Relaxation modulus in PMMA and PTFE fitting by fractional Maxwell model

A study of stress relaxation in samples of polymers PMMA and PTFE (Methylmethacrylate and Polytetrafluorethylene) has been carried out, pointing out that there exists not only one time of relaxation as the classic Maxwell model predicts but two distributions of relaxation time. These can be approached by using a fractional Maxwell's model in which the stress appears as two non-integer order derivatives of the strain. For short times the pattern has an order of the smaller derivative. This fact indicates a more elastic behavior, closer to the Hooke's model. For longer times the order is bigger, showing a behaviour that rather approaches the Newtonian pattern. The two polymers studied in this article, PMMA and PTFE, present a clearly viscoelastic behavior where the deformation of the sample is not instantaneous when applying a load. As a consequence, after the initial deformation process, if we keep the total strain constant, the plastic deformation of the sample increases and the value of their elastic deformation decreases and therefore the stress also decreases — the phenomenon of stress relaxation.