A theory of fatigue crack initiation at inclusions

Abstract

The dislocation dipole accumulation model for fatigue crack initiation previously proposed by the authors is extended to an analysis of the fatigue strength reduction due to inclusions in high strength alloys. The initiation of a fatigue crack is determined by an energy criterion under the assumption that the crack initiation takes place when the self strain energy of dislocation dipoles accumulated at the damaged part in the material reaches a critical value. Explicit formulae for the crack initiation criterion in several cases are derived as functions of the applied stress, the inclusion size, the slip band shape, and the shear moduli of the inclusion and matrix. The following three types of fatigue crack initiation at inclusions are considered: the slip-band crack emanating from a debonded inclusion, the inclusion cracking due to impinging of slip bands, and the slip-band crack emanating from an uncracked inclusion. The first mechanism was reported to be operative in high strength steels, while the last two mechanisms were reported in high strength aluminum alloys. The present theoretical results are in good agreement with the experimental data published for each case of fatigue crack initiation at inclusions.