Stochastic model of accelerated cooling of eutectoid steel rails

Abstract The paper proposes a methodology for incorporating uncertainties of material behaviours in the microstructure evolution model for eutectoid steels. The stochastic model of phase transformations was developed. The model accounts for a random character of the nucleation of pearlite and bainite and the differential growth equations for these structural components are solved for the stochastic variables. The coefficients in the model were identified using inverse analysis for the results of dilatometric tests. The model was applied to simulations of the cooling of rails by subsequent immersions of the rail head in the polymer solution. Johnson–Mehl–Avrami–Kolmogorow phase transformations model was used to design the optimal cooling cycle. Histograms of the microstructural parameters for this optimal cycle were calculated using the developed stochastic model. It was shown that the probability distributions of the pearlite colony size, the nodule size, the interlamellar spacing and the hardness are asymmetric. The model predicted deviations of microstructural parameters and hardness from the mean values.