Abstract
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.
Highlights
Titanium and its alloys are attractive materials for many structural applications in aerospace, industrial, and marine, because of their excellent specific strength, stiffness, and corrosion resistance
To verify the proposed hydrogen transport equation, the boundary conditions of the physical model were modified, so that the model can be simplified to pure diffusion, and to compare the results with the analytic solution. e load applied on the upper edge DE is set to 0 to avoid the stress effects. e hydrogen of the right edge CD is 40 mol/m3 during the diffusion, which is considered as the hydrogen source. e initial hydrogen in the plate is still uniformly distributed of 20 mol/m3
By incorporating a plate model with a central crack at different remote load conditions, it is found that the hydrogen diffusion near the crack is determined by the stress state
Summary
Titanium and its alloys are attractive materials for many structural applications in aerospace, industrial, and marine, because of their excellent specific strength, stiffness, and corrosion resistance. Dıaz et al [20] repeatedly revisited the coupled hydrogen diffusion simulation proposed by Sofronis et al, but they considered the plastic strain rate, the coupled diffusion, and stress-state dependent boundary conditions in the model. When dealing with the coupled mechanical and hydrogen transport problems, a so-called Oriani’s assumption and McNabb and Foster equation are widely used in the models. Many analytical solutions have been developed for the McNabb and Foster equation, such as approaches proposed by Javanmardi and Bashiri [27] or Azizian [28] to model the adsorption process and by Toribio et al [29, 30] for hydrogen-trapping estimation. A hydrogen transport equation is proposed to determine how hydrogen is distributed in titanium and how the stress state influences the hydrogen diffusion. By using the diffusion model built in this paper, the hydrogen diffusion in titanium structure with crack could be solved, and the quantitative prediction of hydrogen embrittlement could be achieved
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