Cracks and extrusions caused by persistent slip bands

Cottrell's account of persistent slip poses a puzzle which has challenged all subsequent research. Persistent slip bands (PSB) endure repeated plastic shear which constantly produces narrower and narrower dipoles, as observed by Veyssiere. At the same time, because narrow interstitial dipoles have a larger elastic energy than otherwise identical vacancy ones, shear will eject larger interstitial dipoles to the surface, whilst retaining smaller vacancy ones in the interior, thereby producing excess vacancy loops. This causes a longitudinal tensile stress (the fibre stress') inside the band. The ejection process lowers the energy by a term linear in the fibre stress, but increases it by a term quadratic in the fibre stress, giving rise to an equilibrium value of the fibre stress, tensile, in order-of-magnitude agreement with observations of extrusions at low temperatures, where only plasticity can occur. The fibre stress produces logarithmic infinities in the surface stress at the edges of the PSB, and thus can be responsible for sharp stage I fatigue cracks. At higher temperatures which allow pipe diffusion and/or volume diffusion, interstitial loops are drawn by the tensile fibre stress into the PSB. Then, as cyclic plasticity attempts to maintain equilibrium, the loops are ejected where the band meets the surface, producing growing extrusions. Such extrusions can grow almost without limit. At low temperatures, the rate of extrusion formation is maximal at one Burgers vector per cycle, but it will be slower than this if it is diffusion limited.