Asymptotic approaches for dealing with distorted crack geometries

A growing, albeit not predominant, way to contribute to the climate transition in the field of fracture mechanics is to refine predictions from damage tolerance approaches used to assess the durability and reliability of sensitive components such as those found in railway, aeronautics, aerospace or nuclear industries. If it can be certified that the reduced safety margins remain acceptable, the intervals between maintenance operations could be extended, and the replacement of defective parts delayed, thereby reducing the environmental footprint. The aim of Damage Tolerance Approaches is to ensure that the existence of unavoidable defects does not compromise safety. This involves considering the most unfavorable case of brittle fracture and determining the propagation of a preexisting crack under cyclic loading until the Griffith energy fracture threshold is reached. Currently, this is done using simplified, smoothed-out crack geometries, relying either on tabulated values or Finite Element Methods. Since meshing of the entire structure is required, the lattercurrently struggles to accurately account for the small-scale tortuosity of the crack geometry. This paper aims to show that asymptotic approaches are efficient alternatives to address this challenge.Various aspects of these approaches, along with selected applications, will be reviewed. In addition to supporting the reduction of safety margins, these approaches also help to ensure that small geometrical perturbations do not lead to unexpected catastrophic failure. Asymptotic methods aim to provide analytical formulas for the variation of stress intensity factors caused by small-scale crack shape perturbations. Several applications are presented including crack shape evolution, the influence of heterogeneities, and propagation in general mixed-mode I+II+III condition.