Kinetics and kinematics for the metal oxidation on a spherical geometry

The oxidation of a metal sphere is analyzed using a regular perturbation method and an inelastic approach. As shown in our previous work [E.-S. Oh, A diffusional analysis for the oxidation on a plane metal–oxide interface, Chem. Eng. J. 117 (2006) 143–154; E.-S. Oh, A perturbation analysis for the metal oxidation fo cylindrical geometries, J. Chem. Eng. Japan 39 (1) (2006) 57–67], the perturbation analysis provides detailed information on the oxide thickness from the location of both moving metal–oxide and oxide–oxygen (air) interfaces, as well as on the concentration of oxygen in each phase. This is compared to the result numerically calculated in literature [P.B. Entchev, D.C. Lagoudas, J.C. Slattery, Effects of non-planar geometries and volumetric expansion in the modeling of oxidation in titanium, Int. J. Eng. Sci. 39 (2001) 695–714]. In addition, a simple inelastic approach [E.-S. Oh, J.R.Walton, D.C. Lagoudas, J.C. Slattery, Evolution of stresses in a simple class of oxidation problems, Acta Mech. 181 (2006) 231–255] is applied to calculate the stress distribution developed during the oxidation of the metal sphere.