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The role of interstitial carbon atoms on the strain-hardening rate of twinning-induced plasticity steels
Scripta Materialia 178 (2020) 264–268
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
The role of interstitial carbon atoms on the strain-hardening rate of twinning-induced plasticity steels Z.C. Luo a,b, M.X. Huang a,∗ a b
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, PR China Guangdong Institute of Materials and Processing, Guangdong Academy of Science, Guangzhou, PR China
a r t i c l e
i n f o
Article history: Received 3 September 2019 Revised 17 November 2019 Accepted 19 November 2019
Keywords: TWIP steel Strain-hardening Dislocation density Carbon-dislocation interaction Synchrotron X-ray diffraction
a b s t r a c t Synchrotron X-ray diffraction was applied to measure the dislocation density of two twinning-induced plasticity (TWIP) steels with different carbon content but comparable stacking fault energy (SFE). We found that the dislocation density of the carbon-alloyed TWIP is much higher than that of the carbonfree TWIP steel, though these two steels possess similar twin volume fraction. It indicates that the excellent tensile and strain-hardening properties of the carbon-alloyed TWIP steels are mainly caused by the high dislocation density induced by the carbon-dislocation interaction. Carbon-free TWIP steels are conventional low SFE fcc alloys similar to 316L stainless steel.
Twinning-induced plasticity (TWIP) steels possess high strainhardening rate and superior tensile properties (tensile uniform elongation >50% and ultimate tensile strength >10 0 0 MPa), and are potential materials for lightweight structure applications [1–6]. Compared to other metals and alloys, the distinguishing feature of TWIP steels is that extensive deformation twins are generated during deformation. As a result, this category of steels is named as TWIP steels in the metallurgy community. Considering the effect of deformation twins on the tensile properties of TWIP steels, one conventional view considers that the average distance of dislocation glide is reduced effectively by deformation twins, resulting in a high dislocation density and therefore excellent tensile properties [2]. Another traditional opinion considers that dislocations piledup at twin boundaries generate back-stresses, leading to the “dynamic Hall–Petch” effect and therefore excellent tensile properties [7,8]. Both traditional views consider deformation twinning is the decisive mechanism responsible for the excellent tensile properties of TWIP steels. These views have been cited by many researchers without questions in the last two decades [9–14]. Different from the above conventional views, some recent experimental results questioned the role of deformation twins in the tensile properties of TWIP steels [15–17]. It was shown that deformation twins only contribute about 10% of the ultimate tensile strength of a TWIP steel [15]. In addition, it was found that a TWIP ∗
Corresponding author. E-mail address: [email protected] (M.X. Huang).
https://doi.org/10.1016/j.scriptamat.2019.11.047 1359-6462/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
steel deformed at 473 and 298 K possessed comparable dislocation densities and tensile properties [16]. But the deformation twins are largely inhibited at 473 K while intensive deformation twins are generated at 298 K [16]. These new experimental evidence suggest that deformation twins may not be the main mechanism responsible for the high dislocation density and excellent tensile properties of TWIP steels [16]. The present work intends to clarify the undiscovered mechanism that is responsible for the excellent tensile properties of T WIP steels. T WIP steels with and without carbon are investigated. Dislocation density and volume fraction of twins are quantified by detailed experiments. Two TWIP steels with the respective chemical composition of Fe–30Mn–3Al–3Si and Fe–30Mn–0.6C (wt%) were employed in the present work, which were denoted as 30Mn3Al3Si and 30Mn0.6C hereafter. They were cast with vacuum casting, followed by forging at 1173 K into a thickness of 100 mm. Tensile specimens with gauge dimensions of 10 × 4 × 1.8 mm were cut from the plate. Quasi-static tensile tests interrupted at true strains of 0.05, 0.1, 0.2, 0.3 and 0.4 were conducted by using a univervial tensile machine. The interrupted tensile samples were then prepared by electropolishing for scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and synchrotron X-ray diffraction (XRD) experiments. In order to get the best contrast of the twins, the Inlens mode was applied under a working voltage of 5 kV in a LEO 1530 SEM. During image collecting, a line integration method was used to reduce the noise, and the brightness was set
Z.C. Luo and M.X. Huang / Scripta Materialia 178 (2020) 264–268
Fig. 1. (a) and (b) EBSD maps of 30Mn0.6C and 30Mn3Al3Si TWIP steels prior to the tensile test, the color maps indicate the orientation of grains; (c) engineering stress–strain curves of two TWIP steels and (d) the true stress–strain curves and strain-hardening rates. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
to 0 while the contrast was about 44.9. Transmission electron microscopy (TEM) observation is carried out by using a JEM-2100 scanning TEM operated at 200 kV. The synchrotron XRD experiments were carried out at the Shanghai synchrotron facility (beamline No. 14B). The energy of the synchrotron X-ray was 18 keV. LaB6 powders were used to determine the instrumental profile. The XRD line profiles were analyzed by the convolution multiple whole profile (CMWP) method [18]. These two TWIP steels are fully-recrystallized as shown in Fig. 1a and b, respectively. The respetive grain size of the 30Mn3Al3Si and 30Mn0.6C samples are 23.9 and 33.4 μm. Fig. 1c presents the engineering stress-strain curves of 30Mn3Al3Si and 30Mn0.6C steels. Fig. 1d reveals the true stress-strain curves and strain-hardening rate (θ ) of the two TWIP steels. The 30Mn3Al3Si and 30Mn0.6C steels exhibit distinguishable strain-hardening rate and ultimate tensile strength (UTS). It can be seen that the θ of the 30Mn0.6C steel is higher than 2 GPa even at a large true strain of 0.4. For comparison, the θ of 30Mn3Al3Si steel is lower than 1.5 GPa after a small true strain of 0.15. TEM images revealed that deformation twins are formed in the 30Mn0.6C and 30Mn3Al3Si samples deformed at room temperature. Fig. 2a and d shows the scanning TEM images of the 30Mn0.6C and 30Mn3Al3Si TWIP steels deformed to a true strain of 0.3 at room temperature, respectively. Fig. 2b and e shows the details of the deformation twins. Selected area electron diffraction (SAED) patterns taken along the [110] zone axis (Fig. 2c and f) reveal clearly the deformation twins in both TWIP steels. In the present work, the evolution of twin volume fractions is determined by using the SEM images (Fig. 2g). The measurement method was described in [16]. Three images of each condition are used and each image covers tens of grains to ensure the statistical reliability. Fig. 2h shows the evolution of twin fractions with the true strain. The area fraction can be used to represent approximately the volume fraction of deformation twins [19,20]. It is noted that the twin volume fraction in the 30Mn0.6C steel is slightly higher than that in the 30Mn3Al3Si steel. Fig. 3a shows the tangled dislocations in the 30Mn0.6C steel after straining to a true strain of 0.05. As the strain increases to 0.1, high dislocation density walls (HDDW) can be observed in the 30Mn0.6C steel (Fig. 3b). Fig. 3c and d illustrates the dislocation structures of the 30Mn3Al3Si steel strained to 0.05 and 0.1, re-
265
spectively. It demonstrates that planar slip prevails in both TWIP steels due to their low stacking fault energy (SFE). At high strains, synchrotron X-Ray diffraction is employed to measure the dislocation density in both TWIP steels. The CMWP method developed by Ribárik [18] and Ungár et al. [21] is utilized to analyze the diffraction profiles. Fig. 4e shows the dislocation densities of both TWIP steels at the true strains of 0.2 and 0.4. The inserted figure in Fig. 4e presents the normalized {220} Bragg peaks of the sample at the true strain of 0.4. The dislocation density calculated by the CMWP method could be higher than the real value due to its overestimation nature. Nevertheless, it is consistent with our previous results [15,16]. Furthermore, it shows that the 30Mn0.6C steel possesses a higher dislocation density than the 30Mn3Al3Si steel at the same true strain. At a true strain of 0.1, the twin volume fractions of both TWIP steels are smaller than 0.5% as shown in Fig. 2h. It suggests that the contribution of twins to the plastic deformation is negligible at low strains. However, it can be seen in Fig. 1d that, at the true strain of 0.05, the θ value of the 30Mn0.6C steel is about 2900 MPa, while it is about 1880 MPa for the 30Mn3Al3Si steel. As the true strain increases to 0.1, the θ of 30Mn0.6C and 30Mn3Al3Si steels become 2690 MPa and 1600 MPa, respectively. The difference of θ in these two steels can be as high as 10 0 0 MPa. Such a large difference should not be related to the deformation twins since the twin volume fractions in both steels are negligibly small at the true strain of 0.1. In other words, the strain-hardening of TWIP steels at low strains only depends on the accumulation of dislocations, which is not controlled by the deformation twins. Remarkably, slip planarity of dislocations has been characterized in both steels as shown in Fig. 3. It suggests that the planar slip alone is also not the cause for the different accumulation rate of dislocations. By combining Figs. 2h and 3e, one can find that the twin volume fraction increases with strain in both TWIP steels, but they show distinguishable dislocation density after the same level of tensile deformation. We also examined the dislocation density of 30Mn0.6C steel deformed at 573 K to a true strain of 0.4. It is found that the dislocation density is as high as 1.4 × 1016 m−2 , though the microstructure contains no deformation twins, which is higher than that of 30Mn3Al3Si TWIP steel with abundant twins deformed to the same strain level at room temperature (Fig. 3e). It indicates that the deformation twins are not the dominant mechanism responsible for the high dislocation density in TWIP steels. The conventional view considers that deformation twins in TWIP steels are responsible for the uphill stage of the strainhardening rate, e.g., 30Mn0.6C in Fig. 1d. However, this conventional view may be questionable according to the present investigation. At room temperature, the strain-hardening rate of the 30Mn0.6C TWIP steel starts to increase at a true strain of about 0.25 as shown in Fig. 1d. But the strain-hardening rate of the 30Mn3Al3Si steel decreases monotonically with strain. These two steels possess similar volume fraction of deformation twin (Fig. 2). Nevertheless, one contains the uphill stage and the other does not. Therefore, the presence of deformation twins is not responsible for the uphill stage of the strain-hardening rate in TWIP steels. The uphill stage of the strain-hardening rate can be explained by the interaction between carbon atoms and dislocations. For the carbon-alloyed TWIP steel, the short-range diffusion of carbon atoms into dislocations are less activated at low strain due to a relative low dislocation density. As a result, the uphill stage at low strain in the carbon-alloyed TWIP steel is not observed. The short-range diffusion of carbon atoms into dislocations can be significantly promoted when more dislocations are presented at high strain. Therefore, the uphill stage appears at a relative large strain (30Mn0.6C in Fig. 1d). In addition, the 30Mn3Al3Si steel does not
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Fig. 2. (a) and (d) STEM image of the microstructure after 0.3 true strain of 30Mn0.6C and 30Mn3Al3Si steels; (b) and (e) high magnification image shows the deformation twins; (c) and (f) The diffraction patterns from (b) and (e); (g) typical SEM image of 30Mn0.6C steel at the true strain of 0.4; (h) the evolution of volume fraction of deformation twins in two TWIP steels.
Fig. 3. (a) and (b) Dislocation structures of 30Mn0.6C TWIP steel after a true strain of 0.05 and 0.1, respectively; (c) and (d) dislocation structures of 30Mn3Al3Si TWIP steel after a true strain of 0.05 and 0.1, respectively; (e) The measured dislocation density of two TWIP steels at high strains, the inserted figure in (e) is the normalized {220} synchrotron diffraction peaks at the true strain of 0.4
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Fig. 4. The dependence of strain-hardening rate on the stacking fault energy and carbon content of TWIP steels.
have the carbon-dislocaiton interaction mechanism so that the uphill stage is not present at all strains (Fig. 1d). It is noted that the SFE of 30Mn3Al3Si and 30Mn0.6C steels at room temperature are 49.1 and 41.9 mJ/m2 , respectively, according to the thermodynamics model [22,23]. Nevertheless, the dislocation density and strain-hardening rate of the 30Mn3Al3Si steel are much lower than that of the 30Mn0.6C steel. It is interesting to note that the strain-hardening rate of the 30Mn3Al3Si steel is similar to that of 316L austenitic steel [24], while the strainhardening rate of high nitrogen austenitic stainless steel has a very high strain-hardening rate similar to the TWIP steels containing carbon (30Mn0.6C) [24,25]. In addition, face-centered cubic (FCC) Ni-C alloys also show that a higher carbon content can lead to a higher strain-hardening rate [26]. Furthermore, it is notable that significant improvement of strain-hardening rate is achieved by carbon addition in high entropy alloys with FCC single-phase structure [27–29]. From all these conclusive experimental evidence, one can draw the conclusion that interstitial carbon solute plays the key role in the high dislocation density and hence high strainhardening rate in TWIP steels. Fig. 4 surveys the strain-hardening rates of various TWIP steels with similar grain size but different carbon content and stacking fault energy [4,5,30–40]. The strain-hardening capacity (θ c ) is defined by
θc =
σ0.4 − σys 0.4
,
(1)
where σ 0.4 is the true stress at a true strain of 0.4, σ ys is the yield stress. It shows that the strain-hardening capacity of TWIP steels slightly depends on the SFE. Instead, the strain-hardening capacity increases significantly with carbon content. It is noted that the carbon-dislocation interaction cannot only affect the dislocation glide in the slip plane [41]. More importantly, the carbondislocation interaction can hinder the cross-slip of dislocations [5,42,43], resulting in a lower rate of dynamic recovery and therefore a higher rate of dislocation accumulation. In summary, the present experimental results demonstrate that the carbon atoms play a vital role in the accumulation of dislocations and therefore the strain-hardening rate of T WIP steels. T WIP steels with carbon possess much higher dislocation density compared to the carbon-free TWIP steels because of the important role of carbon-dislocation interaciton. Carbon-free TWIP steels are conventional low SFE fcc alloys similar to 316L stainless steel.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments M.X. Huang acknowledges the financial support from the National Key Research and Development Program of China (No. 2019YFA0209900), Guangzhou Municipal Science and Technology Project (No. 201807010079), National Natural Science Foundation of China (No. U1764252, U1560204), and Hong Kong Research Grants Council (No. 17255016, 17210418, R7066-18). Z.C Luo acknowledges the financial support from National Natural Science Foundation of China (No. 51901049). The Shanghai Synchrotron Radiation Facility (beamline No. 14B) was acknowledged for providing the beam time and assistance. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.scriptamat.2019.11. 047. References [1] O. Grässel, L. Krüger, G. Frommeyer, L. Meyer, Int. J. Plast. 16 (10) (20 0 0) 1391–1409. [2] O. Bouaziz, N. Guelton, Mater. Sci. Eng.: A 319 (2001) 246–249. [3] S. Allain, J.-.P. Chateau, O. Bouaziz, Mater. Sci. Eng.: A 387 (2004) 143–147. [4] H. Idrissi, K. Renard, L. Ryelandt, D. Schryvers, P.J. Jacques, Acta Mater. 58 (7) (2010) 2464–2476. [5] S.J. Lee, J. Kim, S.N. Kane, B.C. De Cooman, Acta Mater. 59 (17) (2011) 6809–6819. [6] B.C. De Cooman, Y. Estrin, S.K. Kim, Acta Mater. 142 (Supplement C) (2018) 283–362. [7] O. Bouaziz, S. Allain, C. Scott, Scr. Mater. 58 (6) (2008) 484–487. [8] O. Bouaziz, Scr. Mater. 66 (12) (2012) 982–985. [9] Y. Wei, Y. Li, L. Zhu, Y. Liu, X. Lei, G. Wang, Y. Wu, Z. Mi, J. Liu, H. Wang, H. Gao, Nat. Commun. 5 (2014) 3580. [10] Z. Zhang, H. Sheng, Z. Wang, B. Gludovatz, Z. Zhang, E.P. George, Q. Yu, S.X. Mao, R.O. Ritchie, Nat. Commun. 8 (2017) 14390. [11] B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, Science 345 (6201) (2014) 1153–1158. [12] Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Nature 534 (7606) (2016) 227–230. [13] Z. Zhang, M.M. Mao, J. Wang, B. Gludovatz, Z. Zhang, S.X. Mao, E.P. George, Q. Yu, R.O. Ritchie, Nat. Commun. 6 (2015) 10143.
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Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
The role of interstitial carbon atoms on the strain-hardening rate of twinning-induced plasticity steels Z.C. Luo a,b, M.X. Huang a,∗ a b
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, PR China Guangdong Institute of Materials and Processing, Guangdong Academy of Science, Guangzhou, PR China
a r t i c l e
i n f o
Article history: Received 3 September 2019 Revised 17 November 2019 Accepted 19 November 2019
Keywords: TWIP steel Strain-hardening Dislocation density Carbon-dislocation interaction Synchrotron X-ray diffraction
a b s t r a c t Synchrotron X-ray diffraction was applied to measure the dislocation density of two twinning-induced plasticity (TWIP) steels with different carbon content but comparable stacking fault energy (SFE). We found that the dislocation density of the carbon-alloyed TWIP is much higher than that of the carbonfree TWIP steel, though these two steels possess similar twin volume fraction. It indicates that the excellent tensile and strain-hardening properties of the carbon-alloyed TWIP steels are mainly caused by the high dislocation density induced by the carbon-dislocation interaction. Carbon-free TWIP steels are conventional low SFE fcc alloys similar to 316L stainless steel.
Twinning-induced plasticity (TWIP) steels possess high strainhardening rate and superior tensile properties (tensile uniform elongation >50% and ultimate tensile strength >10 0 0 MPa), and are potential materials for lightweight structure applications [1–6]. Compared to other metals and alloys, the distinguishing feature of TWIP steels is that extensive deformation twins are generated during deformation. As a result, this category of steels is named as TWIP steels in the metallurgy community. Considering the effect of deformation twins on the tensile properties of TWIP steels, one conventional view considers that the average distance of dislocation glide is reduced effectively by deformation twins, resulting in a high dislocation density and therefore excellent tensile properties [2]. Another traditional opinion considers that dislocations piledup at twin boundaries generate back-stresses, leading to the “dynamic Hall–Petch” effect and therefore excellent tensile properties [7,8]. Both traditional views consider deformation twinning is the decisive mechanism responsible for the excellent tensile properties of TWIP steels. These views have been cited by many researchers without questions in the last two decades [9–14]. Different from the above conventional views, some recent experimental results questioned the role of deformation twins in the tensile properties of TWIP steels [15–17]. It was shown that deformation twins only contribute about 10% of the ultimate tensile strength of a TWIP steel [15]. In addition, it was found that a TWIP ∗
Corresponding author. E-mail address: [email protected] (M.X. Huang).
https://doi.org/10.1016/j.scriptamat.2019.11.047 1359-6462/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
steel deformed at 473 and 298 K possessed comparable dislocation densities and tensile properties [16]. But the deformation twins are largely inhibited at 473 K while intensive deformation twins are generated at 298 K [16]. These new experimental evidence suggest that deformation twins may not be the main mechanism responsible for the high dislocation density and excellent tensile properties of TWIP steels [16]. The present work intends to clarify the undiscovered mechanism that is responsible for the excellent tensile properties of T WIP steels. T WIP steels with and without carbon are investigated. Dislocation density and volume fraction of twins are quantified by detailed experiments. Two TWIP steels with the respective chemical composition of Fe–30Mn–3Al–3Si and Fe–30Mn–0.6C (wt%) were employed in the present work, which were denoted as 30Mn3Al3Si and 30Mn0.6C hereafter. They were cast with vacuum casting, followed by forging at 1173 K into a thickness of 100 mm. Tensile specimens with gauge dimensions of 10 × 4 × 1.8 mm were cut from the plate. Quasi-static tensile tests interrupted at true strains of 0.05, 0.1, 0.2, 0.3 and 0.4 were conducted by using a univervial tensile machine. The interrupted tensile samples were then prepared by electropolishing for scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and synchrotron X-ray diffraction (XRD) experiments. In order to get the best contrast of the twins, the Inlens mode was applied under a working voltage of 5 kV in a LEO 1530 SEM. During image collecting, a line integration method was used to reduce the noise, and the brightness was set
Z.C. Luo and M.X. Huang / Scripta Materialia 178 (2020) 264–268
Fig. 1. (a) and (b) EBSD maps of 30Mn0.6C and 30Mn3Al3Si TWIP steels prior to the tensile test, the color maps indicate the orientation of grains; (c) engineering stress–strain curves of two TWIP steels and (d) the true stress–strain curves and strain-hardening rates. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
to 0 while the contrast was about 44.9. Transmission electron microscopy (TEM) observation is carried out by using a JEM-2100 scanning TEM operated at 200 kV. The synchrotron XRD experiments were carried out at the Shanghai synchrotron facility (beamline No. 14B). The energy of the synchrotron X-ray was 18 keV. LaB6 powders were used to determine the instrumental profile. The XRD line profiles were analyzed by the convolution multiple whole profile (CMWP) method [18]. These two TWIP steels are fully-recrystallized as shown in Fig. 1a and b, respectively. The respetive grain size of the 30Mn3Al3Si and 30Mn0.6C samples are 23.9 and 33.4 μm. Fig. 1c presents the engineering stress-strain curves of 30Mn3Al3Si and 30Mn0.6C steels. Fig. 1d reveals the true stress-strain curves and strain-hardening rate (θ ) of the two TWIP steels. The 30Mn3Al3Si and 30Mn0.6C steels exhibit distinguishable strain-hardening rate and ultimate tensile strength (UTS). It can be seen that the θ of the 30Mn0.6C steel is higher than 2 GPa even at a large true strain of 0.4. For comparison, the θ of 30Mn3Al3Si steel is lower than 1.5 GPa after a small true strain of 0.15. TEM images revealed that deformation twins are formed in the 30Mn0.6C and 30Mn3Al3Si samples deformed at room temperature. Fig. 2a and d shows the scanning TEM images of the 30Mn0.6C and 30Mn3Al3Si TWIP steels deformed to a true strain of 0.3 at room temperature, respectively. Fig. 2b and e shows the details of the deformation twins. Selected area electron diffraction (SAED) patterns taken along the [110] zone axis (Fig. 2c and f) reveal clearly the deformation twins in both TWIP steels. In the present work, the evolution of twin volume fractions is determined by using the SEM images (Fig. 2g). The measurement method was described in [16]. Three images of each condition are used and each image covers tens of grains to ensure the statistical reliability. Fig. 2h shows the evolution of twin fractions with the true strain. The area fraction can be used to represent approximately the volume fraction of deformation twins [19,20]. It is noted that the twin volume fraction in the 30Mn0.6C steel is slightly higher than that in the 30Mn3Al3Si steel. Fig. 3a shows the tangled dislocations in the 30Mn0.6C steel after straining to a true strain of 0.05. As the strain increases to 0.1, high dislocation density walls (HDDW) can be observed in the 30Mn0.6C steel (Fig. 3b). Fig. 3c and d illustrates the dislocation structures of the 30Mn3Al3Si steel strained to 0.05 and 0.1, re-
265
spectively. It demonstrates that planar slip prevails in both TWIP steels due to their low stacking fault energy (SFE). At high strains, synchrotron X-Ray diffraction is employed to measure the dislocation density in both TWIP steels. The CMWP method developed by Ribárik [18] and Ungár et al. [21] is utilized to analyze the diffraction profiles. Fig. 4e shows the dislocation densities of both TWIP steels at the true strains of 0.2 and 0.4. The inserted figure in Fig. 4e presents the normalized {220} Bragg peaks of the sample at the true strain of 0.4. The dislocation density calculated by the CMWP method could be higher than the real value due to its overestimation nature. Nevertheless, it is consistent with our previous results [15,16]. Furthermore, it shows that the 30Mn0.6C steel possesses a higher dislocation density than the 30Mn3Al3Si steel at the same true strain. At a true strain of 0.1, the twin volume fractions of both TWIP steels are smaller than 0.5% as shown in Fig. 2h. It suggests that the contribution of twins to the plastic deformation is negligible at low strains. However, it can be seen in Fig. 1d that, at the true strain of 0.05, the θ value of the 30Mn0.6C steel is about 2900 MPa, while it is about 1880 MPa for the 30Mn3Al3Si steel. As the true strain increases to 0.1, the θ of 30Mn0.6C and 30Mn3Al3Si steels become 2690 MPa and 1600 MPa, respectively. The difference of θ in these two steels can be as high as 10 0 0 MPa. Such a large difference should not be related to the deformation twins since the twin volume fractions in both steels are negligibly small at the true strain of 0.1. In other words, the strain-hardening of TWIP steels at low strains only depends on the accumulation of dislocations, which is not controlled by the deformation twins. Remarkably, slip planarity of dislocations has been characterized in both steels as shown in Fig. 3. It suggests that the planar slip alone is also not the cause for the different accumulation rate of dislocations. By combining Figs. 2h and 3e, one can find that the twin volume fraction increases with strain in both TWIP steels, but they show distinguishable dislocation density after the same level of tensile deformation. We also examined the dislocation density of 30Mn0.6C steel deformed at 573 K to a true strain of 0.4. It is found that the dislocation density is as high as 1.4 × 1016 m−2 , though the microstructure contains no deformation twins, which is higher than that of 30Mn3Al3Si TWIP steel with abundant twins deformed to the same strain level at room temperature (Fig. 3e). It indicates that the deformation twins are not the dominant mechanism responsible for the high dislocation density in TWIP steels. The conventional view considers that deformation twins in TWIP steels are responsible for the uphill stage of the strainhardening rate, e.g., 30Mn0.6C in Fig. 1d. However, this conventional view may be questionable according to the present investigation. At room temperature, the strain-hardening rate of the 30Mn0.6C TWIP steel starts to increase at a true strain of about 0.25 as shown in Fig. 1d. But the strain-hardening rate of the 30Mn3Al3Si steel decreases monotonically with strain. These two steels possess similar volume fraction of deformation twin (Fig. 2). Nevertheless, one contains the uphill stage and the other does not. Therefore, the presence of deformation twins is not responsible for the uphill stage of the strain-hardening rate in TWIP steels. The uphill stage of the strain-hardening rate can be explained by the interaction between carbon atoms and dislocations. For the carbon-alloyed TWIP steel, the short-range diffusion of carbon atoms into dislocations are less activated at low strain due to a relative low dislocation density. As a result, the uphill stage at low strain in the carbon-alloyed TWIP steel is not observed. The short-range diffusion of carbon atoms into dislocations can be significantly promoted when more dislocations are presented at high strain. Therefore, the uphill stage appears at a relative large strain (30Mn0.6C in Fig. 1d). In addition, the 30Mn3Al3Si steel does not
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Fig. 2. (a) and (d) STEM image of the microstructure after 0.3 true strain of 30Mn0.6C and 30Mn3Al3Si steels; (b) and (e) high magnification image shows the deformation twins; (c) and (f) The diffraction patterns from (b) and (e); (g) typical SEM image of 30Mn0.6C steel at the true strain of 0.4; (h) the evolution of volume fraction of deformation twins in two TWIP steels.
Fig. 3. (a) and (b) Dislocation structures of 30Mn0.6C TWIP steel after a true strain of 0.05 and 0.1, respectively; (c) and (d) dislocation structures of 30Mn3Al3Si TWIP steel after a true strain of 0.05 and 0.1, respectively; (e) The measured dislocation density of two TWIP steels at high strains, the inserted figure in (e) is the normalized {220} synchrotron diffraction peaks at the true strain of 0.4
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Fig. 4. The dependence of strain-hardening rate on the stacking fault energy and carbon content of TWIP steels.
have the carbon-dislocaiton interaction mechanism so that the uphill stage is not present at all strains (Fig. 1d). It is noted that the SFE of 30Mn3Al3Si and 30Mn0.6C steels at room temperature are 49.1 and 41.9 mJ/m2 , respectively, according to the thermodynamics model [22,23]. Nevertheless, the dislocation density and strain-hardening rate of the 30Mn3Al3Si steel are much lower than that of the 30Mn0.6C steel. It is interesting to note that the strain-hardening rate of the 30Mn3Al3Si steel is similar to that of 316L austenitic steel [24], while the strainhardening rate of high nitrogen austenitic stainless steel has a very high strain-hardening rate similar to the TWIP steels containing carbon (30Mn0.6C) [24,25]. In addition, face-centered cubic (FCC) Ni-C alloys also show that a higher carbon content can lead to a higher strain-hardening rate [26]. Furthermore, it is notable that significant improvement of strain-hardening rate is achieved by carbon addition in high entropy alloys with FCC single-phase structure [27–29]. From all these conclusive experimental evidence, one can draw the conclusion that interstitial carbon solute plays the key role in the high dislocation density and hence high strainhardening rate in TWIP steels. Fig. 4 surveys the strain-hardening rates of various TWIP steels with similar grain size but different carbon content and stacking fault energy [4,5,30–40]. The strain-hardening capacity (θ c ) is defined by
θc =
σ0.4 − σys 0.4
,
(1)
where σ 0.4 is the true stress at a true strain of 0.4, σ ys is the yield stress. It shows that the strain-hardening capacity of TWIP steels slightly depends on the SFE. Instead, the strain-hardening capacity increases significantly with carbon content. It is noted that the carbon-dislocation interaction cannot only affect the dislocation glide in the slip plane [41]. More importantly, the carbondislocation interaction can hinder the cross-slip of dislocations [5,42,43], resulting in a lower rate of dynamic recovery and therefore a higher rate of dislocation accumulation. In summary, the present experimental results demonstrate that the carbon atoms play a vital role in the accumulation of dislocations and therefore the strain-hardening rate of T WIP steels. T WIP steels with carbon possess much higher dislocation density compared to the carbon-free TWIP steels because of the important role of carbon-dislocation interaciton. Carbon-free TWIP steels are conventional low SFE fcc alloys similar to 316L stainless steel.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments M.X. Huang acknowledges the financial support from the National Key Research and Development Program of China (No. 2019YFA0209900), Guangzhou Municipal Science and Technology Project (No. 201807010079), National Natural Science Foundation of China (No. U1764252, U1560204), and Hong Kong Research Grants Council (No. 17255016, 17210418, R7066-18). Z.C Luo acknowledges the financial support from National Natural Science Foundation of China (No. 51901049). The Shanghai Synchrotron Radiation Facility (beamline No. 14B) was acknowledged for providing the beam time and assistance. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.scriptamat.2019.11. 047. References [1] O. Grässel, L. Krüger, G. Frommeyer, L. Meyer, Int. J. Plast. 16 (10) (20 0 0) 1391–1409. [2] O. Bouaziz, N. Guelton, Mater. Sci. Eng.: A 319 (2001) 246–249. [3] S. Allain, J.-.P. Chateau, O. Bouaziz, Mater. Sci. Eng.: A 387 (2004) 143–147. [4] H. Idrissi, K. Renard, L. Ryelandt, D. Schryvers, P.J. Jacques, Acta Mater. 58 (7) (2010) 2464–2476. [5] S.J. Lee, J. Kim, S.N. Kane, B.C. De Cooman, Acta Mater. 59 (17) (2011) 6809–6819. [6] B.C. De Cooman, Y. Estrin, S.K. Kim, Acta Mater. 142 (Supplement C) (2018) 283–362. [7] O. Bouaziz, S. Allain, C. Scott, Scr. Mater. 58 (6) (2008) 484–487. [8] O. Bouaziz, Scr. Mater. 66 (12) (2012) 982–985. [9] Y. Wei, Y. Li, L. Zhu, Y. Liu, X. Lei, G. Wang, Y. Wu, Z. Mi, J. Liu, H. Wang, H. Gao, Nat. Commun. 5 (2014) 3580. [10] Z. Zhang, H. Sheng, Z. Wang, B. Gludovatz, Z. Zhang, E.P. George, Q. Yu, S.X. Mao, R.O. Ritchie, Nat. Commun. 8 (2017) 14390. [11] B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, Science 345 (6201) (2014) 1153–1158. [12] Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, C.C. Tasan, Nature 534 (7606) (2016) 227–230. [13] Z. Zhang, M.M. Mao, J. Wang, B. Gludovatz, Z. Zhang, S.X. Mao, E.P. George, Q. Yu, R.O. Ritchie, Nat. Commun. 6 (2015) 10143.
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