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The effects of Si on the mechanical twinning and strain hardening of Fe–18Mn–0.6C twinning-induced plasticity steel
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Acta Materialia 61 (2013) 3399–3410 www.elsevier.com/locate/actamat
The effects of Si on the mechanical twinning and strain hardening of Fe–18Mn–0.6C twinning-induced plasticity steel Kookhyun Jeong, Jae-Eun Jin, Yeon-Seung Jung, Singon Kang, Young-Kook Lee ⇑ Department of Materials Science and Engineering, Yonsei University, Seoul 120-749, Republic of Korea Received 28 January 2013; accepted 14 February 2013 Available online 16 March 2013
Abstract The stacking-fault energy (SFE), dislocation slip, mechanical twinning, strain hardening, and yield and tensile strengths were systemically investigated in Fe–18Mn–0.6C–1.5Si twinning-induced plasticity (TWIP) steel. The results were also compared with those for Fe– 18Mn–0.6C and Fe–18Mn–0.6C–1.5Al TWIP steels. The SFE decreased by 4 mJ m2 per 1 wt.% Si. The addition of Si increased both the yield strength, due mainly to solid solution hardening, and the tensile strength, owing to the high strain hardening that occurred while maintaining a large elongation of over 60%. To examine this high strain hardening, especially at low strains, the volume fractions of the primary and secondary mechanical twins were quantitatively evaluated by combining the merits of electron backscattered diffractometry and transmission electron microscopy. The volume fractions of both the primary and secondary twins were the highest in the Fe–18Mn– 0.6C–1.5Si TWIP steel, which had the lowest SFE of the three TWIP steels. In particular, the volume fraction of the secondary mechanical twins increased rapidly with the addition of Si. The contributions of dislocation storage, mechanical twinning and dynamic strain aging (DSA) to the strain hardening were also quantitatively evaluated in the three TWIP steels. The Si-added TWIP steel had the highest strain hardening, due mainly to the active primary and secondary twinning, and experienced negligible DSA. In contrast, the Al-added TWIP steel exhibited the lowest strain hardening due to the reductions in both the mechanical twinning and DSA. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Twinning-induced plasticity (TWIP) steel; Stacking-fault energy; Mechanical twin; Strain hardening; Dynamic strain aging
1. Introduction High-Mn austenitic steels have recently attracted a great deal of attention because of their high tensile strength and extraordinary ductility arising from the many mechanical twins generated during plastic deformation, which is termed twinning-induced plasticity (TWIP) [1–3]. Of the TWIP steels, the Fe–Mn–C ternary system has frequently been studied due to the easy control of both the stackingfault energy (SFE) and austenite stability by regulating the Mn and C concentrations [4,5]. Idrissi et al. [2] investigated the relationship between high strain hardening and mechanical twinning in Fe–22Mn–1.2C TWIP steel and found that mechanical twins contain a high level of sessile ⇑ Corresponding author. Tel.: +82 2 2123 2831; fax: +82 2 312 5375.
E-mail address: [email protected] (Y.-K. Lee).
dislocations and act as strong barriers to dislocation gliding, resulting in high strain hardening. Gil Sevillano [6] reported that mechanical twins contribute to the reduction of the effective grain size in Fe–22Mn–0.6C TWIP steel, which is referred to as the dynamic Hall–Petch effect. Despite its outstanding tensile properties, Fe–Mn–C TWIP steel has some shortcomings, such as low yield strength (YS) [2,7], carbide precipitation [8] and hydrogen delayed fracture [9–11]. To solve these problems, the addition of an alloying element such as Al has been considered by different researchers [5,8,10–15]. The Al effectively suppresses the hydrogen delayed fracture [10,11,14,15] and cementite precipitation [8,12,13], and stabilizes the austenite phase against the strain-induced martensitic transformation in Fe–Mn–C TWIP steel [5]. However, the addition of Al is not effective at improving the YS in TWIP steel [15–17].
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.02.031
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Dyson and Holmes [18] quantitatively investigated the solid solution hardening effects of various alloying elements on the YS of Fe–16Cr–25Ni stainless steel. They found that Si causes greater improvement of the YS than Al. Ohkubo et al. [19] reported that the YS increases from 161 to 213 MPa with the addition of 1 wt.% Si to Fe–17Cr–12Ni austenitic stainless steel and found that the Si causes high dislocation densities at low strains. Furthermore, it is known that Si decreases the SFE in Fe–17Cr–14Ni austenitic stainless steel [20] and Fe–31 Mn–0.8 C shape-memory alloys [21]. The decreased SFE restrains the cross-slip of dislocations [22,23], promotes planar slip [24,25] and enhances mechanical twinning [26,27]. Therefore, Si is expected to improve both the yield and tensile strengths through solid solution hardening, dislocation hardening and mechanical twinning in high Mn TWIP steels. Nevertheless, the effects of Si on the SFE, dislocation slip, mechanical twinning, strain hardening, and yield and tensile strengths of C-bearing high-Mn TWIP steels are yet to be reported. Meanwhile, both the dislocation storage and mechanical twinning contribute to strain hardening in TWIP steels with low SFE [3,7,28–30]. Dini et al. [29] investigated the change in dislocation density with strain in Fe–31Mn– 3Si–3Al TWIP steel using an X-ray diffractometer (XRD) and evaluated the contribution of dislocation storage to strain hardening. Allain et al. [7] analyzed the contribution of mechanical twinning to the strain hardening in terms of a dislocation mean free path (MFP) in Fe–22Mn–0.6C TWIP steel. However, the detailed experimental method for measuring the twin fractions, which are an essential parameter for determining the MFP, has not been introduced in the literature. Therefore, the quantitative analysis of mechanical twins, such as the area fraction of twinned grains, twin density and twin volume fraction, must still be performed to examine the relationship between strain hardening and mechanical twinning. Shun et al. [31] attempted to measure the area fraction of twinned grains, defined as the ratio of the number of grains containing mechanical twins to the total observed grains in Fe–30Mn–1.0C–(0 and 3)Al austenitic steels using an optical microscope (OM). However, the measured area fraction of the twinned grains seems to be inaccurate because there has been no evidence that all of the etched regions are twins and that all twins are etched. Li et al. [32] investigated the twin density, defined as the total length of the twin boundaries in the area observed in a nanostructured Cu–Zn alloy using a transmission electron microscope (TEM). Mechanical twins have been confirmed by means of selected area electron diffraction (SAED), and fine twins have also been observed. However, due to the limitations of the observed area, TEM observation is not suitable for the quantitative analysis of mechanical twins in high-Mn TWIP steel. McCabe et al. [33] measured the twin volume fraction in highly purified Zr from electron backscattered diffractometer (EBSD) images, defined as the ratio between the total
area of mechanical twins and the observed area. Although EBSD provides a larger observable area than TEM, the spatial resolution is not high enough to observe extremely thin mechanical twins [34,35]. Recently, Gutierrez-Urrutia and Raabe [36] succeeded in more clearly observing mechanical twins in Fe–22Mn–0.6C TWIP steels using an electron channeling contrast imaging (ECCI) method, compared with the EBSD method, and quantitatively evaluated the area fraction of the twinned grains. However, the ECCI still has a lower spatial resolution than that of TEM [34,35] and has yet to become a conventional electron microscopic technique like TEM and EBSD. Therefore, no qualified experimental methods have been performed to measure the twin fraction. As a result, the following three subjects were investigated in the present study. First, the effects of Si on the SFE, dislocation slip, mechanical twinning, strain hardening and yield and tensile strengths in Fe–18Mn–0.6C– 1.5Si TWIP steel were examined and compared with those in Fe–18 Mn–0.6C and Fe–18Mn–0.6C–1.5Al TWIP steels. Second, the twin volume fractions of the three TWIP steels were quantitatively measured using both EBSD and TEM to compensate for the shortcomings of each method and obtain more accurate analysis of the mechanical twinning. Finally, using the measurements of the dislocation density and twin volume fraction, the contributions of dislocation storage, mechanical twinning and dynamic strain aging (DSA) to the strain hardening of each TWIP steel were quantitatively evaluated to identify a predominant hardening mechanism. 2. Experimental procedure Three ingots, weighing 30 kgf each, with the chemical compositions listed in Table 1, were prepared by vacuum induction melting. The ingots were homogenized at 1200 °C for 12 h in a protective nitrogen gas atmosphere and hot-rolled at temperatures between 1000 and 1100 °C into a plate 5 mm thick. To eliminate the decarburized layers of the plate, surface grinding was performed that removed 1 mm from each side of the plate. The surfaceground plate was cold-rolled at room temperature to make sheets 1.4 mm thick, corresponding to a thickness reduction of 55%. The cold-rolled sheets were annealed at 900 °C for 5 min using a vacuum tube furnace, followed by oil quenching to prevent carbide precipitation. The microstructures of the annealed specimens were observed using an electron backscattered diffractometer
Table 1 Chemical compositions (wt.%) of the TWIP steels used in the present study. TWIP steel
Mn
C
Si
Al
Fe
T618 T618–Al T618–Si
17.65 17.51 17.70
0.62 0.58 0.59
0.01 0.05 1.59
0.01 1.54 0.03
Bal. Bal. Bal.
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(EBSD, EDAX, Hikari) attached to a field-emission scanning electron microscope (FE-SEM, TESCAN, Mira-3). The EBSD specimens were prepared by mechanical polishing with an aqueous solution containing colloidal silica particles. The mean grain size of the annealed specimens was determined using a mean equivalent circle diameter on EBSD boundary maps with and without annealing twin boundaries. Uniaxial tensile tests were conducted at a constant strain rate of 1 104 s1 using an Instron machine (Instron, 3382) at room temperature. The gauge portion of the tensile specimens was 6 mm wide, 25 mm long and 1.3 mm thick. Mechanical twins were observed using both EBSD and a field-emission TEM (FE-TEM, JEOL, JEM2000EX) operated at 200 kV. Thin foils for TEM observations were prepared by twin-jet polishing in a mixed solution of 90% acetic acid and 10% perchloric acid at 15 °C and an applied potential of 20 V. The foils were additionally thinned by an ion beam with an incidence angle of 4° using a precision ion polishing system (Gatan, 691). To investigate the specimens’ phase constituents, stacking-fault energies (SFEs) and dislocation densities, an X-ray diffractometer (XRD, RIGAKU, D/MAX-2500) ˚ operated was used with Cu Ka radiation (k ¼ 1:54056A), at 30 kV at room temperature. The scanning range and speed were 40–100° and 1° min1, respectively. The SFE was determined using the following equation proposed by Schramm and Reed [37]: c¼
K 1 1 1 x0 Gð1 1 1Þ a0 A0:37 he250 i1 1 1 pffiffiffi a p 3
ð1Þ
where K 1 1 1 x0 is a proportionality constant with a value of 6.6 [21,37], Gð1 1 1Þ is the shear modulus of 65 GPa in the (1 1 1) fault plane, a0 is the lattice parameter and A is the Zener anisotropy of 3.43. The mean square microstrain (he250 i1 1 1 ) was determined using a Willamson–Hall plot [38] obtained from the XRD profiles. The stacking-fault probability (a) was obtained using the following equation for both annealed (ANN) and cold-worked (CW) specimens [37]: D2h ¼ ð2h2 0 0 2h1 1 1 ÞCW ð2h2 0 0 2h1 1 1 ÞANN pffiffiffi 45 3 1 ¼ 2 tan h2 0 0 þ tan h1 1 1 a p 2
ð2Þ
where 2h is the XRD peak position. The shear modulus (G) was measured using a resonant frequency and damping analyzer (RFDA, IMCE, HTVP1600) at room temperature. The specimen used to measure the shear modulus was 15 mm wide, 50 mm long and 3.5 mm thick. 3. Results and discussion 3.1. Microstructure Fig. 1a–c shows the EBSD boundary maps of the T618, T618–Al and T618–Si TWIP steels, respectively, which were taken from the normal planes of the annealed speci-
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mens. The blue and black lines correspond to low- and high-angle boundaries whose misorientation angles are 3–15° and 15–180°, respectively. The red lines denote annealing twin boundaries determined by the coincidence site lattice (CSL) boundaries of R3. The austenite grain sizes (AGSs) of the T618, T618–Al and T618–Si TWIP steels with annealing twin boundaries were 10.0, 11.7 and 8.5 lm, respectively, which indicated a slight decrease in AGS with the addition of Si. In addition, the three TWIP steels possessed no deformed grains and were fully recrystallized into an austenite single phase with equiaxed grains (Fig. 1d). The austenite single phase remained devoid of emartensite formation, even after tensile tests were performed to fracture (Fig. 1e). 3.2. Stacking-fault energy The SFE and AGS are important factors contributing to the tensile properties of high-Mn austenitic steels because these steels’ deformation mechanisms are greatly influenced by the SFE [7,17,22]. The SFE is usually either calculated using thermodynamic models [39–41] or measured experimentally with TEM [12,20], XRD [12,21] or neutron diffraction [16]. Fig. 2 shows the changes in the measured (closed marks) and calculated (open marks) SFE values with Si content for several austenitic steels. The measured SFE values decreased with Si content in the Fe–17Cr–14Ni [20] and Fe–31Mn–0.8C [21] steels, regardless of the experimental method or alloy composition used. However, the calculated SFE values increased with Si content in the Fe–28Mn–2Al [39] and Fe–22 Mn–0.6C [40] TWIP steels and the Fe– 31Mn–0.8C shape-memory alloy [41]. This result was most likely due to a lack of accurate interaction parameters in the Mn–Si and Si–C. Therefore, the SFE values of the three TWIP steels in the present study were measured using XRD, according to Schramm and Reed’s method [37]. The measured SFE values of the T618 and T618–Si TWIP steels were 19.3 and 13.8 mJ m2, respectively, implying a reduction from the 4 mJ m2 per 1 wt.% Si, which were similar to those of other austenitic steels, as shown in Fig. 2. Meanwhile, the measured SFE value of the T618–Al TWIP steel was 29.1 mJ m2, which was even higher than that of the T618 TWIP steel. This result shows good agreement with previous reports stating that Al increases the SFE of austenite in high-Mn TWIP steels [12,17,40]. 3.3. Tensile properties Fig. 3 shows the engineering stress–strain (s–e) curves for the T618, T618–Al and T618–Si TWIP steels. The T618–Si TWIP steel exhibited the highest yield strength (YS) and ultimate tensile strength (UTS), while the T618–Al TWIP steel had an unimproved YS and a lower UTS, as was expected based on the results of previous reports [16,17]. It is worth noting that the total elongation
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Fig. 1. EBSD boundary maps of (a) T618, (b) T618–Al and (c) T618–Si TWIP steels. The blue and black lines indicate the low-angle (3° < h < 15°) and high-angle (h > 15°) boundaries, respectively. The red lines indicate the annealing twin boundaries of the R3 CSL. The figure also shows the XRD patterns of (d) annealed and (f) fractured specimens. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Variations in the calculated and measured SFE values with Si content in various austenitic steels.
of the T618–Si TWIP steel did not decrease significantly and was still over 60%, in spite of the increased strengths. The increased YS of the T618–Si TWIP steel was thought to be associated with several factors, including a reduction in the effective grain size, as shown in Fig. 1a–c, the solid solution hardening of Si [18,42] and the restraint of cross-slip due to its decreased SFE [22,27], considering no precipitation hardening. Meanwhile, the T618– Si TWIP steel exhibited continuous yielding similar to that of the T618 TWIP steel, whereas the T618–Al TWIP steel showed a yield point elongation (YPE) [13]. The appearance of a YPE was probably attributed to a lack of strain hardening, which stemmed from the low dislocation density and delayed mechanical twinning at low strain due to the increased SFE caused by the addition of Al [12,40]. The UTS values of the T618, T618–Al and T618–Si TWIP steels were 1104, 925 and 1187 MPa, respectively. The Al lowers the UTS of these C-bearing high-Mn TWIP
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Fig. 3. Engineering stress–strain (s–e) curves for the T618, T618–Al and T618–Si TWIP steels measured at room temperature and a constant strain rate of 104 s1. The inset shows an enlarged graph of the yielding part of the curve, where YPE is the yield point elongation.
steels because of reductions in both the DSA, due to the decrease in C diffusivity [8,31], and the mechanical twinning, owing to the increased SFE [12,40]. The T618–Si TWIP steel’s stress–strain curve had fewer serrations than those of the T618 and T618–Al TWIP steels, and these serrations are known to be formed by the DSA in C-containing high-Mn TWIP steels [43,44]. The diminished serrations implied a weakened DSA, probably due to the reduced C diffusivity caused by the addition of Si. Actually, Darken [45] has reported that the C diffusivity decreases with the addition of Si in Fe–0.6C weld steel when its temperature has been elevated to the austenitic region. Although the DSA was greatly weakened by the addition of Si, the strain hardening of the T618–Si TWIP steel (742 MPa) was comparable to that of the T618 TWIP steel (738 MPa) with strong DSA effects, probably due to a more active mechanical twinning based on the reduction in SFE caused by the addition of Si. The reason why the T618–Si TWIP steel exhibited the highest UTS among the three TWIP steels was thought to be attributed mainly to its vigorous mechanical twinning. 3.4. Strain hardening behavior Fig. 4a shows the true stress–strain (r–e) and strain hardening rate (SHR, dr/de) curves of the three TWIP steels. The T618–Si TWIP steel exhibited the highest SHR among the three TWIP steels up to a true strain of 0.37. At the onset of plastic deformation in particular, the T618–Si TWIP steel exhibited a very high SHR of 4735 MPa, probably due to the high density of partial dislocations and active mechanical twinning, even at such a low strain. To investigate the strain hardening behavior of the three TWIP steels in more detail, a modified Crussard–Jaoul (C– J) analysis [12,46–49] was performed based on the Swift equation [47] (Fig. 4b–d). As expected based on the results
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of a previous report [50], the plastic deformation region of the T618 TWIP steel (Fig. 4b) could be divided into five stages: the dynamic recovery of dislocations and no twinning (stage A), active primary mechanical twinning (stage B), less active primary mechanical twinning (stage C), active secondary mechanical twinning (stage D) and thicker twin bundle formation (stage E). The T618–Al TWIP steel exhibited three stages (stages A, C and E) on the SHR curve, as shown in Fig. 4c. The disappearance of stages B and D resulted from less active primary and secondary mechanical twinning due to the increased SFE caused by the addition of Al [12]. The T618–Si TWIP steel also exhibited three stages on the SHR curve similar to those of the T618–Al TWIP steel, but it had a different slope at the intermediate stage (stage II, as shown in Fig. 4d). After the SHR decreased up to a true strain of 0.04, it increased linearly with a positive slope to a true strain of 0.27, unlike the T618 and T618–Al TWIP steels, which had almost constant and negative slopes, respectively. The positive slope of the SHR in the T618– Si TWIP steel was thought to be due to the active mechanical twinning caused by the decreased SFE. The positive slope of the SHR occurred over a wide strain range of 0.04–0.27, which has yet to be reported for other TWIP steels [12,46,50,51]. To confirm the active mechanical twinning in the T618– Si TWIP steel, the microstructural evolution of the T618–Si TWIP steel was observed at true strains of 0.02, 0.05, 0.1 and 0.25. Planar dislocation (PD) arrangements and stacking faults (SFs) were clearly observed in a TEM bright field image of the specimen strained by 0.02, taken in a reflecting plane of g = 002 (Fig. 5). It is known that SFs are readily formed in face centered cubic (fcc) materials with low SFE values and that PD arrangements are mainly favored by low SFE, high friction stress and short-range ordering (SRO) [24–26]. Because the T618–Si TWIP steel did not exhibit the SRO, but rather SFs like the Fe–22 Mn–0.6C TWIP steel [36], it was thought that PD arrangements were probably promoted by the low SFE and increased friction stress caused by the addition of Si [18,20,21]. Some primary mechanical twins (TW1) 30 nm thick, along with PDs and SFs, were also observed near the austenite grain boundaries at the same strain of 0.02 (Fig. 6a). As a result, the microstructure of the T618–Si TWIP steel exhibiting SFs, PDs and mechanical twins apparently shows good agreement with previous reports stating that mechanical twinning is favored in fcc materials with PD arrangements [24–26]. However, microbands formed instead of mechanical twins in a recent study on Fe–28Mn–0.8C–9Al steel, although PD arrangements have been clearly observed at low strains [52]. The PD arrangements in the Fe–28Mn–0.8C–9Al steel with a high SFE value of 85 mJ m2 has been attributed mainly to the SRO [52]. Accordingly, not all materials with PD arrangements exhibit mechanical twinning, and it was thought that the crystal defectsobserved in the T618–SiTWIP steel, such as SFs, partial dislocations, PD arrangements and mechanical twins, stemmed from the low SFE of the steel.
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Fig. 4. (a) True stress–strain (r–e) curves and strain hardening rate (dr/de) curves for the T618, T618–Al and T618–Si TWIP steels; ln(dr/de)–ln r plots for the modified Crussard–Jaoul (C–J) analysis [12,46–49] of the (b) T618, (c) T618–Al and (d) T618–Si TWIP steels.
Fig. 5. Bright-field TEM images of the T618–Si TWIP steel deformed at a true strain of 0.02 and taken with a two-beam diffraction condition. PD and SFs are planar dislocation and stacking faults, respectively.
Meanwhile, a true strain of 0.02 corresponded to stage A without mechanical twinning in the T618 and T618–Al TWIP steels. Accordingly, the first stage in Fig. 4d of the
T618–Si TWIP steel was considered a mixture of stages A and B in the T618 TWIP steel. Therefore, a new nomenclature of stages was employed, dividing the curve into stages I, II and III, for the T618–Si TWIP steel. Both primary mechanical twins (TW1) (Fig. 6b) and secondary mechanical twins (TW2), which exhibited a different variant from that of the TW1, were observed at a true strain of 0.05 (Fig. 6c). The SAED pattern illustrated in Fig. 6f shows that primary and secondary mechanical twinning occurred on the ð1 1 1Þ plane in the ½1 1 1 direction and the ð1 1 1Þ plane in the ½1 1 1 direction, respectively, as has been previously reported in the literature [50]. The interior angle between the primary and secondary mechanical twin directions was measured by TEM to be 69°, which was in good agreement with the calculated angle of 70° between the ½1 1 1 and ½1 1 1 directions. This result agrees with those of previous reports giving the measured angle between the directions of the primary and secondary mechanical twins as 71° in Fe–22Mn–0.6C TWIP steel [50]. Therefore, this result confirmed that both secondary and primary mechanical twinning occurred at a low strain of 0.05, corresponding to the transition strain between stages I and II. Accordingly, stage II in Fig. 4d of the T618–Si TWIP steel was considered to be a combination
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Fig. 6. Bright-field TEM images of the T618–Si TWIP steel at various true strains of (a) 0.02, (b and c) 0.05, (d) 0.1 and (e) 0.25. TW1, TW2 and G.B. are the primary and secondary mechanical twins and grain boundaries, respectively. The insets of each image show the SAED patterns of the mechanical twins. (f) Index of the SAED patterns of the mechanical twins at a true strain of 0.05.
of stages B and D in the T618 TWIP steel, skipping stage C. At a true strain of 0.25, which almost corresponded to the end of stage II, both the primary and secondary mechanical twins grew in number, becoming denser and indicating a continuous generation of mechanical twins during stage II (Fig. 6e). 3.5. Quantitative analysis of the twin volume fraction To examine the cause of the high SHR in the T618–Si TWIP steel, especially at low strains, the twin volume fraction, which is defined as the total area of the mechanical
twins per observed area, was quantitatively measured by the steel deformation at a true strain of 0.1 and compared to that of the T618 and T618–Al TWIP steels. For a more accurate and reliable measurement of the twin volume fraction, both EBSD with a large observable area and high resolution TEM were utilized to compensate for each method’s respective shortcomings. Fig. 7a shows the EBSD Kikuchi pattern quality (KPQ) map of the T618–Si TWIP steel deformed at a true strain of 0.1. The EBSD KPQ map shows some annealing twins (ATs) and many mechanical twins (MTs). The apparent widths of the mechanical twins were between 190 and
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230 nm from a misorientation angle map (Fig. 7b), as drawn by scanning perpendicular the mechanical twins along a black line in Fig. 7a. The average apparent width of the mechanical twins was 210 nm, which is similar to those observed from the EBSD KPQ maps in previous reports [50,53]. A TEM image (Fig. 7c) taken from the same strained T618–Si TWIP steel sample shows a bundle of several parallel mechanical twins. The width of the bundle was 190 nm, which was similar to the apparent twin width measured by EBSD (Fig. 7b). Each mechanical twin inside the bundle had an average width of 30 nm, which is similar to TEM results in the literature [28,46]. Therefore, we found that a single mechanical twin on the EBSD KPQ map was actually a bundle of several thin mechanical twins, and that the twin volume fraction measured from the EBSD KPQ map was an overestimation. To measure the average number of mechanical twins in each twin bundle observed on the EBSD KPQ map, the number of twin bundles per unit area was measured using these maps and compared to the number of mechanical twins per unit area measured using the TEM images. 15 TEM images covering an area of 1400 lm2 were obtained from each 0.1-strained TWIP steel specimen. All of the TEM images were taken along the [0 1 1] zone axis, which is typically adopted for mechanical twin observation [46,50]. Four EBSD KPQ maps were obtained from each
deformed TWIP steel specimen, covering an area of 12,500 lm2. Of the total area observed by EBSD, the number of twin bundles per unit area of the {0 1 1} grains (3900 lm2) was compared with the number of mechanical twins per unit area measured by TEM, and is presented in Table 2. As expected, the number of twin bundles per unit area of the {0 1 1} grains determined from the EBSD KPQ maps was less than that of the mechanical twins observed per unit area by TEM, regardless of the TWIP steels’ chemical compositions. This result was probably due to the limited resolution of the EBSD for the observation of thin mechanical twins. Therefore, a compensating factor was determined by dividing the number of mechanical twins per unit area obtained from the TEM images by the number of twin bundles measured from the EBSD KPQ maps. The compensating factors were 2.56, 2.53 and 2.64 for the T618, T618–Al and T618–Si TWIP steels, respectively. Therefore, an average compensating factor (k) of 2.58 was used for the calculation of the volume fraction of mechanical twins (F) in the three TWIP steels as follows: F¼
RlEBSD wEBSD AEBSD k
ð3Þ
where RlEBSD and wEBSD are the total length and apparent average width (210 nm) of the twin bundles measured by
Fig. 7. (a) Electron backscattered diffraction (EBSD) Kikuchi pattern quality map of the T618–Si TWIP steel deformed at a true strain of 0.1. AT and MT are the annealing and mechanical twins, respectively. (b) Misorientation angle map scanned along the thick black line in (a). (c) TEM image taken from the same strained T618–Si TWIP steel.
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Table 2 Measured values used for the calculation of the compensating factor (k) using both EBSD and TEM. A{0 1 1} and n are the total observed area of the {0 1 1} grains and the number of mechanical twins, respectively. Measured value 2
A{0 1 1} (lm ) n n/A{0 1 1} (102 lm2) k (n/A{0 1 1})TEM/(n/A{0 1 1})EBSD
T618 steel
T618–Al steel
T618–Si steel
EBSD
TEM
EBSD
TEM
EBSD
TEM
3692 107 2.90 2.56
1319 98 7.43
4286 54 1.26 2.53
1475 47 3.19
3813 194 5.09 2.64
1431 192 13.42
Fig. 8. EBSD Kikuchi pattern quality maps of the (a) T618, (b) T618–Al and (c) T618–Si TWIP steels at a true strain of 0.1. The solid line indicates the intersections of the primary and secondary mechanical twins.
EBSD KPQ maps, respectively, and AEBSD is the total observed area of the {0 1 1} grains on the EBSD KPQ maps. Representative EBSD KPQ maps of the three TWIP steels used to measure the twin volume fraction are presented in Fig. 8. While even primary mechanical twins were barely observed in the T618–Al TWIP steel (Fig. 8b), the T618–Si TWIP steel exhibited well-developed secondary mechanical twins along with primary mechanical twins (solid lines in Fig. 8c). Accordingly, not only the total twin volume fraction but also the volume fractions of primary and secondary mechanical twins were separately evaluated from the EBSD KPQ maps. Fig. 9 shows the change in twin volume fraction with the change in SFE in the three TWIP steels deformed by a true strain of 0.1. The total twin volume fraction (open marks) linearly decreased with a slope of 0.13% per SFE of 1 mJ m2. The total twin volume fraction was only a few percentage points due to both the small strain of 0.1 used and the nanometer-sized twin width [28,46]. Meanwhile, the changes in volume fraction of the primary and secondary mechanical twins (closed marks) with the change in SFE did not exhibit similar behavior. The volume fraction
Fig. 9. Change in the twin volume fraction with SFE in the T618, T618– Al and T618–Si TWIP steels deformed at a true strain of 0.1.
of the primary mechanical twins increased almost linearly with decreasing SFE, from 30 to 20 mJ m2, and then increased slightly below 20 mJ m2 in the low SFE range. This result was contrary to the behavior of the volume fraction of the secondary mechanical twins, which rapidly
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increased when the SFE was less than 20 mJ m2, resulting in additional strain hardening in the T618–Si TWIP steel. 3.6. Quantitative analysis of the strain hardening Both dislocation storage and mechanical twinning can contribute to strain hardening in TWIP steels with low SFE values [3,28,29,36,54]. The DSA also increases the strain hardening of C-bearing TWIP steels [12,44]. Therefore, the total flow stress of the three C-bearing TWIP steels deformed by a true stress of 0.1 (r0.1) can be expressed as follows: r0:1 ¼ r0 þ Drd þ Drt þ DrD
ð4Þ
where r0 is the lattice friction stress, the values of which were taken from the y-intercepts of the Hall–Petch plots of the Fe–22Mn–0.6C [28], Fe–18Mn–0.6C–1.5Al [13] and T618–Si TWIP steels. The r0 values were 132 MPa for the T618, 155 MPa for the T618–Al and 190 MPa for the T618–Si TWIP steels. The T618–Si TWIP steel possessed the highest r0 value, indicating the significant solid solution hardening induced by Si. Drd, Drt and DrD are the increments in flow stress caused by dislocation storage, mechanical twinning and DSA, respectively. The r0.1 values of the three TWIP steels were 720, 602 and 823 MPa for the T618, T618–Al and T618–Si TWIP steels, respectively. The Drd value was calculated by the following equation [29,54]: pffiffiffi Drd ¼ MaGb q ð5Þ where M is an average Taylor factor of 3.06 for fcc crystals [3,28,29], a is a constant value of 0.26 [3,28,29] and b is the Burgers vector. The shear modulus (G) of the T618–Si TWIP steel was measured with a resonant frequency and damping analyzer (RFDA) to be 72.5 GPa at room temperature. This value was slightly higher than those of Fe– 18Mn–0.6C (71.0 GPa) [55] and Fe–18Mn–0.6C–1.5Al TWIP steels (70.4 GPa) [55]. The dislocation density (q) was calculated using the following equation [29,54]: pffiffiffiffiffiffi 3 2phe250 i1 1 1 q¼ ð6Þ Db where D is the average crystallite size determined using the Sherrer formula [56], as obtained from the XRD profiles. The dislocation densities (q) of the T618, T618–Al and T618–Si TWIP steels at a strain of 0.1 were determined using XRD to be 8.5 1014, 7.6 1014 and 9.2 1014 m2, respectively, and there was little difference in the dislocation density between the Fe–18Mn–0.6C and Fe–18Mn–0.6C–1.5Al TWIP steels at low strains when the dislocation densities were measured using neutron diffraction [57]. The amount of dislocation hardening (Drd) in the three TWIP steels at a strain of 0.1 was calculated using Eq. (5) and is plotted in Fig. 10. The Drd values were 420, 395 and 445 MPa for the T618, T618–Al and T618–Si TWIP steels, respectively. The contribution of dislocation hardening to
the total flow stress at a true strain of 0.1 was 58%, 66% and 54% in the T618, T618–Al and T618–Si TWIP steels, respectively, which is in good agreement with previous reports suggesting that dislocation storage causes high strain hardening at low strains in Fe–22Mn–0.6C TWIP steel [36]. The T618–Al TWIP steel exhibited the lowest dislocation hardening among the three TWIP steels because it had the lowest density of dislocations, making cross-slip easier due to the increased SFE caused by the addition of Al [12,17,40]. The amount of strain hardening caused by mechanical twinning (Drt) and DSA (DrD) without dislocation storage was 168, 52 and 188 MPa in the T618, T618–Al and T618– Si TWIP steels, respectively. The Drt values of the primary (Drpt ) and secondary (Drst ) twins were calculated using the following equation with the dislocation mean free path (MFP) approach [29,54]: MbGb ð7Þ L where b is a constant with a value of 0.24, which is indistinguishable between the primary and secondary twins [29,54]. The grain and twin boundaries were regarded as the main microstructural obstacles to dislocation gliding, and the dislocation MFP (L) was written as follows [3,28,29,54]:
Drt ¼
1 1 1 ¼ þ L d t
ð8Þ
where d is the effective grain size of the annealed specimen, and measured 10.0, 11.7 and 8.2 lm for the T618, T618–Al and T618–Si TWIP steels, respectively (Fig. 1). According to the Fullman’s stereological analysis [30], the mean twin spacing (t) has the following relationship with both the volume fraction (F) and the width (e) of the mechanical twins: 1 1 F ¼ t 2e ð1 F Þ
ð9Þ
Fig. 10. Contributions of the dislocation multiplication (Drd), primary (Drpt ) and secondary (Drst ) twins, and DSA (DrD) to the strain hardening of the T618, T618–Al and T618–Si TWIP steels deformed at a true strain of 0.1.
K. Jeong et al. / Acta Materialia 61 (2013) 3399–3410
for which the e values of the primary and secondary mechanical twins were obtained from TEM images and measured 30 nm, regardless of the TWIP steels’ chemical compositions. The F values were obtained separately for the primary and secondary mechanical twins (Fig. 8). The Drt values of the primary (Drpt ) and secondary (Drst ) mechanical twins were calculated using the following equation, which combines Eqs. (8) and (9) with Eq. (7): 1 1 F Drt ¼ MbGb þ ð10Þ d 2e ð1 F Þ The contributions of the primary and secondary twins to the strain hardening in the three TWIP steels at a strain of 0.1 are plotted in Fig. 10. While the Drt value of the T618–Al TWIP steel with only primary mechanical twins was 48 MPa, the Drt values of the T618 TWIP steel were 103 MPa for the primary twins (Drpt ) and 25 MPa for the secondary twins (Drst ). The Drt values of the T618–Si TWIP steel with well-developed primary and secondary twins (Fig. 7c) were calculated to be 120 MPa for the primary twins (Drpt ) and 65 MPa for the secondary twins (Drst ). The contribution of Drt to the overall strain hardening in the T618, T618–Al and T618–Si TWIP steels at a strain of 0.1 was 18%, 8% and 23%, respectively. The strain hardening (DrD) of the T618 TWIP steel caused by the DSA was calculated to be 40 MPa by subtracting the r0, Drd and Drt values from the total flow stress of 720 MPa (Fig. 10). However, the DrD values of the T618–Al and T618–Si TWIP steels were negligible, at 4 and 3 MPa, respectively. The above results demonstrated that the reason why the addition of Si in the Fe–18Mn–0.6C (T618) TWIP steel increased the strain hardening, while greatly reducing the DrD value, was attributed to the increases in Drd (445 MPa), Drt (185 MPa) and especially Drst (65 MPa), as a result of the secondary twins. In a similar fashion, the reason for the decreased strain hardening with the addition of Al to the Fe–18Mn–0.6C (T618–Al) TWIP steel could be attributed to reductions in Drd (395 MPa), Drt (48 MPa) and DrD (4 MPa), with the reduction in Drt being the greatest due to the increased SFE value caused by the addition of Al [12,17,40]. 4. Conclusions
(1) The SFE of a Fe–18Mn–0.6C TWIP steel measured by XRD was shown to decrease by 4 mJ m2 per 1 wt.% Si and up to 1.5 wt.% Si, resulting in active primary and secondary twinning. (2) The volume fractions of the primary and secondary mechanical twins were quantitatively evaluated by combining the advantages of EBSD and TEM. The total twin volume fraction increased linearly with decreasing SFE. However, when the SFE was less
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than 20 mJ m2, the volume fraction of the primary twins increased slowly, while that of the secondary twins increased rapidly. (3) The addition of Si to the Fe–18Mn–0.6C TWIP steel increased both the yield strength due to solid solution hardening and the ultimate tensile strength due to significant strain hardening, with a large elongation of over 60%. (4) The contributions of dislocation storage, mechanical twinning and DSA to the strain hardening behavior were quantitatively evaluated in Fe–18Mn–0.6C, Fe–18Mn–0.6C–1.5Al and Fe–18Mn–0.6C–1.5Si TWIP steels deformed by a true strain of 0.1. The addition of Si to the Fe–18Mn–0.6C TWIP steel raised the strain hardening, due primarily to the primary and secondary twins, although the DSA was greatly weakened by the addition of Si. Conversely, the addition of Al to the Fe–18Mn–0.6C TWIP steel resulted in a decrease in strain hardening due to a reduction in both the mechanical twinning and DSA.
Acknowledgements The authors are grateful for a grant from the Fundamental R&D Program for Core Technology of Materials funded by the Ministry of Commerce, Industry and Energy of the Republic of Korea. References [1] Gra¨ssel O, Kru¨ger L, Frommeyer G, Meyer LW. Int J Plast 2000;16:1391. [2] Idrissi H, Renard K, Ryelandt L, Schryvers D, Jacques PJ. Acta Mater 2010;58:2464. [3] Shiekhelsouk MN, Favier V, Inal K, Cherkaoui M. Int J Plast 2009;25:105. [4] Lee YK, Choi CS. Metall Mater Trans A 2000;31:355. [5] Saeed-Akbari A, Imlau J, Prahl U, Bleck W. Metall Mater Trans A 2009;40:3076. [6] Gil Sevillano J. Scripta Mater 2009;60:336. [7] Allain S, Chateau JP, Bouaziz O. Mater Sci Eng A 2004;387–389:143. [8] Zuidema BK, Subramanyam DK, Leslie WC. Metall Mater Trans A 1987;18:1629. [9] Koyama M, Akiyama E, Tsuzaki K. Corros Sci 2012;54:1. [10] Chin KG, Kang CY, Shin SY, Hong S, Lee S, Kim HS, et al. Mater Sci Eng A 2011;528:2922. [11] Kim Y, Kang N, Park Y, Choi I, Kim G, Kim S, et al. J Kor Inst Met Mater 2008;46:780. [12] Jin JE, Lee YK. Acta Mater 2012;60:1680. [13] Kang S, Jung YS, Jun JH, Lee YK. Mater Sci Eng A 2010;527:745. [14] So KH, Kim JS, Chun YS, Park KT, Lee YK, Lee CS. ISIJ Int 2009;49:1952. [15] Park IJ, Jeong KH, Jung JG, Lee CS, Lee YK. Int J Hydrogen Energy 2012;37:9925. [16] Jeong JS, Woo W, Oh KH, Kwon SK, Koo YM. Acta Mater 2012;60:2290. [17] Park KT, Jin KG, Han SH, Hwang SW, Choi K, Lee CS. Mater Sci Eng A 2010;527:3651. [18] Dyson DJ, Holmes B. J Iron Steel Res Int 1970;208:469. [19] Ohkubo N, Miyakusu K, Uematsu Y, Kimura H. ISIJ Int 1994;34:764.
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[41] Tian X, Zhang Y. Mater Sci Eng A 2009;516:78. [42] Tsuzaki K, Natsume Y, Tomota Y, Maki T. Scripta Mater 1995;33:1087. [43] Renard K, Ryelandt S, Jacques PJ. Mater Sci Eng A 2010;527:2969. [44] Dastur YN, Leslie WC. Metall Mater Trans A 1981;12:749. [45] Darken LS. Trans AIME 1948;180:430. [46] Jin JE, Lee YK. Mater Sci Eng A 2009;527:157. [47] Swift HW. J Mech Phys Solids 1952;1:1. [48] Colla V, De Sanctis M, Dimatteo A, Lovicu G, Solina A, Valentini R. Metall Mater Trans A 2009;40:2557. [49] Umemoto M, Liu ZG, Sugimoto S, Tsuchiya K. Metall Mater Trans A 2000;31:1785. [50] Barbier D, Gey N, Allain S, Bozzolo N, Humbert M. Mater Sci Eng A 2009;500:196. [51] Dini G, Najafizadeh A, Ueji R, Monir-Vaghefi SM. Mater Des 2010;31:3395. [52] Yoo JD, Park KT. Mater Sci Eng A 2008;496:417. [53] Bracke L, Verbeken K, Kestens L, Penning J. Acta Mater 2009;57:1512. [54] Hutchinson B, Ridley N. Scripta Mater 2006;55:299. [55] Kim J, Lee SJ, De Cooman BC. Scripta Mater 2011;65:363. [56] Ortiz AL, Shaw L. Acta Mater 2004;52:2185. [57] Jeong JS, Koo YM, Jeong IK, Kim SK, Kwon SK. Mater Sci Eng A 2011;530:128.
Acta Materialia 61 (2013) 3399–3410 www.elsevier.com/locate/actamat
The effects of Si on the mechanical twinning and strain hardening of Fe–18Mn–0.6C twinning-induced plasticity steel Kookhyun Jeong, Jae-Eun Jin, Yeon-Seung Jung, Singon Kang, Young-Kook Lee ⇑ Department of Materials Science and Engineering, Yonsei University, Seoul 120-749, Republic of Korea Received 28 January 2013; accepted 14 February 2013 Available online 16 March 2013
Abstract The stacking-fault energy (SFE), dislocation slip, mechanical twinning, strain hardening, and yield and tensile strengths were systemically investigated in Fe–18Mn–0.6C–1.5Si twinning-induced plasticity (TWIP) steel. The results were also compared with those for Fe– 18Mn–0.6C and Fe–18Mn–0.6C–1.5Al TWIP steels. The SFE decreased by 4 mJ m2 per 1 wt.% Si. The addition of Si increased both the yield strength, due mainly to solid solution hardening, and the tensile strength, owing to the high strain hardening that occurred while maintaining a large elongation of over 60%. To examine this high strain hardening, especially at low strains, the volume fractions of the primary and secondary mechanical twins were quantitatively evaluated by combining the merits of electron backscattered diffractometry and transmission electron microscopy. The volume fractions of both the primary and secondary twins were the highest in the Fe–18Mn– 0.6C–1.5Si TWIP steel, which had the lowest SFE of the three TWIP steels. In particular, the volume fraction of the secondary mechanical twins increased rapidly with the addition of Si. The contributions of dislocation storage, mechanical twinning and dynamic strain aging (DSA) to the strain hardening were also quantitatively evaluated in the three TWIP steels. The Si-added TWIP steel had the highest strain hardening, due mainly to the active primary and secondary twinning, and experienced negligible DSA. In contrast, the Al-added TWIP steel exhibited the lowest strain hardening due to the reductions in both the mechanical twinning and DSA. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Twinning-induced plasticity (TWIP) steel; Stacking-fault energy; Mechanical twin; Strain hardening; Dynamic strain aging
1. Introduction High-Mn austenitic steels have recently attracted a great deal of attention because of their high tensile strength and extraordinary ductility arising from the many mechanical twins generated during plastic deformation, which is termed twinning-induced plasticity (TWIP) [1–3]. Of the TWIP steels, the Fe–Mn–C ternary system has frequently been studied due to the easy control of both the stackingfault energy (SFE) and austenite stability by regulating the Mn and C concentrations [4,5]. Idrissi et al. [2] investigated the relationship between high strain hardening and mechanical twinning in Fe–22Mn–1.2C TWIP steel and found that mechanical twins contain a high level of sessile ⇑ Corresponding author. Tel.: +82 2 2123 2831; fax: +82 2 312 5375.
E-mail address: [email protected] (Y.-K. Lee).
dislocations and act as strong barriers to dislocation gliding, resulting in high strain hardening. Gil Sevillano [6] reported that mechanical twins contribute to the reduction of the effective grain size in Fe–22Mn–0.6C TWIP steel, which is referred to as the dynamic Hall–Petch effect. Despite its outstanding tensile properties, Fe–Mn–C TWIP steel has some shortcomings, such as low yield strength (YS) [2,7], carbide precipitation [8] and hydrogen delayed fracture [9–11]. To solve these problems, the addition of an alloying element such as Al has been considered by different researchers [5,8,10–15]. The Al effectively suppresses the hydrogen delayed fracture [10,11,14,15] and cementite precipitation [8,12,13], and stabilizes the austenite phase against the strain-induced martensitic transformation in Fe–Mn–C TWIP steel [5]. However, the addition of Al is not effective at improving the YS in TWIP steel [15–17].
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.02.031
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Dyson and Holmes [18] quantitatively investigated the solid solution hardening effects of various alloying elements on the YS of Fe–16Cr–25Ni stainless steel. They found that Si causes greater improvement of the YS than Al. Ohkubo et al. [19] reported that the YS increases from 161 to 213 MPa with the addition of 1 wt.% Si to Fe–17Cr–12Ni austenitic stainless steel and found that the Si causes high dislocation densities at low strains. Furthermore, it is known that Si decreases the SFE in Fe–17Cr–14Ni austenitic stainless steel [20] and Fe–31 Mn–0.8 C shape-memory alloys [21]. The decreased SFE restrains the cross-slip of dislocations [22,23], promotes planar slip [24,25] and enhances mechanical twinning [26,27]. Therefore, Si is expected to improve both the yield and tensile strengths through solid solution hardening, dislocation hardening and mechanical twinning in high Mn TWIP steels. Nevertheless, the effects of Si on the SFE, dislocation slip, mechanical twinning, strain hardening, and yield and tensile strengths of C-bearing high-Mn TWIP steels are yet to be reported. Meanwhile, both the dislocation storage and mechanical twinning contribute to strain hardening in TWIP steels with low SFE [3,7,28–30]. Dini et al. [29] investigated the change in dislocation density with strain in Fe–31Mn– 3Si–3Al TWIP steel using an X-ray diffractometer (XRD) and evaluated the contribution of dislocation storage to strain hardening. Allain et al. [7] analyzed the contribution of mechanical twinning to the strain hardening in terms of a dislocation mean free path (MFP) in Fe–22Mn–0.6C TWIP steel. However, the detailed experimental method for measuring the twin fractions, which are an essential parameter for determining the MFP, has not been introduced in the literature. Therefore, the quantitative analysis of mechanical twins, such as the area fraction of twinned grains, twin density and twin volume fraction, must still be performed to examine the relationship between strain hardening and mechanical twinning. Shun et al. [31] attempted to measure the area fraction of twinned grains, defined as the ratio of the number of grains containing mechanical twins to the total observed grains in Fe–30Mn–1.0C–(0 and 3)Al austenitic steels using an optical microscope (OM). However, the measured area fraction of the twinned grains seems to be inaccurate because there has been no evidence that all of the etched regions are twins and that all twins are etched. Li et al. [32] investigated the twin density, defined as the total length of the twin boundaries in the area observed in a nanostructured Cu–Zn alloy using a transmission electron microscope (TEM). Mechanical twins have been confirmed by means of selected area electron diffraction (SAED), and fine twins have also been observed. However, due to the limitations of the observed area, TEM observation is not suitable for the quantitative analysis of mechanical twins in high-Mn TWIP steel. McCabe et al. [33] measured the twin volume fraction in highly purified Zr from electron backscattered diffractometer (EBSD) images, defined as the ratio between the total
area of mechanical twins and the observed area. Although EBSD provides a larger observable area than TEM, the spatial resolution is not high enough to observe extremely thin mechanical twins [34,35]. Recently, Gutierrez-Urrutia and Raabe [36] succeeded in more clearly observing mechanical twins in Fe–22Mn–0.6C TWIP steels using an electron channeling contrast imaging (ECCI) method, compared with the EBSD method, and quantitatively evaluated the area fraction of the twinned grains. However, the ECCI still has a lower spatial resolution than that of TEM [34,35] and has yet to become a conventional electron microscopic technique like TEM and EBSD. Therefore, no qualified experimental methods have been performed to measure the twin fraction. As a result, the following three subjects were investigated in the present study. First, the effects of Si on the SFE, dislocation slip, mechanical twinning, strain hardening and yield and tensile strengths in Fe–18Mn–0.6C– 1.5Si TWIP steel were examined and compared with those in Fe–18 Mn–0.6C and Fe–18Mn–0.6C–1.5Al TWIP steels. Second, the twin volume fractions of the three TWIP steels were quantitatively measured using both EBSD and TEM to compensate for the shortcomings of each method and obtain more accurate analysis of the mechanical twinning. Finally, using the measurements of the dislocation density and twin volume fraction, the contributions of dislocation storage, mechanical twinning and dynamic strain aging (DSA) to the strain hardening of each TWIP steel were quantitatively evaluated to identify a predominant hardening mechanism. 2. Experimental procedure Three ingots, weighing 30 kgf each, with the chemical compositions listed in Table 1, were prepared by vacuum induction melting. The ingots were homogenized at 1200 °C for 12 h in a protective nitrogen gas atmosphere and hot-rolled at temperatures between 1000 and 1100 °C into a plate 5 mm thick. To eliminate the decarburized layers of the plate, surface grinding was performed that removed 1 mm from each side of the plate. The surfaceground plate was cold-rolled at room temperature to make sheets 1.4 mm thick, corresponding to a thickness reduction of 55%. The cold-rolled sheets were annealed at 900 °C for 5 min using a vacuum tube furnace, followed by oil quenching to prevent carbide precipitation. The microstructures of the annealed specimens were observed using an electron backscattered diffractometer
Table 1 Chemical compositions (wt.%) of the TWIP steels used in the present study. TWIP steel
Mn
C
Si
Al
Fe
T618 T618–Al T618–Si
17.65 17.51 17.70
0.62 0.58 0.59
0.01 0.05 1.59
0.01 1.54 0.03
Bal. Bal. Bal.
K. Jeong et al. / Acta Materialia 61 (2013) 3399–3410
(EBSD, EDAX, Hikari) attached to a field-emission scanning electron microscope (FE-SEM, TESCAN, Mira-3). The EBSD specimens were prepared by mechanical polishing with an aqueous solution containing colloidal silica particles. The mean grain size of the annealed specimens was determined using a mean equivalent circle diameter on EBSD boundary maps with and without annealing twin boundaries. Uniaxial tensile tests were conducted at a constant strain rate of 1 104 s1 using an Instron machine (Instron, 3382) at room temperature. The gauge portion of the tensile specimens was 6 mm wide, 25 mm long and 1.3 mm thick. Mechanical twins were observed using both EBSD and a field-emission TEM (FE-TEM, JEOL, JEM2000EX) operated at 200 kV. Thin foils for TEM observations were prepared by twin-jet polishing in a mixed solution of 90% acetic acid and 10% perchloric acid at 15 °C and an applied potential of 20 V. The foils were additionally thinned by an ion beam with an incidence angle of 4° using a precision ion polishing system (Gatan, 691). To investigate the specimens’ phase constituents, stacking-fault energies (SFEs) and dislocation densities, an X-ray diffractometer (XRD, RIGAKU, D/MAX-2500) ˚ operated was used with Cu Ka radiation (k ¼ 1:54056A), at 30 kV at room temperature. The scanning range and speed were 40–100° and 1° min1, respectively. The SFE was determined using the following equation proposed by Schramm and Reed [37]: c¼
K 1 1 1 x0 Gð1 1 1Þ a0 A0:37 he250 i1 1 1 pffiffiffi a p 3
ð1Þ
where K 1 1 1 x0 is a proportionality constant with a value of 6.6 [21,37], Gð1 1 1Þ is the shear modulus of 65 GPa in the (1 1 1) fault plane, a0 is the lattice parameter and A is the Zener anisotropy of 3.43. The mean square microstrain (he250 i1 1 1 ) was determined using a Willamson–Hall plot [38] obtained from the XRD profiles. The stacking-fault probability (a) was obtained using the following equation for both annealed (ANN) and cold-worked (CW) specimens [37]: D2h ¼ ð2h2 0 0 2h1 1 1 ÞCW ð2h2 0 0 2h1 1 1 ÞANN pffiffiffi 45 3 1 ¼ 2 tan h2 0 0 þ tan h1 1 1 a p 2
ð2Þ
where 2h is the XRD peak position. The shear modulus (G) was measured using a resonant frequency and damping analyzer (RFDA, IMCE, HTVP1600) at room temperature. The specimen used to measure the shear modulus was 15 mm wide, 50 mm long and 3.5 mm thick. 3. Results and discussion 3.1. Microstructure Fig. 1a–c shows the EBSD boundary maps of the T618, T618–Al and T618–Si TWIP steels, respectively, which were taken from the normal planes of the annealed speci-
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mens. The blue and black lines correspond to low- and high-angle boundaries whose misorientation angles are 3–15° and 15–180°, respectively. The red lines denote annealing twin boundaries determined by the coincidence site lattice (CSL) boundaries of R3. The austenite grain sizes (AGSs) of the T618, T618–Al and T618–Si TWIP steels with annealing twin boundaries were 10.0, 11.7 and 8.5 lm, respectively, which indicated a slight decrease in AGS with the addition of Si. In addition, the three TWIP steels possessed no deformed grains and were fully recrystallized into an austenite single phase with equiaxed grains (Fig. 1d). The austenite single phase remained devoid of emartensite formation, even after tensile tests were performed to fracture (Fig. 1e). 3.2. Stacking-fault energy The SFE and AGS are important factors contributing to the tensile properties of high-Mn austenitic steels because these steels’ deformation mechanisms are greatly influenced by the SFE [7,17,22]. The SFE is usually either calculated using thermodynamic models [39–41] or measured experimentally with TEM [12,20], XRD [12,21] or neutron diffraction [16]. Fig. 2 shows the changes in the measured (closed marks) and calculated (open marks) SFE values with Si content for several austenitic steels. The measured SFE values decreased with Si content in the Fe–17Cr–14Ni [20] and Fe–31Mn–0.8C [21] steels, regardless of the experimental method or alloy composition used. However, the calculated SFE values increased with Si content in the Fe–28Mn–2Al [39] and Fe–22 Mn–0.6C [40] TWIP steels and the Fe– 31Mn–0.8C shape-memory alloy [41]. This result was most likely due to a lack of accurate interaction parameters in the Mn–Si and Si–C. Therefore, the SFE values of the three TWIP steels in the present study were measured using XRD, according to Schramm and Reed’s method [37]. The measured SFE values of the T618 and T618–Si TWIP steels were 19.3 and 13.8 mJ m2, respectively, implying a reduction from the 4 mJ m2 per 1 wt.% Si, which were similar to those of other austenitic steels, as shown in Fig. 2. Meanwhile, the measured SFE value of the T618–Al TWIP steel was 29.1 mJ m2, which was even higher than that of the T618 TWIP steel. This result shows good agreement with previous reports stating that Al increases the SFE of austenite in high-Mn TWIP steels [12,17,40]. 3.3. Tensile properties Fig. 3 shows the engineering stress–strain (s–e) curves for the T618, T618–Al and T618–Si TWIP steels. The T618–Si TWIP steel exhibited the highest yield strength (YS) and ultimate tensile strength (UTS), while the T618–Al TWIP steel had an unimproved YS and a lower UTS, as was expected based on the results of previous reports [16,17]. It is worth noting that the total elongation
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Fig. 1. EBSD boundary maps of (a) T618, (b) T618–Al and (c) T618–Si TWIP steels. The blue and black lines indicate the low-angle (3° < h < 15°) and high-angle (h > 15°) boundaries, respectively. The red lines indicate the annealing twin boundaries of the R3 CSL. The figure also shows the XRD patterns of (d) annealed and (f) fractured specimens. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Variations in the calculated and measured SFE values with Si content in various austenitic steels.
of the T618–Si TWIP steel did not decrease significantly and was still over 60%, in spite of the increased strengths. The increased YS of the T618–Si TWIP steel was thought to be associated with several factors, including a reduction in the effective grain size, as shown in Fig. 1a–c, the solid solution hardening of Si [18,42] and the restraint of cross-slip due to its decreased SFE [22,27], considering no precipitation hardening. Meanwhile, the T618– Si TWIP steel exhibited continuous yielding similar to that of the T618 TWIP steel, whereas the T618–Al TWIP steel showed a yield point elongation (YPE) [13]. The appearance of a YPE was probably attributed to a lack of strain hardening, which stemmed from the low dislocation density and delayed mechanical twinning at low strain due to the increased SFE caused by the addition of Al [12,40]. The UTS values of the T618, T618–Al and T618–Si TWIP steels were 1104, 925 and 1187 MPa, respectively. The Al lowers the UTS of these C-bearing high-Mn TWIP
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Fig. 3. Engineering stress–strain (s–e) curves for the T618, T618–Al and T618–Si TWIP steels measured at room temperature and a constant strain rate of 104 s1. The inset shows an enlarged graph of the yielding part of the curve, where YPE is the yield point elongation.
steels because of reductions in both the DSA, due to the decrease in C diffusivity [8,31], and the mechanical twinning, owing to the increased SFE [12,40]. The T618–Si TWIP steel’s stress–strain curve had fewer serrations than those of the T618 and T618–Al TWIP steels, and these serrations are known to be formed by the DSA in C-containing high-Mn TWIP steels [43,44]. The diminished serrations implied a weakened DSA, probably due to the reduced C diffusivity caused by the addition of Si. Actually, Darken [45] has reported that the C diffusivity decreases with the addition of Si in Fe–0.6C weld steel when its temperature has been elevated to the austenitic region. Although the DSA was greatly weakened by the addition of Si, the strain hardening of the T618–Si TWIP steel (742 MPa) was comparable to that of the T618 TWIP steel (738 MPa) with strong DSA effects, probably due to a more active mechanical twinning based on the reduction in SFE caused by the addition of Si. The reason why the T618–Si TWIP steel exhibited the highest UTS among the three TWIP steels was thought to be attributed mainly to its vigorous mechanical twinning. 3.4. Strain hardening behavior Fig. 4a shows the true stress–strain (r–e) and strain hardening rate (SHR, dr/de) curves of the three TWIP steels. The T618–Si TWIP steel exhibited the highest SHR among the three TWIP steels up to a true strain of 0.37. At the onset of plastic deformation in particular, the T618–Si TWIP steel exhibited a very high SHR of 4735 MPa, probably due to the high density of partial dislocations and active mechanical twinning, even at such a low strain. To investigate the strain hardening behavior of the three TWIP steels in more detail, a modified Crussard–Jaoul (C– J) analysis [12,46–49] was performed based on the Swift equation [47] (Fig. 4b–d). As expected based on the results
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of a previous report [50], the plastic deformation region of the T618 TWIP steel (Fig. 4b) could be divided into five stages: the dynamic recovery of dislocations and no twinning (stage A), active primary mechanical twinning (stage B), less active primary mechanical twinning (stage C), active secondary mechanical twinning (stage D) and thicker twin bundle formation (stage E). The T618–Al TWIP steel exhibited three stages (stages A, C and E) on the SHR curve, as shown in Fig. 4c. The disappearance of stages B and D resulted from less active primary and secondary mechanical twinning due to the increased SFE caused by the addition of Al [12]. The T618–Si TWIP steel also exhibited three stages on the SHR curve similar to those of the T618–Al TWIP steel, but it had a different slope at the intermediate stage (stage II, as shown in Fig. 4d). After the SHR decreased up to a true strain of 0.04, it increased linearly with a positive slope to a true strain of 0.27, unlike the T618 and T618–Al TWIP steels, which had almost constant and negative slopes, respectively. The positive slope of the SHR in the T618– Si TWIP steel was thought to be due to the active mechanical twinning caused by the decreased SFE. The positive slope of the SHR occurred over a wide strain range of 0.04–0.27, which has yet to be reported for other TWIP steels [12,46,50,51]. To confirm the active mechanical twinning in the T618– Si TWIP steel, the microstructural evolution of the T618–Si TWIP steel was observed at true strains of 0.02, 0.05, 0.1 and 0.25. Planar dislocation (PD) arrangements and stacking faults (SFs) were clearly observed in a TEM bright field image of the specimen strained by 0.02, taken in a reflecting plane of g = 002 (Fig. 5). It is known that SFs are readily formed in face centered cubic (fcc) materials with low SFE values and that PD arrangements are mainly favored by low SFE, high friction stress and short-range ordering (SRO) [24–26]. Because the T618–Si TWIP steel did not exhibit the SRO, but rather SFs like the Fe–22 Mn–0.6C TWIP steel [36], it was thought that PD arrangements were probably promoted by the low SFE and increased friction stress caused by the addition of Si [18,20,21]. Some primary mechanical twins (TW1) 30 nm thick, along with PDs and SFs, were also observed near the austenite grain boundaries at the same strain of 0.02 (Fig. 6a). As a result, the microstructure of the T618–Si TWIP steel exhibiting SFs, PDs and mechanical twins apparently shows good agreement with previous reports stating that mechanical twinning is favored in fcc materials with PD arrangements [24–26]. However, microbands formed instead of mechanical twins in a recent study on Fe–28Mn–0.8C–9Al steel, although PD arrangements have been clearly observed at low strains [52]. The PD arrangements in the Fe–28Mn–0.8C–9Al steel with a high SFE value of 85 mJ m2 has been attributed mainly to the SRO [52]. Accordingly, not all materials with PD arrangements exhibit mechanical twinning, and it was thought that the crystal defectsobserved in the T618–SiTWIP steel, such as SFs, partial dislocations, PD arrangements and mechanical twins, stemmed from the low SFE of the steel.
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Fig. 4. (a) True stress–strain (r–e) curves and strain hardening rate (dr/de) curves for the T618, T618–Al and T618–Si TWIP steels; ln(dr/de)–ln r plots for the modified Crussard–Jaoul (C–J) analysis [12,46–49] of the (b) T618, (c) T618–Al and (d) T618–Si TWIP steels.
Fig. 5. Bright-field TEM images of the T618–Si TWIP steel deformed at a true strain of 0.02 and taken with a two-beam diffraction condition. PD and SFs are planar dislocation and stacking faults, respectively.
Meanwhile, a true strain of 0.02 corresponded to stage A without mechanical twinning in the T618 and T618–Al TWIP steels. Accordingly, the first stage in Fig. 4d of the
T618–Si TWIP steel was considered a mixture of stages A and B in the T618 TWIP steel. Therefore, a new nomenclature of stages was employed, dividing the curve into stages I, II and III, for the T618–Si TWIP steel. Both primary mechanical twins (TW1) (Fig. 6b) and secondary mechanical twins (TW2), which exhibited a different variant from that of the TW1, were observed at a true strain of 0.05 (Fig. 6c). The SAED pattern illustrated in Fig. 6f shows that primary and secondary mechanical twinning occurred on the ð1 1 1Þ plane in the ½1 1 1 direction and the ð1 1 1Þ plane in the ½1 1 1 direction, respectively, as has been previously reported in the literature [50]. The interior angle between the primary and secondary mechanical twin directions was measured by TEM to be 69°, which was in good agreement with the calculated angle of 70° between the ½1 1 1 and ½1 1 1 directions. This result agrees with those of previous reports giving the measured angle between the directions of the primary and secondary mechanical twins as 71° in Fe–22Mn–0.6C TWIP steel [50]. Therefore, this result confirmed that both secondary and primary mechanical twinning occurred at a low strain of 0.05, corresponding to the transition strain between stages I and II. Accordingly, stage II in Fig. 4d of the T618–Si TWIP steel was considered to be a combination
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Fig. 6. Bright-field TEM images of the T618–Si TWIP steel at various true strains of (a) 0.02, (b and c) 0.05, (d) 0.1 and (e) 0.25. TW1, TW2 and G.B. are the primary and secondary mechanical twins and grain boundaries, respectively. The insets of each image show the SAED patterns of the mechanical twins. (f) Index of the SAED patterns of the mechanical twins at a true strain of 0.05.
of stages B and D in the T618 TWIP steel, skipping stage C. At a true strain of 0.25, which almost corresponded to the end of stage II, both the primary and secondary mechanical twins grew in number, becoming denser and indicating a continuous generation of mechanical twins during stage II (Fig. 6e). 3.5. Quantitative analysis of the twin volume fraction To examine the cause of the high SHR in the T618–Si TWIP steel, especially at low strains, the twin volume fraction, which is defined as the total area of the mechanical
twins per observed area, was quantitatively measured by the steel deformation at a true strain of 0.1 and compared to that of the T618 and T618–Al TWIP steels. For a more accurate and reliable measurement of the twin volume fraction, both EBSD with a large observable area and high resolution TEM were utilized to compensate for each method’s respective shortcomings. Fig. 7a shows the EBSD Kikuchi pattern quality (KPQ) map of the T618–Si TWIP steel deformed at a true strain of 0.1. The EBSD KPQ map shows some annealing twins (ATs) and many mechanical twins (MTs). The apparent widths of the mechanical twins were between 190 and
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230 nm from a misorientation angle map (Fig. 7b), as drawn by scanning perpendicular the mechanical twins along a black line in Fig. 7a. The average apparent width of the mechanical twins was 210 nm, which is similar to those observed from the EBSD KPQ maps in previous reports [50,53]. A TEM image (Fig. 7c) taken from the same strained T618–Si TWIP steel sample shows a bundle of several parallel mechanical twins. The width of the bundle was 190 nm, which was similar to the apparent twin width measured by EBSD (Fig. 7b). Each mechanical twin inside the bundle had an average width of 30 nm, which is similar to TEM results in the literature [28,46]. Therefore, we found that a single mechanical twin on the EBSD KPQ map was actually a bundle of several thin mechanical twins, and that the twin volume fraction measured from the EBSD KPQ map was an overestimation. To measure the average number of mechanical twins in each twin bundle observed on the EBSD KPQ map, the number of twin bundles per unit area was measured using these maps and compared to the number of mechanical twins per unit area measured using the TEM images. 15 TEM images covering an area of 1400 lm2 were obtained from each 0.1-strained TWIP steel specimen. All of the TEM images were taken along the [0 1 1] zone axis, which is typically adopted for mechanical twin observation [46,50]. Four EBSD KPQ maps were obtained from each
deformed TWIP steel specimen, covering an area of 12,500 lm2. Of the total area observed by EBSD, the number of twin bundles per unit area of the {0 1 1} grains (3900 lm2) was compared with the number of mechanical twins per unit area measured by TEM, and is presented in Table 2. As expected, the number of twin bundles per unit area of the {0 1 1} grains determined from the EBSD KPQ maps was less than that of the mechanical twins observed per unit area by TEM, regardless of the TWIP steels’ chemical compositions. This result was probably due to the limited resolution of the EBSD for the observation of thin mechanical twins. Therefore, a compensating factor was determined by dividing the number of mechanical twins per unit area obtained from the TEM images by the number of twin bundles measured from the EBSD KPQ maps. The compensating factors were 2.56, 2.53 and 2.64 for the T618, T618–Al and T618–Si TWIP steels, respectively. Therefore, an average compensating factor (k) of 2.58 was used for the calculation of the volume fraction of mechanical twins (F) in the three TWIP steels as follows: F¼
RlEBSD wEBSD AEBSD k
ð3Þ
where RlEBSD and wEBSD are the total length and apparent average width (210 nm) of the twin bundles measured by
Fig. 7. (a) Electron backscattered diffraction (EBSD) Kikuchi pattern quality map of the T618–Si TWIP steel deformed at a true strain of 0.1. AT and MT are the annealing and mechanical twins, respectively. (b) Misorientation angle map scanned along the thick black line in (a). (c) TEM image taken from the same strained T618–Si TWIP steel.
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Table 2 Measured values used for the calculation of the compensating factor (k) using both EBSD and TEM. A{0 1 1} and n are the total observed area of the {0 1 1} grains and the number of mechanical twins, respectively. Measured value 2
A{0 1 1} (lm ) n n/A{0 1 1} (102 lm2) k (n/A{0 1 1})TEM/(n/A{0 1 1})EBSD
T618 steel
T618–Al steel
T618–Si steel
EBSD
TEM
EBSD
TEM
EBSD
TEM
3692 107 2.90 2.56
1319 98 7.43
4286 54 1.26 2.53
1475 47 3.19
3813 194 5.09 2.64
1431 192 13.42
Fig. 8. EBSD Kikuchi pattern quality maps of the (a) T618, (b) T618–Al and (c) T618–Si TWIP steels at a true strain of 0.1. The solid line indicates the intersections of the primary and secondary mechanical twins.
EBSD KPQ maps, respectively, and AEBSD is the total observed area of the {0 1 1} grains on the EBSD KPQ maps. Representative EBSD KPQ maps of the three TWIP steels used to measure the twin volume fraction are presented in Fig. 8. While even primary mechanical twins were barely observed in the T618–Al TWIP steel (Fig. 8b), the T618–Si TWIP steel exhibited well-developed secondary mechanical twins along with primary mechanical twins (solid lines in Fig. 8c). Accordingly, not only the total twin volume fraction but also the volume fractions of primary and secondary mechanical twins were separately evaluated from the EBSD KPQ maps. Fig. 9 shows the change in twin volume fraction with the change in SFE in the three TWIP steels deformed by a true strain of 0.1. The total twin volume fraction (open marks) linearly decreased with a slope of 0.13% per SFE of 1 mJ m2. The total twin volume fraction was only a few percentage points due to both the small strain of 0.1 used and the nanometer-sized twin width [28,46]. Meanwhile, the changes in volume fraction of the primary and secondary mechanical twins (closed marks) with the change in SFE did not exhibit similar behavior. The volume fraction
Fig. 9. Change in the twin volume fraction with SFE in the T618, T618– Al and T618–Si TWIP steels deformed at a true strain of 0.1.
of the primary mechanical twins increased almost linearly with decreasing SFE, from 30 to 20 mJ m2, and then increased slightly below 20 mJ m2 in the low SFE range. This result was contrary to the behavior of the volume fraction of the secondary mechanical twins, which rapidly
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increased when the SFE was less than 20 mJ m2, resulting in additional strain hardening in the T618–Si TWIP steel. 3.6. Quantitative analysis of the strain hardening Both dislocation storage and mechanical twinning can contribute to strain hardening in TWIP steels with low SFE values [3,28,29,36,54]. The DSA also increases the strain hardening of C-bearing TWIP steels [12,44]. Therefore, the total flow stress of the three C-bearing TWIP steels deformed by a true stress of 0.1 (r0.1) can be expressed as follows: r0:1 ¼ r0 þ Drd þ Drt þ DrD
ð4Þ
where r0 is the lattice friction stress, the values of which were taken from the y-intercepts of the Hall–Petch plots of the Fe–22Mn–0.6C [28], Fe–18Mn–0.6C–1.5Al [13] and T618–Si TWIP steels. The r0 values were 132 MPa for the T618, 155 MPa for the T618–Al and 190 MPa for the T618–Si TWIP steels. The T618–Si TWIP steel possessed the highest r0 value, indicating the significant solid solution hardening induced by Si. Drd, Drt and DrD are the increments in flow stress caused by dislocation storage, mechanical twinning and DSA, respectively. The r0.1 values of the three TWIP steels were 720, 602 and 823 MPa for the T618, T618–Al and T618–Si TWIP steels, respectively. The Drd value was calculated by the following equation [29,54]: pffiffiffi Drd ¼ MaGb q ð5Þ where M is an average Taylor factor of 3.06 for fcc crystals [3,28,29], a is a constant value of 0.26 [3,28,29] and b is the Burgers vector. The shear modulus (G) of the T618–Si TWIP steel was measured with a resonant frequency and damping analyzer (RFDA) to be 72.5 GPa at room temperature. This value was slightly higher than those of Fe– 18Mn–0.6C (71.0 GPa) [55] and Fe–18Mn–0.6C–1.5Al TWIP steels (70.4 GPa) [55]. The dislocation density (q) was calculated using the following equation [29,54]: pffiffiffiffiffiffi 3 2phe250 i1 1 1 q¼ ð6Þ Db where D is the average crystallite size determined using the Sherrer formula [56], as obtained from the XRD profiles. The dislocation densities (q) of the T618, T618–Al and T618–Si TWIP steels at a strain of 0.1 were determined using XRD to be 8.5 1014, 7.6 1014 and 9.2 1014 m2, respectively, and there was little difference in the dislocation density between the Fe–18Mn–0.6C and Fe–18Mn–0.6C–1.5Al TWIP steels at low strains when the dislocation densities were measured using neutron diffraction [57]. The amount of dislocation hardening (Drd) in the three TWIP steels at a strain of 0.1 was calculated using Eq. (5) and is plotted in Fig. 10. The Drd values were 420, 395 and 445 MPa for the T618, T618–Al and T618–Si TWIP steels, respectively. The contribution of dislocation hardening to
the total flow stress at a true strain of 0.1 was 58%, 66% and 54% in the T618, T618–Al and T618–Si TWIP steels, respectively, which is in good agreement with previous reports suggesting that dislocation storage causes high strain hardening at low strains in Fe–22Mn–0.6C TWIP steel [36]. The T618–Al TWIP steel exhibited the lowest dislocation hardening among the three TWIP steels because it had the lowest density of dislocations, making cross-slip easier due to the increased SFE caused by the addition of Al [12,17,40]. The amount of strain hardening caused by mechanical twinning (Drt) and DSA (DrD) without dislocation storage was 168, 52 and 188 MPa in the T618, T618–Al and T618– Si TWIP steels, respectively. The Drt values of the primary (Drpt ) and secondary (Drst ) twins were calculated using the following equation with the dislocation mean free path (MFP) approach [29,54]: MbGb ð7Þ L where b is a constant with a value of 0.24, which is indistinguishable between the primary and secondary twins [29,54]. The grain and twin boundaries were regarded as the main microstructural obstacles to dislocation gliding, and the dislocation MFP (L) was written as follows [3,28,29,54]:
Drt ¼
1 1 1 ¼ þ L d t
ð8Þ
where d is the effective grain size of the annealed specimen, and measured 10.0, 11.7 and 8.2 lm for the T618, T618–Al and T618–Si TWIP steels, respectively (Fig. 1). According to the Fullman’s stereological analysis [30], the mean twin spacing (t) has the following relationship with both the volume fraction (F) and the width (e) of the mechanical twins: 1 1 F ¼ t 2e ð1 F Þ
ð9Þ
Fig. 10. Contributions of the dislocation multiplication (Drd), primary (Drpt ) and secondary (Drst ) twins, and DSA (DrD) to the strain hardening of the T618, T618–Al and T618–Si TWIP steels deformed at a true strain of 0.1.
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for which the e values of the primary and secondary mechanical twins were obtained from TEM images and measured 30 nm, regardless of the TWIP steels’ chemical compositions. The F values were obtained separately for the primary and secondary mechanical twins (Fig. 8). The Drt values of the primary (Drpt ) and secondary (Drst ) mechanical twins were calculated using the following equation, which combines Eqs. (8) and (9) with Eq. (7): 1 1 F Drt ¼ MbGb þ ð10Þ d 2e ð1 F Þ The contributions of the primary and secondary twins to the strain hardening in the three TWIP steels at a strain of 0.1 are plotted in Fig. 10. While the Drt value of the T618–Al TWIP steel with only primary mechanical twins was 48 MPa, the Drt values of the T618 TWIP steel were 103 MPa for the primary twins (Drpt ) and 25 MPa for the secondary twins (Drst ). The Drt values of the T618–Si TWIP steel with well-developed primary and secondary twins (Fig. 7c) were calculated to be 120 MPa for the primary twins (Drpt ) and 65 MPa for the secondary twins (Drst ). The contribution of Drt to the overall strain hardening in the T618, T618–Al and T618–Si TWIP steels at a strain of 0.1 was 18%, 8% and 23%, respectively. The strain hardening (DrD) of the T618 TWIP steel caused by the DSA was calculated to be 40 MPa by subtracting the r0, Drd and Drt values from the total flow stress of 720 MPa (Fig. 10). However, the DrD values of the T618–Al and T618–Si TWIP steels were negligible, at 4 and 3 MPa, respectively. The above results demonstrated that the reason why the addition of Si in the Fe–18Mn–0.6C (T618) TWIP steel increased the strain hardening, while greatly reducing the DrD value, was attributed to the increases in Drd (445 MPa), Drt (185 MPa) and especially Drst (65 MPa), as a result of the secondary twins. In a similar fashion, the reason for the decreased strain hardening with the addition of Al to the Fe–18Mn–0.6C (T618–Al) TWIP steel could be attributed to reductions in Drd (395 MPa), Drt (48 MPa) and DrD (4 MPa), with the reduction in Drt being the greatest due to the increased SFE value caused by the addition of Al [12,17,40]. 4. Conclusions
(1) The SFE of a Fe–18Mn–0.6C TWIP steel measured by XRD was shown to decrease by 4 mJ m2 per 1 wt.% Si and up to 1.5 wt.% Si, resulting in active primary and secondary twinning. (2) The volume fractions of the primary and secondary mechanical twins were quantitatively evaluated by combining the advantages of EBSD and TEM. The total twin volume fraction increased linearly with decreasing SFE. However, when the SFE was less
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than 20 mJ m2, the volume fraction of the primary twins increased slowly, while that of the secondary twins increased rapidly. (3) The addition of Si to the Fe–18Mn–0.6C TWIP steel increased both the yield strength due to solid solution hardening and the ultimate tensile strength due to significant strain hardening, with a large elongation of over 60%. (4) The contributions of dislocation storage, mechanical twinning and DSA to the strain hardening behavior were quantitatively evaluated in Fe–18Mn–0.6C, Fe–18Mn–0.6C–1.5Al and Fe–18Mn–0.6C–1.5Si TWIP steels deformed by a true strain of 0.1. The addition of Si to the Fe–18Mn–0.6C TWIP steel raised the strain hardening, due primarily to the primary and secondary twins, although the DSA was greatly weakened by the addition of Si. Conversely, the addition of Al to the Fe–18Mn–0.6C TWIP steel resulted in a decrease in strain hardening due to a reduction in both the mechanical twinning and DSA.
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