Microstructural development involving nucleation and growth phenomena simulated with the Phase Field method

A Phase Field model is developed for non-isothermal heat treatment conditions. Nucleation and growth occur on different time scales, to sample frequently enough to observe nucleation would require an impractically large number of integration cycles to be performed in order to observe growth kinetics in real alloys. For this reason, the Langevin noise terms in the Phase Field equations were replaced with a Poisson seeding algorithm, in which viable nuclei were introduced in the microstructure at a rate matched by the observed nucleation rate. The interparticle spacing for isothermal simulations was observed to be Dt, in agreement with hypothesis that nucleation stalls in isothermal simulations because of soft impingement. Kinetics were observed to give the correct Avrami exponent in the constant nucleation rate extreme, but deviated from the Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory with nucleation rates that varied with time. This was explained as being due to soft impingement, where JMAK theory is known to break down. Results of continuous cooling simulations showed a window of quench rates that would form bimodal particle size distributions, in agreement with recent experimental studies in superalloys.