Determination of internal stresses in cyclically deformed copper single crystals using convergent-beam electron diffraction and dislocation dipole separation measurements

Single crystals of copper were cyclically deformed, in single slip, to presaturation at 298 K. The dislocation substructure was analyzed using conventional bright-field and dark-field transmission electron microscopy with particular attention directed towards the dislocation dipole spacing. It was found that, in both metals, the dipole spacing and statistical distribution of spacings were independent of the location in the heterogeneous substructure, which consisted of dense dipole bundles (or veins) and channels with relatively low dislocation density. Furthermore, the stress to separate the dipoles with largest spacing (upper-bound separation for stable dipoles) can be used to calculate the stress at the dipole location. This stress is within a factor of about two of the applied stress in both channels and veins. The stress necessary to pass dislocations through the dense veins was calculated to also be within a factor of about two of the applied stress. Convergent-beam electron diffraction (CBED) experiments were also performed at several locations very near the dipole bundles and within the channels. The lattice parameter measurements also suggested an absence of long-range internal stresses. The observations and calculations suggest a uniform state of stress throughout the heterogeneous dislocation substructure, without the presence of significant internal stresses.