**1. Introduction**

The plasticity of crystalline materials results primarily from motion and multiplication of dislocations. Both theoretical and experimental investigations show that the mechanical properties of metals depend on the density, the distribution, the nucleation, and the mobility of dislocations. In particular, the mechanical properties of polycrystals depend on the presence of grain boundaries (GBs), such as the elastic limit and strain hardening. More specifically, these properties are greatly dependent on the interaction mechanisms between dislocations and GBs (dislocation transmission or absorption at GB, formation of a dislocation pile-up, etc.). Indeed, GBs generally present themselves as obstacles to dislocation motion.

In the case of grain size reduction, which means the increase of GB fraction in the material, the material strength is increased following the Hall–Petch's relationship [1–3]. Experimental observations of collective dislocation distributions in the neighborhood of GBs have also made it possible to characterize slip lines using electron microscopy. The interaction between dislocations and GB can be directly observed through in-situ mechanical tests in a Transmission Electron Microscope (TEM). From TEM, it is also possible to obtain the position of each dislocation in a discrete dislocation pile-up, which can be used to calculate stress concentrations at GB [4]. Electron Back Scattered Diffraction (EBSD) measurements in Scanning Electron Microscopes (SEM)

are able to measure the local crystallographic orientations during deformation and therefore the evolution of intra-granular lattice rotations and geometrically dislocation densities [5,6]. Moreover, the coupling of Electron Channelling Contrast Imaging (ECCI) and EBSD permits characterizing single dislocations, dislocation densities, and dislocation substructures in deformed bulk materials [7]. Recently, Atomic Force Microscopy (AFM) makes it possible to analyze the topography and surface roughness of a material following the emergence of dislocations (slip step heights) during mechanical loading of single and poly-crystals [8–10]. Moreover, based on experimental observations, multi-scale simulations involving Crystal Plasticity Finite Element Method (CPFEM), Discrete Dislocation Dynamics (DDD), and Molecular Dynamics (MD) have been developed during these last decades. These methods aim at deeply understanding slip mechanisms and the interactions between dislocations and GBs, and to predict mechanical properties of crystalline materials. However, CPFEM can only consider averaged slip in continuum mechanics, which cannot be used to investigate the discrete interactions between dislocations and GBs. DDD can be performed to study the motion of each individual dislocation, but the complex properties of GBs are missing in this method and elastic anisotropy calculations remain tedious. MD can show the precise structure of dislocation cores and GBs at atomic scale, but it can be only used for simulations at the nanoscale and within a small period of time due to intensive required computing resources.

As the simplest system containing GB, the bi-crystal configuration has been extensively studied. Dehm et al. [11] have reported a comprehensive review on micro-/nanomechanical testing at small scale, especially about GB effect in plasticity and the interactions between dislocations and GBs. Based on many experimental results, there are mainly four mechanisms of dislocation-GB interactions which have been studied: dislocation transmission across GB [12], GB as a dislocation source for lattice dislocation [13], formation of a dislocation pile-up [4] and dislocation absorption at GB [14]. The dislocation transmission is largely investigated through the geometrical transmission factor as reviewed by Bayerschen et al. [15] and the critical stress for transmission as reviewed by Hunter et al. [16]. The geometrical transmission factor has been firstly proposed by Livingston and Chalmers [17] considering only slip system orientations. Then, Shen et al. [4] have proposed another transmission factor considering both slip systems and GB orientations, which has been successfully applied to the prediction of slip activity due to a dislocation pile-up in a 304 stainless steel. Afterwards, Beyerlein et al. [18] have proposed another transmission factor considering threshold angles for the slip systems and GB. It is conjectured that the slip transfer is not possible if at least one of these two angles is bigger than a critical angle [18,19]. The critical transmission stress is generally studied based on image force on dislocations due to the moduli mismatch [20–24]. Furthermore, the interaction between dislocations and special boundaries like twin boundaries has been investigated by many researchers [25–28]. As discussed above, it is believed that a critical stress is needed for the dislocation to get from one grain to the other grain across the GB. The GB will dominate the overall material's behavior when this critical stress is higher than the size-dependent single crystalline flow stress. However, Imrich et al. [25] have showed that, at a critical small sample size, the coherent Σ3 twin GB may not have an impact on the overall mechanical property of micro-beam since the critical stress for transmission is quite low in this case, as shown also by Malyar et al. [28]. In general, however, a large angle random GB does have an evident influence on slip transmission mechanism [29].

In this study, the objective is to develop a new experimental/theoretical methodology suitable for investigating the effects of elastic and plastic anisotropies on the interactions between dislocations and GBs in bi-crystalline micro-pillars. We will consider the effects of GB stiffness, free surfaces, and critical force (lattice friction force and other forces due to obstacles to dislocation motion) on discrete dislocation pile-ups at grain boundaries. In order to reach this objective, both an experimental study based on compression tests on bi-crystalline micro-pillars and a theoretical investigation of discrete dislocation pile-ups in heterogeneous and anisotropic media are performed. Among the different possible mechanisms involving collective dislocation behavior, dislocation pile-ups at GBs and slip transfer are essentially studied. The experimental procedure of in-situ micro-compression

tests on Nickel (Ni) and *α*-Brass bi-crystals is first described in Section 2. Then, slip line height profiles analyzed by SEM and AFM are presented in Section 3. Moreover, the simulation of the slip step height profiles using an anisotropic and heterogeneous discrete dislocation pile-up model in a bi-crystalline configuration are given in Section 4. All the simulation results and the important material parameters for both Ni and *α*-Brass samples are discussed. Section 5 provides the conclusions.
