MODELING OF ISOTHERMAL AUSTENITE TO FERRITE TRANSFORMATION IN A Fe-CALLOY BY PHASE-FIELD METHOD
Jun ZHANG1,2,Chengwu ZHENG2(),Dianzhong LI2
1 School of Chemistry and Materials Science, University of Science and Technology of China, Hefei 230026, China 2 Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China;
Cite this article:
Jun ZHANG,Chengwu ZHENG,Dianzhong LI. MODELING OF ISOTHERMAL AUSTENITE TO FERRITE TRANSFORMATION IN A Fe-CALLOY BY PHASE-FIELD METHOD. Acta Metall Sin, 2016, 52(11): 1449-1458.
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 their properties. 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 numerical models for adequate quantitative descriptions of the nucleation and growth of ferrite grains as well as the overall transformation kinetics. In this work, a modified multi-phase field model has been developed to simulate the isothermal γ-α transformation in a Fe-C alloy. This model takes both the effect 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 γ-α 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 have been imulated. The simulation results indicate that the nucleation density of ferrite increases with decreasing the 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. The simulation results also indicate that the transformation mode from austenite to ferrite varies from essentially diffusion-controlled at high temperature towards interface-controlled at low temperature.
Fig.1 Profiles of order parameter of grain i, ηi(r, t) (a) and carbon concentration x(r, t) (b) across the interface between austenite and ferrite (δ denotes the interface width; xγ and xα are the carbon contents in γ and α, respectively; x is the actual carbon content)
Fig.2 Simulation results of the temporal evolutions of the microstructure (a1~a4) and carbon concentration field (b1~b4) by phase-field at 1050 K during the isothermal transformations at time t =2 s (a1, b1), t =16 s (a2, b2), t =48 s (a3, b3) and t =60 s (a4, b4)
Fig.3 Profiles of carbon concentration across the interface along the growth direction shown in Fig.2a2 during the ferrite growth (xcγ,eq is the local-equilibrium carbon concentration andx0is the nominal carbon concentration, the arrow indicates the growth direction of the ferrite)
Fig.4 Effect of carbon diffusional mobility Mcγ on carbon concentration profile across the austenite-ferrite interface at different times (Arrow indicates the growth direction of the ferrite)
Fig.5 Driving forces for austenite-to-ferrite transformation as a function of carbon concentration in austenite
Fig.6 Simulation results of the microstructure evolution during the austenite-to-ferrite transformation at different isothermal temperatures (T) and t(a1) T=1010 K, t =2 s (a2) T=1010 K, t =16 s (a3) T=1010 K, t =32 s (a4) T=1010 K, t =48 s(b1) T=1048 K, t =2 s (b2) T=1048 K, t =16 s (b3) T=1048 K, t =48 s (b4) T=1048 K, t =60 s(c1) T=1087 K, t =2 s (c2) T=1087 K, t =16 s (c3) T=1087 K, t =48 s (c4) T=1087 K, t =100 s
Fig.7 Kinetics of austenite-to-ferrite transformation at different isothermal temperatures
Fig.8 Simulation results of carbon concentration field at different times during the austenite-ferrite transformation at different T and t(a1) T=1010 K, t =2 s (a2) T=1010 K, t =16 s (a3) T=1010 K, t =32 s (a4) T=1010 K, t =48 s(b1) T=1048 K, t =2 s (b2) T=1048 K, t =16 s (b3) T=1048 K, t =48 s (b4) T=1048 K, t =60 s(c1) T=1087 K, t =2 s (c2) T=1087 K, t =16 s (c3) T=1087 K, t =48 s (c4) T=1087 K, t =100 s
Fig.9 Profiles of carbon concentration across moving interface along the growth direction shown in Fig.8 at T=1010 K (a), T=1048 K (b) and T=1087 K (c) (Solid lines represent the carbon concentration profiles at different times. The circles indicate the carbon concentrations calculated by the interface-controlled model)
Fig.10 Mode parameter S as a function of ferrite fraction at different temperatures
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