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On the feasibility of twinning nucleation via extrinsic faulting in twinning-induced plasticity steel
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Scripta Materialia 68 (2013) 436–439 www.elsevier.com/locate/scriptamat
On the feasibility of twinning nucleation via extrinsic faulting in twinning-induced plasticity steel Azdiar A. Gazder,a,b Ahmed A. Saleha,⇑ and Elena V. Perelomaa,b a
School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, New South Wales 2522, Australia b Electron Microscopy Centre, University of Wollongong, New South Wales 2522, Australia Received 14 September 2012; revised 13 November 2012; accepted 13 November 2012 Available online 24 November 2012
Schmid’s law is used to predict the tendency of different grain orientations to deform via perfect slip, twinning, intrinsic and extrinsic faulting in a twinning-induced plasticity steel subjected to uniaxial tension. While the Schmid factors for twinning and intrinsic faulting are equivalent, the present analysis underscores the feasibility of twin nucleation at high strains via extrinsic faulting in the near-h1 0 0i-oriented grains that are nominally regarded as being unfavourably oriented for twinning. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: TWIP; Schmid factor; Tension; Electron back-scattering diffraction
The evolution of the microstructure and bulk texture in a fully recrystallized Fe–24Mn–3Al–2Si– 1Ni–0.06C twinning-induced plasticity (TWIP) steel subjected to interrupted tensile loading was investigated in Ref. [1]. Similar to earlier work [2–5], uniaxial tension promoted twinning in near-h1 1 1i orientations parallel to the tensile axis. This dependence of deformation twinning on grain orientation follows Schmid’s law, as the Schmid factor (m) for twinning is higher than that for slip in the h1 1 1i orientations. Here twinning activity is sustained with increasing tensile strain as more grains progressively rotate towards the h1 1 1i fibre [4]. To date, studies on the tensile loading of TWIP steels suggest that a deviation from Schmid’s law occurs at higher strains. This deviation is manifested by the delayed onset of twinning in the near-h1 0 0i grains that are nominally regarded as being unfavourably oriented for twinning [2,5]. Gutierrez-Urrutia et al. [5] ascribed this deviation to the stress concentration effect induced by neighbouring grain interactions. Alternatively, the present analysis hypothesizes that the presumed deviation from Schmid’s law could be the result of the increased feasibility of twin nucleation via extrinsic stacking faults at high tensile strains. For a given stress state, the Schmid factor is a geometric or crystallographic measure of the tendency of a certain orientation to deform by a particular deforma-
⇑ Corresponding author. Tel.: +61 4221 3034; fax: +61 4221 3662; email: [email protected]
tion mode. While Schmid’s law inherently assumes that all deformation systems have an equal value of critical resolved shear stress (CRSS), the actual activation of a deformation mode is dictated by its characteristic CRSS. Consequently, Schmid’s law predicts a plastic response without enforcing strain compatibility and gives a lower bound (or Sachs) estimate for the onset of plastic deformation [6]. Despite these assumptions, the Schmid factor analysis is effective in explaining the dependence of deformation twinning on grain orientation in low stacking fault energy face-centred cubic materials [2,5,7–9] as their deformation approaches the “lower-bound” Sachs type more than the “higher-bound” Taylor type [10]. The Schmid factor of each orientation was calculated using 24 f1 1 1gh1 1 0i perfect slip systems (counting both forward and reverse slip directions) and 12 f1 1 1gh1 1 2i forward twinning systems. Furthermore, dislocations gliding on the {1 1 1} plane in the h1 1 0i direction can easily dissociate into h1 1 2i Shockley partials bounding a stacking fault [11]. The character of the stacking fault is governed by the movement of the partial dislocation. The motion of a Shockley partial on a close-packed plane produces an intrinsic stacking fault while the motion on two consecutive close packed planes creates an extrinsic stacking fault. Previous Schmid factor analyses on TWIP steels subjected to tension [2,5] have implied that twins nucleate via intrinsic stacking faults as the m-values of twinning and the leading partial of intrinsic faults are equivalent [9]. However, as pointed out in Ref. [8], the Schmid factor for twinning will depend on whether it is the intrinsic
1359-6462/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2012.11.014
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Figure 1. /2 = 0° and 45° ODF sections depicting the variation in Schmid factor during uniaxial tension for (a) perfect slip and the leading partial of (b) intrinsic and (c) extrinsic stacking faults. In (a–c), h1 1 1i = red, h1 0 0i = blue, h1 1 0i = green. The ratio between the Schmid factors of (d) perfect slip and the leading partial of intrinsic stacking faults, (e) the leading partials of intrinsic and extrinsic stacking faults, and (f) perfect slip and the leading partial of extrinsic stacking faults. Contour levels = 0.02 for (a–c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
or the extrinsic stacking fault that acts as the twin nucleus. In this regard, calculations considering twin nucleation via extrinsic faulting are usually overlooked. Consequently, the Schmid factors of the leading partials of the intrinsic and extrinsic stacking faults were calculated following Karaman et al. [8,9]. A generalized Schmid’s law was used such that: X ð1Þ m¼ bgrgT nT where b is the slip direction, g is the orientation matrix in Euler angles, r is the stress tensor for uniaxial tension along the prior rolling direction (RD) and n is the slip plane. In order to account for the directionality of the twinning shear, an additional constraint was applied for the twinning modes such that only positive Schmid factors are considered (i.e. the shear stress across the twinning plane and resolved in the twinning direction must be positive) [12]. In Figure 1a–c, the tendency of orientations to deform via perfect slip, intrinsic or extrinsic faulting during uniaxial tension are shown by plotting their Schmid factors for the /2 = 0° and 45° orientation distribution function (ODF) sections. As stated above and following Ref. [9], the Schmid factors for twinning are not shown as they are the same as those of the leading partial of intrinsic stacking faults (Fig. 1b). Here, higher Schmid factors (or lighter areas) indicate the greater propensity of an orientation to deform by a particular deformation mode. The locations of the h1 1 1i, h1 0 0i and h1 1 0i fibres parallel to the tensile axis (or prior RD) are superimposed on the ODF sections with a spread of 15° around their ideal skeleton lines, and their respective Schmid factors are given in Table 1.
Table 1. Schmid factors for the perfect slip systems and the leading partials of the intrinsic and extrinsic stacking faults. Fibre
Schmid factor Slip
Twinning/intrinsic
Extrinsic
h1 1 1i h1 0 0i h1 1 0i
0.28 0.41 0.41
0.32 0.24 0.47
0.16 0.47 0.24
Figure 1d–f shows the ratios between the Schmid factors of perfect slip and the leading partial of intrinsic stacking faults (ms/mIn, Fig. 1d), between the leading partials of intrinsic and extrinsic stacking faults (mIn/ mEx, Fig. 1e) and between perfect slip and the leading partial of extrinsic stacking faults (ms/mEx, Fig. 1f). While the solid, dashed and dotted lines denote orientations where either deformation mode is equally favoured (as the Schmid factor ratio = 1), regions where a single deformation mode is more likely are indicated as marked. It is clear in Figure 1b, d and e that intrinsic faulting is favoured along the h1 1 1i and h1 1 0i fibres, whereas the orientations along the h1 0 0i fibre tend to favour extrinsic faulting (Fig. 1c, e and f). The inverse pole figure (IPF) maps in Figure 2a and c show the microstructures at a tensile strain of 20.9% from Ref. [1] and after repolishing the same sample at a tensile strain of 48%, respectively. In Figure 2b and d, the orientations of twin-free and twinned grains are depicted as clear blue and solid red circles, respectively. Both IPFs contain the same solid, dashed and dotted black lines, which are equivalent to the solid (ms/mIn = 1), dashed (mIn/mEx = 1) and dotted (ms/mEx = 1) black lines from Figure 1d–f. The following paragraphs discuss only a sin-
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Figure 2. (a and c) IPF maps at tensile strains of 20.9% and 48%, respectively. LAGBs = silver, HAGBs = black, 60° h1 1 1i, R3 TBs = red lines and rolling direction (RD) = horizontal. The orientations of some twin-free and twinned grains from (a) and (c) are shown on the IPFs in (b) and (d) as clear blue and solid red circles, respectively. The solid, dashed and dotted black lines on the IPFs correspond to those in Figure 1d–f, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
gle black line (or a pair of deformation modes) on the IPFs at any given instance. For example, on comparing slip with intrinsic faulting (or twinning), the area between the solid black line and the h1 0 0i pole comprises orientations with higher Schmid factors that favour slip. It follows that the region between the solid black line and the h1 1 1i h1 1 0i line denotes orientations with higher Schmid factors that favour intrinsic faulting. Figure 2b and d shows some twinned grains (solid red circles) falling to the left of the solid black line and lying within the region that favours slip. This observation agrees with previous TWIP steel investigations that correlate twinning activity with the crystallographic orientation [2,3,5]. While Refs. [2,3,5] are limited to comparing the Schmid factors for slip and twinning (or the leading partial of the intrinsic stacking faults), we emphasize that the Schmid factor predictions can be extended to include the possibility of twin nucleation via extrinsic stacking faults. Consequently, on comparing intrinsic faulting (or twinning) with extrinsic faulting, the area between the dashed black line and the h1 0 0i pole comprises orientations with higher Schmid factors that favour extrinsic faulting. The region between the dashed black line and the h1 1 1i h1 1 0i line denotes orientations with higher Schmid factors that favour intrinsic faulting. In Figure 2b and d, some twinned grains (solid red circles) fall to the left of the dashed black line and lie within the region that favours extrinsic faulting. Lastly, on comparing slip with extrinsic faulting, the area between the dotted black line and the h1 0 0i pole comprises orientations with higher Schmid factors that favour extrinsic faulting. The region between the dotted black line and the h1 1 1i h1 1 0i line denotes orienta-
tions with higher Schmid factors that favour slip. While the grains around the h1 0 0i pole are twin-free at 20.9% tensile strain (Fig. 2b), twinning is clearly seen in nearh1 0 0i oriented grains at 48% strain, which corresponds to the ultimate tensile strength of 1080 MPa (Fig. 2d). This is in agreement with previous studies on TWIP steels that observed twinning in such orientations at tensile strains of 30% (Fe–22Mn–0.6C) [5] and 55% (Fe– 18Mn–0.6C–1.5Al) [13]. Thus, based on the above observations and on Schmid factor considerations, it is argued that the presumed deviation from Schmid’s law [2,3,5] could just as well be ascribed to the orientation dependency of the character of the stacking fault acting as a twin nucleus. It is therefore plausible that twins in grains with h1 1 1i orientations nucleate via intrinsic stacking faults whereas twins in the near-h1 0 0i-oriented grains nucleate via extrinsic stacking faults. Transmission electron microscopy (TEM)-based characterization has identified intrinsic stacking faults as a precursor for deformation twinning in TWIP steels with different compositions (Fe–21Mn–1.2C deformed at room temperature and Fe–17Mn–3Al–3Si deformed at 186 °C) [14,15]. However, (i) the TEM analyses in Refs. [14,15] were undertaken at low strain levels (<10%), (ii) the observed faults were not correlated with the grain orientation and (iii) there is alternative experimental evidence suggesting that extrinsic stacking faults may also act as nuclei for deformation twinning. With respect to point (iii), Coupeau et al. [16] concluded that both intrinsic and extrinsic stacking faults need to be accounted for in order to explain the twinning events observed during the in situ atomic force
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stress levels achieved during uniaxial tensile testing (Figure 1a in Ref. [1], 0.2% proof stress = 290 MPa and ultimate tensile strength = 1080 MPa) and further underscores the feasibility of twinning via extrinsic faulting. Consequently, the observation of a delayed initiation of twinning in the h1 0 0i-oriented grains can be ascribed to the formation of dislocation cells via cross-slip, which, in turn, has the effect of relieving the local stress concentration required to nucleate twinning [18]. In summary, Schmid factor predictions indicate the feasibility of extrinsic stacking faults acting as twin nuclei at high strains in orientations with low Schmid factors for twinning. Further TEM characterization should be undertaken in order to correlate the character of the stacking fault with the crystallographic orientation and the strain level. Figure 3. The texture-weighted Schmid factor for perfect slip and the leading partials of intrinsic and extrinsic stacking faults vs. tensile strain.
microscopy of a low stacking fault energy Cu–13.7Al h1 1 1i single crystal undergoing compression. Extrinsic stacking faults and twinning have also been observed by Karaman et al. [8,17] during the tensile loading of h1 0 0i single crystals of Hadfield steel [8] and 316L austenitic stainless steel [17]. Interestingly, Karaman et al. [8] postulated a dislocation model to explain the formation of extrinsic stacking faults and the subsequent evolution of twinning in “unfavourable” orientations like h1 0 0i, which have high extrinsic Schmid factors. Their model has two prerequisites: (1) The mobility of the leading partial of the extrinsic stacking fault should be faster than the trailing partial. This condition is inherently satisfied as the Schmid factor for the leading partial is higher (and therefore more mobile) than that for the trailing partial. (2) The shear stress applied on the leading partial of the extrinsic stacking fault has to overcome the fault tension. If a stacking fault energy (SFE) range of 15–30 mJ m–2 and a partial Burgers vector (bP) of 1.47 1010 m are used, the fault tension is approximated as SFE/bP [8], which returns a shear stress of 102–203 MPa. If the average Schmid factor for extrinsic stacking faults is 0.35 (see Fig. 31), a normal stress of 290–580 MPa is calculated. This range of normal stresses are within the 1
The texture-weighted average Schmid factors for perfect slip, intrinsic and extrinsic faulting shown in Figure 3 were calculated using the experimental bulk ODFs (Figure 5a–g in Ref. [1]). With increasing tensile strain, the decline in the texture-weighted Schmid factors for slip and intrinsic faulting is ascribed to the progressive strengthening of orientations with relatively lower Schmid factors along the h1 1 1i and h1 0 0i fibres (Fig. 1a and b). This alludes to texture hardening effects, as orientations with higher Schmid factors rotate towards orientations with lower Schmid factors with greater tensile strain. On the other hand, the levelling-off in the weighted Schmid factor of the extrinsic stacking faults beyond 20.9% tensile strain is due to the progressive strengthening of orientations along the h1 0 0i fibre, the Schmid factors of which are relatively higher than other grains (Fig. 1c).
The authors thank Prof. D.B. Santos of UFMG, Brazil for the source material and the UOW Small Grant Scheme for funding. [1] A.A. Saleh, E.V. Pereloma, A.A. Gazder, submitted for publication. [2] P. Yang, Q. Xie, L. Meng, H. Ding, Z. Tang, Scripta Mater. 55 (2006) 629. [3] R. Ueji, N. Tsuchida, D. Terada, N. Tsuji, Y. Tanaka, A. Takemura, K. Kunishige, Scripta Mater. (2008) 963. [4] D. Barbier, N. Gey, S. Allain, N. Bozzolo, M. Humbert, Mater. Sci. Eng. A 500 (2009) 196. [5] I. Gutierrez-Urrutia, S. Zaefferer, D. Raabe, Mater. Sci. Eng. A 527 (2010) 3552. [6] H.R. Piehler, W.A. Backofen, in: J Grewen, G. Wassermann (Eds.), Textures in Research and Practice, Proceedings of the International Symposium, Clausthal-Zellerfeld, October 2–5, 1968, Springer, Berlin, 1969, p. 436. [7] I. Karaman, H. Sehitoglu, A.J. Beaudoin, Y.I. Chumlyakov, H.J. Maier, C.N. Tome´, Acta Mater. 48 (2000) 2031. [8] I. Karaman, H. Sehitoglu, Y.I. Chumlyakov, H.J. Maier, I.V. Kireeva, Scripta Mater. 44 (2001) 337. [9] I. Karaman, H. Sehitoglu, K. Gall, Y.I. Chumlyakov, H.J. Maier, Acta Mater. 48 (2000) 1345. [10] T. Leffers, R.K. Ray, Prog. Mater. Sci. 54 (2009) 351. [11] R.E. Reed-Hill, R. Abbaschian, Physical Metallurgy Principles, PWS-Kent, Boston, MA, 1992. [12] J.W. Christian, S. Mahajan, Prog. Mater. Sci. 39 (1995) 1. [13] H. Beladi, I.B. Timokhina, Y. Estrin, J. Kim, B.C. De Cooman, S.K. Kim, Acta Mater. 59 (2011) 7787. [14] H. Idrissi, K. Renard, L. Ryelandt, D. Schryvers, P.J. Jacques, Acta Mater. 58 (2010) 2464. [15] H. Idrissi, L. Ryelandt, M. Veron, D. Schryvers, P.J. Jacques, Scripta Mater. 60 (2009) 941. [16] C. Coupeau, F. Tranchant, J. Vergnol, J. Grilhe´, Eur. Phys. J. Appl. Phys. 6 (1999) 1. [17] I. Karaman, H. Sehitoglu, H.J. Maier, Y.I. Chumlyakov, Acta Mater. 49 (2001) 3919. [18] S. Miura, J.-I. Takamura, N. Narita, Trans. JIM 9 (1968) 555.
Scripta Materialia 68 (2013) 436–439 www.elsevier.com/locate/scriptamat
On the feasibility of twinning nucleation via extrinsic faulting in twinning-induced plasticity steel Azdiar A. Gazder,a,b Ahmed A. Saleha,⇑ and Elena V. Perelomaa,b a
School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, New South Wales 2522, Australia b Electron Microscopy Centre, University of Wollongong, New South Wales 2522, Australia Received 14 September 2012; revised 13 November 2012; accepted 13 November 2012 Available online 24 November 2012
Schmid’s law is used to predict the tendency of different grain orientations to deform via perfect slip, twinning, intrinsic and extrinsic faulting in a twinning-induced plasticity steel subjected to uniaxial tension. While the Schmid factors for twinning and intrinsic faulting are equivalent, the present analysis underscores the feasibility of twin nucleation at high strains via extrinsic faulting in the near-h1 0 0i-oriented grains that are nominally regarded as being unfavourably oriented for twinning. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: TWIP; Schmid factor; Tension; Electron back-scattering diffraction
The evolution of the microstructure and bulk texture in a fully recrystallized Fe–24Mn–3Al–2Si– 1Ni–0.06C twinning-induced plasticity (TWIP) steel subjected to interrupted tensile loading was investigated in Ref. [1]. Similar to earlier work [2–5], uniaxial tension promoted twinning in near-h1 1 1i orientations parallel to the tensile axis. This dependence of deformation twinning on grain orientation follows Schmid’s law, as the Schmid factor (m) for twinning is higher than that for slip in the h1 1 1i orientations. Here twinning activity is sustained with increasing tensile strain as more grains progressively rotate towards the h1 1 1i fibre [4]. To date, studies on the tensile loading of TWIP steels suggest that a deviation from Schmid’s law occurs at higher strains. This deviation is manifested by the delayed onset of twinning in the near-h1 0 0i grains that are nominally regarded as being unfavourably oriented for twinning [2,5]. Gutierrez-Urrutia et al. [5] ascribed this deviation to the stress concentration effect induced by neighbouring grain interactions. Alternatively, the present analysis hypothesizes that the presumed deviation from Schmid’s law could be the result of the increased feasibility of twin nucleation via extrinsic stacking faults at high tensile strains. For a given stress state, the Schmid factor is a geometric or crystallographic measure of the tendency of a certain orientation to deform by a particular deforma-
⇑ Corresponding author. Tel.: +61 4221 3034; fax: +61 4221 3662; email: [email protected]
tion mode. While Schmid’s law inherently assumes that all deformation systems have an equal value of critical resolved shear stress (CRSS), the actual activation of a deformation mode is dictated by its characteristic CRSS. Consequently, Schmid’s law predicts a plastic response without enforcing strain compatibility and gives a lower bound (or Sachs) estimate for the onset of plastic deformation [6]. Despite these assumptions, the Schmid factor analysis is effective in explaining the dependence of deformation twinning on grain orientation in low stacking fault energy face-centred cubic materials [2,5,7–9] as their deformation approaches the “lower-bound” Sachs type more than the “higher-bound” Taylor type [10]. The Schmid factor of each orientation was calculated using 24 f1 1 1gh1 1 0i perfect slip systems (counting both forward and reverse slip directions) and 12 f1 1 1gh1 1 2i forward twinning systems. Furthermore, dislocations gliding on the {1 1 1} plane in the h1 1 0i direction can easily dissociate into h1 1 2i Shockley partials bounding a stacking fault [11]. The character of the stacking fault is governed by the movement of the partial dislocation. The motion of a Shockley partial on a close-packed plane produces an intrinsic stacking fault while the motion on two consecutive close packed planes creates an extrinsic stacking fault. Previous Schmid factor analyses on TWIP steels subjected to tension [2,5] have implied that twins nucleate via intrinsic stacking faults as the m-values of twinning and the leading partial of intrinsic faults are equivalent [9]. However, as pointed out in Ref. [8], the Schmid factor for twinning will depend on whether it is the intrinsic
1359-6462/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2012.11.014
A. A. Gazder et al. / Scripta Materialia 68 (2013) 436–439
437
Figure 1. /2 = 0° and 45° ODF sections depicting the variation in Schmid factor during uniaxial tension for (a) perfect slip and the leading partial of (b) intrinsic and (c) extrinsic stacking faults. In (a–c), h1 1 1i = red, h1 0 0i = blue, h1 1 0i = green. The ratio between the Schmid factors of (d) perfect slip and the leading partial of intrinsic stacking faults, (e) the leading partials of intrinsic and extrinsic stacking faults, and (f) perfect slip and the leading partial of extrinsic stacking faults. Contour levels = 0.02 for (a–c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
or the extrinsic stacking fault that acts as the twin nucleus. In this regard, calculations considering twin nucleation via extrinsic faulting are usually overlooked. Consequently, the Schmid factors of the leading partials of the intrinsic and extrinsic stacking faults were calculated following Karaman et al. [8,9]. A generalized Schmid’s law was used such that: X ð1Þ m¼ bgrgT nT where b is the slip direction, g is the orientation matrix in Euler angles, r is the stress tensor for uniaxial tension along the prior rolling direction (RD) and n is the slip plane. In order to account for the directionality of the twinning shear, an additional constraint was applied for the twinning modes such that only positive Schmid factors are considered (i.e. the shear stress across the twinning plane and resolved in the twinning direction must be positive) [12]. In Figure 1a–c, the tendency of orientations to deform via perfect slip, intrinsic or extrinsic faulting during uniaxial tension are shown by plotting their Schmid factors for the /2 = 0° and 45° orientation distribution function (ODF) sections. As stated above and following Ref. [9], the Schmid factors for twinning are not shown as they are the same as those of the leading partial of intrinsic stacking faults (Fig. 1b). Here, higher Schmid factors (or lighter areas) indicate the greater propensity of an orientation to deform by a particular deformation mode. The locations of the h1 1 1i, h1 0 0i and h1 1 0i fibres parallel to the tensile axis (or prior RD) are superimposed on the ODF sections with a spread of 15° around their ideal skeleton lines, and their respective Schmid factors are given in Table 1.
Table 1. Schmid factors for the perfect slip systems and the leading partials of the intrinsic and extrinsic stacking faults. Fibre
Schmid factor Slip
Twinning/intrinsic
Extrinsic
h1 1 1i h1 0 0i h1 1 0i
0.28 0.41 0.41
0.32 0.24 0.47
0.16 0.47 0.24
Figure 1d–f shows the ratios between the Schmid factors of perfect slip and the leading partial of intrinsic stacking faults (ms/mIn, Fig. 1d), between the leading partials of intrinsic and extrinsic stacking faults (mIn/ mEx, Fig. 1e) and between perfect slip and the leading partial of extrinsic stacking faults (ms/mEx, Fig. 1f). While the solid, dashed and dotted lines denote orientations where either deformation mode is equally favoured (as the Schmid factor ratio = 1), regions where a single deformation mode is more likely are indicated as marked. It is clear in Figure 1b, d and e that intrinsic faulting is favoured along the h1 1 1i and h1 1 0i fibres, whereas the orientations along the h1 0 0i fibre tend to favour extrinsic faulting (Fig. 1c, e and f). The inverse pole figure (IPF) maps in Figure 2a and c show the microstructures at a tensile strain of 20.9% from Ref. [1] and after repolishing the same sample at a tensile strain of 48%, respectively. In Figure 2b and d, the orientations of twin-free and twinned grains are depicted as clear blue and solid red circles, respectively. Both IPFs contain the same solid, dashed and dotted black lines, which are equivalent to the solid (ms/mIn = 1), dashed (mIn/mEx = 1) and dotted (ms/mEx = 1) black lines from Figure 1d–f. The following paragraphs discuss only a sin-
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Figure 2. (a and c) IPF maps at tensile strains of 20.9% and 48%, respectively. LAGBs = silver, HAGBs = black, 60° h1 1 1i, R3 TBs = red lines and rolling direction (RD) = horizontal. The orientations of some twin-free and twinned grains from (a) and (c) are shown on the IPFs in (b) and (d) as clear blue and solid red circles, respectively. The solid, dashed and dotted black lines on the IPFs correspond to those in Figure 1d–f, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
gle black line (or a pair of deformation modes) on the IPFs at any given instance. For example, on comparing slip with intrinsic faulting (or twinning), the area between the solid black line and the h1 0 0i pole comprises orientations with higher Schmid factors that favour slip. It follows that the region between the solid black line and the h1 1 1i h1 1 0i line denotes orientations with higher Schmid factors that favour intrinsic faulting. Figure 2b and d shows some twinned grains (solid red circles) falling to the left of the solid black line and lying within the region that favours slip. This observation agrees with previous TWIP steel investigations that correlate twinning activity with the crystallographic orientation [2,3,5]. While Refs. [2,3,5] are limited to comparing the Schmid factors for slip and twinning (or the leading partial of the intrinsic stacking faults), we emphasize that the Schmid factor predictions can be extended to include the possibility of twin nucleation via extrinsic stacking faults. Consequently, on comparing intrinsic faulting (or twinning) with extrinsic faulting, the area between the dashed black line and the h1 0 0i pole comprises orientations with higher Schmid factors that favour extrinsic faulting. The region between the dashed black line and the h1 1 1i h1 1 0i line denotes orientations with higher Schmid factors that favour intrinsic faulting. In Figure 2b and d, some twinned grains (solid red circles) fall to the left of the dashed black line and lie within the region that favours extrinsic faulting. Lastly, on comparing slip with extrinsic faulting, the area between the dotted black line and the h1 0 0i pole comprises orientations with higher Schmid factors that favour extrinsic faulting. The region between the dotted black line and the h1 1 1i h1 1 0i line denotes orienta-
tions with higher Schmid factors that favour slip. While the grains around the h1 0 0i pole are twin-free at 20.9% tensile strain (Fig. 2b), twinning is clearly seen in nearh1 0 0i oriented grains at 48% strain, which corresponds to the ultimate tensile strength of 1080 MPa (Fig. 2d). This is in agreement with previous studies on TWIP steels that observed twinning in such orientations at tensile strains of 30% (Fe–22Mn–0.6C) [5] and 55% (Fe– 18Mn–0.6C–1.5Al) [13]. Thus, based on the above observations and on Schmid factor considerations, it is argued that the presumed deviation from Schmid’s law [2,3,5] could just as well be ascribed to the orientation dependency of the character of the stacking fault acting as a twin nucleus. It is therefore plausible that twins in grains with h1 1 1i orientations nucleate via intrinsic stacking faults whereas twins in the near-h1 0 0i-oriented grains nucleate via extrinsic stacking faults. Transmission electron microscopy (TEM)-based characterization has identified intrinsic stacking faults as a precursor for deformation twinning in TWIP steels with different compositions (Fe–21Mn–1.2C deformed at room temperature and Fe–17Mn–3Al–3Si deformed at 186 °C) [14,15]. However, (i) the TEM analyses in Refs. [14,15] were undertaken at low strain levels (<10%), (ii) the observed faults were not correlated with the grain orientation and (iii) there is alternative experimental evidence suggesting that extrinsic stacking faults may also act as nuclei for deformation twinning. With respect to point (iii), Coupeau et al. [16] concluded that both intrinsic and extrinsic stacking faults need to be accounted for in order to explain the twinning events observed during the in situ atomic force
A. A. Gazder et al. / Scripta Materialia 68 (2013) 436–439
439
stress levels achieved during uniaxial tensile testing (Figure 1a in Ref. [1], 0.2% proof stress = 290 MPa and ultimate tensile strength = 1080 MPa) and further underscores the feasibility of twinning via extrinsic faulting. Consequently, the observation of a delayed initiation of twinning in the h1 0 0i-oriented grains can be ascribed to the formation of dislocation cells via cross-slip, which, in turn, has the effect of relieving the local stress concentration required to nucleate twinning [18]. In summary, Schmid factor predictions indicate the feasibility of extrinsic stacking faults acting as twin nuclei at high strains in orientations with low Schmid factors for twinning. Further TEM characterization should be undertaken in order to correlate the character of the stacking fault with the crystallographic orientation and the strain level. Figure 3. The texture-weighted Schmid factor for perfect slip and the leading partials of intrinsic and extrinsic stacking faults vs. tensile strain.
microscopy of a low stacking fault energy Cu–13.7Al h1 1 1i single crystal undergoing compression. Extrinsic stacking faults and twinning have also been observed by Karaman et al. [8,17] during the tensile loading of h1 0 0i single crystals of Hadfield steel [8] and 316L austenitic stainless steel [17]. Interestingly, Karaman et al. [8] postulated a dislocation model to explain the formation of extrinsic stacking faults and the subsequent evolution of twinning in “unfavourable” orientations like h1 0 0i, which have high extrinsic Schmid factors. Their model has two prerequisites: (1) The mobility of the leading partial of the extrinsic stacking fault should be faster than the trailing partial. This condition is inherently satisfied as the Schmid factor for the leading partial is higher (and therefore more mobile) than that for the trailing partial. (2) The shear stress applied on the leading partial of the extrinsic stacking fault has to overcome the fault tension. If a stacking fault energy (SFE) range of 15–30 mJ m–2 and a partial Burgers vector (bP) of 1.47 1010 m are used, the fault tension is approximated as SFE/bP [8], which returns a shear stress of 102–203 MPa. If the average Schmid factor for extrinsic stacking faults is 0.35 (see Fig. 31), a normal stress of 290–580 MPa is calculated. This range of normal stresses are within the 1
The texture-weighted average Schmid factors for perfect slip, intrinsic and extrinsic faulting shown in Figure 3 were calculated using the experimental bulk ODFs (Figure 5a–g in Ref. [1]). With increasing tensile strain, the decline in the texture-weighted Schmid factors for slip and intrinsic faulting is ascribed to the progressive strengthening of orientations with relatively lower Schmid factors along the h1 1 1i and h1 0 0i fibres (Fig. 1a and b). This alludes to texture hardening effects, as orientations with higher Schmid factors rotate towards orientations with lower Schmid factors with greater tensile strain. On the other hand, the levelling-off in the weighted Schmid factor of the extrinsic stacking faults beyond 20.9% tensile strain is due to the progressive strengthening of orientations along the h1 0 0i fibre, the Schmid factors of which are relatively higher than other grains (Fig. 1c).
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