Abstract
A computational 3D model that accounts for both nucleation and interface migration is a very useful tool to monitor and grasp the complexity of microstructure formation in low-alloyed steels. In the present study we have developed a 3D mixed-mode multigrain model for the austenite-ferrite and the austenite-ferrite-austenite formation capable of following diffusional phase transformations under arbitrary thermal routes. This new model incorporates the solute drag effect of a substitutional element (in this case Mn) and ensures an automatic change in transformation direction when changing from heating to cooling and vice-versa. An analytical solution for calculating the energy dissipation of solute drag together with multiple regression approximations for chemical potentials are proposed which significantly accelerate the computation. The modelling results are first benchmarked for an Fe-0.1C-0.5Mn (wt.%) alloy under different continuous cooling and isothermal holding conditions. The model revealed relatively large variations in transformation kinetics of individual grains as a result of interactions with neighboring grains. Then the model is applied to predict the transformation kinetics of a series of Fe-C-Mn alloys during cyclic partial phase transformations. The comparison with experimental dilatometer results nicely validates the predictions of this model regarding the change in overall transformation kinetics of the ferrite transformation as a function of the Mn content. New features of this model are its efficient algorithm to compute energy dissipation by solute drag, its capabilities of predicting the microstructural state for spatially resolved grains and the minimal fine tuning of modelling parameters. The code to implement this model is publicly available.
Highlights
The kinetics of the austenite (γ ) to ferrite (α) phase transformation in steels has been studied for decades using both experimental and modelling approaches [1,2]
For the same grain nucleated at the same temperature and the same position but exposed to a higher cooling rate, the Mn concentration across the interface is much lower and the C diffusion gradient is much higher, indicating that in this case the transformation kinetics is mainly controlled by C diffusion
The modelling results of the transformation kinetics during continuous cooling demonstrate that: 1) the model performs well in predicting the overall transformation kinetics during continuous cooling; 2) the development of physical and chemical characteristics can be monitored for each individual grain and 3) the contribution and dissipations of the Gibbs free energies can be calculated to understand the mechanism for the change in interfacial velocity
Summary
The kinetics of the austenite (γ ) to ferrite (α) phase transformation in steels has been studied for decades using both experimental and modelling approaches [1,2]. Given the heavy computational demands after incorporating solute drag, most established models are limited to 1D, with the exception of one 2D cellular automaton model [41], and all of these models only focus on the interface migration itself These studies provide a detailed insight into the transformation behavior during linear cooling, isothermal annealing and thermal cycling, two key parameters that need to be included to make the step to model transformation kinetics in real (3D) steels are still missing. These expressions were shown to be correct regardless of transformation directions (i.e. ferrite grains are growing or austenite grains are growing)
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