Abstract
A numerical finite difference method is developed here to solve the diffusion equation for hydrogen in presence of trapping sites. A feature of our software is that an optimization of diffusion and trapping parameters is achieved via a non linear least squares fit. On the other hand, we have demonstrated that usual electrochemical hydrogen permeation tests are enough to assess hydrogen free energies of trapping in the range of −35 kJ/mol to −70 kJ/mol. These conclusions are obtained by assuming the presence of saturable traps in local equilibrium with hydrogen and are validated by means of simulated permeation and degassing transients. In addition, we check our model performing electrochemical hydrogen permeation tests at 30°C, 50°C, and 70°C, on an API 5L X60 as received steel state to study its trapping and diffusion properties considering only one type of trapping site. The binding energies (ΔG) and the trap densities (N) are determined by fitting the theoretical model to the experimental permeation data. The steel presents a high density of weak traps, |ΔG|<35 KJ/mol, namely, N=1.4×10−5 mol cm−3. Strong trapping sites which alter the shape of the permeation transient are also detected; their ΔG values ranged from 57 to 72 KJ/mol.
Highlights
In the literature it is possible to find different approaches to fit simulated hydrogen permeation transients to experimental ones, generally based on the model of McNabb and Foster [1]
For the as received-API 5L X60 condition we assume only one kind of trapping site, and we demonstrate that it is enough to achieve an excellent fit of the calculated transient to the experimental one
The permeation transients calculated in this way with the software of [7] are presented in Figures 10, 11, and 12 together with the theoretical permeation transients calculated with the software used in the present work
Summary
In the literature it is possible to find different approaches to fit simulated hydrogen permeation transients to experimental ones, generally based on the model of McNabb and Foster [1] Nowadays, this formulation is the most accepted model of hydrogen permeation in presence of one type of traps, with kinetic trapping and detrapping parameters k and p, respectively. Following the formulation and methods of Ferris and Turnbull, Ramunni et al obtained trapping parameters for a steel with different microstructures, where the cementite morphology is changed through selected thermal treatments [7] They are able to simulate permeation transients covering the whole possibilities of the McNabb and Foster formulations, they restricted themselves to the case of local equilibrium, by setting the kinetic parameters high enough to guarantee a fast hydrogen exchange between traps and normal lattice sites. A brief conclusion to summarize the relevant points of the present work is presented
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