Optimization of the Inspection Schedule for Surface-Breaking Cracks under Fatigue Loading

Inspections play an essential role in the damage tolerance approach to control fatigue damage. In this paper a method is presented to optimize the cost-effectiveness of inspection scheduling for single and multiple inspections during the expected lifetime. Detailed results are given for a surface-breaking crack of depth a in a cyclic tension field. The original crack depth is treated as a random variable with a known probability density function. The crack growth is governed by Paris law, and the inspection technique has a known probability of detection. The component fails when the crack depth reaches a critical value cr a . As a part of the damage tolerant approach the component is replaced only when the depth of the detected crack is larger than a pre-defined value r a . The analysis is based on theoretical considerations, which take into account three aspects of fatigue damage using a statistical approach. • Stage 1: Development of pre-crack fatigue damage leading to the formation of a very small macrocrack • Stage 2: Growth of the macrocrack • Stage 3: Determination of the probability of a detected crack with crack length r a a > The authors have discussed Stage 1 in considerable detail elsewhere. Here, the emphasis will be on Stages 2 and 3. The point of departure is a macrocrack, represented by a probability distribution 0 ( ; ) f a N of surface breaking macrocracks that Stage 1 has yielded, with known statistics. By the use of an evolution law (for example, Paris law) we can then compute the probability distribution ( ; ) f a N after N cycles. We take into account that cracks can only be detected with a known probability of detection (POD). For a pre-determined number of cycles that defines the expected lifetime, we obtain the