While the Forman Equation in particular might yield some nice physical insight, one can tackle the whole problem of structure lifetime directly, using the stress intensity factor and so called fracture toughness. This requires application of fracture mechanics, a detailed explanation of which is beyond the scope of this dissertation, and which, in any case, is well covered in numerous texts such as [45].
It is sufficient to note that application of fracture mechanics, with the appropriate examination of the crack geometry, nature of stress applied, and length of crack to date, along with experimental data for materials, can give an idea of when failure may be likely to occur.