**5. Conclusions**

In this work, experimental studies of Burgers vector distribution in discrete dislocation pile-ups at GB were performed in Ni and *α*-Brass bi-crystalline micro-pillars. Ex-situ AFM measurements were carried out after a compression test with a flat punch nanoindenter. The measured slip step heights were simulated using a three anisotropic layers model combined with image stress calculation [42], which was more suitable for a single-ended dislocation pile-up configuration with single slip compared to multi-slip configurations. In this model, GB was regarded as an elastic interphase with a thickness *H*GB = 0.9 nm, which was obtained from MS simulations. Meanwhile, the effects of two free surfaces around micro-pillars were considered. It was found that, for the Ni sample, the best solution of this simulation was obtained considering anisotropic elasticity, the effect of free surfaces, a critical shear stress *τ<sup>c</sup>* = 12 MPa, a homogeneous external stress, and the same Burgers vector of incoming dislocations and interfacial dislocations. However, for the *α*-Brass sample, still considering anisotropic elasticity, the best solution was obtained with free surfaces, a homogeneous external stress field, and a larger critical shear stress of *τ<sup>c</sup>* = 43 MPa. In addition, the Burgers vector of interfacial dislocations was modeled as a residual Burgers vector because there was a huge number of transmitted and/or absorbed dislocations.

**Author Contributions:** Conceptualization, X.C., T.R., C.M., and S.B.; methodology, X.C., T.R., C.M., and S.B.; software, X.C.; validation, T.R., C.M., and S.B.; formal analysis, X.C., T.R., C.M., and S.B.; investigation, X.C.; resources, C.M. and S.B.; data curation, X.C.; writing—original draft preparation, X.C.; writing—review and editing, T.R., C.M., and S.B.; visualization, X.C.; supervision and project administration, S.B.; funding acquisition, C.M. and S.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors are grateful to the French Ministry of Higher Education and Scientific Research and the French-German University (UFA-DFH) for financial supports. The authors are also grateful to Experimental Methodology in Materials Science (MWW) in Saarland University and the French State (ANR) through the program "Investment in the future" (LabEx "DAMAS" referenced as ANR-11-LABX-0008-01) for additional financial supports. We also would like to thank the Deutsche Forschungsgemeinschaft DFG for the financing of the AFM microscope, Grant No. INST 256/455-1 FUGG.

**Acknowledgments:** The authors would like to thank J. Rafael Velayarce for his help with the experiments.

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