A Note on a Nonlinear Version of Wagner's Classical Model of Internal Oxidation

A nonlinear version of Wagner's classical model of internal oxidation is presented. This version accounts for the fact that precipitates may act as diffusion barriers by introducing a heuristic dependence of the diffusion coefficients of elements upon the local volume fraction of oxides formed. Remarkably, the now nonlinear problem still admits an analytic solution. This solution reveals a sudden and discontinuous transition from internal oxidation to formation of some external oxidized scale, when the fraction of oxide precipitates reaches some critical value which can be calculated explicitly in terms of the respective specific volumes of the matrix and the oxide.