Nonlinear rheological models and their application to describe the mechanical behavior of highly oriented polymer materials

The nonlinear viscoelasticity of uniaxial oriented polymer materials is considered. To explain the deformation mechanisms of oriented polymers and the possibility of predicting their mechanical behavior in various operating modes, new nonlinear rheological models have been proposed. The application of the simplest rheological model of a real viscoelastic solid to the description and explanation of the recovery process in polymer materials is studied. From the standpoint of rheology, a model of an ideal viscoelastic solid is introduced. Using the balance equation for the number of transitions through energy barriers, a method for calculating the new nonlinear rheological model has been proposed. To eliminate the shortcomings of the ideal viscoelastic solid model associated with the impossibility of predicting creep and stress relaxation modes for long times, a generalized rheological model of a real viscoelastic solid was obtained. In the corrected model, the simplest elements are connected in parallel, which means the presence of not one, but several energy barriers in the materials, the transmission through which have their own relaxation times. To describe the recovery processes in polymer materials, the model of an ideal viscoelastic solid is supplemented by a parallel connected elastic spring. An additional Hooke spring replaces the interfibrillar interaction between the individual elements of the structure and is responsible for possible obstacles during jump-like transitions through the energy barrier. Using the method of rheological models and describing interfibrillar bonds within the framework of the theory of elasticity, a constitutive equation was obtained for the case of recovery processes. Based on the constitutive equation of viscoelasticity for uniaxial oriented polymer materials, a new nonlinear highly elastic element is introduced, which replaces the Maxwell's element in the theory of linear viscoelasticity. A new rheological model of parallel connection of elastic elements is shown. An explanation of the retardation of the recovery process in polymers is given. The simplest rheological model of a real viscoelastic solid is proposed, in which an elastic spring is responsible for interfibrillar bonds. A constitutive equation is obtained that describes the recovery process in polymers. This equation can be integrated by quadratures and gives a solution that is an analogue of the Newton-Leibniz formula for the proposed model. It is shown that the deformation recovery process in polymer does not depend on the level of initial deformation and the loading method. The obtained result is confirmed by experimental data for polyamide and polyethylene film yarns. When specifying a certain initial level of deformation, generalized recovery curves of these materials are obtained. The proposed simplest rheological model of a real viscoelastic solid makes it possible to predict the reducing properties of polymer materials. And also makes it possible to determine the height of the energy barrier and the magnitude of the elastic modulus in the model. Based on the new rheological models, it is planned in the future to consider the issues of modeling and forecasting different modes of deformation.