Thermorheological response

We have characterized these polymers with respect to their thermorheological response in tension, in the linear viscoelastic regime. Then their performance in a shape-memory sequence was computed from the theory of temperature-dependent linear viscoelasticity, allowing comparisons to be made between them [63]. 

Yes, it sometimes happens to us. The thermorheological response of each polymer in Table 6.1 was characterized by us in the Oxford laboratory. Fortunately after doing this study no equipment was ruined . 

For linear thermorheologically simple materials a single temperature-dependent shift factor, aT T), can be used to predict the transient thermal response [20]. The mechanical response is history dependent and involves the use of reduced times, ( ) and (t), which can be found from the shift factor as... 

However, for thermorheologically simple materials, that is, for those materials for which the time-temperature superposition principle holds, the mechanical properties data can be shifted parallel to the time or frequency axis. This fact suggests an additional hypothesis that can be very useful in solving some specific thermoviscoelastic problems. According to this hypothesis, the net effect of temperature in the response must be equivalent to a variation in the rates of creep or relaxation of the material. Thus for T > Tq the process occurs at a higher rate than at Tq. 

The Eqs. (2.1a) and (2.1b) apply thus actually to a rate scale and, in the frequait case of cyclic exposure, to a frequency scale co. If a thermorheologically simple system is considei ed the fr juency scale can be replaced by a temperature sale 1/T. Steps A that satisfy Eqs. (2.1a) and (2.1b) appear then in the response-functions for systmis of this nature that are measured as a function of temperatiue at pven, fixed paturbation rate. The temperature at whidi the steps occur depends, however, on the rate of external i rturbution. The temperature-dependent thawing of conformational isomers in thermorheologically complicated systems can be similariy observed in the response-functions, but the steps no longer satisfy Eqs. (2.1 a) and (2.1 b). These two equations lose, in addition, their validity with rrapect to the rate scale if, as is the case of polymers, several mutually independent, internal variables are required in order to uniquely define the conformational isomerism. In this case. Eqs. (2.1a) and (2.1b) become inequalities... 

T > To are shifted to longer times, and measurements for T < Tq aie shifted to shorter times. A well-defined reduced curve means the viscoelastic response is thermorheologically simple (Schwarzl and Staverman, 1952). It represents log Jp(t) at To over an extended time range. The time scale shift factors aj that were used in the reduction of the creep compliance curves to obtain the reduced curve constitute the temperature dependence, ar is fitted to an analytical form, which is often chosen to be the Williams-Landel-Ferry (WLF) equation (Ferry, 1980),... 

The most common means to extend the frequency scale is to invoke time-temperature superpositioning (Ferry, 1980). If all motions of a polymer contributing to a particular viscoelastic response are affected the same by temperature, then changes in temperature only alter the overall time scale such a material is thermorheologically simple. Thermorheological simplicity means conformance to the time-temperature superposition principle, whereby lower and higher strain rate data can be obtained from measurements at higher and lower temperatures, respectively. 

Often the assumption is made that a material is thermorheologically simple, meaning all mechanisms contributing to the response have the same temperature dependence. In this situation, temperature only changes the relrixation time, not the shape of the relaxation function. Accordingly, the principle of time-temperature superpositioning can be applied. The measured quantities are shifted... 

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