Cyclic hardening mechanisms in [001] copper single crystals

Abstract

Friction stress and back stress of [001] Cu single crystals during cyclic deformation were derived from cyclic stress–strain hysteresis loops by using the Cottrell method and the results are compared with those for single slip crystals. The cyclic hardening features of the [001] crystals are described in terms of the friction stress and back stress. Specific, detailed study was carried out on the sample cycled with a plastic strain amplitude of 1.8×10 –3. It has been shown that both the ‘true’ friction stress, i.e. the cyclic yield stress, and the back stress in the [001] crystals increase much more rapidly than those in single slip crystals in the hardening stage. In the saturation stage, however, only the friction stress in the [001] crystal is higher than its correspondent in the single slip crystals, while the back stresses in these two types of crystals are close to each other. The higher friction stress in the [001] crystal is related to the higher density of jogs produced by the dislocation reactions between the primary and critical slip systems, and the existence of secondary dislocations in channels. The higher back stress in the hardening stage is attributed to the higher dislocation density in loop patches introduced by dislocation reactions in the first dozen of cycles. By modifying the Kulhlmann-Wilsdorf and Laird model, it is possible now to express quantitatively both the back stress and the shear stress in a cyclically deformed crystal with a particular orientation as functions of the applied strain amplitude as well as an orientation-dependent factor: the hardening coefficient for the first stage of unidirectional deformation. The predictions from these expressions for multiple slip crystals are in very good agreement with experimental data.