Dislocation plasticity in persistent slip bands

Abstract

Persistent slip bands dominate plastic flow under conditions of ‘saturation’, i.e. when a ductile material is cycled at constant plastic strain amplitude, the maximum stress in one cycle rises and then saturates. The saturation stress is identified as being to an excellent approximation equal to the endurance limit of the material, as measured by conventional stress cycling tests. When saturation is attained, plastic flow is confined to well-defined slip bands, which persist after electropolishing and resuming cyclic straining. These persistent slip bands have a well-defined dislocation structure, characterised by a length, which separates walls of dislocation dipoles. The persistent slip bands have a unique stress–strain curve, caused by the backward and forward motion of screw dislocations between the walls. Many authors have worked on these structures, and their main features are widely agreed. Persistent slip bands lead to the initiation of fatigue cracks, because where they intersect the external surface of the material, they cause stress concentrations and generate intrusions, which follow the interface between the persistent slip band and the matrix within which it is embedded. Many features of the cyclic plastic flow can be understood in terms of two basic concepts. Firstly, it is assumed that the bands are dissipative structures, shear structures, with a spacing determined by dynamic processes including the laying down of edge dislocation dipoles and the forces on groups of dipoles resulting from the motion of the screw dislocations producing them. Secondly, the mean free path of screw dislocations in the bands is determined by the probability of meeting and annihilating another screw dislocation of opposite sign. Very simple equations show that the saturation stress is equal to the plastic strain in the band multiplied by the elastic shear modulus divided by 4 π. This very simple result is borne out to within a few percent by recent data on copper single crystals. Other data relating the wall spacing to the saturation stress and the minimum distance apart of stable screw dislocations is accurately rationalised by the theory. Several aspects of the theory deserve comment. The theory indicates that the dislocation density does not matter. The strong temperature dependence of the wall spacing and the saturation stress receive natural explanation. And if the saturation stress is equal to the stress for the onset of stage III unidirectional work-hardening, one can rationalise one of the oldest rules in fatigue strength — the so-called ‘fatigue ratio’, whereby the endurance limit is proportional to the ultimate tensile strength. The picture of cyclic hardening implies that materials with steep initial hardening rates show low saturation stresses; cyclic hardening curves always cross. This is in agreement with observation. Objections raised by other authors are analysed briefly. The existence of internal stress in the structures, as deduced by Mughrabi in neutron irradiated copper, can be re-interpreted on the basis of the normally assumed variation of dislocation line tension with character. The picture of cross-slip which emerges, implies that cross-slip occurs at all stages in the stress–strain curve, but at the onset of stage III, every screw dislocation cross-slips to annihilation — no screw dipoles are possible. This seems consistent with observation.