A model for precipitation-temperature-time curve calculation

Nanometer precipitation is of great importance to the mechanical properties of the low carbon micro-alloyed steel. Precipitation process is controlled by the driving force for precipitation and the diffusion rate of atoms. Under the influence of these two factors, the fastest precipitation temperature for (M_x¹M_v²M_1-x-v³)(C_yN_1-y) phase is available, which is also known as nose temperature. The maximum number density of precipitates can be obtained through isothermal treatment at the nose temperature. The most effective tool for getting the value of nose temperature is the precipitation-temperature-time (PTT) curve. Due to that the diffusivity of substitutional atom is several orders of magnitude smaller than that of interstitial atom, the nucleation process and growth process of complex precipitation are controlled by the diffusion of substitutional atoms. So far no model has been established for calculating PTT curve of complex precipitation. All the existing models are established for simple precipitation. In this work, a kinetic model, based on the classical nucleation and growth theories and Johnson-Mehl-Avrami equation, employing Adrian thermodynamic model and L-J model, using average diffusivity to demonstrate the effects of forming elements on precipitation process, has been adapted to describe the precipitation kinetics following high temperature deformation in micro-alloy steels alloying with V, Nb and Ti. Using this model, the PTT curves for the kinetics of second phase were easily obtained. In the experiment, within the temperature range from 660 to 540℃, the nose temperature of carbonitride precipitation is equal to or slightly higher than 620℃. The value of nose temperature estimated from PTT curve is 628℃ which is consistent with the experimental observation. There are enough reasons to believe that the model proposed in this work can estimate accurately the nose temperature information in relatively small experiment case. This model has outstanding advantages in comparison with existing models: the mole fraction of precipitation and the driving force for precipitation per unit volume ΔG_v can be calculated directly without calculating the solubility formula of complex carbide in matrix; The proposed model can also be used to calculate the absolute solution temperature and the constituent of initial complex precipitation forming at critical temperature of precipitation, which can be used as the iterative initial values for calculating the equilibrium information between matrix and precipitation at relatively low temperatures.