Asymptotic approaches for dealing with distorted crack geometries

Abstract

A growing, albeit not predominant, way to contribute to the climate transition in the field of fracturemechanics is to refine predictions from damage tolerance approaches used to assess the durability andreliability of sensitive components such as those found in railway, aeronautics, aerospace or nuclearindustries. If it can be certified that the reduced safety margins remain acceptable, the intervals betweenmaintenance operations could be extended, and the replacement of defective parts delayed, therebyreducing the environmental footprint.The aim of Damage Tolerance Approaches is to ensure that the existence of unavoidable defects does notcompromise safety. This involves considering the most unfavorable case of brittle fracture and determiningthe propagation of a preexisting crack under cyclic loading until the Griffith energy fracture thresholdis reached. Currently, this is done using simplified, smoothed-out crack geometries, relying either ontabulated 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 tosupporting the reduction of safety margins, these approaches also help to ensure that small geometricalperturbations do not lead to unexpected catastrophic failure. Asymptotic methods aim to provide analyticalformulas 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, andpropagation in general mixed-mode I+II+III condition