Tensile force-temperature relationship

The value fe can be expressed in terms of the tensile force-temperature relationship by the equation... 

This system is expanded to the thermomechanical analysis capability which requires the measurement of length in a penetration, expansion, or extension mode. The basis of this analysis has been discussed in the literature. The relationships of the thermal expansivity a and the length 1 of a sample with respect to temperature and tensile force f are expressed as follows... 

The essential requirement for a substance to be rubbery is that it consist of long flexible chainlike molecules. The molecules themselves must therefore have a backbone of many noncolinear single valence bonds, about which rapid rotation is possible as a result of thermal agitation. Some representative molecular subunits of rubbery polymers are shown in Fig. 1 thousands of these units linked together into a chain constitute a typical molecule of the elastomers listed in Fig. 1. Such molecules change their shape readily and continuously at normal temperatures by Brownian motion. They take up random conformations in a stress-free state but assume somewhat oriented conformations if tensile forces are applied at their ends (Fig. 2). One of the first questions to consider, then, is the relationship between the applied tension / and the mean chain end separation r, averaged over time or over a large number of chains at one instant in time. 

As long ago as 1935 Meyer and Ferri [2] showed that the tensile force at constant length was very nearly proportional to the absolute temperature, i.e. f=aT. Differentiating this relationship we obtain... 

Phase equilibrium between the crystalline and disordered state has been demonstrated by the application of the Clapeyron equation to the relationship between melting temperature and applied hydrostatic pressure. In a one-dimensional analogue to the Clapeyron equation, applicable to oriented fibrous systems, the relationship between tensile force and length can be established. It is found that " " ... 

Although difficult, it is possible to measure stress vs. strain curves of PSAs. Examples of such work include that of Christenson et al. [.3J and Piau et al. [23J. One can do this at various elongation rates and temperatures and create a material response function. Of course, it is much easier to obtain rheological data at small strains than to obtain tensile stress-strain data. One can assume a shape of the stress vs. strain function (i.e. a constitutive relationship) and then use the small strain data to assign values to the parameters in such a function. In order for a predictive model of peel to be useful, one should be able to use readily obtained rheological parameters like those obtained from linear viscoelastic master curve measurements and predict peel force master curves. 

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