Time Temperature-Superposition-Principle TTSP Master Curves

Development of Time Temperature-Superposition-Principle (TTSP) Master Curves 

While data was collected from room temperature ( 25° C) to 130° C, only the data above 90° C is shown as it was not possible to shift data below this temperature to form a realistic extension to the data shown. Note that the TTSP method is an outgrowth of the kinetic theory of polymers which is only strictly valid above the Tg. While the TTSP is thought to be valid for temperatures below the Tg, the exact lower limit is not well defined. A guiding rule of thumb is that TTSP may be used below the Tg as long as data is shiftable to form a smooth master curve. 

The 120° C master curve can now be shifted to determine a new master curve for any temperature between 90° C and 130° C. If shifted to the right to form a master curve for 90° C, the data would span the time from about 0.5 minutes to lO minutes (or nearly 200 years). On the other hand, if the data were shifted to the left to form a master curve for 130° C, the data would span the time from about 10 minutes to 10 minutes. In other 

Plotting the reciprocal of creep compliance for a time of 0.5 minutes from each of the curves in Fig, 7,3 with temperature results in the data previously discussed and given in Fig, 7,2. This curve verifies the various stages for a polymer as described by Fig, 3,16 in Chapter 3 and Fig, 7,1 in this chapter. Here, however, as mentioned earlier no rubbery flow or liquid 

An additional decade of shifting to be roughly equivalent to a master curve for 78° would provide data over approximately 200 years. Clearly with this method a prediction of behavior over a design lifetime of 40 or 50 years is possible though no experimental data has ever been collected for such an extended period providing proof that the approach is valid. 

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However, it is also necessary to discuss how broadband bulk, shear and Poisson s ratio are measured. The measurement of the broadband shear modulus is easily accomplished using the time-temperature-superposition-principle (TTSP) and a torsion test. See Kenner, Knauss and Chai (1982) for a description of a simple torsiometer and the measurement of a master curve for a structural epoxy adhesive, FM-73, at 20.5° C. 

The Schapery method given by Eqs. 10.25 and 10.26 is a mathematical definition of a time-stress-superposition-principle or TSSP that is analogous to the TTSP. Later it will be shown how to obtain stress dependent compliance and modulus master curves from experimental data using TSSP much in the same manner as temperature dependent master curves were determined from experimental data using the TTSP. 

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