear equations which describe the dynamics of macromolecules with relaxing friction. Non-linear optical relaxation of polymers under conditions of uniaxial elongation is discussed.

Nonisothermal flow of polymer melts

The Curtiss-Bird theory for polymer melts is modified to allow the temperature to be a function of time. The resulting constitutive equation involves integrals over the temperature history of the polymer. The predictions of this constitutive equation for the inception of uniaxial elongation with simultaneous cooling at a constant rate are calculated and compared with the experimental data of Matsumoto and Bogue. Qualitative agreement between the theory and the data is obtained when the link tension coefficient in the Curtiss-Bird theory is not equal to zero, but such agreement cannot be obtained when this coefficient is equal to zero. The extension of the theory to include spatially varying temperature is also discussed.

Efficiency of antiozonants under conditions of static load. Dependence on deformation, content of the additive and ozone concentration

The influence of uniaxial elongation (10 to 160%) on the efficiency of various antiozonants was studied in radiation and sulphur-crosslinked synthetic rubber SKI-3 (poly- cis-1,4-isoprene). The activity of the antiozonant was evaluated from the time dependence of stress. The experimental data are explained by assuming that the antiozonant fulfils two simultaneous functions by reacting with ozone and participating in the formation of a protective surface layer.

Strain in self-implanted silicon

Direct measurements of perpendicular strain by channeling presented here show that self-implantations (50 keV at 20 K) at dose levels up to amorphization of silicon induce a uniaxial elongation of the lattice parameter. The maximum strain is proportional to the implanted dose up to the amorphous threshold, and the strain varies with depth as the nuclear energy distribution. The relation of such an elongation to the co-existence of disordered amorphous (clusters) and crystalline phases in the implanted layer is discussed.

Prediction of Elastic Strains of Polymer Melts in Shear and Elongation

Transient and steady‐state recoverable strains in shear and uniaxial elongation were measured with rheometers of different type. Results on melts of linear and branched polyethylenes, polypropylene, polystyrene, polyamide 6, and a PIB solution are reported. To represent the linear viscoelastic behavior, the essential basis of the theoretical treatment, discrete relaxation time spectra have been determined from the dynamic moduli in oscillatory shear. Calculations of the primary normal stress and of the shear and elongational viscosities in the non‐Newtonian range are based on a single integral constitutive equation with strain‐dependent memory function. Recoverable strains observed after unloading the samples from steady‐state flow are calculated by means of a quasilinear treatment of the materials, making use of deformation rate dependent effective relaxation strengths. The agreement of predicted and measured recoverable strains over a very wide range of shear and elongation rates strongly supports this new concept, which does not involve an inversion of the integral constitutive equation. In addition, the applicability of two empirical equations that relate the primary normal stress coefficient and the recoverable strain in steady shear flow to the dynamic moduli are checked on the same materials.

A streamline element scheme for solving viscoelastic flow problems. Part I. Differential constitutive equations

A finite element program for solving viscoelastic flow problems in plane and axisymmetric geometries is described. The program is based on a streamline element scheme (S.E.S.). One of the principal features of the program is that it employs an iterative process to treat elastic stresses as pseudo-body forces; during each iteration it generates updated streamline-based elements and integrates Maxwell-type constitutive equations along the streamlines forming the element boundaries. The performance of this method was satisfactory, considering both accuracy and efficiency. Results of two simple test problems and two complex flow problems are shown. These problems are simple shearing flow, uniaxial and biaxial elongation, extrudate swelling and flow around a sphere in a long cylinder. In the simple test problems the results were very accurate and were compared with exact solutions and inthe more complex flows the results were in close agreement with data from other programs based on different methods. Some limitations and the current state of development of the program are also discussed.

Coil Relaxation in Uniaxially Deformed Polymer Melt

AbstractSANS studies on the relaxation of an amorphous polymer melt is reported. Just after the uniaxial elongation the chains deform affinely. Shortly thereafter the SANS results give evidence of chain contraction. Some randomization is observed long before the reptation time is reached.

Rheo‐optical Fourier‐transform infrared spectroscopy of polymers. VII. Uniaxial deformation of heat‐set poly‐(ethylene terephthalate) film

AbstractPoly(ethylene terephthalate) (PET) film was uniaxially stretched to a draw ratio of 2.5. Two samples were prepared from this oriented film by heat‐setting it at 493 K while free to relax and when held at constant length. The structural changes occurring during uniaxial elongation up to fracture of these two oriented crystalline samples and their stress–strain characteristics were simultaneously monitored by rapid‐scanning Fourier‐transform infrared (FTIR) spectroscopy. In the free‐annealed sample, the orientation of the molecules in the amorphous phase shows a gradual improvement throughout the test, while chain unfolding occurs above 20% strain. This indicates that the predominant mechanism of deformation in this sample could be chain uncoiling in the amorphous phase followed by longitudinal slip processes within the sample. In the taut‐annealed sample, chain unfolding occurs at low strains accompanied by slight improvements in amorphous and crystalline orientation. Thus, in this sample longitudinal slip would appear to be the main deformation mechanism. The results of the FTIR measurements are discussed with reference to the dependence of the deformation mechanisms on the initial structure of the samples.

Harmonic and impulse rheological tests of biomaterials.

Up to now, not so much attention has been paid concerning the dynamic rheological behaviour of soft tissues although non linear viscoelastic effects have often been reported when mechanical properties of biomaterials are concerned. In order to characterize such properties different rheological tests have been proposed, the two principal being the study of the sample stresses responses to applied strains which are either harmonic with time or of step function type. Two different apparatus have been designed in our laboratory which allow specific rheological tests on biological materials under controlled environmental conditions. With one of them, harmonic uniaxial extension tests are performed in a large domain of frequencies (.001 Hz to 100 Hz) and forces (up to 20 daN); with the other, the samples are submitted to relaxation tests in uniaxial elongation up to 5 cm deformation within time duration of the order of 20 ms. The principal characteristics, limitations and performances of such apparatus are presented and few examples of data thus obtained are given. On the basis of quasi linear viscoelasticity models, it can be shown that both two types of tests with their proper limitations are leading to the same rheological parameters.

Rheo-optical Fourier-Transform Infrared Spectroscopy (FTIRS) of polymers—6: Changes of crystal-axes orientation and state of order during uniaxial elongation of high-density polyethylene

The transient structural changes of high-density polyethylene during uniaxial elongation have been studied by simultaneous mechanical and Fourier-transform infrared spectroscopic (FTIRS) measurements at ambient and elevated temperatures. The experimental results of these rheo-optical FTIRS investigations are discussed in terms of the orientational changes of the crystal axes and the crystal-phase transformation of the polymer during the mechanical treatment, and the microstructural consequences are correlated with the macroscopic mechanical properties.

Orientation effects and rheology of short glass fiber-reinforced thermoplastics

The rheology of polyolefines, polyamide 6, and polystyrene-acrylonitrile filled with glass fibers of different concentrations and aspect ratios have been investigated in simple shear flow, capillary rheometry, and uniaxial elongation. A comparison is made with unfilled and glass bead-filled melts. Fiber orientation was investigated by X-ray microradiography. Steady-state viscosities are obtained on fibers aligned parallel to the direction of flow. Entrance pressure losses, the shape of the viscosity function, and the appearance of a yield stress are depending on the fiber aspect ratio. The temperature dependence of the viscosity function is not significantly different from that of the unfilled melt. Transient shear stresses were measured on samples of different initial orientations of the fibers. The change of fiber orientation during shear flow gives rise to a pronounced overshoot of shear stress and normal stress difference. Elastic strains in shear are increased by the fibers but elastic elongational strains are reduced. Mechanisms are proposed to explain the experimental observations.

Extensional flows of oldroyd fluids

The complete equations for a general extensional flow of the eight-constant Oldroyd fluid are presented. The type of flow, described by a single parameter m, is fixed but the rate of strain and the stress components may vary with time. The conditions under which stresses reach steady values in stretching at constant rate of strain are investigated and specific results obtained for uniaxial, equibiaxial and planar elongation. Creep is discussed for a restricted (Maxwell-like) model, and the same critical value of a combination of parameters is obtained. The problem of possible loss of symmetry of the axisymmetric flows under certain conditions is discussed briefly.

Rheo-optical fourier transform IR (FTIR) spectroscopy of polyurethane elastomers

In the preceding papers of this study (SIESLER 1983, 1983a) the results of rheo-optical FTIR investigations at ambient and elevated temperature obtained from a series of model polyester urethanes with varying composition have been discussed in terms of the phase separation and segmental orientation of these polymers. The present work demonstrates the potential of this technique applied to NH-deuterated specimens of these polyester urethanes with reference to a more detailed insight into phase separation and the orientation mechanism of the phase-separated hard segments during uniaxial elongation and recovery.

Principal possibility of strength reinforcement of polypropylene during uniaxial elongation in an oxidizing medium

It was shown that isothermal curves of the durability of oriented films of isotactic PP at 120° and with P O 2=600 torr are extremal in nature. Comparison of the concentration of carbonyl groups in the termination zone of samples with properties of the polymer under stress showed the role of variation of kinetics of oxidizing processes in the existence of non-monotonous dependence of durability on stress. PP is oxidized in the free and stressed state by a heterogeneous mechanism. The local nature of failure under conditions of thermal-oxidative breakdown was established. It was shown that the strength stabilization and strength reinforcement of the polymer are possible, in principle, in the oxidizing medium. A scheme was proposed for the fracture of the polymer under stress under conditions of thermal-oxidative breakdown.

Rheo-optical fourier transform IR (FTIR) spectroscopy of polyurethane elastomers

In a preceding paper of this study (SIESLER 1983) the application of rheo-optical FTIR spectroscopy to a series of model polyester urethanes at ambient temperature has been discussed with reference to the phase separation and segmental orientation of these polymers during uniaxial elongation and recovery. Here, the results of variable-temperature FTIR measurements and rheo-optical FTIR investigations at elevated temperature are presented and interpreted in terms of the temperature dependence of hydrogen bonding and structural organization of the hard segments.