Viscoelastic Meaning of Force-Temperature Relationship at Constant Length in Crystalline High Polymers

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Equations describing force-temperature characteristics at constant length with constant rate of cooling are derived in two ways from the theory of linear viscoelasticity.The first method based upon the relaxation time spectrum and the time-temperature superposition principle gives Eq. (8). Secondly, Eq. (9) is deduced from the approximate consideration that the stress relaxation due to the contraction of original length with descending temperature is estimated by step-wise cooling approximation and use of relaxation modulus corresponding to the time of each step.Force-temperature measurement and its analysis are conducted on unoriented crystalline polyethylene terephthalate.The first and the second theoretical deductions are successfully applied to these results as shown in Figs. (3) and (4). While verifications of the first method are confined to the temperature range only above the second-order transition temperature (95°C, Fig. (1)) due to the limitation of the applicability of time-temperature superposition principle, those of the second method are done over the whole temperature range of measurements.
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