Sensitivity analysis of an algorithm for applying the time‐temperature superposition principle

Abstract

The measurements of the dynamic complex modulus of viscoelastic materials on any apparatus is confined to a limited frequency and temperature range. It has been observed that an increase in temperature produces an identical effect in a viscoelastic material as a decrease in frequency and vice versa. Empirically, then, there is a correspondence between temperature and frequency. The time‐temperature superposition principle with reduced variables provides a method of extending the effective frequency range of the dynamic modulus and loss factor. This technique involves measuring the complex modulus over a limited frequency range and a variety of temperatures. The data at different temperatures are then plotted versus frequency and shifted along the frequency axis until a smooth curve results over a broad frequency range at some fixed temperature. This paper reviews the time‐temperature superposition principle, and presents an implementation algorithm and an ad hoc error analysis.