On the key role of crack surface area on the lifetime of arbitrarily shaped flat cracks

Accurate fatigue lifetime prediction is a central element in many industries. Often, a damage tolerant approach is used to ensure that some given imperfections are safe. In this context, these lifetime predictions are frequently made using simplified crack geometries leading to costly conservatism. In particular for a closed crack front, a circular or elliptical crack enclosing the real defect is generally used leading to an underestimation of the real lifetime. Using an iterative perturbation method to simulate the fatigue growth of many tensile complexly shaped cracks, we show that in the absence of any additional complexity, (i) the front quickly becomes circular; (ii) its evolution with the number of loading cycles can be obtained analytically using a circular crack of same area as the original distorted defect. In practice, it means that replacing a complex crack front shape with this simple, analytically solvable configuration is an effective way to improve predictions and that it is not useful to invoke more complex shapes such as elliptical cracks. These take-home messages are illustrated by an example from the aviation industry.