Study On Fractional Maxwell Model Of Polymer Stress Relaxation Process

Polymers are typical viscoelastic materials. The study of the viscoelasticity is important to understand their structure, motion and phase transition as well as the relation between structure and properties. The introduction of fractional calculus provided new tool and methods for studying viscoelasticity, corresponding study is quite lack. In this paper, The stress relaxation procession of PTFE is studied by using fractional Maxwell model.The asymptotic solution of fractional Maxwell model are assumed to be the starting point to decide the parameters (β,α,τ,Ε), but the relaxation timeτfitted by experimental data is in contradiction with the conditions of the asymptotic solutions. Relaxation timer fitted may be larger than the testing time, the result doesn't satisfy the condition of t >>τ.After discussing the determination of the parameters of fractional Maxwell model, the results show that the parameters of fractional Maxwell model exist certain adjusting freedom. The relaxation exponentβandα(order of the fractional derivatives) can be decided according to the experimental data of the initial and terminal time, respectively. Different the relaxation exponent is given out by choosing different experimental data. To certain extent, the relaxation time is not sensitive to the fitting results.Because the relaxation time and modulus are not independent parameters, relaxation timer can be chosen properly in order to avoid contradiction with asymptotic conditions. The modulusΕcan be determined by using the experimental data of the initial time. The fractional Maxwell model can describe the viscoelastic stress relaxation by optimizing the parameters properly very well.