We propose a theoretical-experimental approach to the determination of the concentration of hydrogen in the process zone. The plots of the dependences of the concentration of hydrogen on the mechanical characteristics of the material and external load are constructed.In the contemporary science, much attention is given to the development of the method aimed at the evaluation of the concentration of hydrogen in metals; in particular, in the process zone, where the material is deformed under stresses exceeding the yield strength. In [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], the influence of the stress-strain state on the distribution of hydrogen in the process zone was investigated in various specific cases.
Formulation of the Problem and Its SolutionThe distribution of the concentration of hydrogen near the crack tip was found on the basis of the solution of the Fick equation, which takes into account the influence of the gradient of mechanical stresses on the diffusion of hydrogen in the process zone [12]:where C = C x, y, t ( ) is the hydrogen concentration, ∇ = ∂/∂x, ∂/∂y ( ) is the Hamiltonian operator, D is the diffusion coefficient, R is the universal gas constant, T is absolute temperature, V H is the partial molar volume of hydrogen in the metal, σ h is the hydrostatic component of the stress tensor in the metal, and t is time.The Fick equation (1) is solved in a two-dimensional domain S (Fig. 1). In this case, it is assumed that the hydrogen distribution in the domain S is uniform and equal to C 0 . Hence, we use the following initial conditions for the distribution of hydrogen:(2)
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