Predicting the Transition between Upper and Lower Bainite via a Gibbs Energy Balance Approach

doi:10.1016/j.jmst.2016.11.028

Abstract

Abstract:

The transition temperature between upper bainite and lower bainite is calculated with an extended Gibbs energy balance model, which is able to quantitatively describe the evolution of carbon supersaturation within bainitic ferrite sheaves during the entire thickening process. The nucleation rate of intra-lath cementite precipitation on a dislocation is calculated based on of the degree of carbon supersaturation. Upper bainite and lower bainite are thus distinguished by the effective nucleation density and therefore a numerical criterion can be set to define the transition. The model is applied to Fe-xC-1Mn/2Mn/1Mo ternary alloys. Results show that the transition temperature increases with bulk carbon content at lower carbon concentration but decreases in the higher carbon region. This prediction agrees very well with the experimental observations in Mn and Mo alloyed systems. Moreover, the highest transition temperature and the carbon content at which it occurs in the Fe-xC-2Mn system are in good agreement with reported experimental data. The inverse “V” shaped character of the carbon concentration-transition temperature curve indicates two opposite physical mechanisms operating at the same time. An analysis is carried out to provide an explanation.

Key words: Bainite, Interface migration, Carbon diffusion, Gibbs energy balance, Low-alloy steel

Yang Zenan, Xu Wei, Yang Zhigang, Zhang Chi, Chen Hao, van der Zwaag Sybrand. Predicting the Transition between Upper and Lower Bainite via a Gibbs Energy Balance Approach[J]. J. Mater. Sci. Technol., 2017, 33(12): 1513-1521.

Figures/Tables 12

Fig. 1. Schematic illustration of quadratic profiles of carbon concentration in the non-overlapping diffusion stage in austenite but overlapping in ferrite. The shape of the carbon profile in bainite is presented by the quadratic Taylor expansion.

Fig. 2. Schematic illustration of quadratic profiles of carbon concentration in the overlapping diffusion stage in both austenite and ferrite.

Fig. 3. 3-D morphology of critical nucleus.

Fig. 4. Dimension parameters of critical nucleus and the ratio of Gibbs energy barrier for nucleation on dislocation to homogeneous as a function of β[26].

Table 1 Physical parameters for nucleation rate calculation

Physical parameter	Symbol	Value	Ref.
Burgers vector	b	2.5·10^-10m	^[33,34]
Cementite nucleation driving force	FV	TCFE6 Database	^[35]
Shear modulus	G	8.3·10⁹ Pa	^[36,37]
Dislocation density	Nd	10¹⁴m^-2	^[38]
Diffusivity of iron on grain boundary	Qdα	155 kJ/mol	^[39]
Cementite molar volume	Vmθ	6.0·10^-6 m³/mol	^[35]
Interfacial energy between α and θ	σα/θ	0.55J/ m²
Debye temperature of ferrite	θD	430 K	^[40]

Fig. 5. Series of steady state carbon profiles of an Fe-0.1C-1Mn alloy at 470 °C.

Fig. 6. Evolution of carbon supersaturation in the middle point of bainitic ferrite for Fe-xC-1Mn alloy at 470 °C for different initial bulk carbon concentrations.

Fig. 7. Intra-lath cementite density vs temperature for different bulk carbon content in the Fe-xC-1Mn alloy. The horizontal dashed line is the critical nucleus density [N?] distinguishing upper and lower bainite, set as 1021 m-3.

Fig. 8. (a) Calculated variation of transition temperature separating upper bainite and lower bainite region for Fe-xC-1Mn, Fe-xC-2Mn and Fe-xC-1Mo ternary alloys. (b) Experimental determined transition temperature for Fe-xC-2Mn[9], Mo alloyed steel[7] and Ni, Cr, Mo steels[8].

Fig. 9. Thickening rate vs time at 470°C for 1Mn alloy with different carbon content.

Fig. 10. Variation of transition temperature separating upper bainite and lower bainite region by different criterion for effective nucleation density for Fe-xC-1Mn ternary alloy.

Fig. 11. Carbon profile during the development of seemingly up-hill diffusion.

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