*3.1. Preliminary Slip Analysis Using Schmid Factors and Incompatibility Stresses*

Based on the local crystalline orientation, the mechanical and geometrical information of each slip system in the studied grains were firstly analyzed. The slip analysis results for Ni sample and *α*-Brass sample are reported in Tables 1 and 2, respectively. The results include the Schmid factors, the resolved shear stresses normalized by the applied stress considering elastic incompatibility stresses as detailed in [37,38], the angles between the slip line and the GB line on the upper surface *θ*Up, the angles between the slip line and the upper edge of sample on the side surface *θ*Side (see Figure 1e) and the maximum transmission factor with corresponding slip system in the adjacent grain. Here, slip systems in FCC crystals are indicated by Schmid and Boas's notation [39]. The analysis of Schmid factors and resolved shear stresses can be used to predict the first active slip systems (with the maximum Schmid factor or the maximum resolved shear stress) during compressive loading. Schmid factor are computed directly from the projection of the homogeneous external applied stress. However, for the analysis of the resolved shear stresses considering incompatibility stresses, the stresses in the two crystals are the sum of the external applied stress and incompatibility stresses due to heterogeneous elasticity coming from misorientation and anisotropic elasticity [37,38,40]. In some cases, the first active slip system with maximum Schmid factor can be different from the one obtained when considering incompatibility stresses [38,40]. After the mechanical tests, the activated slip lines could be observed by SEM (see Figure 3a for Ni and Figure 4a for *α*-Brass) and by AFM (see Figure 5a for Ni and Figure 6a for *α*-Brass). Then, both angles *θ*Up and *θ*Side were experimentally determined as shown in Figure 3a (right) for Ni and in Figure 4a (right) for *α*-Brass. By comparing these angles to the theoretical analyses as described in Tables 1 and 2 (see also Figure 3b for Ni and Figure 4b for *α*-Brass), the active slip planes were identified. For the present experiments, the onset of plasticity occurred in crystal II for the Ni sample and in crystal I for the *α*-Brass sample. In both grains, the first active slip system is always the same, either considering a simple Schmid analysis or elastic incompatibility stresses [37,38,40], as marked in red in Tables 1 and 2. However, for the *α*-Brass sample, combining the analyses provided by Schmid factor and incompatibility stresses, a second slip system could be active as well and is marked in blue in Table 2.


**Table 1.** Slip system analyses for Ni micro-pillar. The first active slip system is marked in red. The compressive direction is along X, the GB normal along Y and the upper face normal along Z as presented in Figure 1e.

∗1 RSS: Resolved shear stress normalized by the applied stress when considering elastic incompatibility stresses (IS) following the formula reported by Richeton and Berbenni [37,38,40]. ∗2 MTF: Maximum transmission factor based on the formula given by Shen et al. [4] with corresponding slip system (CSS) [39] in the adjacent grain.


**Table 2.** Slip system analyses for *α*-Brass micro-pillar. The first active slip system is marked in red and the second one in blue. The compressive direction is along X, the GB normal along Y and the upper face normal along Z as presented in Figure 1e.
