**1. Introduction**

Hydrogen may cause a significant reduction of ductility of metallic materials which leads to a premature fracture of engineering components and structures. This so-called hydrogen embrittlement was already extensively studied in the last century with the help of experimental [1,2] as well as theoretical methods [3–13]. The most accepted theoretical concepts explaining the embrittlement at the atomistic level are the Hydrogen-Enhanced Decohesion (HEDE) [14] and the Hydrogen-Enhanced Localized Plasticity (HELP) [15]. The HEDE concept deals with a hydrogen-induced reduction of the cohesive strength of grain boundaries (GBs), while the HELP model is based on the hydrogen-enhanced dislocation mobility. At high tensile triaxialities, the HELP mechanism accelerates the necking failure of microvoids and, at low triaxialities, it induces their shearing coalescence and failure (see e.g., [16,17]). The relevance of HEDE and HELP damage mechanisms should be identified for each particular case of the hydrogen-assisted fracture.

Decohesion processes in polycrystalline metallic materials are mostly restricted to a vicinity of planar defects like grain boundaries and, as a rule, they are affected by a presence of hydrogen and impurity atoms segregating at these defects [18–20]. This was also the case of the H-charged nickel-based superalloy that exhibited quasi-brittle fracture surfaces of a mixed intergranular and transgranular morphology in Ni matrice as reported in the experimental study [1]. Surprisingly, the most frequent crack initiation sites reported by Seita et al. [1] were Σ3 coherent twin boundaries, in spite of their lowest energy and hydrogen solubility. Other low-Σ GBs (Σ = 1 − 29) were less susceptible to crack initiation but less resistant to crack propagation. General GBs (Σ > 29) exhibited the highest resistance to crack initiation but the lowest resistance to crack propagation. Since the plane of Σ3 GB is also the plane of dislocation glide and many of fractured Σ3 GBs were inclined by 60◦ to the tensile axis, the authors assumed that a shear deformation by dislocation glide in the GB plane assisted the crack initiation process, along with dislocations trapped to this plane from other (111) slip planes. Such a damage process resembles the shearing failure induced by the HELP mechanism at low triaxialities [16]. Further crack propagation followed along general grain boundaries due to their highest energy (lowest separation energy and cohesive strength) and the highest hydrogen concentration.

However, such an interpretation of the peculiar fracture behavior is certainly not exhaustive without exploring the effect of hydrogen segregation on the cohesive strength of GBs in H-charged nickel specimens—i.e., without also taking the HEDE mechanism into account. This is the main objective of our ab-initio study. In the first principles calculations, the mechanical properties of GBs are usually characterized by strengthening/embrittlening energies [18], cleavage energies (work of separation) [20,21], and/or by the cohesive strength related to uniaxial loading (or deformation). However, GBs in metallic engineering components are rather subjected to an external multiaxial loading/deformation. Moreover, a superposition of local stresses of various kind often leads to a multiaxial stress state, even in the case of uniaxial external loading. Tensile triaxial stresses ahead of crack fronts or tensile/compressive internal stresses induced by thermomechanical and surface treatments can serve as good examples of such local stresses. For the purpose of practical applications of grain boundary engineering, therefore, it is also useful to understand the effect of multiaxial loading on the cohesive strength of GBs. Let us note that cracks not only induce triaxial stress state but also act as stress concentrators that can significantly raise the local stress level.

In this paper, we present values of cohesive strength of clean and hydrogen segregated GBs in fcc nickel. We also studied the aforementioned effect of triaxiality of the stress state on the strength response of GBs in our ab initio predictions. Namely, we studied the Σ5, Σ3, and Σ11 coherent GBs. The Σ5 served as an example of GBs with an excess volume (void space) at GBs where impurities tend to segregate. One can therefore expect locally increased hydrogen concentration at the GB affecting its cohesion. The other two considered low-angle GBs have rather negligible excess volume. In such a case, one could expect that these GBs do not affect H distribution in the crystal. However, as was shown in the work of Stefano et al. [7], Σ3 GB can serve as a two-dimensional barrier for H migration. Moreover, the GBs included in our study have been studied theoretically and there is enough data for comparison in the literature.
