A model for the fatigue of copper at low plastic strain amplitudes

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Abstract
Single crystals of pure copper oriented for single slip were fatigued in air at room temperature at low constant plastic strain amplitudes in the range 0·1 % ≤ e p≤ 0·6%. After a few thousand cycles the specimens entered what appeared to be an equilibrium state which contained two phases: a hard and almost inactive ‘matrix’ and the softer ‘persistent slip bands’ (PSBs) into which the deformation tended to concentrate. In the equilibrium state the stress amplitude, the shape of the stress-strain loop and the volume fraction of the specimen occupied by the PSBs were invariant. Furthermore, the volume fraction occupied by the PSBs was found to be linearly related to the plastic strain amplitude. Thus, no matter what the average strain amplitude in the crystal (so long as both phases were present) the PSBs suffered a fixed amplitude which was measured as 0·90%; the specimen adapted itself to the applied amplitude by adjusting the relative amounts of the two phases. A number of predictions of this model were experimentally verified. For example the stress amplitude in the saturation state is merely the stress amplitude required to produce a plastic strain amplitude of 0·90% in the PSBs and therefore does not depend on the strain amplitude. In addition, by analogy with other simple two-phase systems, the behaviour of copper in fatigue tests at constant stress amplitude can be correctly predicted. The analogy has one serious limitation, however, in that the formation of PSBs is found not to be reversible. Although the experiments were done exclusively with single crystals of pure copper it is hoped that the results will be applicable to polycrystalline specimens and to other materials.