**4. Conclusions**

The lattice parameter assessment through convergent beam electron diffraction patterns recorded in the channels and close to the walls of the labyrinth dislocation structure suggest very low long range internal stresses (LRIS). Our earlier dipole height work on the same cyclically deformed copper also suggests low internal stresses. The stress to separate dipoles with the widest height was independent of the location. Therefore, the results of the current CBED analysis study is consistent with our earlier maximum dipole height measurement work.

Minimal changes (less than 10−<sup>4</sup> nm) were observed in the lattice parameters recorded throughout a single channel. These values are less than 6.5% of the applied stress. Hence, negligible internal stresses in the channel interior and near the dislocation walls were observed. The Kassner et al. X-ray synchrotron study on monotonically deformed (to 30% strain at ambient temperature) copper single crystals [32] suggest that long range internal stresses were nearly 10% of the applied stress. Thus, the outcome of the present cyclic deformation study is consistent with the earlier monotonic deformation work. Although the changes in the lattice parameter in a channel are very minimal (less than 10−<sup>4</sup> nm), chi-squared analysis suggest that the difference between the lattice parameter values of the cyclically deformed copper and the unstrained copper are slightly higher in the proximity of the walls in comparison with the channel interior. These internal stresses are less than 6.5% of the applied stress. This is consistent with the composite model originally suggested by Mughrabi but with perhaps lower values of internal stresses. Therefore, it appears that a low proportion of the Bauschinger effect may be influenced by the existence of long range internal stresses. The dominant feature of the Bauschinger effect may include the Orowan–Sleeswyk [6] mechanism type of explanation, since both the maximum dipole height measurements and the lattice parameter assessment through CBED analysis suggest a relatively homogenous stress state within the heterogeneous dislocation microstructure.

**Author Contributions:** M.E.K. conceived of and designed the project; R.E., M.S., and M.E.K. contributed to theoretical analysis and conceptualization; M.S. prepared the fatigued samples and was involved in fundamental discussions with M.E.K.; R.E. prepared the TEM samples; R.E. and M.H.M. performed TEM studies and data analysis; Literature searches were performed by R.E.; Manuscript preparation and proof-reading were performed by R.E., M.E.K., M.S., and M.H.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Foundation under grant DMR-1401194.

**Acknowledgments:** The authors greatly appreciate the assistance of Professor Marc Legros and Tannaz Sattari Tabrizi.

**Conflicts of Interest:** The authors declare no conflict of interest.
