Predicting Deformation and Relaxation Processes in Uniaxially Oriented Polymers

Abstract

A physical theory of the structure of uniaxially oriented polymers is used to propose a new mechanical model that makes it possible to predict deformation processes in polymers. Polycaproamide-film fibers are used as an example to illustrate the use of the model to predict deformation and relaxation in polymers. Making optimum use of both new and traditional polymers in different sectors of industry would be impossible without proper study of their viscoelastic properties. Such studies can be performed by mathematically modeling the deformation processes which take place in these materials. In practice, an attempt is made to quantitatively predict the behavior of polymers by using various methods that involve mathematical modeling and numerical projection [1-5]. However, as is known, these methods are valid for a relatively narrow range of mechanical loads, strains, and temperatures and cannot predict certain features of the materials’ behavior. In addition, such methods do not embrace or explain all of the processes that take place in synthetic fibers and filaments because the physical features of polymers are not accounted for in the integral equations of viscoelasticity [1-12]. Thus, in this article we propose to model deformation and relaxation processes by using a nonlinear mechanical model that includes physical properties. This will make it possible to determine the mechanical characteristics of polymeric materials under conditions that correspond to different types of loading, which in turn will allow the materials’ properties to be predicted within a wide range of loads and temperatures. The supermolecular structure of oriented amorphous-crystalline polymers is variegated and complex. Thus, the polymers can be in different quasi-equilibrium states when loaded. The viscoelastic component of deformation is a subject worthy of special attention when studying the deformation of materials of the given class. In accordance with modern physics, materials may undergo viscoelastic deformation due to the rearrangement of different stable structures (clusters) which are in different states separated by energy barriers. These clusters or active conformation elements (ACEs) [13] - the nature of which is not germane to mechanical descriptions - can be in one of two stable states. The stable state in which the linear dimension is minimal - state 1 - will be referred to as being conditionally convolute and will be represented as . We will call the second stable state - state 2 - conditionally involute and will represent it as . For example, an elastic spring can either be convolute or involute. On the one hand, this element is elastic. On the other hand, it is also nonlinear. Thus, instead of using classical mechanical models in the form of Hookean springs, dampers, and combinations thereof, i.e. classical linear Maxwell elements, Kelvin-Voigt elements, etc., we are proposing to use a nonlinear model (elastic spring) which is based on energy barriers. These barriers will be represented in the form of the energy diagram shown in Fig. 1. In accordance with the proposed physical and mechanical model, an unloaded cluster can be in one of two stable states - state 1 or state 2. These states are separated by an energy gap of the width U and a barrier of the height H. A deformation