Invited Lecture
Numerical analysis of diffusion-controlled internal corrosion by the cellular automata approach

For nearly all high-temperature applications of engineering alloys, diffusion-controlled internal corrosion processes are of particular technical relevance and high complexity. In general, an internal-corrosion process is considered to be a diffusion-controlled chemical reaction of a less-noble alloying element with a nonmetallic penetrating species such as oxygen, nitrogen, carbon, or sulfur. Kinetics are determined by the diffusivities and solubilities of the reacting species, as well as by the thermodynamic stability of the precipitates formed. Under well-defined simplified conditions, internal precipitation can be described by Wagner’s theory of internal oxidation where the diffusive fluxes of both reacting species are combined by mass equilibrium at the internal reaction front. However, important aspects of the mechanism like the possibility of less stable precipitates, nucleation and growth, mechanical stress effects and the transition from internal precipitation to external scale formation are neglected by Wagner`s theory. Therefore, numerical tools, using the finite-difference or the cellular automata concept, have been developed that are more flexible in accounting for such aspects and are introduced in the present paper.

Cellular automata (CA) represent distributed dynamical systems whose structure is particularly well suited to determine the temporal evolution of the system. By a meaningful definition of states and transformation rules, CA can be adapted to complex diffusion processes. It is shown that the model is able to consider nucleation and growth aspects, the transition from internal precipitation to superficial scale formation, interdiffusion between scales, and high diffusivity paths like grain boundaries and dislocations. This has been verified by applying CA to (i) internal nitridation of nickel-base superalloys, (ii) internal oxidation of low-alloy Cr steel, and (iii) interdiffusion within protective coating systems on plain carbon steel.