Application of minimum energy formalism in a multiple slip band model for fatigue—II. Crack nucleation and derivation of a generalised Coffin-Manson law

Abstract

A situation of multiple parallel slip bands is considered. Each slip band is modelled as an accumulation of edge dipoles. The dislocation dipole density within the slip bands continually increases with fatigue cycling. The strain energy density within the slip bands consequently builds up with cycling until a critical cycle number when it becomes energetically favorable to nucleate a microcrack within one of the slip bands. This is proposed to be the crack nucleation cycle number. The above criterion based on the strain energy density is used to derive an explicit expression for the number of cycles for crack nucleation. It is shown that there is a parallel between this criterion for crack nucleation and other criteria that are based on the accumulation of a certain critical amount of damage. A generalised Coffin-Manson law for crack initiation is also derived. The size and most likely site of the just-nucleated crack is discussed.