In order to estimate the reliability of real components which undergo varying conditions and stresses at different times in their lifetime, cumulative damage theories were introduced. The idea behind these is that failure is due to a structure accumulating damage at different stress levels until finally fracture occurs. Initially, it was proposed that such accumulation was just a linear combination of damages, but this was subsequently modified to give a non-linear accumulation rule.
A continuous version of the accumulation rule, a damage function, was proposed in the
1950s by Kachanov [22]. This whole area is called continuum damage
mechanics. The use of the damage function allows one to take into account the many and
varied mechanisms that affect useful lifetime. As well as the actual crack growth
process, one may be interested in the effect that such things as weather plays in the
accumulation of damage. Indeed, it is possible to consider damage at the initial
stages of the damage process, by determining a general ``pattern'' of damage, from
experiment, rather than trying to observe the initiation process directly. Such
consideration may be made in the specification of the damage function. Indeed much of
the previous work on short cracks has concentrated on an examination of damage
functions such as total length of cracks per unit area, 
[4].