Micromechanical analysis of crack initiation and hysteresis loops of aluminium single crystals under high-cycle fatigue

Abstract

The micromechanical model of extrusion formation in a polycrystal under high-cycle fatigue is briefly reviewed. Following the same general approach, and guided by the observations of Mecke and Blochwitz on the subgrain boundary displacement in a single crystal, a micromechanic model of extrusions and intrusions in an aluminum single crystal with multiple fatigue bands under stress-controlled loading is presented. The microstress and strain fields in the crystal are calculated by the boundary element method for the three-dimensional elasto-plastic solids. From these microfields, the macroscopic stress and strain of the crystal at different stages of loading are calculated. The numerical analysis gives the changes in hysteresis loop shape with loading cycles. The incremental plastic strain distribution and the incremental residual stress in each cycle depend on the initial shear stresses. Two sets of initial stresses are taken to calculate the hysteresis loops. This shows the dependence of the shape and size of the hysteresis loops on the distribution of initial shear stresses. The size and distribution of persistent slip bands (PSBs) on the front surface of the present model are the same as those on the side surface. This agrees with the experiments of Zhai et al. Both the calculated and the experimental PSBs on the side surfaces are concave. The calculated extrusion height and intrusion depth at stress saturation seem to agree with the experimental values. This model seems to provide an explanation for a number of observations in a fatigued single crystal oriented for single slip.