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Acta Metall Sin  2015, Vol. 51 Issue (9): 1136-1144    DOI: 10.11900/0412.1961.2015.00091
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SIMULATION OF GROWTH KINETICS OF PRO-EUTECTOID FERRITE USING MIXED CONTROL MODEL WITH CONSIDERATION OF DISLOCATION INTERACTION
Huidong WU,Chi ZHANG,Wenbo LIU,Zhigang YANG()
Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084
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Huidong WU,Chi ZHANG,Wenbo LIU,Zhigang YANG. SIMULATION OF GROWTH KINETICS OF PRO-EUTECTOID FERRITE USING MIXED CONTROL MODEL WITH CONSIDERATION OF DISLOCATION INTERACTION. Acta Metall Sin, 2015, 51(9): 1136-1144.

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Abstract  

During austenite to ferrite transformation, the lattice structure transforms from fcc to bcc, resulting in a clearly distinguishable austenite and ferrite interface. The short range diffusion of the Fe and C atoms across the interface causes its movement, referred to as interface migration. On the other hand, the C rejected by the ferrite during the austenite to ferrite transformation in Fe-C alloys accumulates ahead of the moving interface. This pile-up of C atom is dependent on the long range diffusion of C in austenite and also influences the ferrite growth kinetics. Experimental observations indicate that dislocations are always migrating with ledges during ledgewise growth. The local stress field of dislocations is considered to alter the solute concentration at the riser of ledges and causes a complex diffusion field interaction among ledges as they migrate. Some established works by other researchers have already taken the effect into consideration when studying phase transformation kinetics. However, these works were limited in diffusion control cases and could hardly explain some experimental results. In this work, a ledgewise growth model considering migration of austenite/ferrite interface, C diffusion in austenite and especially elastic interactions between dislocations moving with ferrite ledges was established, and all the simulated results were qualitatively similar to the reported experimental results. Calculated results showed that the C concentration at the riser of ledges was changed by the elastic stress of these dislocations, which would further change the growth behavior of ledges. In the growth behavior simulations of two ledges, the horizontal distance of the two ledges was found to be a key role to determine the growth kinetics. When the horizontal distance of two ledges was larger than the critical distance, an attractive phenomenon of the two ledges was found to decelerate the leading step; while a repulsive phenomenon of the two ledges which would accelerate the leading ledge if the horizontal distance was smaller than this value. Compared with the simulation results without considering elastic interactions between dislocations, however, in the growth behavior simulations of multi-ledge with elastic dislocation interactions, the coalescence behavior of ledges and growth rate of the leading step were both changed.

Key words:  pro-eutectoid ferrite      mixed-control model      ledgewise growth kinetics     
Fund: Supported by National Natural Science Foundation of China (Nos.51171087 and 51471094)

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https://www.ams.org.cn/EN/10.11900/0412.1961.2015.00091     OR     https://www.ams.org.cn/EN/Y2015/V51/I9/1136

Fig.1  Schematic of each ledges with one dislocation(Burgers vector b is parallel to the terrace plane, vi is the velocity of ledge i, "⊥" represents one edge dislocation)
Fig. 2  Schematic of C diffusion flux at austenite/ferrite interface ( Jint and Jint+Δx are C fluxes flowing into and out of interface in volume element Dx, respectively)
Fig.3  Graphical constructions for determination of cm2 and cm’2 ’ in cases of ΔG’th >0 (a) and ΔG′th <0 (b)( ΔGth, ΔGF, ΔG’th are free energy changes attending to phase transformation, dislocation interaction and combinationof the two, respectively. c0 is bulk carbon concentration. cm1,cm2, cm’2 are carbon concentrations of austenite at the interface without considering dislocation interaction, when ΔGF >0 and ΔGF <0 , respectively. ca is equilibrium carbon concentration of ferrite)
Fig.4  Influence of horizontal distance Xd between two ledges on elastic force acting on the unit length of ledge Fx (a) and carbon concentration change at the riser of ledge 1 Δcm resulting from Fx (b) ( ceq —equilibrium carbon concentration of austenite)
Fig.5  Simulation morphologies of two ledges pro-eutectoid ferrite during isothermal transformation of Fe-0.34%C alloy at 720 ℃ for normalized total isothermal transformation time T1 with (a) and without (b) considering dislocation interaction (X and Y correspond to normalized horizontal and vertical ordinates, respectively and both ordinates are four times expanded)
Fig.6  Normalized carbon concentration of austenite at the interface U (a) and ledge velocity V (b) evolutions with normalized transformation time T during isothermal transformation of Fe-0.34%C alloy at 720 ℃ with and without considering dislocation interaction with total transformation time T1
Fig.7  Simulation morphologies of two ledges pro-eutectoid ferrite during isothermal transformation of Fe-0.34%C alloy at 720 ℃ for normalized total isothermal transformation time T2 with (a) and without (b) considering dislocation interaction
Fig.8  U (a) and V (b) evolutions with T during isothermal transformation of Fe-0.34%C alloy at 720 ℃ with and without considering dislocation interaction with total transformation time T2
Fig.9  Simulation morphologies of 10 ledges pro-eutectoid ferrite during isothermal transformation of Fe-0.34%C alloy at 720 ℃ for normalized total isothermal transformation time T2 with (a) and without (b) considering dislocation interaction
Fig.10  Evolutions of growth velocity v1 (a) and length L1 (b) of ledge 1 with transformation time t
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