applied fracture mechanics

342Applied Fracture Mechanicsin incorrect conclusions. Flaws can be incorrectly classified as benign if their measured sizesare less than the sizes of the governing flaw acceptance criteria used to dictate repairdecisions.Figure 2. Field Observations of Leak Probabilities Compared with pc-PRAISE Results for VariousValues of the Residual Stress Adjustment Factors and Plant Cycles (Large Diameter Pipes) (Khaleel MA.et al., 1995)The procedures shown in Fig. 3 are applicable to a given location in a structure. The cracksize distribution is combined with the non-detection probability to provide the postinspectiondistribution. The manner in which the cracks that escape detection grow is thencalculated by fracture mechanics techniques. The cumulative probability of failure at anytime is simply the probability of having a crack at that time equal to or larger than thecritical crack size. The crack size distribution at the time of the first ISI can be calculated.This pre-inspection distribution is combined with the non-detection probability to providethe post-inspection distribution. Fracture mechanics calculations then proceed up to the nextISI, at which time the procedures are again applied. Calculations of the failure probabilityfor the general model are performed numerically because of the complexity of the fracturemechanics calculations of the growth of two-dimensional cracks as well as the complicatedbivariate nature of the crack size distribution.4.1. One-dimensional modelConsideration of one-dimensional cracks greatly simplifies the probabilistic fracturemechanics model. The two-dimensional surface of the initial crack size shown in Fig. 1becomes a line that is a function of only one length, which will be taken to be crack depth a.Additionally, the fracture mechanics calculations are considerably simplified, because onlyone dimension of crack growth has to be considered. However, if one-dimensional cracks in