Using fractional derivatives for improved viscoelastic modeling of textile composites. Part II: Fabric under different temperatures

Abstract

An improved modelling of the viscoelastic behavior of fabric composites at different temperatures is presented by a new means of fractional calculus. To this end, a four-parameter fractional derivative Zener model is first used to describe the dynamic behavior of the fabric, where the constitutive relation’s response to a unit step of strain (for determination of the time dependent stress relaxation modulus) can be readily found in the literature. This response function is then fitted to the experimental data of samples of a typical prepreg composite made of E-glass fibers comingled with polypropylene fibers, both at the dry and consolidated conditions. It is shown that the Zener model can better capture the experimental data when compared to the conventional approaches such as integer order modelling and Prony series. The results, particularly, showed that the viscoelastic behavior of the material at lower temperature regimes is far more accurate using the fractional derivatives approach. Finally, the variation of storage and loss moduli of the dry fabric with external cyclic loading were scrutinized, to determine the rubbery and glassy regions of the frequency response.