Mathematical modeling of residual stresses and distortions induced by gas nitriding of 32CrMoV13 steel

The aim of this paper is to provide a model simulating the nitriding of 32CrMoV13 low alloy steels. The model is based on thermodynamics of irreversible processes and chemical kinetics. The mechanical approach is based on the mechanics of continuous media and considers an elasto-viscoplastic constitutive law. A self-consistent scale transition scheme establishes the link between chemical and mechanical calculations. The simulation describes the diffusion of nitrogen and carbon, the main precipitations with the associated volume changes, the residual stresses developed during treatment, and the distortions of complex structural parts. It enables evaluating the macroscopic volumetric eigenstrains, the thermal strain and the variation of Young’s modulus induced by the treatment. The problem is solved by Finite Element calculations. The unknown inputs of the model are identified through an inverse method using different kinds of experimental data such as nitrogen and carbon mass fractions, distortions and residual stresses. Flat and cylindrical samples are employed for that purpose. These specimens are gas nitrided during 120 h at 550 °C. The simulation program is finally validated on a sample of complex geometry treated in the same conditions. The distortions predicted by the model are therefore compared to results of measurements carried out by 3D full-field optical scanning.