Phase Field Simulation Of Martensitic Transformation In Steel

As one of the important phases in steel,the martensite has been suggested as a predominant role to accommodate the strength and toughness of steel,which means that it should be an effective method to improve the steel performance by the means of controlling martensitic transformation and reverse transformation.A complex heat treatment process is always adopted in industry to regulate the proportion of martensite and retained austenite.However,it should be noted that the complex microstructural evolution is accompanied within martensitic transformation and reverse transformation in such heat treatment process,which is difficult to be observed and predicted accurately by current experimental or theoretical methods.On the other hand,phase field models are reasonably effective at providing microscopic-scale simulations by predicting microstructural morphologies,and have recently emerged as a versatile tool for describing microstructural evolution during material processing.Nonetheless,the present phase field simulations are mainly implemented with regard to simple martensitic transformation behavior,such as the realization of martensitic transformation,the orientation relationship of martensite variants,nucleation factors and some specific phenomena during martensitic transformation,while little attention has been paid to related behaviors of martensitic transformation and reverse transformation in complex process.Simulations for such complex microstructural evolution are helpful to make up for the shortcomings of experimental and theoretical methods in microscale,and deepen the understanding for phase transformation and microstructural morphology with the perspective of thermodynamics.In the present study,based on the phase field microelasticity model,a time-dependent Ginzburg-Landau equation for microscopic plastic flow,a muti-parameters Allen-Cahn equation and a Cahn-Hilliard equation are coupled respectively,to realize the prediction of complex martensitic transformation and reverse transformation.Both finite element and finite difference methods are applied to realize numerical solution of such models,to ensure the accuracy and efficiency of simulations.As a result,the complex martensitic transformation behavior in the Q&P process,the reverse martensitic transformation phenomenon during intercritical annealing process and the martensitic transformation plasticity for transformation loading process are studied respectively,and such simulation results are in good agreement with the existing experimental results or theories.The main achievements of the present work are:A modified parameter is introduced into the phase field microelasticity model of Fe-0.22C-1.58Mn-0.81Si(wt.%)steel to modify simulated results,making the martensite fractions of athermal martensitic transformation predicted by phase field model are agree with experimental values well.Simulation results suggest that volume fractions of retained austenite after the secondary quenching are higher than the value after direct quenching,due to the contribution of carbon redistribution to austenite stability enhancement.Meanwhile,results also demonstrate that such values are lower compared to values after the first quenching,indicating that the stability of such untransformed austenite is incompletely although the carbon redistribution has evolved for 80 s during partitioning process.A dependence of martensitic transformation dynamics on the quenching temperature is confirmed,and an optimal temperature(290 ℃ or 300 ℃)can be predicted to obtain the maximum amount of retained austenite.A coupled phase field model is applied to investigate the isothermal transformation behavior and carbon diffusion during partitioning process.As the coupled modelling contained both the Allen-Cahn and Cahn-Hilliard equations is developed,an assumption is adopted that microstructural evolution controlled by the Allen-Cahn equation has always kept in the stable state to combine the real and dimensionless temporal scales.Simulation results reveal that the interfacial migration is confirmed in the early stage during partitioning step and shown as reverse martensitic transformation.Such migration behavior keeps a weak dependence on the partitioning temperature and shows an anisotropic migrating process due to the heterogeneous distribution of elastic strain energy.Formation of isothermal martensite is predicted after an incubation period,which is attributed to both the elastic and chemical driving forces.The isothermal martensitic transformation is significantly affected by temperatures,resulting in obvious difference of the transformation kinetics curves at various partitioning temperatures.To replicate the microstructural evolution produced during reverse transformation,both the displacive and diffusional transformation mechanisms are considered by a coupled modelling approach,in which both phase field microelasticity and multi-phase field models are contained.Fully martensitic structures of Fe-9.6Ni-7.1Mn(at.%)steel at room temperature are taken as starting microstructures to exclude the influence of retained austenite during simulations.Simulation results demonstrate that the acicular reverse austenite firstly formed along the martensite lath boundaries at 600 ℃ under the displacive mechanism,and continue to grow during the subsequent diffusional transformation.The globular reverse austenite can be formed at high prior austenite grain boundaries by diffusional transformation under various temperatures,and holds a partial non-orientation relationship with neighboring martensite laths.As time progresses,the globular austenite grows preferentially toward the martensite laths those lie on one side of the prior austenite grain boundary.Partitioning behavior of Mn and Ni elements is considered in simulations,and an alloy influence coefficient is introduced to illustrate the contribution of different alloy elements to the chemical Gibbs free energy.Result shows a high enrichment of alloying elements within the acicular austenite,which indicates that the transformation can be described by a mixed-controlled mode dominated by the interface-controlled part.On the other hand,diffusioncontrolled part of the mixed-controlled mode plays a predominant effect for the growth of globular austenite,resulting in an almost partitionless process for the formation of globular austenite.Invasive growth behavior of globular austenite to acicular austenite can be observed upon impingement at the later stage during diffusional transformation,which is attributed to the minimization of gradient energy in the system and the concentration difference of alloying elements within the two types of reversed austenite.This behavior can be considered as a possible mechanism for grain refinement during intercritical annealing process.A time-dependent Ginzburg-Landau equation is coupled with the phase field microelasticity model,to investigate microscopic transformation flow during martensitic transformation,which is referred to as the elastoplastic phase field model.This model is applied in conjunction with Fe-0.22C-1.58Mn-0.81Si(wt.%)steel to investigate transformation plasticity of martensitic transformation in response to uniaxial,biaxial,shear and axialshear loadings below half the yield strength of austenite.The simulation results clearly suggest that the transformation plasticity coefficient is independent of external stress.Similar microstructural evolution and deformation behaviors are identified in response to both uniaxial and biaxial loadings when the uniaxial stress is equal to the difference in applied stresses along both axes during biaxial loading,and the equivalent values of transformation plastic strains are roughly the same regardless of the stress components in the combined axial and shear loadings.The simulation results also demonstrate that the preferential orientation can occur under both axial and shear loading conditions,in which the loading direction determines the variant type of preferential orientation and the load value can affect the magnitude of preferential orientation.It is also evident that different preferential orientation trends are obtained under axial and shear loads,which can be attributed to different contribution of the external energy term in the total Gibbs free energy,resulting in a lack of regular relationships between preferential orientations and axial-shear loads.The transformation plastic strain generated during martensitic transformation is controlled by both the Magee and Greenwood-Johnson mechanisms,with the Magee mechanism playing a more dominant role.