Modeling of Pitting Corrosion Using Fick's Law of Diffusion Through XFEM

The mass-transport characteristics of the pit influence the pit growth kinetics through the pit electrolyte concentration. The ionic flux in the pit solution is driven by Fick’s law of diffusion [ 163 ]. Formation of salt layer on the pit surface is enforced due to the increase in ionic concentration within the pit solution, which reaches a supersaturation condition [ 292 , 318 ]. The ionic concentration of the salt layer is known as saturation concentration , as a notion of chemical equilibrium [ 61 , 399 ] between anodic and cathodic reactions. The movement of the dissolved metal ions in the pit governs the movement of the electrode boundary of the pit, making it a diffusion-controlled process. Thus, stable pitting corrosion of the metal is a diffusion-controlled dissolution process with a moving boundary. Such a problem is known as the classic Stefan problem [ 315 ]. This problem requires a detailed mass balance formulation between the metal and electrolytic solution, which can model a sharp moving electrode boundary [ 225 ]. The mass balance between the metal and the electrolytic solution, separated by a moving interface, in a stable pit growth condition, results in a set of governing equations that are solved for the concentration field and interface position (pit boundary evolution). The interface experiences a jump discontinuity in metal concentration. Because the problem involves moving boundary, modeling this process through conventional FEM is very cumbersome. Hence, we use the XFEM model with enriched functions to handle the moving boundaries. XFEM handles this jump discontinuity by using a discontinuous-derivative enrichment formulation, along with the level set method, which is employed for tracking the interface explicitly and updating it over time. A combined XFEM and level set method is developed in this chapter. A number of results for pitting corrosion of stainless steel 304 are presented. The above proposed model is validated by comparing the numerical results with experimental results, exact solutions, and some other approximate solutions.