Constitutive equations are derived for the non-isothermal viscoelastic behavior of polymers at finite strains. The model is based on the concept of transient reversible networks with temperature-dependent rates of creation and breakage for active chains. It is demonstrated that the constitutive relations adequately predict the response of polyisobutylene in isothermal and non-isothermal static tests.

A constitutive model in finite thermoviscoelasticity based on the concept of transient networks

The viscoelastic behavior of polymeric systems based upon the Leonov model has been examined for (i) the stress growth at constant strain rate, (ii) the stress growth at constant speed and (iii) the elastic recovery in elongational flow. The model parameters have been determined from the available rheological data obtained either in steady shear flow (shear viscosity and first normal-stress difference as a function of shear rate) or oscillatory flow (storage and loss moduli as a function of frequency in the linear region) or from extensional flow at very small strain rates (time-dependent elongation viscosity in the linear viscoelastic limit). In addition, the effect of the parameter characterizing the strain-hardening of the material during elongation has also been studied. The estimation of this parameter has been based upon the structural characteristics of the polymer chain which include the critical molecular weight and molecular weight of an independent segment. Five different polymer melts have been considered with varying number of modes (maximum four modes). Resulting predictions are in fair agreement with corresponding experimental data in the literature.

Elongational flow behavior of polymeric fluids according to the Leonov model

A model of non-linear viscoelasticity with relaxation times dependent upon free volume is here proposed. The free volume is related to the isotropic part of the stress tensor by means of a simple differential equation. The model predictions are compared with a large amount of experimental results taken on polymeric melts or concentrated solutions and reported in the literature. The single parameter of the model is determined, within each set of data, by fitting of the viscosity curve. A satisfactory agreement is obtained with data taken under both elongation and shear for which also the relaxation behavior after single and double strain steps is considered.

Testing of a constitutive equation with free volume dependent relaxation spectrum

Many theories about the rheological behaviour of melts and concentrated solutions of high molecular weight polymers are based upon the transientnetwork model, originally developed by Green and Tobolsky [l], Lodge [2], and Yamamoto [ 31. Among these theories a model proposed by Marrucci and coworkers [4,5] turns out to be rather successful [6-111. The basic equations of this model, as formulated in ref. [ 51, are:

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Derivation of the Marrucci model from transient-network theory

A non-linear viscoelastic model has been used to interpret transient flow birefringence in changing shear flow for a polymer melt. It is shown how the new model is consistent with the basic hypothesis of the linear stress-optical law. Stress growth in shear flow and relaxation after different amounts of shearing are compared with the predictions of the non-linear model. A good agreement between experimental data and theoretical predictions is found.

Transient birefringence of polymer melts in intermittent shear flow: Model analysis of the non-linear viscoelastic behaviour

For a commercial polyisobutylene, at room temperature, stress relaxation after a sudden imposition of a shear or elongational strain has been performed in the limit of linear viscoelasticity. Transient shear and elongational stresses have been determined in the non‐linear region by using a Universal Instron Testing Machine. While for shear flow steady‐state conditions were reached in some cases, the elongational results are only transient because the experimental procedure gives a rate of stretching which decreases in time. Some steady shear results have been obtained at higher temperatures with a capillary viscometer. The results have been interpreted by means of a one‐parameter model which attributes the non‐linearities arising from the change in the spectrum of relaxation times to modification of the entangled network. The Bogue‐White model has been also considered for comparison.

Bruno De Cindio

Papers

Transient Shear and Elongational Data for Polyisobutylene Melts