Computer simulation of thermochemical treatments: modelling diffusion and precipitation in metals

A model for simultaneous diffusion and precipitation in metals has been recently incorporated into a finite element computer code 1]2]. This model allows now for numerical simulations of various thermochemical treatments such as nitriding or carburizing. Subsequent quenching simulations are then made more accurate, by introducing the influence of the carbon content on the thermo-metallurgical and mechanical properties of the materials 3]. After recalling the mathematical equations used to model simultaneous diffusion and precipitation and their implementation into a finite element code, this paper deals with the method used to obtain the local fractions of precipitates as functions of the local content in each chemical element. The law of mass action is employed to calculate the fractions of precipitates obtained at thermodynamic equilibrium. This leads to a nonlinear complementarity problem. The method used to solve this problem is described in detail, and is validated by computing the phase diagram of a micro-alloyed steel. Finally, numerical simulations of combined diffusion and precipitation in steels point out the efficiency of the approach presented, as well as the important role played by precipitation during diffusion in metals.