Critical assessment 19: stacking fault energies of austenitic steels

Abstract

The stacking fault energy (SFE) can play a key role in the deformation mechanism (e.g. transformation-induced plasticity and twinning-induced plasticity) of austenitic steels. Therefore, tremendous efforts have been devoted to exploring the evaluation methods and controlling parameters (e.g. alloying elements and temperature) that determine the SFE and its relationship to mechanical twinning. We provide here a summary of recent progress in studies of the SFE of austenite and of unsolved issues that may stimulate further investigation.

Keywords:

• Stacking fault energy
• Austenitic steels
• Twinning-induced plasticity
• Transformation-induced plasticity
• Mechanical twin
• ε martensite

Introduction

An earnest demand for high performance steels that can be used to reduce the impact on the environment and minimise the use of energy has provided the motivation to explore a new concept in steel design, viz. a change in focus from the body-centred cubic matrix of ferrite to the face-centred cubic (fcc) matrix. This is because the fcc steels have a variety of plasticity-enhancing mechanisms, such as transformation-induced plasticity and twinning-induced plasticity (TWIP).^1–11 The strengthening mechanism of the fcc steels is strongly dependent upon the stacking fault energy (SFE) of γ austenite.^{1,4,8,10–21} It is known that whereas the mechanical stimulation of ε martensite is a dominant strengthening mechanism when the SFE value is less than approximately 20 mJ m⁻², TWIP begins to dominate as the SFE value ranges from 20 to 40 mJ m⁻².^1,2,8,9 For TWIP steels, the SFE influences a ‘critical stress’ for mechanical twinning,^13,22–26 the twin fraction^27–29 and the twin thickness.^30–32

Until now, many researchers have investigated the effects of both alloying elements and temperature on the SFE value in various austenitic steels by means of X-ray^27,33–43 and in situ neutron^9,29,43–47 diffractometry, transmission electron microscopy,^43,48–64 thermodynamic calculation^{,5,12,23,28,65–82} ab initio simulations^83–86 or molecular dynamics simulations.⁸⁷ Therefore, in the present assessment we summarise the definition and evaluation methods of the SFE and its dependence on solute content and temperature. In addition, the dependency of mechanical twinning on the SFE is discussed.

Stacking fault and SFE

The atomic arrangement at the stacking fault in γ increases the total energy of the lattice due to its non-equilibrium structure.⁸⁸ The energy per unit area of the faulted region is the SFE.⁵ The fault has been considered both as a volumetric defect^5,89,90 and a planar defect.^88,91 When the fault is regarded as a volumetric embryo of hexagonal close-packed ε martensite in the γ matrix, the SFE can be thermodynamically calculated based on the classical nucleation model^{,12,26,65,68,69,72,73,75,78,79} which consists of chemical and magnetic Gibbs free energies, γ/ε interfacial energy and elastic strain energy. When the fault is considered as a planar defect, the SFE is experimentally measured through transmission electron microscopic observation of the extended dislocation nodes^{43,48–50,52,54,57,58,63} or the separation width between partial dislocations.^{51,53,55,56,59,62}

It is not in fact verified whether all faults have a volume change normal to the fault plane, consistent with the greater density of the ε phase relative to the γ phase, since the classic work of Brooks et al.^89,90 has not been systematically followed in studies of stacking fault structures.

Evaluation methods of SFE

Thermodynamics calculation

The SFE is usually calculated using a subregular solution model based on the classical nucleation theory.⁵ (1) where Γ is the SFE, ρ is the molar surface density along the atomic plane of (111) in mol m⁻², is the difference in Gibbs free energy between γ and ε phases in J mol⁻¹, E_str is the elastic strain energy caused by the difference in specific volumes between γ and ε phases in J mol⁻¹ and σ is the γ/ε interfacial energy in mJ m⁻².

is composed of the following terms:(2) where χ is a molar fraction of an alloying element. is the change in partial molar Gibbs free energy between γ and ε phases in J mol⁻¹. is the change in the thermodynamic interaction parameter between the elements in γ and ε phases. The sum of the first and the second terms in equation (2)(2) is the change of chemical Gibbs free energy between γ and ε phases . is the change of magnetic Gibbs free energy between γ and ε phases; the magnetic properties of each phase, such as the Néel temperature (T_N), the magnetic moment and the Bohr magneton, are varied by the addition of alloying elements, resulting in the change of magnetic Gibbs free energy of each phase. is an excess free energy introduced by grain refinement of the γ phase; this term considers the suppressive effect of the γ → ε transformation by grain refinement.⁹²

For accurate calculation of the SFE value, each term in equations (1)(1) and (2)(2) has been intensively re-evaluated or newly investigated. According to the Eshelby's inclusion theory,⁹³ the E_str consists of both pure dilatational energy and pure shear energy. A homogeneous-state model using the same elastic modulus for γ and ε phases and an inhomogeneous-state model using different elastic moduli are used for the calculation of E_str. Recently, the present authors reported that homogeneous- and inhomogeneous-state models do not show a significant difference in E_str value in Fe–15Mn–(0–0.37)C (wt-%) steels, and that E_str should be considered particularly for low C high Mn steels.⁷³

Because the σ value is difficult to be measured experimentally, the σ value is indirectly determined by subtracting the and E_str values from the measured SFE value of each austenitic steel^56,68,80 or the σ value at zero K is calculated by ab initio simulation for pure Fe.⁹⁴ Pierce et al.⁵⁶ obtained the σ values by subtracting the and E_str values from the SFE values measured using the TEM. The σ values range from 8.6 to 11.8 mJ m⁻² for Fe–(22,25,28)Mn–3Al–3Si and Fe–18Mn–0.6C–(0,1.5)Al–(0,1.5)Si (wt-%) steels; the σ value decreases from 32.5 to 15.7 mJ m⁻² with increasing Mn concentration in Fe–(16–25)Mn (wt-%) binary steels.

The effects of both alloying elements and the temperature on the value have been studied by evaluating the enthalpy change⁷² and a critical temperature^72,75 for the phase transformation between γ and ε phases in Fe–(0–29)Mn (wt-%) steels. Both and for Fe-high Mn^72,95–102 and Fe–Cr^103,104 steels have been recently revised using ab initio simulation or a sublattice model. Nevertheless, the state of the thermodynamic data for the γ → ε martensitic transformation (M_s), such as , , , , and , has been shown to be rather poor in a recent analysis.¹⁰⁵

Regarding , the prediction of the Néel temperature (T_N) is important because the value sharply changes near T_N, leading to a sudden change of SFE.^12,63 The T_N represents a magnetic transition temperature between anti-ferromagnetism and para-magnetism. Therefore, Jin et al.¹⁰⁶ reviewed empirical equations for estimating the T_N of austenitic stainless steels^107,108 and Fe-high Mn austenitic steels^12,109; they additionally measured the T_N of austenitic Fe–17.9Mn–2.7C–(0, 2.2 and 4.3)Al (at.-%) TWIP steels, suggesting a more accurate predictive equation using 116 measured T_N values as follows:(3)

The applicable composition range of this equation is 3.0–53.0 at.-% Mn, 0–5.33 at.-% C, 0–9.78 at.-% Al, 0–11.72 at.-% Si and 0–7.22 at.-% Cr. The error range is ±8.86 K.

Regarding the term, strictly speaking, this term is not necessary to predict the intrinsic SFE value because the intrinsic SFE value depends on the chemical composition and temperature, not on the grain size of the γ phase. However, when the grain size is fine, it is difficult for the front partial dislocation to be sufficiently extended due to the interruption by neighbouring dislocations or the grain boundary. This suppression of the dislocation extension makes the SFE value increased apparently.⁷⁵ In addition, in reality the γ → ε transformation and mechanical twinning are suppressed in the fine-grained austenitic steels.^{75,92,105,110–112} Therefore, based on Takaki et al.⁹²'s experimental data on the relationship between the M_s and the γ grain size,⁹² Lee and Choi⁷⁵ proposed the following equation: , d is the γ grain size (μm). Because the value increases dramatically as the grain size is less than approximately 30 μm, the term should be considered for the SFE calculation of fine-grained austenitic steels.

X-ray and in situ neutron diffractometry

When the SFE is measured using an X-ray diffractometer (XRD) and an in situ neutron diffractometer (ND), its value is calculated using the following equation.³⁸ (4) where K₁₁₁ ω₀ is a proportionality constant of 6.6,³⁸ a₀ is a lattice parameter of the γ phase and C₁₁, C₁₂ and C₄₄ are the elastic stiffness coefficients evaluated by ab initio simulation^113–116 or nanoindentation testing.⁵⁶ is a mean square strain when the Fourier length of 50 Å is normal to the (111) plane, and P_sf is a stacking fault probability. was obtained from peak broadening using the Williamson–Hall plot³⁸ or the Voigt approximation.¹¹⁷ In most cases, P_sf is determined from the shifts of diffraction peaks of (111) and (200) or (111) and (222) in both annealed and deformed specimens.

For instance, the SFE values of Fe–15Mn–2Cr–0.6C–(0.02–0.21)N (wt-%) TWIP steels were measured using both the XRD and the in situ ND⁴³; they showed good agreement between two diffraction tests; 14 mJ m⁻² for the 0.02N steel and approximately 33 mJ m⁻² for the 0.21N steel. This result indicates that the effect of a static load applied during in situ neutron diffraction tests on the SFE value is insignificant.

Recently, deformation-dependent SFE values were measured by adopting an equation of as a function of dislocation density in Fe–27Mn–3.5Al–2.5Si (wt-%) TWIP steel using the XRD.³⁴ The SFE increased from 18.3 to 40.1 mJ m⁻² with increasing tensile true strain from 2 to 46% because the value became greater with increasing dislocation density from 1.2 × 10¹⁴ to 44.2 × 10¹⁴ m⁻². The SFE values measured at different strains using the XRD matched well with those measured using a transmission electron microscope (TEM); the difference in SFE value measured two different apparatuses was only approximately 2 mJ m⁻².

Transmission electron microscopy

In general, the following two TEM techniques have been widely employed for the SFE measurement based on the observation of dislocation configurations,¹¹⁸ such as extended dislocation nodes^{43,48–50,52,54,57,58,63} and the separation width between partial dislocations, viz. the width of a stacking fault.^{51,53,55,56,59,62}

When the SFE value is measured using geometrical information in the vicinity of extended dislocation nodes, it is calculated by the following equation:^118–120 (5) where μ is a shear modulus, ʋ is the Poisson's ratio, b_p is the magnitude of the Burgers vector of partial dislocations, ε_i is an inner cutoff radius of the dislocation core and α is an angle between a node arm and the Burgers vector. y and R are inscribed and outer radii of extended dislocation nodes, respectively.

Meanwhile, when the SFE value is measured using the separation width between partial dislocations, the following equation is used.¹²¹ (6) where d is the separation width between partial dislocations. β is an angle between a dislocation line and the Burgers vector.

The aforementioned two TEM techniques assume that the dislocation configuration is in an elastic equilibrium, resulting from a balance between the repulsion of partial dislocations and the surface energy of the stacking fault. However, the dislocation configuration can be influenced by pinning of partial dislocations by the local segregation of solute atoms or by the interaction of dislocations, resulting in the scattering of the SFE value.^122,123 In addition, there is a difficulty in the accurate measurement of an inscribed radius (y) in equation (5)(5) or the separation width between partial dislocations (d) in equation (6)(6) because both y or d values are too small to be measured when the SFE value is higher than approximately 20 mJ m⁻².^43,122 For example, the SFE value of Fe–15Mn–2Cr–0.6C–0.21N (wt-%) TWIP steel was measured using the XRD, in situ ND and TEM.⁴³ The SFE value (25 mJ m⁻²) measured using the TEM was lower than the SFE values (approximately 33 mJ m⁻²) measured using the XRD and in situ ND due to the difficulty in accurate measurement of the small y.

Recently, to obtain both μ and ʋ values in the (111) fault plane instead of those of a bulk specimen, elastic stiffness coefficients were measured based on an equilibrium configuration of partial dislocations in the (111) plane of Fe–(22, 25, 28)Mn–3Al–3Si (wt-%) TWIP steels.⁵⁶ Regarding Fe–22Mn–3Al–3Si (wt-%) TWIP steel, whereas the μ and ʋ values of the bulk specimen were 72 GPa and 0.24, the μ and ʋ values in the (111) fault plane were 67 GPa and 0.30. The SFE value (16 ± 4 mJ m⁻²) measured using isotropic elastic constants was slightly higher than that (15 ± 3 mJ m⁻²) measured using anisotropic elastic constants.

The effects of alloying elements and temperature on the SFE

The SFE value of austenitic steels is greatly influenced by alloying elements, such as Mn, Ni, Cr, Cu, Si, Al, C and N. In the present review, the dependency of the SFE value on alloying elements is categorised as follows:

Alloying elements increasing the SFE (C, Al, Ni and Cu)

It is well known that C raises the SFE value in Fe–Mn–C ternary steels according to thermodynamic calculations.^13,69,72,73 For example, the SFE linearly increased from −16.6 to −0.4 mJ m⁻² by 43.8 mJ m⁻² per wt-% C with increasing C concentration in Fe–15Mn–(0–0.37)C (wt-%) steels,⁷³ and from 2.2 to 23.0 mJ m⁻² by 40.8 mJ m⁻² per wt-% C in Fe–22Mn–(0.06–0.57)C (wt-%) steels.¹³

Al, Ni and Cu also raise the SFE of austenitic steels. Both thermodynamic calculations⁶⁹ and the in situ ND tests²⁹ revealed that the SFE values of Fe–18Mn–0.6C–(0–3)Al (wt-%) steels linearly increased from 21 to 44 mJ m⁻² by approximately 9 mJ m⁻² per wt-% Al with an increase in Al concentration.

Vitos et al.⁸⁶ compared the SFE values of Fe–(17–19)Cr–(8–20)Ni (at.-%) austenitic stainless steels measured using the TEM and the XRD with those of the steels calculated by ab initio simulation, and concluded that the addition of Ni to austenitic stainless steels increases their SFE values. Recently, Park et al.⁵⁸ measured the SFE values of C-bearing austenitic stainless steels, i.e. Fe–12Cr–0.4C–(5.07–9.91)Ni (wt-%) steels, using the TEM; the SFE value linearly increased from 31.2 to 45.8 mJ m⁻² by approximately 3 mJ m⁻² per wt-% Ni with increasing Ni concentration.

Regarding the effect of Cu on the SFE, the SFE values of Fe–20Mn–1.3C–(0–3)Cu (wt-%) TWIP steels linearly increased from 24.4 to 28.7 mJ m⁻² with the addition of Cu¹²⁴ and those of Fe–22Mn–0.6C–(0–7.4)Cu (wt-%) TWIP steels rose from 22.7 to 31.3 mJ m^{−2 77}; these results show that the SFE value increases by approximately 1 mJ m⁻² per wt-% Cu in Cu-bearing high Mn steels.

Alloying elements decreasing the SFE (Cr and Si)

Vitos et al.⁸⁶ also collected the SFE values of Fe–(13–25)Cr–(13–16)Ni (at.-%) steels measured using the TEM and the XRD from the literature, and compared them with the values calculated using ab initio simulation. They found that the addition of Cr to austenitic stainless steels lowers their SFE values.⁸⁶

Regarding the Si effect, Tian and Zhang⁶⁷ reported that the SFE value, which was measured using the XRD, linearly decreases from 17.4 to 6.3 mJ m⁻² by 1.3 mJ m⁻² per at.-% Si in Fe–31Mn–0.77C–(0.25–8.67)Si (at.-%) steels. Jeong et al.²⁷ also measured the SFE values of Fe–18Mn–0.6C–(0 and 1.5)Si (wt-%) TWIP steels using the XRD, and realised that the SFE linearly decreased from 19.3 to 13.8 mJ m⁻² by 4 mJ m⁻² per wt-% Si (or 1.8 mJ m⁻² per at.-% Si) with increasing Si concentration.

Parabolic change in SFE due to Mn

For Fe–(0–29)Mn (wt-%) binary steels, the SFE drops with increasing Mn concentration up to approximately 13 wt-%, and then rises again with the addition of Mn further according to the thermodynamic calculation.^69,75 When C is added to the binary steels, a parabolic SFE curve is still maintained with a critical Mn concentration of 13 wt-%.⁷² These predicted Mn effects were recently confirmed by the direct measurement using the TEM. Whereas the SFE values of Fe–12Cr–0.4C–(4.87–10.23)Mn (wt-%) steels linearly decreased from 19.4 to 10.5 mJ m⁻² with increasing Mn concentration,⁵⁸ the SFE values of Fe–(22–28)Mn–3Al–3Si (wt-%) steels increased from 15 to 39 mJ m⁻² with the addition of Mn.⁵⁶

An alloying element changing the SFE differently according to the chemical composition of a base material (N)

The effect of N on the SFE exhibits different tendencies according to the chemical composition of a base material, such as Fe–Mn–Cr, Fe–Mn–Cr–C and Fe–Cr–Ni–Mn steels. Gavriljuk et al.⁵⁷ investigated the dependency of SFE on the N concentration in Fe–17Mn–15Cr–xN and Fe–18Cr–16Ni–10Mn–xN (wt-%) steels using the TEM. For Fe–17Mn–15Cr–xN (wt-%) steels, the SFE decreased from 26 to 20 mJ m⁻² with increasing N concentration from 0.23 to 0.48 wt-%, and then increased again to 40 mJ m⁻² at a N concentration of 0.8 wt-%. However, for Fe–18Cr–16Ni–10Mn–xN (wt-%) steels, the SFE value increased from 43 to 65 mJ m⁻² with increasing N concentration from 0.08 to 0.4 wt-%, and then decreased again to 53 mJ m⁻² when the N concentration is 0.54 wt-%. Lee et al.⁹ reported that the SFE values, which were measured using the in situ ND, increased from 10.4 to 22.8 mJ m⁻² with increasing N concentration in Fe–18Cr–10Mn–0.2Si–0.03C–(0.39–0.69)N (wt-%) steels. Lee et al.⁴³ measured the SFE values of Fe–15Mn–2Cr–0.6C–(0.02–0.21)N (wt-%) steels using the XRD and the in situ ND, and reported that the SFE value linearly increased from 14.6 to 33.1 mJ m⁻² with the addition of N up to 0.21 wt-%.

The above results clearly show an inconsistent effect of N on the SFE; this is considered to be caused by differences in both chemical compositions of base materials and the range of N concentration.

Temperature effect

The temperature as well as alloying elements is also an important factor for the SFE. Rémy et al.¹²² gave an overview of a temperature dependence of SFE, which was measured using the TEM, in Fe–(17–20)Cr–(13–15)Ni and Fe–20Mn–4Cr–0.5C (wt-%) steels. They reported that the SFE value of Fe–Cr–Ni steels increased by approximately 0.1 mJ m⁻² per K when the temperature rose from 300 to 400 K and that those of Fe–Mn–Cr–C steels were arisen by 0.06 mJ m⁻² per K with increasing temperature from 300 to 390 K; these results stemmed from the improvement of γ stability with an increase in temperature. However, when the SFE value is measured at elevated temperature using the TEM, the pinning of partial dislocations by the local segregation of solute atoms may influence the y value in equation (5)(5) or the d value in equation (6)(6) , careful observation should be carried out.

Meanwhile, Saeed-Akbari et al.⁶⁹ evaluated the SFE values of Fe–Mn–C and Fe–Mn–Al–C steels as a function of temperature through thermodynamics calculations. As a result, the SFE values of Fe–22Mn–0.6C (wt-%) steels linearly increased from 16 to 52 mJ m⁻² by 0.2 mJ m⁻² per K with increasing temperature from 300 to 473 K. Lan et al.¹²⁵ also performed thermodynamic calculations of the SFE value of Fe–22Mn–0.7C (wt-%) TWIP steel at the temperatures ranging from 273 to 1473 K. The SFE value linearly rose from 25 to 243 mJ m⁻² by 0.18 mJ m⁻² per K. These results inform that the SFE value of austenitic steels is almost linearly proportional to the temperature. However, there is still a lack of experimental data on the variation of interfacial energy as a function of temperature.⁷⁶

The effect of SFE on mechanical twinning

The SFE has a crucial effect on the behaviour of mechanical twinning, such as a ‘critical stress’ required for mechanical twinning,^{6,13,22,26,126} the twin fraction^27,28 and the twin thickness.^{30–32,127,128} Jeong et al.²⁷ measured both the SFE values and the volume fractions of mechanical twins using the TEM and an electron backscatter diffractometer (EBSD) in Fe–18Mn–0.6C–1.5Si, Fe–18Mn–0.6C and Fe–18Mn–0.6C–1.5Al (wt-%) TWIP steels, which were tensile deformed by a true strain of 0.1.²⁷ Whereas the addition of Al to the Fe–18Mn–0.6C (wt-%) TWIP steel raised the SFE value from 19.3 to 29.1 mJ m⁻², the addition of Si lowered the SFE value to 13.8 mJ m⁻². The lower the SFE value the higher the total volume fraction of mechanical twins. Especially, when the SFE value is less than 20 mJ m⁻², the volume fraction of secondary mechanical twins rapidly increased.

Regarding the effect of SFE on the twin thickness, Yang et al.¹²⁸ examined the relationship between the SFE value calculated by thermodynamic calculation and the twin thickness in Fe–22Mn–0.6C–(0 and 1.5)Al (wt-%) TWIP steels, which were tensile deformed by a true strain of 0.3. They found that when the Al was added, the SFE value increased from 19 to 30 mJ m⁻² and the twin thickness also increased from 17 to 120 nm. However, for Fe–15Mn–2Cr–0.6C–(0.02–0.21)N (wt-%) TWIP steels deformed by a true strain of 0.2,³² although the SFE value rose from 15 to 33 mJ m⁻² by the addition of N, the twin thickness was rather reduced from 56 to 19 nm.⁴³ This result indicates that interstitial N atoms suppressed the thickening of mechanical twins. Idrissi et al.¹²⁷ also measured the twin thickness in Fe–20Mn–1.2C and Fe–28Mn–3.5Si–2.8Al (wt-%) TWIP steels deformed by a true strain of 0.1. Whereas the twin thickness of the C-bearing TWIP steel (SFE of 15 mJ m⁻²)⁵³ ranged from 20 to 70 nm, that of the C-free TWIP steel (SFE of 39 mJ m⁻²)⁵⁶ ranged from 100 to 700 nm. However, because the C-bearing TWIP with the lower SFE value exhibited the thinner twins compared to the C-free TWIP steel, it is difficult to judge whether the thin twins of the C-bearing TWIP steel was caused by the low SFE or by interstitial C atoms. Accordingly, it is necessary to scrutinise the relationship between the twin thickness, interstitial atoms and the SFE value.

The critical twinning stress (σ_T) has been described by various equations according to the mechanisms of twin nucleation.^6,22,129,130 Byun²² proposed the following equation for the σ_T by considering the stress required for the infinite separation between partial dislocations on a slip plane.(7)

According to this equation, the σ_T value of 316 austenitic stainless steel with the SFE value of 14.2 mJ m⁻² is approximately 600 MPa.

Ghasri-Khouzani and McDermid¹³ examined the σ_T values by observing the onset of mechanical twinning in Fe–22Mn–(0.4 and 0.6)C (wt-%) TWIP steels using the EBSD, and reduced a constant in Byun's equation as follows, considering their own σ_T values and the σ_T values measured previously in other Fe-high Mn steels.(8)

This equation shows that the onset of mechanical twinning was retarded from 300 to 400 MPa with increasing SFE from 17.2 mJ m⁻² for the 0.4C steel to 23.0 mJ m⁻² for the 0.6C steel.

Mahato et al.³⁴ investigated the twinning mechanism and the σ_T value in Fe–27Mn–2.5Si–3.5Al (wt-%) TWIP steel with the SFE value of 18.3 mJ m⁻² using the TEM. They observed that mechanical twinning of the C-free TWIP steel took place by the three-layer stacking fault mechanism,¹²⁹ and calculated the σ_T value (615 MPa) by employing the following equation,¹²⁶ which was proposed on the basis of the three-layer stacking fault mechanism.¹²⁹ (9) where M is the Taylor factor (3.06) and L₀ is the width of a twin embryo (approximately 200 nm).

The above equations (7)(7) –(9)(9) commonly reveal that the σ_T value is proportional to the SFE value regardless of the twinning mechanism; this means that it is difficult for mechanical twinning to occur as the SFE value is high.

Summary and perspective

In the present article, we briefly reviewed the definition, evaluation methods and influential parameters (alloying elements and temperature) of the SFE and consequences on mechanical twinning. Of them, recent improvements are summarised as follows: for thermodynamic calculation of the SFE value, chemical, magnetic, elastic strain and interfacial energies terms have been revised. For X-ray and neutron diffractometry of the SFE value, the SFE value was measured with the value as a function of dislocation density. For TEM observation, both μ and ʋ values in the (111) fault plane were newly obtained instead of their bulk properties. Regarding the effects of alloying elements on the SFE value, whereas N raises the SFE, Si lowers it in Fe-high Mn TWIP steels. The volume fraction of twins increased and the σ_T value decreased with lowering SFE value. Meanwhile, whereas the twin thickness increased with increasing SFE value by the addition of Al to TWIP steels, it was reduced with the addition of N, although the SFE value increased.

Despite of above-mentioned recent advances in both experiments and calculations of the SFE values of austenitic steels, the following several issues are still waiting for in-depth studies.

1. It is not clear whether there is always a volume change associated with the formation of a stacking fault, or only when ε martensite is favoured. The electron microscopy techniques first used by Brook et al.^89,90 should be exploited in characterising this aspect in future studies of the SFE.

2. For more accurate calculation and measurement of the SFE value, the influence of the segregation of interstitial atoms to the stacking faults^74,81,131 and the accurate values of interfacial energy are needed to be considered, particularly at elevated temperatures.

3. The effects of interstitial atoms, such as C and N, on the nucleation and thickening of mechanical twins are necessary to be investigated in austenitic steels with the same SFE value.

4. The concept of a critical stress for mechanical twinning needs further investigation as to whether it is fundamentally justified or is simply a pragmatic approach towards a practical parameter.