Numerical simulation of internal oxidation of steels during annealing treatments

This paper presents a new model for simultaneous diffusion and precipitation of chemical elements in metallic matrices, a scheme for its numerical solution, and several applications to problems of internal oxidation. The model basically stands as an extension of the classical Wagner model for internal oxidation of steels, but is more much general in that it allows for an arbitrary number of diffusing chemical elements, an arbitrary number of precipitate phases with arbitrary compositions, dependence of diffusion coefficients and solubility products upon (time-dependent) temperature, etc., thus allowing for a much broader range of applications. As a counterpart, it is generally impossible to solve the complex, non-linear equations of the model analytically, but this can be done numerically. The simple but efficient numerical scheme proposed is based on explicit 1D finite differences. Experience has shown that this scheme, in spite of its rusticity and the restrictions it imposes on the time-step, is more efficient than more elaborate strategies based on the finite-element method. The applications presented are concerned with internal oxidation of steels during annealing processes. The model and associated numerical scheme allow for evaluation of the amounts of the various oxide precipitates in the external layer of the sheet. This opens the way, through numerical parametric studies of the influence of the process parameters and the chemical composition, to the improvement of existing treatments and the development of new steel grades.