Thermo-chemical-mechanical simulation of low temperature nitriding of austenitic stainless steel; inverse modelling of surface reaction rates

A multi-physics thermo-chemical-mechanical 1-dimensional implicit finite difference model is presented to simulate the evolution of composition and residual stress profiles over the expanded austenite case developing during low temperature nitriding of austenitic stainless steels. The model combines 1-dimensional diffusion of nitrogen in the depth direction with a concentration-dependent diffusivity, elasto-plastic accommodation of the lattice expansion, stress gradient-induced diffusion of nitrogen, solid solution-strengthening by nitrogen and trapping of nitrogen by chromium atoms. The rate of the surface reaction governing the transfer of nitrogen from the gas to the solid is unknown and was evaluated by inverse modelling. The modelling was applied adopting the surface reaction rate as the only fitting parameter and taking mass-uptake curves (thermogravimetry) as the constraint, while all other data were taken from established literature values. Very good agreement is achieved between the predicted and experimental composition-depth profiles. Further, the applicability of the present model to plasma nitriding was verified by simulating (not fitting) the evolution of composition-depth profiles obtained after plasma nitriding of stainless steel. The good to very good agreement of the present model's predictions with experimental data for gaseous and plasma nitriding, indicates that the essential multi-physics influences and parameters are taken into account, with a minimum of adjustable parameters.