Generic relaxation spectra of solid polymers. I. Development of spectral distribution model and its application to stress relaxation of polypropylene

Abstract

An important aspect of designing polymeric articles for engineering applications and predicting their properties over their lifetime is the computation of their time-dependent viscoelastic behavior. A simplified numerical computational technique based on a Gaussian spectral distribution model was developed to describe this behavior over a wide range of time and temperature. The model was used to describe the stress-relaxation behavior of isotactic polypropylene (iPP) over a wide range of strain, time, and temperature. It appears that a spectrum with two components (one distribution for the amorphous zone and the other for the crystalline zone ) is sufficient to describe the viscoelastic behavior of iPP. The parameters specifying the distributions (mean relaxation time, standard deviation, and relaxation strength) may be obtained by nonlinear regression analysis and the temperature dependence of the distributions may be evaluated experimentally. An excellent fit between experimental data and the mathematical model is observed. The method may be applied generally for any linear viscoelastic property (e.g., static and dynamic relaxation and creep in tensile or shear) and for any polymer.