Nonlinear Viscoelastic Polymer Research Articles

Towards a universal shear correction factor in filament stretching rheometry

Filament stretching rheometry is a prominent experimental method to determine rheological properties in extensional flow whereby the separating plates determine the extension rate. In literature, several correction factors that can compensate for the errors introduced by the shear contribution near the plates have been introduced and validated in the linear viscoelastic regime. In this work, a systematic analysis is conducted to determine if a material-independent correction factor can be found for non-linear viscoelastic polymers. To this end, a finite element model is presented to describe the flow and resulting stresses in the filament stretching rheometer. The model incorporates non-linear viscoelasticity and a radius-based controller for the plate speed is added to mimic the typical extensional flow in filament stretching rheometry. The model is validated by comparing force simulations with analytical solutions. The effects of the end-plates on the extensional flow and resulting force measurements are investigated, and a modification of the shear correction factor is proposed for the non-linear viscoelastic flow regime. This shows good agreement with simulations performed at multiple initial aspect ratios and strain rates and is shown to be valid for a range of polymers with non-linear rheological behaviour.

A comparison between $K$ and $G$ approaches for a viscoelastic material: the case of environmental stress cracking of HDPE

According to linear elastic fracture mechanics the stress intensity factor and the energy release rate are two fracture parameters linked by the elastic modulus and Poisson’s ratio of the considered material. This concept has been extended to the analysis of linear viscoelastic materials, by introducing time-dependent quantities; it is also used for nonlinear viscoelastic polymers, even if its accuracy in this case is still an open question. In this work the slow crack growth and the environmental stress cracking resistance of two high-density polyethylene grades were investigated, differing for their molecular weight distribution and fracture resistance. The description of the fracture behavior of the two materials provided by the stress intensity factor or the energy release rate turned out to be equivalent, despite the nonlinear mechanical behavior exhibited by the two polymers. Moreover, a time-dependent effective modulus, related to the two fracture parameters, was evaluated: its value was in good agreement with the modulus experimentally determined from tensile tests. A constant relevant effective strain was found despite the different testing conditions (i.e. applied mechanical loading, temperature and presence of an active environment), its value being equal for the two considered polyethylenes.

Development of experimental methods for impact testing by combining Hopkinson pressure bar with other techniques

The split Hopkinson pressure bar (SHPB) technique and the wave propagation inverse analysis (WPIA) technique are both extensively used to experimentally investigate the impact behavior of materials, although neither of them alone provides a fully satisfactory analysis. In the present paper, attention is given to new experimental techniques by incorporating a damage-modified constitutive model into the SHPB technique and combining the Hopkinson pressure bar (HPB) technique with WPIA. First, to distinguish the response due to dynamic constitutive behavior and the response due to dynamic damage evolution, the SHPB method incorporating a damage-modified constitutive model is developed, including an explicit damage-modified Zhu-Wang-Tang model and an implicit damage-modified constitutive model. Second, when the SHPB results become invalid, a method of combining new Lagrange inverse analyses with the HPB technique is developed, including cases of the HPB arranged in front of a long specimen and behind the specimen. As examples of these new methods, typical results are given for nonlinear viscoelastic polymers and concretes considering damage evolution, a super-elastic Ti-Ni alloy with phase transformation and an aluminum foam with shock waves propagating within it.

Analysis of reversible and irreversible strains in the creep of a nonlinear viscoelastic polymer

The results of an experimental investigation and analytical description of creep of a nonlinear viscoelasticplastic material (a Upilex-S polyimide film) in tension are presented. The elastic modulus, yield stress, and ultimate strength were found from quasi-static tests with a constant deformation rate. The total strain of the material was assumed to be the sum of elastic, viscoelastic, and irreversible strains. The reversible elastic and viscoelastic and the irreversible deformation of the material were investigated in experiments on creep with the subsequent recovery of deformations (creep recovery). The nonlinearity of its viscoelastic behavior was taken into account using the principle of stress-time superposition. The results obtained allow one to describe the creep behavior of a material at various stages of loading and unloading.

Effect of Stress-Induced Damage Evolution on Long-Term Creep Behavior of Nonlinear Viscoelastic Polymer

The mechanical behaviors were investigated by nonlinear creep tests of poly(methyl methacrylate) under different temperatures. The test duration was 4000 seconds. The corresponding temperature shift factors, stress shift factors and temperature-stress shift factors were obtained according to time-temperature superposition principle, the time-stress superposition principle and the time-temperature-stress superposition principle (TTSSP). The master creep compliance curve up to about 1-month at a reference temperature 22 degrees centigrade and a reference stress 14 MPa was constructed, and the effect of stress-induced damage evolution on the long-term creep behavior of polymeric material was accounted. It was shown that TTSSP provides an effective accelerated test technique in the laboratory, the results obtained from a short-term creep test of poly(methyl methacrylate) specimen at high temperature and stress level can be used to construct the master creep compliance curve for prediction of the long-term mechanical properties at relatively lower temperature and stress level, and the master creep compliance curve with damage considered can be applied to accurately characterize the long-term creep behavior of nonlinear viscoelastic polymer.

Solution strategies for FEM analysis with nonlinear viscoelastic polymers

The Schapery model is a very common model for nonlinear viscoelastic behaviour of polymers. Therefore this model has been implemented with a user subroutine into the FEM package MARC. Since explicit integration is relatively fast but is often accompanied by numerical instabilities and implicit integration is relatively slow but numerically stable, combined strategies have been programmed. Results show that the viscoelastic response of complex products can be calculated without numerical instabilities and with short calculation times. Full viscoelastic calculations and calculations using creep isochrones on dead weight loading of an HDPE bottle crate only differ from the onset of creep buckling.

A discrete complex compliance spectra model of the nonlinear viscoelastic creep and recovery of microcellular polymers

The present work reports a discrete stress-dependent, complex compliance spectra method that may be used to predict the mechanical response of nonlinear viscoelastic polymers during creep and recovery processes. The method is based on the observation that the real and imaginary parts of a discrete complex compliance frequency spectra obtained from creep and recovery measurements are smooth, easily fit functions of stress. The new method is applied to a set of microcellular polycarbonate materials with differing relative density. The nonlinear viscoelastic characteristics of a microcellular polycarbonate material system are very sensitive to relative density and therefore, this material system is a particularly difficult modeling challenge. However, the present model was able to exhibit excellent quantitative agreement with the basis creep and recovery measurements at all experimental stress levels for each of the experimental relative density material types. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 691–697, 2000

Damage theory for polymeric material

In this paper, the effects of extenal environment such as corrosion medium, radiation and non-consistent materials on deformation of polymers are discussed. Damage constitutive equations for non-linear elastic and non-linear viscoelastic polymers and a variational principle for viscoelastic damage are also given.

Stress-dependent dynamic compliance spectra approach to the nonlinear viscoelastic response of polymers

The present work reports a discrete, stress-dependent dynamic compliance spectra method which may be used to predict the mechanical response of nonlinear viscoelastic polymers during strain-defined processes. The method is based on the observation that the real and complex parts of the discrete dynamic compliance frequency components obtained from creep measurements are smooth, easily fit functions of stress. Comparisons between experimental measurements and model calculations show that the model exhibits excellent quantitative agreement with the basis creep measurements at all experimental stress levels. The model exhibits good quantitative agreement with stress relaxation measurements at moderate levels of applied strain. However, the model underestimates the experimental stress relaxation at an applied strain of 3.26%. The stress relaxation error appears to be a real material effect resulting from the different strain character of creep and stress relaxation tests. The model provides a good quantitative agreement with experimental constant strain rate measurements up to approximately 4% strain, after which the model underestimates the experimental flow stress. This effect is explained by the time dependence of the stress-activated configurational changes necessary for large strains in glassy polymers. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2301–2309, 1998

Flow-rate characteristics for the pulsating flow of a nonlinear viscoelastic polymer solution in a pipe

The mean flow rate in a channel remains constant for a given mean pressure gradient for pulsating and stationary flows of a Newtonian liquid. Theory and measurements on nonlinear viscous [1-4] and nonlinear viscoelastic [5-13] liquids in the 1970s and 1980s showed that pressure-gradient pulsations can increase the flow rate, and if the increase is fairly large, flow pulsation can be a way of raising the throughput. However, this is attained at the expense of increasing the power consumed in pumping the liquid.

The dynamic performance of the Weissenberg Rheogoniometer

The dynamic performance of a standard Model R18 Weissenberg Rheogoniometer has been studied in detail. The Rheogoniometer was carefully calibrated and used to measure accurately the rheological behaviour of a highly nonlinear viscoelastic polymer solution (1% polyacrylamide in 50% glycerol/water).

An Experimental Study of a Nonlinear Material with Memory

The applicability of a functional polynomial of third degree for the constitutive equation of a nonlinear viscoelastic polymer has been investigated. A method for the determination of the kernel functions appearing in the one-dimensional creep formulation has been discussed. Creep measurements of tension and compression in low density polyethylene under single step, two step, and three step loading histories are described. The analysis of this data has provided a basis for determination of the creep kernel functions. For the loading range used in the test, the Volterra-Fréchet multiple integral expansion of the constitutive functional of low density polyethylene has been found to be adequately represented by the three-term integral representation. A number of cases of general load histories was investigated. A close comparison between the experimental response to these loading histories and the response predicted by the three-term integral representation was obtained.