One-dimensional governing equations for the creep under hydrogen diffusion flow

Saturation of some metals with hydrogen, in particular α-iron, immediately in the process of loading can cause a great increase of their deformation response. The study is aimed at the macroscopic description of this phenomenon. The constructed governing equations are based on the concept of the equation of state with internal parameters. The modeled experiment involves saturation of a cylindrical specimen with hydrogen from the electrolyte, loaded torque. The analysis of both research literature and experimental data justified the applicability of the linear boundary conditions of the first and third kinds. This made it possible to use the analytical solutions in the form of Fourier series of Bessel functions for the classical diffusion equation. It turned out that the scatter of diffusivity, reported by different authors, can result in a significantly different interpretation of the experiments. For the most common value of D of the order 10 -9m 2s 4, the calculated time for the complete saturation of the specimen was approximately a few minutes, which diverged from the characteristic times of the experiment. The explanation could have been either a lower value of diffusivity, or the presence of the so-called “traps”. Inclusion of the limited capacity traps with the irreversible capture into the model has also enabled us to explain the presence of a noticeable incubation period. The study did not take into account the dependencies of D on the accumulated plastic strain, the stress gradient, and concentration. From the time dependences of the concentration and its derivatives the authors concluded that the hydrogen concentration should be the first to be considered as a parameter of the state. Furthermore, the creep power index was kept constant but the creep coefficient was assumed to be dependent on hydrogen concentration as well as on the accumulated plastic strain. The latter dependence was justified by the gradual strain rate deceleration for the loading below the macroscopic yield stress. The numerical results have demonstrated the principal possibility of macroscopic modeling of deformation synergistic effects under hydrogen absorption.