Modeling of isothermal bainite formation based on the nucleation kinetics

Abstract

Abstract Using a new approach to modeling bainite nucleation, the kinetics of isothermal bainite formation have been calculated under the assumption of displacive growth. The nucleation rate is assumed to depend on the number density of potential nucleation sites N i, a factor λ accounting for autocatalytic nucleation, and an activation energy Q*. Compatible with the theory for athermal martensite nucleation, N i is assumed to be proportional to the driving pressure. Analogous to the Koistinen – Marburger model for martensite formation, the average volume of bainitic sub-units is assumed to be constant over the extent of the transformation and the growth of sub-units is very fast, and thus the change in fraction is directly related to the nucleation rate of bainite. The model results in an analytical expression for the fraction bainite as a function of time that contains only two adjustable parameters: a (temperature independent) autocatalytic parameter λ and a rate parameter κ, which has a temperature dependence that is mainly governed by Q*. The calculations are compared with experimental fraction curves measured isothermally with dilatometry for the carbon steels C45, C50 and C60 at a range of temperatures. From the best agreement between the calculations and the experimental data it follows that Q* decreases linearly with temperature, which is consistent with other bainite nucleation models. By austenitizing steel C60 at different temperatures it is found that λ depends on the austenite grain size: when the austenite grain size is increased, λ becomes larger.