A Semiempirical Model for Sigma-Phase Precipitation in Duplex and Superduplex Stainless Steels

Sigma phase is known to reduce the mechanical properties and corrosion resistance of duplex and superduplex stainless steels. Therefore, heat treatments and welding must be carefully performed so as to avoid the appearance of such a detrimental phase, and clearly, models suitable to faithfully predict σ-phase precipitation are very useful tools. Most fully analytical models are based on thermodynamic calculations whose agreement with experimental results is not always good, so that such models should be used for qualitative purposes only. Alternatively, it is possible to exploit semiempirical models, where time-temperature-transformation (TTT) diagrams are empirically determined for a given alloy and the continuous-cooling-transformation (CCT) diagram is calculated from the TTT diagram. In this work, a semiempirical model for σ-phase precipitation in duplex and superduplex stainless steels, under both isothermal and unisothermal conditions, is proposed. Model parameters are calculated from empirical data and CCT diagrams are obtained by means of the additivity rule, whereas experimental measurements for model validation are taken from the literature. This model gives a satisfactory estimation of σ-phase precipitates during both isothermal aging and the continuous cooling process.