A Note on Automated Time-Temperature and Time-Pressure Shifting

Time-dependent material functions of engineering plastics within the exploitation range of temperatures extend over several decades of time. For this reason material characterization is carried out at different temperatures and/or pressures within a certain experimental window, which for practical reasons extends typically over four decades of time. For example, when relaxation experiments in shear, are performed at different constant temperatures and/or pressures, a set of segments is obtained. Using the time-temperature and/or time-pressure superposition principle, these segments can be shifted along the logarithmic time-scale to obtain a master curve at a selected reference conditions. This shifting is commonly performed manually (“by hand”), and requires some experience. Unfortunately, manual shifting is not based on a commonly agreed mathematical procedure which would, for a given set of experimental data, yield always exactly the same master curve, independently of a person who executes the shifting process. Thus, starting from the same set of experimental data two different researchers could, and very likely will, construct two different master curves. In this paper we propose mathematical methodology which completely removes ambiguity related to the manual shifting procedures. Paper presents the derivation of the shifting algorithm and its validation using several simulated- and real- experimental data.