Method of modeling viscoelastic properties of oriented polymer materials using multi-barrier theory

Abstract

The results of modeling deformation processes of uniaxially oriented polymer materials are presented. The discription of two-barrier model is given, according to which polymer macromolecules can be in three stable states. The constitutive equation of the oriented polymer material is obtained. The solution of this equation is shown for the case of a deformation mode with a constant load level. Based on the energy barriers theory, as a result of the transformation of the balance equations of the occupation numbers of steady states, the constitutive equation of the polymer material is obtained. This equation is a second-order differential equation in time. For the deformation process with a constant stress level, the constitutive equation takes the form of a linear inhomogeneous second-order differential equation with constant coefficients. A general solution of this equation is given in explicit form. The solution of the Cauchy problem gives a general solution of the constitutive equation for the considered case. The analysis and transformation of the general solution leads to dependencies that determine the deformation of the oriented polymer material for creep and recovery processes. The use of a two-barrier model with three steady states of macromolecules made it possible to obtain a constitutive equation which is a second-order differential equation in time. As an example, the application of the constitutive equation to the deformation mode with a constant stress level is considered and its general solution is obtained. A universal function has been introduced with the help of which it is possible to calculate the deformation of a polymer material in the creep and recovery mode. By combining the theoretical curve with the experimental creep curves of polyethylene terephthalate filaments, the applicability of the considered modeling method is shown. The obtained constitutive equation makes it possible to describe and predict both static and dynamic deformation modes. The applicability of the obtained model to the static mode of deformation is shown. It should be noted that the solution of the obtained constitutive equation in certain cases leads to an oscillatory relaxation mode.

Keywords

• energy barrier theory
• two-barrier model
• energy diagram
• highly elastic deformation
• constitutive equation
• oriented polymers