Empirical Approach To Time-Stress-Superposition TSSP

Empirical Approach To Time-Stress-Superposition (TSSP) 

The development of master curves using a semi-empirical TTSP approach was discussed in Chapter 7. A similar semi-empirical TSSP is can also be used to obtain a master curve valid over a long time at one stress level by shifting and superposing creep compliance (or relaxation modulus) data obtained at other stress levels in a short term test. This principle is illustrated in Fig, 10.14. 

Hiel has used both the TSSP and the Schapery procedure to produce master curves of the shear behavior of a carbon epoxy composite. An example of his results is given in Fig. 10.15. The shear creep compliance of a carbon epoxy composite is shown for various stress levels. The data were shifted horizontally to form a smooth master curve for the lowest stress level as illustrated by the open symbols. The Schapery procedure was also used independently on this data set and the resulting master curve prediction is indicated by the solid line. For more details, see the cited reference in Fig. 10.15. 

The TTSP and the TSSP can be combined to produce a master curve that can be shifted both as a function of temperature and stress. The shift factors are therefore multiplicative or additive on a logarithmic time scale. This process is shown in Fig. 10.16 where two paths are indicated to find the final master curve. In both cases, creep curves at different stress and temperature levels are found experimentally. Following the left path, the family of curves for each stress level is assembled on one graph and TTSP used to obtain TTSP master curves of the response at a reference temperature one master curve for each stress level is obtained. Subsequently, 

TTSP was also used to form a master curve for the same material and the combined shift function surface is shown in Fig. 10.19. 

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