Effects of mechanical stress, chemical potential, and coverage on hydrogen solubility during hydrogen-enhanced decohesion of ferritic steel grain boundaries: A first-principles study

Hydrogen-enhanced decohesion (HEDE) is one of the many mechanisms of hydrogen embrittlement, a phenomenon that severely impacts structural materials such as iron and iron alloys. Grain boundaries (GBs) play a critical role in this mechanism, where they can provide trapping sites or act as hydrogen diffusion pathways. The interaction of H with GBs and other crystallographic defects, and thus the solubility and distribution of H in the microstructure, depends on the concentration, chemical potential, and local stress. Therefore, for a quantitative assessment of HEDE, a generalized solution energy in conjunction with the cohesive strength as a function of hydrogen coverage is needed. In this paper, we carry out density functional theory calculations to investigate the influence of H on the decohesion of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="normal">Σ</a:mi><a:mn>5</a:mn><a:mo>(</a:mo><a:mn>310</a:mn><a:mo>)</a:mo><a:mo>[</a:mo><a:mn>001</a:mn><a:mo>]</a:mo></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi mathvariant="normal">Σ</c:mi><c:mn>3</c:mn><c:mrow><c:mo>(</c:mo><c:mn>112</c:mn><c:mo>)</c:mo></c:mrow><c:mrow><c:mo>[</c:mo><c:mn>1</c:mn><c:mover accent="true"><c:mn>1</c:mn><c:mo>¯</c:mo></c:mover><c:mn>0</c:mn><c:mo>]</c:mo></c:mrow></c:mrow></c:math> symmetrical tilt GBs in bcc Fe, as examples for open and close-packed GB structures. A method to identify the segregation sites at the GB plane is proposed. The results indicate that at higher local concentrations, H leads to a significant reduction of the cohesive strength of the GB planes, significantly more pronounced at the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi mathvariant="normal">Σ</f:mi><f:mn>5</f:mn></f:mrow></f:math> than at the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi mathvariant="normal">Σ</h:mi><h:mn>3</h:mn></h:mrow></h:math> GB. Interestingly, at finite stress, the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi mathvariant="normal">Σ</j:mi><j:mn>3</j:mn></j:mrow></j:math> GB becomes more favorable for H solution, as opposed to the case of zero stress, where the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mi mathvariant="normal">Σ</l:mi><l:mn>5</l:mn></l:mrow></l:math> GB is more attractive. This suggests that, under certain conditions, stresses in the microstructure can lead to a redistribution of H to the stronger grain boundary, which opens a path to designing H-resistant microstructures. To round up our study, we investigate the effects of typical alloying elements in ferritic steel, C, V, Cr, and Mn, on the solubility of H and the strength of the GBs.