分数Maxwell模型应用于PTFE松弛模量的研究

Relaxation Modulus of PTFE Studied by Fractional Maxwell Model

用分数M axwell模型对聚合物PTFE(Polytetrafluoethylene)的应力松弛过程进行了研究.分数M axwell模型的渐近行为是确定其参数的基本依据,但根据实验数据确定的松弛时间与渐近解成立的条件并不自恰.通过适当选定松弛时间,利用起始时段的实验数据确定初始松弛指数和松弛模量,并适当优化末端松弛指数,分数M axwell模型可以对粘弹性应力松弛过程给出非常好的描述.

The stress relaxation modulus of PTFE （polytetrafluorethylene） was studied by using fractional Maxwell model. The asymptotic solutions of fractional Maxwell model were assumed to be the starting point to decide the parameters（β, α, T E） , but the relaxation time T fitted by experimental data is in contradiction with the conditions of the asymptotic solutions. The principles for choosing the parameters were discussed. The relaxation exponent β and α （ the order of the fractional derivatives） can be decided according to the relaxation behavior of the initial and terminal time respectively. Choosing the relaxation time T properly, the modulus E can be determined by using the experimental data of the initial time. By optimizing the parameters T and α, the fractional Maxwell model can describe viscoelastic relaxation process very well. The relative error of the relaxation modulus of PTFE fitted by fractional Maxwell model is 0.64%.