Particle-size-grouping model of precipitation kinetics in microalloyed steels

The formation, growth, and size distribution of precipitates greatly affects the microstructure and properties of microalloyed steels. Computational particle-size-grouping (PSG) kinetic models based on population balances are developed to simulate precipitate particle growth resulting from collision and diffusion mechanisms. First, the generalized PSG method for collision is explained clearly and verified. Then, a new PSG method is proposed to model diffusioncontrolled precipitate nucleation, growth, and coarsening with complete mass conservation and no fitting parameters. Compared with the original population-balance models, this PSG method saves significant computation and preserves enough accuracy to model a realistic range of particle sizes. Finally, the new PSG method is combined with an equilibrium phase fraction model for plain carbon steels and is applied to simulate the precipitated fraction of aluminum nitride and the size distribution of niobium carbide during isothermal aging processes. Good matches are found with experimental measurements, suggesting that the new PSG method offers a promising framework for the future development of realistic models of precipitation.