In the article titled “Numerical Analysis of the Coupling between Hydrogen Diffusion and Mechanical Behavior near the Crack Tip of Titanium” [1], there was a spelling error in author Wen-juan Zhan’s name in the authors’ list, where “Wen-juan Zhan” should have read “Wen-juan Zhang.”

Hydrogen embrittlement, as one of the major concerns for austenitic stainless steel, is closely linked to the diffusion of hydrogen through the grain boundary of materials. The phenomenon is still not well understood yet, especially the full interaction between hydrogen diffusion and the misorientation of the grains. This work aimed at the development of a robust numerical strategy to model the full coupling of the hydrogen diffusion and the anisotropic behavior of crystals in 316 stainless steel. A constitutive model, which allows easy incorporation of crystal orientation, various loading conditions, and arbitrary model geometries, was established by using the finite element package ABAQUS. The study focuses on three different bicrystal models composed of misoriented crystals, and the results indicate that the redistribution of hydrogen is significant closely to the grain boundary, and the redistribution is driven by the hydrostatic pressure caused by the misorientation of two neighboring grains. A higher elastic modulus ratio along the tensile direction will lead to a higher hydrogen concentration difference in the two grains equidistant from the grain boundary. The hydrogen concentration shows a high value in the crystal along the direction with stiff elastic modulus. Moreover, there exists a large hydrogen concentration gradient in a narrow region very close to the grain boundary to balance the concentration difference of the neighboring grains.

Hydrogen plays a detrimental effect on the degeneration of titanium and its alloys, and it is very important to quantify the hydrogen concentration when estimating the microstructure evaluation of titanium and its alloys in a hydrogen environment. In this paper, the hydrogen atoms are assumed to reside in interstitial sites and in trapping sites such as dislocations, and a mechanic-diffusion coupled model was proposed to describe the stress effects on the diffusion of hydrogen in titanium. A titanium plate with a central crack was modeled to verify the mechanic-diffusion model, and it is solved by the finite element method in commercial software COMSOL. The results indicate that hydrogen diffusion near the crack is determined by the stress state. When the stress state of the crack tip is elastic, the hydrogen will diffuse from both sides of the crack towards the tip and lead to the highest hydrogen concentration in the crack tip. When a plastic zone exists in front of the crack tip, the highest hydrogen concentration at crack surface deviates to the side near the crack tip; a hydrogen concentration peak exists at a characterized distance in front of crack tip initially and then diminishes with the diffusion process. The proposed model is expected to solve the hydrogen concentration under stress in more complex structures.