Thermodynamic calculation of the stacking fault energy in Fe-Cr-Mn-C-N steels

doi:10.1016/j.jallcom.2018.03.296

Journal of Alloys and Compounds

Volume 749, 15 June 2018, Pages 776-782

https://doi.org/10.1016/j.jallcom.2018.03.296 Get rights and content

Highlights

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Stacking fault energy in Fe-Cr-Mn-C-N steels was thermodynamically calculated.
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For accurate stacking fault energy, measured and predicted energies were compared.
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Cr increases stacking fault energy, then decreases it again over a critical value.
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Mn, C and N continuously increase stacking fault energy.

Abstract

To determine the thermodynamic parameters for the calculation of the accurate stacking fault energy (SFE) in Fe-Cr-Mn-C-N steels using the sublattice model, the comparison between the calculated and experimental SFE values was conducted. It was realized that the relationship between SFE and alloying elements in Fe-Cr-Mn-C-N steels was different from that of the conventional Fe-Cr-Ni stainless steels. The SFE increased with the increasing Cr concentration up to a critical value, then decreased again with further increased Cr concentration. The critical value decreased with the addition of Mn, C and N. In contrast to Cr, the addition of Mn continuously increased the SFE, regardless of the additions of C and N. Regarding the C and N, they also increased the SFE linearly and the impact of N on the SFE was only slightly effective relative to that of C. Accordingly, we realized that the thermodynamic calculation using the suggested combination of thermodynamic parameters should be considered for more accurate SFE calculation in Fe-Cr-Mn-C-N steels.

Graphical abstract

Introduction

Austenitic Fe-Cr-Mn-C-N steels exhibit the remarkable combination of tensile strength and ductility of over 60,000 MPa% [1,2] and corrosion resistance [3] due to the transformation- and twinning-induced plasticity (TRIP and TWIP) and the formation of a passive film, respectively. The dominant strengthening mechanism is the TRIP when the stacking fault energy (SFE) is below 20 mJ m⁻², and with an increasing SFE up to ∼40 mJ m⁻², it exhibits the TWIP [4,5]. Accordingly, the evaluation of an accurate SFE in the Fe-Cr-Mn-C-N steels has been actively conducted using the X-ray and neutron diffractometry (XRD and ND) [4,6,7], transmission electron microscopy (TEM) [[8], [9], [10], [11]] and thermodynamic calculation [10,12,13].

Each method has its own disadvantages [4,14,15] as follows: (1) For the XRD, the limitation of an observation area in the surface of the specimen and the error by the peak doublet of Kα1 and Kα2, (2) For the ND, the difficulty to utilize to the equipment and the long processing time, (3) For the TEM, the scattering of data caused by the segregation of the alloying atoms (C and N) in the stacking fault and the difficulty in measuring the high SFE due to the size reduction of the dislocation configurations such as extended node and stacking fault tetrahedral, (4) For the thermodynamic calculation, the discrepancy due to different thermodynamic databases for the same elements with respect to the authors. It is necessary to determine a more reliable SFE based on the comparison between the calculated and measured SFE values using the abovementioned techniques. However, the systematic thermodynamic calculation of the SFE has not yet been established in the Fe-Cr-Mn-C-N system with respect to the alloying elements with a wide range probably due to the presence of various interaction parameters on the same elements such as L_Fe,Mn:Va, L_Fe:C,Va, L_Fe:N,Va and L_Fe:C,N. It leads to a difficulty in designing the new Fe-Cr-Mn-C-N steels, considering the strengthening mechanisms (TRIP, TWIP) based on the accurate SFE. Although the empirical equations of the SFE in conventional Fe-Cr-Ni based stainless steels have been reported [[16], [17], [18]], it is difficult to calculate the SFE for Fe-Cr-Mn-C-N steels because of the following reasons; (1) there are difference of the SFE in two systems due to the effect of specific alloying elements (Ni, Mo, Si) on the SFE, (2) the range of the alloying elements for the SFE calculation is significantly limited, and (3) the dependence of the SFE on the additions of C and/or N over ∼0.3 wt.% for various Fe-Cr-Mn-C-N steels has not been considered.

Therefore, in the present study, we carried out the thermodynamic calculation of the SFE in Fe-Cr-Mn-C-N steels using the sublattice model. This model assumed that each element and vacancy separately occupy the substitutional and interstitial sites with random mixing in each sublattice to reflect the real crystalline structure, relative to the widely used subregular model [12,14]. It was suggested to use the combination of the thermodynamic databases for comparison between the calculated and reported experimental SFEs was preferable for more reliable SFE values. Consequently, the effect of the alloying elements on the SFE was systematically investigated using the thermodynamic calculation, discussed and verified in comparison of the results of previous research.

Section snippets

Thermodynamic calculation of stacking fault energy

For this purpose, the SFE was calculated based on the classical nucleation theory, because the stacking fault is a volumetric embryo of the hcp ε phase in the fcc γ matrix [12,14]. The SFEs were thermodynamically calculated using the sublattice model as follows: $S F E = 2 ρ (Δ G_{c h}^{γ \to ε} + Δ G_{m g}^{γ \to ε}) + 2 σ$ where ρ is the molar surface density along the atomic plane of (111) in mol m⁻² which was determined from the equation $4 / (\sqrt{3} a_{γ}^{2} N_{A})$ [12,14], where N_A is Avogardo's number of 6.022 $\times$ 10²³ mol⁻¹ and a_γ is the γ

Comparison of the calculated and measured stacking fault energies

Fig. 1a through c shows the relationship between the measured and calculated SFEs using types I through III, respectively, together with three different indexes of accuracy. Parameter E is the average distance between the line in the figure and markers, parameter D is the average absolute distance between the line, and the parameter S is the standard error in the figure and markers as follows: $E_{i} = \frac{(S F E_{C a l .} - S F E_{M e a .})}{\sqrt{2}}$ $E = \frac{\sum_{i = 1}^{N} E_{i}}{N}$ $D_{i} = | E_{i} |$ $D = \frac{\sum_{i = 1}^{N} D_{i}}{N}$ $S = \sqrt{\frac{\sum_{i = 1}^{N} {(S F E_{c a l .} - S F E_{m e a .})}^{2}}{N}}$ where both the SFE_Cal. and SFE

Conclusion

In the present study, we investigated the thermodynamic calculations of the accurate stacking fault energy (SFE) in Fe-Cr-Mn-C-N steels using the sublattice model based on the comparison between the calculated and experimentally measured SFEs.

(1)
The calculated SFE more closely agreed with the measured SFE when using the combination of thermodynamic databases based on the interaction parameters (L_Fe,Mn:Va, L_Fe:C,N, L_Fe:C,Va and L_Fe:N,Va) suggested by Djurovic et al. [25] and Gӧhring et al. [27].
(2)
The

Acknowledgements

This study was partly supported by the New Energy and Industrial Technology Development Organization (NEDO) under the “Innovation Structural Materials Project (Future Pioneering Projects)” and a Grant-in-Aid for Science Research from the Japan Society for the Promotion of Science. LSJ acknowledges support from the “Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A03002080)”.

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Thermodynamic calculation of the stacking fault energy in Fe-Cr-Mn-C-N steels

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Thermodynamic calculation of stacking fault energy

Comparison of the calculated and measured stacking fault energies

Conclusion

Acknowledgements

Mater. Sci. Eng. A

Mater. Sci. Eng. A

Scripta Mater.

Acta Mater.

Acta Mater.

Scripta Mater.

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Mater. Sci. Eng. A

Acta Mater.

Acta Mater.

Acta Mater.

J. Nucl. Mater.

Scripta Mater.

J. Alloys Compd.