Mathematical Model of Hydrogen Permeability of Metals with Impurities Traps in the Presence of Internal Stresses of Various Physical Nature

The interaction of hydrogen with metals is the main process of at least two areas of scientific research. One of the research directions is hydrogen energy. The second one is the development of effective coatings with the aim of keeping hydrogen atoms in the near-surface layer of structural elements for various purposes. The paper shows the process of creating a physical and mathematical model of the hydrogen permeability of electrochemical alloys synthesized by electrolysis depending on the level, sign, and nature of the distribution of internal stresses. We have analyzed the causes, nature and levels of internal stresses of various physical nature. Diffusion flows are shown through the external surface of a hollow cylinder depending on the sign of internal stresses. The diffusion of hydrogen atoms through a cylindrical shell with impurity traps is described by a non-stationary equation under the corresponding initial and boundary conditions. The choice of such a model system is due to the fact that cylindrical shells are the most common structural elements, and the complication of the mathematical model would not lead to a change in the qualitative picture of the concentration field of hydrogen atoms. For the fields of hydrogen atom concentration, we have used the corresponding analytical dependences which are the basis for mathematical modeling of diffusion processes and demonstrate the ability to control the hydrogen permeability of metals. The hydrogen permeability of a hollow cylinder primarily is shown to depend on the level and nature of the distribution of internal stresses (tensile and compressive). Internal stresses with a logarithmic dependence on coordinates have a single mathematical description, and using the superposition principle allows you to display a picture of the joint interactions of internal stress fields of various origins. When describing diffusion fluxes, two approaches are used. In the first approach, taking into account internal stresses that change the diffusion equation reduces to the introduction of some dimensionless parameters that are easily calculated, while using the principle of superposition, their algebraic summation is allowed. This allows parametrically controlling the internal stresses of different physical nature. The second one allows us to describe a mathematical model of the diffusion process of hydrogen atoms in a medium with the formation and decomposition of fixed metal − impurity − hydrogen complexes, taking into account the probability of their formation and disintegration.

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