Fig. 1 Atomic configurations of the nanocrystalline Fe-Cr alloys: a grain arrangement of the BCC pure Fe model, b Cr distribution of the model before MC swaps of Fe5.6Cr, c Cr distribution of the model after MC swaps of Fe5.6Cr, d hydrogen distribution of the model after hydrogen diffusion equilibration of Fe5.6Cr with hydrogen concentrations of 0.018 wt%

Fig. 2 Stress-strain curves of the nanocrystalline Fe-Cr alloys with hydrogen concentrations of 0.0000 wt%, 0.0018 wt%, 0.009 wt%, 0.018 wt% and Cr concentrations of 0.0 wt%, 5.6 wt% at with different strain rates of 107 s−1, 108 s−1, 109 s−1, 1010 s−1. In each sub-figure, a CH = 0.0000 wt%, CCr = 0.0 wt%; b CH = 0.0000 wt%, CCr = 5.6 wt%; c CH = 0.0018 wt%, CCr = 0.0 wt%; d CH = 0.0018 wt%, CCr = 5.6 wt%; e CH = 0.009 wt%, CCr = 0.0 wt%; f CH = 0.009 wt%, CCr = 5.6 wt%; g CH = 0.018 wt%, CCr = 0.0 wt%; h CH = 0.018 wt%, CCr = 5.6 wt%

Fig. 3 Peak stress, b fracture strain, c Young's modulus, and d toughness of the nanocrystalline Fe-Cr alloys with different Cr concentrations plotted against hydrogen concentration

Fig. 4 Microstructure evolution of the nanocrystalline Fe-Cr alloys at a strain rate of 108 s−1 with different hydrogen concentrations of 0.0018 wt%, 0.009 wt%, 0.018 wt% and Cr concentrations of 0.0 wt%, 5.6 wt% at the strain of 10%, 30%, 60%, respectively

Fig. 5 Shear strain distribution of the nanocrystalline Fe-Cr alloys at the strain rate of 108 s−1 with different hydrogen concentrations of 0.0018 wt%, 0.009 wt%, 0.018 wt%, Cr concentrations of 0.0 wt%, 5.6 wt% and strain of 3%, 5%, respectively

Fig. 6 Arrhenius plots of hydrogen diffusion coefficient with respect to temperature. a Total diffusion coefficient ${D}_{\mathrm{eff}}$, the ${D}_{\mathrm{bulk}}$ and ${D}_{\mathrm{GB}}$ of Fe-Cr alloys with b 0.0018 wt% H, c 0.009 wt% H, d 0.018 wt% H