V.V. Afansiev, M.P. Danilaev, Yu.E. Polsky, A.A. Tsentsevitsky
Wide application of polymeric materials is required the development of methods for producing these materials with pre-defined and reproducible properties. As the specifics of the deformation properties of polymeric materials due to feature molecular and supramolecular structure of these materials, it is a very urgent task of revealing the relationship between the strain tensor and the stress tensor, time, temperature, and the parameters describing the structure of the polymer material in the process of its formation.
One promising theoretical method of study of the properties of polymeric materials is based on the use of differential equations with fractional derivatives. Promising approximate method for studying the processes, described by differential equations with fractional derivatives, is based on the use of non-harmonic spectrum analysis with the definition of the parameters of fractional power spectra of the investigated processes.
Purpose of article is estimate fractional exponents deformation of polymers with non-harmonic spectrum analysis.
Study fractional power spectrum generated by time-dependent changes in the load voltage and emerging strains of the polymer is appropriate for estimate the fractional-power integrated indicator.
Research of the characteristics non-harmonic spectra processes generated by emerging strains of the polymer, conducted for the Kelvin-Fogt – a simple rheological model that takes into account the presence of the elastic polymer material due to the deployment of the polymer macromolecules.
The modeling found that:
1) The parameters of fractional-power-law spectrum are non-stationary over time, which indicates the need to use time-dependent derivatives of fractional order to describe the dynamics of deformation of polymers.
2) The mutual dependence of the parameters of fractional-power-law spectrum unambiguously characterizes the ratio of the viscosity or elasticity in the polymer material.