A number of structural risk assessments have been performed in which damage in the structural detail is modeled in terms of the distribution of cracks or equivalent cracks.  Examples of such risk analyses can be found in Lincoln [1985], Berens, et al. [1991], Alford, et al. [1992] and Lincoln [1997].  If the risk analysis calculations start with a virgin structure the crack sizes are equivalent initial cracks.  If the risk analysis is being performed for in-service or aging aircraft, the crack size distribution is usually obtained either from the sizes of the cracks discovered during fleet inspections or from tear down inspections of structures removed from the fleet.  The cracks detected during fleet inspections would have experienced different total service times and would have to be translated to a common service age to obtain a representative crack size distribution for the population of details.  The cracks from tear down inspections may be from one or many airframes.  In either case, the crack sizes usually need to be translated to a common or different service age.  Typically, to locate the crack sizes at a common number of flight hours, the crack sizes are translated using a fracture mechanics based crack size versus flight hour curve for expected or observed usage.  This process is illustrated in Figure 3.2.11.  After all cracks have been translated to a common service age, a crack size distribution can be established for use in calculating probability of failure as a function of flight hours.

Figure 3.2.11.  Schematic Demonstrating the Translation of Crack Sizes to a Common Size Using Predicted a versus T