Critical verification of the effective diffusion concept

Knowing the hydrogen distribution c(x,t) and local hydrogen concentration gradients grad(c) in ferritic steel components is crucial with respect to hydrogen embrittlement. Basically, hydrogen is absorbed from corrosive or gaseous environments via the surface and diffuses through interstitial lattice sites into bulk. Although, the lattice diffusion coefficient D_L∼0.01mm²/s is in the order of magnitude of those for well-annealed pure iron, trapping sites in the microstructure retard the long-range chemical diffusion j_L=−D_chem(c)grad(c), causing local hydrogen accumulation in near surface regions in limited time. Considering pure ferritic crystals without trapping sites in the microstructure, the limited characteristic diffusion depth x_c∼√D_efft is proportional to the square root of the effective diffusion coefficient D_eff and of time t. Effective diffusion coefficients are measured independently for hydrogen using the electrochemical permeation technique. For pure crystals, the effective diffusion coefficient is constant at given temperature and allows accurate calculations of the diffusion depths. However, with trapping sites in the microstructure the effective diffusion coefficient is not a material property anymore and becomes dependent on the hydrogen charging conditions. In the present work, the theory of hydrogen bulk diffusion is used to verify the concept of effective diffusion. For that purpose, the generalized bulk diffusion equation was solved numerically by using the finite difference method (FDM). The implementation was checked using analytical solutions and a comprehensive convergence study was done to avoid mesh and time dependency of the results. It is shown that effective diffusion coefficients can vary by magnitudes depending on the sub-surface lattice concentration. This limits the application of the effective diffusion concept and also the calculation of the characteristic diffusion depth.