A probabilistic approach to characterizing structural durability has been extensively explored by Manning and Yang [1987, 1989].  For the durability analysis, the growth of a distribution of equivalent initial flaw sizes for a population of structural elements is calculated as a function of flight hours in the expected usage environment.  Durability is then characterized in terms of either the expected number of cracks that will exceed a fixed size as a function of flight hours or in terms of the distribution of flights to reach a crack of given size.  These concepts are illustrated in Figure 3.2.10, from Manning & Yang [1989], in which:

–     EIFSD represents the equivalent initial flaw size distribution of initial quality;

–     p(i,t) represents the distribution of number of cracks of a size larger than x;

–     F_T(x) (t) represents the distribution of service time to reach a crack of size x.

The EIFSD must be projected forward based on a crack growth methodology that is compatible with that used to produce the EIFSD. Manning and Yang recommend a combined deterministic crack growth analysis (DCGA) and stochastic crack growth analysis (SCGA) for projecting the EIFSD.

Figure 3.2.10.  Schematic Using the Equivalent Initial Crack Size Distribution (EIFSD) for Durability Analysis