Phase-Field Modeling Of Austenite-to-Ferrite Transformation In Fe-C-Mn Alloys

With the high and growing demands for materials performance,it has attracted much attention on developing superior mechanical behaviors in alloys,mainly because of strong dependence of the tensile strength and ductility of the material on the microstructure evolution during processing.Austenite-to-ferrite transformation in modern steels is a key metallurgical phenomenon as it can be exploited to produce microstructures that are closely associated with significant improvement of the properties.In order to obtain excellent microstructure characteristics and material mechanical properties by designing the alloy compositions and appropriate processing steps,it is of great importance to investigate the transformation thermodynamics and kinetics,and microstructure evolution during the austenite-to-ferrite transformation.Currently,both experimental and theoretical studies of this transformation have received much attention.In particular,in recent years,considerable efforts have been directed to the development of mesoscopic models for adequate quantitative descriptions of the nucleation and growth of ferrite grains as well as the overall transformation kinetics.In this paper,the phase-field method was used to model the austenite-to-ferrite transformation.A modified multi-phase field model has been developed to simulate the isothermal ?-a transformation in a Fe-C alloy.This model takes both the effects of a finite interface mobility and a finite diffusivity into account,which hence enables a clear description of the mixed-mode nature of the transformation.In contrast to the diffusion-controlled phase transformation model,the carbon concentration in front of the moving ?/? interface is found to be non-equilibrium under this circumstance.In order to study the microstructural behavior and kinetics over the entire temperature range of the phase transformation,three different isothermal transformation processes were simulated.The simulation results indicated that the nucleation density of ferrite increases with decreasing temperature,which thus leads to a larger volume fraction of ferrite.However,the heterogeneous distribution of carbon in the untransformed austenite is intensified.The final microstructural product of the transformation at low temperature of 1010 K consists of fine residual austenite islands surrounded by fine polygonal ferrite grains.The simulation results also indicated that the transformation mode from austenite to ferrite varies from essentially diffusion-controlled at high temperature towards interface-controlled at low temperature.In order to investigate the effect of Mn on the austenite-to-ferrite transformation,a multi-phase-field(MPF)model coupling with a Gibbs-energy dissipation model was developed to simulate the isothermal austenite-to-ferrite transformation in ternary Fe-C-Mn alloys.This model considered the Mn diffusion inside the migrating interface in a physical manner and took its effect on the transformation kinetics into account.Comparison simulations were made to analyze the difference in the transformation kinetics and ferrite morphologies with and without considering the energy dissipation at the moving interface.It showed that the incomplete transformation phenomenon does occur due to the Mn diffusion inside interface.The modified MPF model was then used to study the effect of Mn contents on the microstructures and kinetics of the phase transformations.It was found that the ferrite growth along the austenite/austenite boundaries is faster than that in the perpendicular direction.This difference is intensified with increasing the Mn concentration,which hence leads to the ferrite morphology changed from elliptical to flat alike.It also presents a slower transformation kinetics,a larger degree of the incomplete transformation and a more interface controlled mode when increasing the Mn concentration.In addition,the phase-field method could readily be used to simulate the complex morphological phenomena during the austenite-to-ferrite transformation in steels in view of its convenience to include the material properties,especially the grain boundary properties,in a phenomenological way,and thus to model the microstructural processes in an anisotropic system.Therefore,a modified multi-phase-field model that takes into account various anisotropic interfacial conditions has been developed to simulate the growth morphology of ferrite during the austenite-to-ferrite transformation in a Fe-C-Mn alloy.In this model,a quantitative relation between the MPF model parameters and the physical anisotropic interfacial properties,including the grain-boundary energy and the mobility,was carefully considered,which allowing identical width of the diffuse interface regarding arbitrary interfacial anisotropies in the MPF simulations.In this way,both the accuracy and the numerical stability of the model could be ensured.Using this model,the effects of the grain boundary anisotropy on the ferrite growth were studied.The simulation results indicated that,apart from the interfacial energy of ??.?,the grain boundary energy between the initial austenite grains,??.?,does also significantly influence the growing morphology of ferrite.The ferrite growth along the initial austenite grain boundaries is facilitated when increasing the ratio of ??.?/??.?,and hence leads to a smaller equilibrium angle at the triple junction.The results also indicated that misorientation-dependent grain boundary energy and mobility play important roles in the ferrite growth behavior.The growth of ferrite with a low misorientation a/y interface is greatly inhibited.The ferrites nucleated at the triple junctions of the initial austenite grains present different growth scenarios while assigning different orientation relationships.Finally,comparison simulations of ferrite morphologies in a polycrystalline structure are implemented with and without considering the anisotropic grain boundaries.Futher,the simulated results of anisotropic microstructure were compared with the optical micrograph and were found in good agreement as a result.This MPF model could replicate the morphology diversity of the ferrite grains in the austenite-to-ferrite transformation.