Phenomenological Description of Aging

Damage (aging) is a cumulative process in plastics. Ultimate failure therefore results from an accumulation of material damage over the course of time. The defined shift factor (Eq. 1.10) generally depends not only on temperature T, but also on damage Q  

the time-temperature shift in Eqs. 1.7 to 1.11 is no longer valid. In many cases, the dependencies of temperature and damage can be separated, as suggested by Eq. 1.12. 

We can now introduce a standardized damage Q with 0 Q 1 in the following form  

The time dependence of standardized damage can then be represented in a scaled version, representing standardized damage as a function of a damage variable f/T (0 f/T 1), where r is the failure time of the material at temperature Tor another external parameter  

The variable f/r depends on external conditions. The simplest function that fulfills 0 = 0 for t/t = 0 and 0 = 1 for = 1, is an exponential function. In many cases 0 can in fact be represented by such an exponential function  

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