A viscoelastic model for a biomedical ultra-high molecular weight polyethylene using the time-temperature superposition principle

Abstract

The objective of this study was to obtain a mathematical model of the viscoelastic functions of a medical grade ultra high molecular weight polyethylene (UHMWPE). This model ascertained the applicability of the time-temperature superposition principle (TTSP) to the dynamic viscoelastic properties obtained from dynamic mechanical thermal analysis (DMTA). It was verified that both horizontal and vertical shifts were necessary to superimpose the dynamic modulus/frequency curves. A new methodology is proposed and assessed to determine the horizontal and vertical shift factors for the time-temperature superposition. The present approach is based on a viscoelastic model, a fractional Maxwell model which, associated with the proposed methodology, leads to an easy and effective way to calculate these shift factors. The main advantage relies in the fact that the factors are obtained via a viscoelastic model, not empirically, which provides physical significance to both shift factors.