Abstract
In this work, a conceptual framework is suggested for analyzing thermorheologically simple and complex behavior by using just one approach. Therefore, the linear relation between master time and real time which is required in terms of the time-temperature superposition principle was enhanced to a nonlinear equivalent relation. Furthermore, we evaluate whether there is any relation among well-known existing time-temperature equivalent formulations which makes it possible to generalize different existing formulations. For this purpose, as an example, the power law formulation was used for the definition of the master time. The method introduced here also contributes a further framework for a unification of established time-temperature equivalent formulations, for example the time-temperature superposition principle and time-temperature parameter models. Results show, with additional normalization conditions, most of the developed time-temperature parameter models can be treated as special cases of the new formulation. In the aspect of the arrow of time, the new defined master time is a bended arrow of time, which can help to understand the corresponding physical meaning of the suggested method.
Highlights
Introduction of a Power Law TimeTemperature EquivalentFormulation for the Description of Thermorheologically Simple and Complex BehaviorLinan Qiao *, Sven Nagelschmidt *, Uwe Herbrich and Christian KellerDivision 4—Safety of Storage Containers, Department 3—Containment Systems for Dangerous Goods, Citation: Qiao, L.; Nagelschmidt, S.; Abstract: In this work, a conceptual framework is suggested for analyzing thermorheologically simple and complex behavior by using just one approach
In many physical and engineering applications the fundamental need exists in terms of extending the experimental region—e.g., prediction of long-time properties from tests conducted in a shorter time range
Regarding the effect of temperature, for nonmetallic materials with viscoelastic behavior, the time-temperature dependence is often described using the time-temperature superposition principle (TTS), which has been developed since the 1950s, see F ERRY [2], S CHWARZL and S TAVERMAN [3] and F INDLEY and L AI [4]
Summary
In many physical and engineering applications the fundamental need exists in terms of extending the experimental region—e.g., prediction of long-time properties from tests conducted in a shorter time range. Regarding the effect of temperature, for nonmetallic materials with viscoelastic behavior (for example for polymers and elastomers), the time-temperature dependence is often described using the time-temperature superposition principle (TTS), which has been developed since the 1950s, see F ERRY [2], S CHWARZL and S TAVERMAN [3] and F INDLEY and L AI [4]. Under isothermal conditions, a change between different but constant temperatures is equivalent to a shift in the logarithmic time scale. For thermorheologically complex behavior, under isothermal conditions, a change between different but constant temperatures is equivalent to a stretch in the logarithmic time scale, see for example the works of F ESKO and T SCHOEGL [16] and. In this work it is shown that, for the complex behavior, a change between different but constant temperatures is equivalent to a shift and a stretch in the logarithmic time scale
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