Development of precipitation model with the use of the Lattice Boltzmann Method and its application for the rolling process

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A new precipitation model based on the Lattice Boltzmann Method with elements of Cellular Automata is presented in the paper. The model consists of three submodels: nucleation, precipitation growth, and diffusion of niobium and carbon.The nucleation model used classical nucleation theory and considers homo- and heterogeneous nucleation. The nucleation rate depends on the number of possible nucleation sites, which are defined by dislocation density, i.e. deformation conditions. The nucleation rate depends also on the Zeldowicz parameter, the factor of condensation rate, precipitation work, temperature, and other variables. The nucleation rate is realized in the model by calculating the probability of nucleon appearance in every cell, free of precipitation, and depends on the nucleation rate, the cell volume, and the time step.The growth or dissolution of the precipitation depends on the model on particle size and prevailing local conditions near the particle. The temperature and concentration define the equilibrium size of the particle.LBM model is applied to solve the Fourier equation for niobium and carbon diffusion. Near the precipitations equilibrium concentration of niobium and carbon is established according to precipitations size and temperature, while free diffusion is considered in the other space.Strain-induced precipitation at different temperatures and with the different constant cooling rate was simulated. Results are coincident with theory and experimental researches reported in the scientific literature.Modeling of precipitation during the rolling process with consideration of recrystallization shows an ability of the model to simulate and study the more complex processes that strain-induced precipitation in single deformation. It can be applied for multi-stages deformation processes to design or optimize them in view of precipitation and microstructure evolution.