**Petr Šesták 1,\*, Miroslav Cerný ˇ 1,2, Zhiliang Zhang <sup>3</sup> and and Jaroslav Pokluda 1,2,4**


Received: 29 May 2020; Accepted: 6 July 2020; Published: 8 July 2020

**Abstract:** The cohesive strength of Σ3, Σ5, and Σ11 grain boundaries (GBs) in clean and hydrogen-segregated fcc nickel was systematically studied as a function of the superimposed transverse biaxial stresses using ab initio methods. The obtained results for H-free GBs revealed a quite different response of the coherent twinning boundary Σ3 to the applied transverse stresses in comparison to the other GB types. While the cohesive strength of Σ5 and Σ11 GBs increased with increasing level of tensile transverse stresses, the strength of Σ3 GB remained constant for any applied levels of transverse stresses. In the case of GBs with segregated hydrogen, the cohesive strength of Σ3 was distinctly reduced for all levels of transverse stresses, while the strength reduction of Σ5 and Σ11 GBs was significant only for a nearly isotropic (hydrostatic) triaxial loading. This extraordinary response explains a high susceptibility of Σ3 GBs to crack initiation, as recently reported in an experimental study. Moreover, a highly triaxial stress at the fronts of microcracks initiated at Σ3 boundaries caused a strength reduction of adjacent high-energy grain boundaries which thus became preferential sites for further crack propagation.

**Keywords:** ab initio calculations; hydrogen embrittlement; grain boundary; cohesive strength; multiaxial loading
