Some new operational modes and parameters of stress relaxation for the viscoelastic characterization of solid polymers. I. The “virtual modulus” mode

Abstract

AbstractA new operational (functional) parameter, the so‐called virtual modulus, Ē(t), is introduced. By this, an attempt was made for the approximation of the function of the real modulus E(t), which, as known, is valid only for instantaneous loading, namely, for zero loading times. Thus, through a simple theoretical modeling and an algorithmic approach, the determination of E(t), from Ē(t), sets sail, at the end, to the solution of a Volterra integral equation of the second type, which, in turn, sets sail to the solution of a differential equation. By the aid of numerical integration and also of some experimental evidence, it seems that this solution is valid only for loading times approximately above 0.2 s, thus obtaining, in fact, a “pseudomodulus” of relaxation. To assess the validity of this pseudomodulus, the well‐known Kohlrausch–Williams–Watt (KWW) and the power‐law models were used as some crude “criteria.” By means of best fit, it appeared, at the first instance, that the so‐calculated pseudomodulus better obeys the power‐law model than it does the KWW model. This is a certain contradiction with the so‐called apparent modulus, which was obtained from experiment with a finite loading time superior to 1 s. Two other criteria that were used have shown a satisfactory proof of the validity of this modeling. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 121–137, 2003