Stacking Fault Energy Determination in Fe-Mn-Al-C Austenitic Steels by X-ray Diffraction
Abstract
:1. Introduction
2. About the Stacking Fault and Stacking Fault Energy
3. About the X-ray Diffraction Technique for Determining the SFE
- = stacking fault energy (mJ/m2)
- = 6.6 (constant value)
- , A is the Zener elastic anisotropy and are elastic stiffness coefficients
- is the shear modulus in <111> direction (GPa.)
- = lattice constant ()
- = root mean square microstrain in the <111> direction averaged over the distance of 50
- = stacking fault probability
3.1. XRD Background Setting
3.2. XRD Determination of the Mean Square Microstrain
3.3. Determination of Peak Positions
3.4. Stacking Fault Probability
- = change in the position of the diffraction lines
- = the diffraction angle for each peak
- = constant specific to each h k l reflection (Table 1)
3.5. Elastic Constants
4. Experimental Procedure
4.1. Specimen Preparation
4.2. X-ray Diffraction
4.3. Determination of the SFE
5. Results and Discussions
6. Conclusions
- The flow diagram presents the calculation of the SFE using data obtained by XRD in addition to values of the elastic constants. The procedure was verified with a widely used commercial Hadfield-type alloy, where the values obtained were within the range established by previous investigations.
- Average SFE reference values can be obtained using elastic constants of alloys with similar compositions, which serve an alternative when it is not possible to retrieve the values from experimental tests or computational calculations. However, for Hadfield steel, the variation of the elastic constants in the range in which they have been reported generates a variation in the calculated SFE of 30%.
- and are within the ranges reported for austenitic steels generates variations of 36.6%, 28%, and 28.4% in the value of the SFE for the Fe-22Mn-XAl-0.9C alloys studied with 0%, 3%, and 8% Al, respectively; representing the possibility that these alloys present TRIP or TWIP deformation mechanisms for the case of 0% and TWIP or MBIP for 3% Al content. In the case of the alloy with 8% Al, the probable deformation mechanism is MBIP even with the variation in SFE.
- The SFE variation is 11.6%, 12.3%, and 11.5% for alloys with 0%, 3%, and 8% Al, respectively. When changing between the extreme values reported for this constant reflected in a smaller effect concerning the variations of and .
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Abbreviations
SFE | Stacking fault energy, mJ/m2 |
SFP | Stacking fault probability |
MSM | Mean square microstrain |
A | Zener elastic anisotropy |
G | Shear modulus |
β | Integral Breadth o FWHM |
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Indices of Reflection [H K L] | |
---|---|
1 1 0 | |
2 0 0 | |
2 2 0 | |
3 1 1 | |
2 2 2 | |
4 0 0 |
Alloy | Fe (% wt) | Mn (% wt) | Al (% wt) | C (% wt) |
---|---|---|---|---|
Fe-22Mn-0.9C-0Al | Balance | 20.5 | 0 | 0.87 |
Fe-22Mn-0.9C-3Al | Balance | 22.2 | 3.5 | 0.84 |
Fe-22Mn-0.9C-8Al | Balance | 22.1 | 8.3 | 0.89 |
Reference | Composition of Alloys (wt. pc) | Methodology | C11 [GPa] | C12 [GPa] | C44 [GPa] | Determined SFE of the Hadfield Using These Elastic Constants (mJ/m2) |
---|---|---|---|---|---|---|
Music, et al. [83] | Fe-10Mn | ab initio | 210 | 153 | 135 | 20.53 |
Bampton, et al. [84] | Fe-18Cr-12N-3Mo | Crystal Grown | 235 | 138.5 | 117 | 29.2 |
Endoh, et al. [85] | Fe-30Mn | Atomic Force | 200 ± 9 | 127 ± 6 | 130 ± 3 | 24.1 ± 0.9 |
Gebhardt, Music, Kossmann, Ekholm, Abrikosov, Vitos and Schneider [73] | Fe-25Mn-2Al | ab initio | 153.6 | 105 | 135.5 | 18.5 |
Pierce, Nowag, Montagne, Jiménez, Wittig and Ghisleni [24] | Fe-18Mn-1.5Al-0.6C | Nanoindentation | 169 ± 6 | 82 ± 3 | 96 ± 4 | 26.9 ± 1 |
Lenkkeri [86] | Fe-38.5Mn | Ultrasound | 169.2 | 97.7 | 140.1 | 25.9 |
Cankurtaran, Saunders, Ray, Wang, Kawald, Pelzl and Bach [77] | Fe-40Mn | Ultrasound | 170 | 98 | 141 | 24.27 |
Stinville, et al. [87] | 316L | Nanoindentation | 196 | 129 | 116 | 21.9 |
Pierce, Nowag, Montagne, Jiménez, Wittig and Ghisleni [24] | Fe-22Mn-3Al-3Si | Nanoindentation | 175 ± 7 | 83 ± 3 | 97 ± 4 | 27.3 ± 1.1 |
Alloy | Phase | ± 0.005 | X2 | F2(R) | |
---|---|---|---|---|---|
Fe-22Mn-0.9C-0Al | 3.627 | 47.713 | 5.8 | 0.0431 | |
Fe-22Mn-0.9C-3Al | 3.634 | 47.990 | 3.9 | 0.0383 | |
Fe-22Mn-0.9C-8Al | 3.671 | 49.471 | 5.2 | 0.0523 |
Alloy | SFPx104 | SFE * (mJ/m2) | SFE ** (mJ/m2) | |
---|---|---|---|---|
Fe-22Mn-0.9C-0Al | 9.62 ± 2.68 | 8.92 | 17.53 ± 2.47 | 10.99 |
Fe-22Mn-0.9C-3Al | 6.52 ± 2.96 | 13.56 | 35.61 ± 4.76 | 33.42 |
Fe-22Mn-0.9C-8Al | 7.48 ± 3.24 | 21.86 | 50.76 ± 6.73 | 53.35 |
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Castañeda, J.A.; Zambrano, O.A.; Alcázar, G.A.; Rodríguez, S.A.; Coronado, J.J. Stacking Fault Energy Determination in Fe-Mn-Al-C Austenitic Steels by X-ray Diffraction. Metals 2021, 11, 1701. https://doi.org/10.3390/met11111701
Castañeda JA, Zambrano OA, Alcázar GA, Rodríguez SA, Coronado JJ. Stacking Fault Energy Determination in Fe-Mn-Al-C Austenitic Steels by X-ray Diffraction. Metals. 2021; 11(11):1701. https://doi.org/10.3390/met11111701
Chicago/Turabian StyleCastañeda, Jaime A., Oscar A. Zambrano, Germán A. Alcázar, Sara A. Rodríguez, and John J. Coronado. 2021. "Stacking Fault Energy Determination in Fe-Mn-Al-C Austenitic Steels by X-ray Diffraction" Metals 11, no. 11: 1701. https://doi.org/10.3390/met11111701