A static-dynamic model for the process of cyclic saturation in fatigue of metals

Recent experimental observations of the effects of temperature and cumulative strain on the dislocation structure and cyclic stress-strain behaviour of Cu single crystals show that new ideas are needed for a dislocation theory of cyclic saturation. The observations have enabled a static-dynamic model to be comprehensively checked. The model provides quantitative accounts of the available observations and it shows very clearly that cyclic saturation is not a steady state. It is a dynamic process of continued matrix hardening and persistent slip band (PSB) formation. The model includes a partial static model based on the idea that edge dipole walls in fatigue are metastable but impenetrable to uniform slip. Earlier criticism against this idea has been dealt with in detail on the basis of a simple dislocation account of slip uniformity, which correlates the wall spacings of the static structure with the density of the dynamic structure of gliding dislocations. In addition the present static-dynamic model includes a line tension model for the observed motion of primary matrix and PSB walls. By invoking only conservative dislocation motion the model has the crucial advantage that its validity remains possible even at very low temperatures, where point defects are immobile. The line tension model allows the observed fragmentation of primary matrix walls to be understood, and it accounts for the recently discovered relation between the dislocation density in and the spacing of PSB walls. The model also shows that irreversible matrix hardening drives the continued condensation, whereby matrix walls reduce their volume and cause localization of cyclic strain with slip instabilities and hence fatigue damage.