A model of extrusions and intrusions in fatigued metals II. Surface roughening by random irreversible slip

Abstract A model of the evolution of the surface roughness of persistent slip bands (PSBs) is presented. The physical background of the model is the existence of a dynamic equilibrium between dislocation multiplication and annihilation in PSBs which leads to irreversible microscopic positive and negative slip steps at the surface. The fluctuation of a random distribution of these slip line segments leads to a surface roughness which increases with the square root of the cycle number. The relation between the parameters which characterize the surface relief and the microscopic parameters which control the dislocation glide in PSBs is investigated by computer simulations. Fair agreement is obtained between observed and simulated surface reliefs where such a comparison is possible. The limits of our purely statistical treatment are pointed out.