A discussion of the structure and behaviour of dipole walls in cyclic plasticity

Abstract Assuming that cross-slip by thermally activated migration of jogs can cause annihilation of screw dislocation dipoles without macroscopic crystallographic confinement of cross-slip to the cross-slip plane, an attempt is made to re-derive earlier equations for the saturation stress and the plastic strain amplitude in persistent slip bands. These equations had been based on the assumption that cross-slip could occur only on a cross-slip plane making an obtuse angle with the slip plane, an assumption which limits the mean free path of screw dislocations. The key new assumption is that the walls of edge dislocation dipoles which dominate the structure of persistent slip bands are penetrable obstacles, which increases the mean free paths of the mobile dislocations. Agreement with experiment is obtained if the penetration probability in cyclic saturation is on average one third, a value for which there is a simple rationalization. Estimates can be made of the wall width, which is independent of temperature, in agreement with recent observations by Tippelt et al. However, the main unresolved difficulty is the role of the very fine dipoles, particularly the faulted dipoles, in the walls. A further weakness in the theory is that it ignores the cutting of dipoles by the cross-slipping screw dislocations. Despite these problems, the distribution of dipole heights can be worked out and is found to be in reasonable agreeement with experiment. Acknowledgements I am indebted to Professor C. Holste for an invitation to attend a conference in Dresden, where these ideas were first presented. I am particularly indebted to Dr A. Schwab, who discovered a crucial error in the original version of the paper, and whose work points the way to an understanding of the observed cycle-to-cycle variation in the persistent slip band displacements in terms of a statistical distribution of the penetration probability. I am grateful to Professor H. Mughrabi and to an anonymous referee for critical comments, and also to Robinson College and the Cavendish Laboratory for support. Notes † These data are analysed by L. M. Brown in 'Brief rejoinder' in the same volume.