On the probability of an undetected surface-breaking crack

Surface-breaking fatigue cracks are common defects in metal components subjected to cyclic loads. Such cracks tend to propagate in stress fields that are below the critical stress level for static loading. An important part of a damage tolerant design philosophy is the requirement that surface-breaking cracks should be detectable before they reach a critical depth. In this paper, we consider a surface-breaking crack in a two-dimensional geometry, whose original depth is defined by a probability density function. The increase of the crack depth with number of cycles is governed by Paris law, and the detectability depends on a probability of crack detection (POD). Based on this information we determine the probability that the crack depth will have exceeded a prescribed critical value at a specified number of cycles