On the influence of the initial ramp for a correct definition of the parameters of fractional viscoelastic materials

Abstract

Creep and/or Relaxation tests on viscoelastic materials show a power-law trend. Based upon Boltzmann superposition principle the constitutive law with a power-law kernel is ruled by the Caputo’s fractional derivative. Fractional constitutive law posses a long memory and then the parameters obtained by best fitting procedures on experimental data are strongly influenced by the prestress on the specimen. As in fact during the relaxation test the imposed history of deformation is not instantaneously applied, since a unit step function may not be realized by the test machine. Usually an initial ramp is present in the deformation history and the time at which the deformation attains the maximum value is fixed by the operator. Even though the precharge time is small in comparison with the total duration of the observation time, the parameters obtained by the best fitting procedure leads to relevant error especially for small observation time. In the paper the problem is overcome by considering the time load history for both theoretical and experimental point of view. In order to demonstrate experimentally that the initial ramp of deformation strongly influences the stress history during the relaxation test, different tests were performed on samples of a commercial epoxy resin (SP106) at two different rates of deformation (i.e. 0.2 mm/mm and 2 mm/min). Moreover the corrected approach for the best fitting of the data permits to characterize the viscoelastic materials, in term of fractional viscoelastic parameters, in a short time, and this allows to reduce the long duration of the experimental tests.