Fig. 1 Schematic diagram of the indentation simulation. The gray area represents the fixed layer, the dark blue area represents the thermostatics layer, and the light blue area represents the Newtonian layer

Fig. 2 Snapshots of the nanoindentation simulation at the smaller depth in the [001] model. a1, b1 Hydrogen-free model, c1, d1 hydrogen-charged model at the indentation depth of 9.2 and 11.1 Å, respectively; a2, b2, c2 and d2 the stress distribution of a1, b1, c1 and d1, respectively. The red dots represent hydrogen atoms, and the white blocks represent atomic defect clusters resulted by hydrogen atoms

Fig. 3 Snapshot of nanoindentation simulation at different indentation depth in the [001] model. Top view of hydrogen-free model (a1, c1) and hydrogen-charged model e1, g1 at the indentation depth of 9.5 and 27 Å, respectively; dislocation distribution in the hydrogen-free model b1, d1 and hydrogen-charged model f1, h1 at the indentation depth of 27 and 30 Å; stress distribution a2-h2 corresponding to a1-h1. The atoms are colored according to the CNA value and all BCC Fe atoms are removed

Fig. 4 Effects of hydrogen concentration on the dislocation evolution in the [001] model. Top view of the models at the indentation depth of 30 Å with hydrogen concentration of a 0% H, b 1% H, c 2% H and d 3% H; dislocations distribution at the indentation depth of 30 Å for e 0% H, f 1% H, g 2% H, h 3% H

Fig. 5 Effects of hydrogen concentration on the mechanical properties in the [001] model: a depth-force curves; b depth-hardness curves, c depth-dislocation density curves

Fig. 6 Dislocation spatial distribution at the indentation depth of 30 Å under different indenter radii. Indentation radius of a 15 Å, b 30 Å, c 45 Å and d 60 Å indented for hydrogen-free model and indentation radius of e 15 Å, f 30 Å, g 45 Å and h 60 Å for hydrogen-charged model. All BCC Fe atoms have been removed

Fig. 7 Mechanical properties obtained with varying indentation size and hydrogen concentration. Force-depth curves of models with a 0% H, b 1% H, c 2% H concentrations, d depth-hardness curves of models for different radii

Fig. 8 Depth-force curves under different indenter penetration velocity with/without hydrogen addition. Hydrogen-free models with a [001] surface normal, b [110] surface normal, c [111] surface normal; hydrogen-charged models with d [001] surface normal, e [110] surface normal, f [111] surface normal. All BCC Fe atoms have been removed

Fig. 9 Cross-sectional view of the models with [001] surface normal a without and d with hydrogen addition, the models with [110] surface normal b without and e with hydrogen addition, and the models with [111] surface normal c without and f with hydrogen addition. The blue indicates the BCC atoms are in blue and the FCC atoms are in green

Fig. 10 Snapshots of nanoindentation process in the [110] model at different indentation depth. First dislocation occurred at the depth of a 4.8 Å without hydrogen and d 6.7 Å with hydrogen; top view of the models b without and e with hydrogen addition at the indentation depth of 27 Å; dislocation distribution c without and f with hydrogen addition at the indentation depth of 27 Å. The atoms are colored according to the CNA value and all BCC Fe atoms are removed

Fig. 11 Snapshots of nanoindentation process in the [111] model at different indentation depth. First dislocation occurred at the depth of a 5.8 Å without hydrogen addition and d 6.6 Å with hydrogen addition; top view of the models b without and e with hydrogen addition at the indentation depth of 27 Å, and dislocation distribution c without and f with hydrogen addition at the indentation depth of 27 Å. The atoms are colored according to the CNA value and all BCC Fe atoms are removed

Fig. 12 Mechanical properties of the models with different surface normal and varying hydrogen concentrations. Depth-force curves of the models a without and d with hydrogen addition, depth-hardness curves of the models b without and e with hydrogen addition, and depth-dislocation density curves of the models c without and f with hydrogen addition

Fig. 13 Frequency of Schmid factors in the models with [001], [110] and [111] surface normal