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Pyramidal I slip in c-axis compressed Mg single crystals
SMM-10809; No of Pages 4 Scripta Materialia xxx (2015) xxx–xxx
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Pyramidal I slip in c-axis compressed Mg single crystals Kelvin Y. Xie, Zafir Alam, Alexander Caffee, Kevin J. Hemker ⁎ Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
a r t i c l e
i n f o
Article history: Received 17 August 2015 Received in revised form 7 September 2015 Accepted 8 September 2015 Available online xxxx Keywords: Magnesium Single crystal Plastic deformation Slip trace Pyramidal slip
a b s t r a c t Pyramidal I slip was observed to be the dominant slip mode in magnesium single crystals compressed quasistatically along c-axis at room temperature. The slip trace angles resulted from pyramidal I and pyramidal II slips projected on (0 − 1 1 0) and (2 − 1 − 1 0) surfaces were initially calculated, and then measured on 3% deformed magnesium single crystals. The measured angles indicate the prevalence of pyramidal I slip ({10–11}b11–23 N with the critical resolve shear stress of 54 MPa). The pyramidal slip traces are dense but very fine, suggesting limited b c + aN dislocation activities. © 2015 Published by Elsevier Ltd.
1. Introduction Magnesium (Mg) and its alloys have attracted considerable interest because it is nearly four times lighter than steel, but structural applications of Mg alloys are generally limited to cast components because of its limited formability. Ductility limitations are generally attributed to strong plastic anisotropy that results from its underlying hexagonal lattice [1]. Substantial reduction of this anisotropy has been achieved through rare earth alloying [2], but further development of wrought Mg alloys would benefit from an increased understanding of the mechanisms governing the interactions between various slip and twinning modalities. The critically resolved shear stress (CRSS) for slip on the closepacked basal plane is significantly lower than for the prismatic and pyramidal planes, but basal slip will not accommodate deformation along the c-axis and cannot, by itself, satisfy the Taylor criterion requiring five independent slip systems for the ductility of polycrystalline metals [3]. A number of investigators have performed c-axis compression experiments on single crystals to activate and study non-basal slip [3–8], and the general consensus that has immerged pointing to the importance of bc + a N dislocation slip. TEM studies [3–5,7] have shown that, although compression twins are occasionally observed, non-basal bc + aN dislocations with Burger vectors along b 11–23N are the primary carriers of plastic deformation during c-axis compression and that the interaction of bc + aN dislocations and formation of loops leads to very high strain hardening. Pure Mg sample generally fail after only a few percent deformation when compressed along c-axis; Mg–Li and ⁎ Corresponding author. E-mail address: [email protected] (K.J. Hemker).
Mg–Re alloy exhibit much improved ductility [9–11]. Although the cause is not known, increased activity of b c + a N pyramidal glide has been associated with increased ductility in Mg alloys [9–11]. The bc + aN dislocations lie in and can glide on either {1 0 −1 1} pyramidal I or {1 1 −2 2} pyramidal II slip planes. Detailed TEM tilting experiments can be used to determine slip planes but the easiest and most direct method for identifying active slip systems is to image slip traces on the adjacent faces of single-crystalline specimens. A general trend in the experimental literature for Mg has attributed c-axis deformation to the activation of pyramidal II glide, but closer inspection of individual studies indicate that many investigators have referenced the 1974 work of Obara et al. [3] in lieu of conducting additional slip trace analyses. This point deserves further attention because, as described below, the slip trace observations of Obara et al. [3] are not as straightforward as originally assumed. Moreover, these experimental studies have been paralleled by ab initio and molecular dynamics (MD) simulations, which have predicted various stable dislocation core configurations for bc + a N edge and screw dislocations and been used to estimate the relative mobility of these dislocations on pyramidal I and II glide planes [11–15]. Theoretical studies have the potential to provide atomic-scale insight of dislocation core structures and the kinetics of dislocation glide, but the MD predictions of bc + aN pyramidal glide in Mg have been variable and at times even contradictory. Differences in how the dislocations were created, the empirical potentials used, and applied stresses have resulted in various core configurations and observations of b c + aN glide on pyramidal I planes in some simulations [5,12] and on pyramidal II planes in others [16]. Tang et al. [13] have suggested that bc + aN dislocations are nucleated and glide on pyramidal I planes at relatively low stresses but can cross-slip to pyramidal II planes at much higher stresses. This could be
http://dx.doi.org/10.1016/j.scriptamat.2015.09.016 1359-6462/© 2015 Published by Elsevier Ltd.
Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016
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K.Y. Xie et al. / Scripta Materialia xxx (2015) xxx–xxx
used to rationalize differences in the MD studies, but the importance of pyramidal I glide in this and other theoretical studies remains to be correlated with experimental observations of slip activities. The current study was undertaken to record slip traces on adjacent orthogonal faces of c-axis compressed single-crystalline Mg and to collect experimental data that can be compared and contrasted with the original slip trace measurements of Obara et al. [3]. Rectangular compression samples with dimensions 6 mm × 6.5 mm × 14 mm were electrical discharge machined (EDM) from 99.999% pure bulk [0 0 0 1] Mg single crystals (Metals Crystals and Oxides Ltd, UK). Laue diffraction confirmed that the compression axes of all specimens were aligned to within 1° of the c-axis of the crystals, thus suppressing basal and prismatic slip. The cross-section of the compression samples was cut with (0 −1 1 0) and (2 −1 −1 0) side faces. The EDM parameters were adjusted to low power, low water pressure and low feed rate in order to minimize deformation, and the cut surfaces were chemically polished using 10% nitric acid in water to remove the EDM recast layer. Quasistatic compression tests were conducted in an MTS machine at a strain rate of 10−4 s−1. Deformed samples were imaged immediately after the tests with a confocal microscope (Keyence 3D laser scanning microscope) that accentuated the presence of the slip traces. Fig. 1 provides a geometric summary of all twelve pyramidal I and six pyramidal II systems for an HCP Mg single crystal (a = 3.21 Å and c = 5.21 Å) loaded along the c-axis. The intersections of the various {1 0 − 1 1} and {1 1 − 2 2} planes with the (0 − 1 1 0) front and (2 − 1 − 1 0) side faces can be matched with observed slip traces to identify the active slip systems. Doing so is straightforward but it is important to note that not all slip systems will create a slip step on both faces. As illustrated in Fig. 1, four of the twelve pyramidal I and two of the six pyramidal II slip systems will not produce slip steps on the (0 −1 1 0) face because their Burgers vectors are parallel to that face. Considering all 18 slip systems and the slip traces that they would make on the (0 −1 1 0) and (2 −1 −1 0) faces yields the slip trace angles that are shown in Fig. 1. These values can be compared with experimental observations to determine the relative activity of pyramidal I and II slips. A total of four single-crystalline samples were compressed in this study (Fig. 2a). A typical true stress and strain curve (blue) and
Fig. 2. A typical engineering stress–strain curve and its strain hardening rate curve of Mg single crystal compressed along c-axis at room temperature.
corresponding true strain hardening rate curve (green) are plotted in Fig. 2b. The shape of the flow curves and the measured stress levels are similar to the observations reported by Obara et al. and Syed et al.:
Fig. 1. Summary of all the possible pyramidal slip systems and the corresponding slip traces that may be activated in single crystals Mg compressed along c-axis. Red arrows in the crystal unit cells indicate the Burger's vectors of bc + aN dislocations, colored planes indicate slip planes and bold black boxes highlight the (0 1 1 0) and (2 −1 −1 0) which the slip traces are projected on.
Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016
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no apparent yield point, high flow stress up to 300 MPa before failure and much higher strain hardening rates (~ 5–10 GPa) than pure FCC (e.g. ~ 1.5–2.5 GPa in Ir) and BCC single crystals [3,5,17]. The yield strength at 0.2% strain offset is estimated to be ~135 MPa, comparable to that reported by Syed et al. [5], and this value is used to estimate the critical resolved shear strength (CRSS) for pyramidal slip. All four compressed samples developed slip traces on both (0 −1 1 0) and (2 −1 −1 0) faces. The faces of undeformed samples are free of slip traces as expected (Fig. 3a & b). The speckles in these images are etch pits of pre-existing dislocations from the chemical polishing. After 3% deformation, a high density of inclined and smaller number of coarse horizontal slip traces were observed. Most inclined slip traces on the (0 −1 1 0) faces of all four samples were measured to be ±50° to ±55° to the basal planes (see for example Fig. 3c). This measurement is close to the calculated angle of ±58° for pyramidal I slip and quite different from the angle of ±39° that would be associated with pyramidal II slip. Only occasionally, evidence of slip traces aligned at ±39° on the (0 − 1 1 0) face was observed. The (2 − 1 − 1 0) faces of all four deformed single crystals were also imaged and numerous slip trace angles ranging from ±45° to ±60° were observed (see for example Fig. 3d). This range of inclination angles may be explained by the cross slip of bc + aN dislocations. Geometrically, pyramidal I bc + aN dislocations can cross slip onto another pyramidal I plane. For example, [−1 −1 2 − 3] dislocation can cross slip from (− 1 0 1 1) plane (first crystal in Fig. 1) to (0 −1 1 1) plane (third crystal in Fig. 1). The former produces 43° angle while the latter 62°. Depending on the likelihood and frequency of cross slip, the resultant slip trace angles can be any value between ±43° and ±62°. Comparing these measured values with the calculated angle-pair values in Fig. 1 provides further evidence for the activation of pyramidal I slip, which produce angle-pairs of: ±58° on the (0 −1 1 0) surface and ±0°, ±43°, ±62° on the (2 −1 −1 0) face.
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The coarse horizontal slip traces that occur on both faces are likely associated with basal slip. The compression samples were aligned in a way that basal and prismatic slips are restrained, but the CRSS of basal slip is extremely low (~ 0.5 MPa) [18,19] and slight misalignment or grip constraints could activate basal slip. In revisiting the work of Obara et al. [3], we note that they compressed b 0001 N oriented Mg single crystals, observed non-basal slip traces at an angle of 55° ± 5° on the (0 −1 1 0) surface, and interpreted this to be an indication of {1 1 −2 2} pyramidal II slip. However, close inspection of the geometry associated with the pyramidal I and pyramidal II planes is not consistent with Obara's conclusion; pyramidal II planes do intersect the (0 −1 1 0) face at angles of ±58° or ±39°, but as shown in Fig. 1, the Burger's vector is parallel to the face and does not create a slip step for the planes that intersect at ±58°. Thus, pyramidal II slip systems can only produce ± 39° slip traces on the (0 − 1 1 0) face. By contrast, pyramidal I slip would produce slip traces at ± 58° on this face. Thus the geometry outlined in Fig. 1 suggests that the slip traces presented in Obara's Fig. 2 [3] actually discount pyramidal II slip while leaving open the possibility of pyramidal I slip. The prevalence of pyramidal I slip could be attributed to it having a lower CRSS than pyramidal II slip. The Schmid factor for pyramidal II slip is 10% higher than for pyramidal I slip, but our experiment showed that pyramidal I slip is prevalent, which suggests that the CRSS of pyramidal I slip is lower than for pyramidal II. This interpretation is in good agreement with MD simulations; Tang et al. and Nogaret et al. reported that in their simulations bc + aN dislocations nucleated and multiplied on pyramidal I planes because the lattice friction pyramidal I glide is lower than for pyramidal II [13,20]. For all pyramidal I slip systems, the Schmid factor for c-axis loading is 0.40 and the measured yield strength of 135 MPa translates to a CRSS of 54 MPa, which is 108 times higher than the reported value for basal slip [18,19]. Taken
Fig. 3. Confocal micrographs of the (a) (0 -1 1 0) face and (b) (2 −1 −1 0) face of an undeformed Mg single crystal, (c) (0 -1 1 0) face and (d) (2 −1 −1 0) face of a 3% deformed Mg single crystal. The contrast from pyramidal slip traces is very weak and the images were purposely colored to enhance the contrast.
Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016
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friction, as suggested by MD simulations [13,20], or dislocation debris evidenced in TEM studies [5,6]. In either case, higher stresses are required to support non-basal glide, which leads to very high strain hardening rate and low strain-to-failure (Fig. 2). In conclusion, we identified {1 0 −1 1}b1 1 −2 3N pyramidal I slip as the dominant non-basal slip mode in the pure Mg single crystals compressed along the c-axis. This conclusion is at odds with the highly cited work of Obara et al. [3], but is supported by detailed slip trace analysis of the orthogonal (0 −1 1 0) and (2 −1 −1 0) surfaces and can be explained by the geometry associated with slip step formation. The CRSS for pyramidal I slip is 54 MPa. The diffuse pyramidal I slip traces, high strain rate hardening and low ductility point to limited activity of the bc + a N dislocations. These observations may be used as a benchmark for MD and discrete dislocation dynamics (DDD) simulations of Mg and help guide Mg alloying strategies to improve ductility.
Acknowledgments The authors would like to thank Drs. H.D. Fang, Y.Z. Tang, J. El-Awady and Miss. G. Valentino for extensive and fruitful discussions. This research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-20022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
Fig. 4. (a) High resolution 3-D surface profile of the (0 -1 1 0) face from a 3% deformed sample that contains some basal and pyramidal slip traces. Some slip traces are indicated by arrows. The line profiles across (b) pyramidal slip traces and (c) a basal slip trace.
altogether, these observations indicate that pyramidal I slip is the preferred non-basal deformation mode for accommodating c-axis compression in pure Mg single crystals. In addition to studying the slip trace angles, we also measured the relative height of the surface steps to provide insight on the heterogeneity of slip. A surface profile of pyramidal I and basal slip steps is shown in Fig. 4a. The pyramidal I slip traces are dense, but most of them are faint and many steps are too fine to be resolved. Drawing a line across the pyramidal I slip traces reveals steps on the order of 10 to 20 nm (Fig. 4b). This is much smaller than the ~100 nm steps produced by the unintentionally activated basal slips (Fig. 4c). We note that there are many finer pyramidal I slip traces that were visible in the confocal image but are beyond the resolution limit of the profilometry. These observations suggest that each b c + aN source generates very little plastic strain when activated, which is in contrast to the burst of activity that occurs when basal sources operate. The b c + a N glide may be limited by lattice
References [1] S.R. Agnew, Ö. Duygulu, Int. J. Plast. 21 (2005) 1161–1193. [2] S. Sandlöbes, S. Zaefferer, I. Schestakow, S. Yi, R. Gonzalez-Martinez, Acta Mater. 59 (2011) 429–439. [3] T. Obara, H. Yoshinga, S. Morozumi, Acta Metall. 21 (1973) 845–853. [4] C.M. Byer, B. Li, B. Cao, K. Ramesh, Scr. Mater. 62 (2010) 536–539. [5] B. Syed, J. Geng, R. Mishra, K. Kumar, Scr. Mater. 67 (2012) 700–703. [6] J. Geng, M.F. Chisholm, R. Mishra, K. Kumar, Philos. Mag. Lett. 94 (2014) 377–386. [7] J.F. Stohr, J.P. Poirier, Philos. Mag. 25 (1972) 1313–1329. [8] E. Lilleodden, Scr. Mater. 62 (2010) 532–535. [9] S. Agnew, J. Horton, M. Yoo, Metall. Mater. Trans. A 33 (2002) 851–858. [10] S. Agnew, M. Yoo, C. Tome, Acta Mater. 49 (2001) 4277–4289. [11] S. Sandlöbes, M. Friák, S. Zaefferer, A. Dick, S. Yi, D. Letzig, Z. Pei, L.-F. Zhu, J. Neugebauer, D. Raabe, Acta Mater. 60 (2012) 3011–3021. [12] T. Nogaret, W.A. Curtin, J.A. Yasi, L.G. Hector, D.R. Trinkle, Acta Mater. 58 (2010) 4332–4343. [13] Y. Tang, J.A. El-Awady, Acta Mater. 71 (2014) 319–332. [14] Y. Tang, J.A. El-Awady, Mater. Sci. Eng. A 618 (2014) 424–432. [15] M. Ghazisaeidi, L. Hector, W. Curtin, Scr. Mater. 75 (2014) 42–45. [16] S. Ando, T. Gotoh, H. Tonda, Metall. Mater. Trans. A 33 (2002) 823–829. [17] T.J. Balk, K.J. Hemker, L.P. Kubin, Scr. Mater. 56 (2007) 389–392. [18] H. Yoshinaga, R. Horiuchi, Trans. JIM 4 (1963) 1–8. [19] H. Yoshinaga, R. Horiuchï, Trans. Jpn. Inst. Metals 5 (1963) 14–21. [20] T. Nogaret, W. Curtin, J. Yasi, L. Hector, D. Trinkle, Acta Mater. 58 (2010) 4332–4343.
Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/smm
Pyramidal I slip in c-axis compressed Mg single crystals Kelvin Y. Xie, Zafir Alam, Alexander Caffee, Kevin J. Hemker ⁎ Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
a r t i c l e
i n f o
Article history: Received 17 August 2015 Received in revised form 7 September 2015 Accepted 8 September 2015 Available online xxxx Keywords: Magnesium Single crystal Plastic deformation Slip trace Pyramidal slip
a b s t r a c t Pyramidal I slip was observed to be the dominant slip mode in magnesium single crystals compressed quasistatically along c-axis at room temperature. The slip trace angles resulted from pyramidal I and pyramidal II slips projected on (0 − 1 1 0) and (2 − 1 − 1 0) surfaces were initially calculated, and then measured on 3% deformed magnesium single crystals. The measured angles indicate the prevalence of pyramidal I slip ({10–11}b11–23 N with the critical resolve shear stress of 54 MPa). The pyramidal slip traces are dense but very fine, suggesting limited b c + aN dislocation activities. © 2015 Published by Elsevier Ltd.
1. Introduction Magnesium (Mg) and its alloys have attracted considerable interest because it is nearly four times lighter than steel, but structural applications of Mg alloys are generally limited to cast components because of its limited formability. Ductility limitations are generally attributed to strong plastic anisotropy that results from its underlying hexagonal lattice [1]. Substantial reduction of this anisotropy has been achieved through rare earth alloying [2], but further development of wrought Mg alloys would benefit from an increased understanding of the mechanisms governing the interactions between various slip and twinning modalities. The critically resolved shear stress (CRSS) for slip on the closepacked basal plane is significantly lower than for the prismatic and pyramidal planes, but basal slip will not accommodate deformation along the c-axis and cannot, by itself, satisfy the Taylor criterion requiring five independent slip systems for the ductility of polycrystalline metals [3]. A number of investigators have performed c-axis compression experiments on single crystals to activate and study non-basal slip [3–8], and the general consensus that has immerged pointing to the importance of bc + a N dislocation slip. TEM studies [3–5,7] have shown that, although compression twins are occasionally observed, non-basal bc + aN dislocations with Burger vectors along b 11–23N are the primary carriers of plastic deformation during c-axis compression and that the interaction of bc + aN dislocations and formation of loops leads to very high strain hardening. Pure Mg sample generally fail after only a few percent deformation when compressed along c-axis; Mg–Li and ⁎ Corresponding author. E-mail address: [email protected] (K.J. Hemker).
Mg–Re alloy exhibit much improved ductility [9–11]. Although the cause is not known, increased activity of b c + a N pyramidal glide has been associated with increased ductility in Mg alloys [9–11]. The bc + aN dislocations lie in and can glide on either {1 0 −1 1} pyramidal I or {1 1 −2 2} pyramidal II slip planes. Detailed TEM tilting experiments can be used to determine slip planes but the easiest and most direct method for identifying active slip systems is to image slip traces on the adjacent faces of single-crystalline specimens. A general trend in the experimental literature for Mg has attributed c-axis deformation to the activation of pyramidal II glide, but closer inspection of individual studies indicate that many investigators have referenced the 1974 work of Obara et al. [3] in lieu of conducting additional slip trace analyses. This point deserves further attention because, as described below, the slip trace observations of Obara et al. [3] are not as straightforward as originally assumed. Moreover, these experimental studies have been paralleled by ab initio and molecular dynamics (MD) simulations, which have predicted various stable dislocation core configurations for bc + a N edge and screw dislocations and been used to estimate the relative mobility of these dislocations on pyramidal I and II glide planes [11–15]. Theoretical studies have the potential to provide atomic-scale insight of dislocation core structures and the kinetics of dislocation glide, but the MD predictions of bc + aN pyramidal glide in Mg have been variable and at times even contradictory. Differences in how the dislocations were created, the empirical potentials used, and applied stresses have resulted in various core configurations and observations of b c + aN glide on pyramidal I planes in some simulations [5,12] and on pyramidal II planes in others [16]. Tang et al. [13] have suggested that bc + aN dislocations are nucleated and glide on pyramidal I planes at relatively low stresses but can cross-slip to pyramidal II planes at much higher stresses. This could be
http://dx.doi.org/10.1016/j.scriptamat.2015.09.016 1359-6462/© 2015 Published by Elsevier Ltd.
Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016
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used to rationalize differences in the MD studies, but the importance of pyramidal I glide in this and other theoretical studies remains to be correlated with experimental observations of slip activities. The current study was undertaken to record slip traces on adjacent orthogonal faces of c-axis compressed single-crystalline Mg and to collect experimental data that can be compared and contrasted with the original slip trace measurements of Obara et al. [3]. Rectangular compression samples with dimensions 6 mm × 6.5 mm × 14 mm were electrical discharge machined (EDM) from 99.999% pure bulk [0 0 0 1] Mg single crystals (Metals Crystals and Oxides Ltd, UK). Laue diffraction confirmed that the compression axes of all specimens were aligned to within 1° of the c-axis of the crystals, thus suppressing basal and prismatic slip. The cross-section of the compression samples was cut with (0 −1 1 0) and (2 −1 −1 0) side faces. The EDM parameters were adjusted to low power, low water pressure and low feed rate in order to minimize deformation, and the cut surfaces were chemically polished using 10% nitric acid in water to remove the EDM recast layer. Quasistatic compression tests were conducted in an MTS machine at a strain rate of 10−4 s−1. Deformed samples were imaged immediately after the tests with a confocal microscope (Keyence 3D laser scanning microscope) that accentuated the presence of the slip traces. Fig. 1 provides a geometric summary of all twelve pyramidal I and six pyramidal II systems for an HCP Mg single crystal (a = 3.21 Å and c = 5.21 Å) loaded along the c-axis. The intersections of the various {1 0 − 1 1} and {1 1 − 2 2} planes with the (0 − 1 1 0) front and (2 − 1 − 1 0) side faces can be matched with observed slip traces to identify the active slip systems. Doing so is straightforward but it is important to note that not all slip systems will create a slip step on both faces. As illustrated in Fig. 1, four of the twelve pyramidal I and two of the six pyramidal II slip systems will not produce slip steps on the (0 −1 1 0) face because their Burgers vectors are parallel to that face. Considering all 18 slip systems and the slip traces that they would make on the (0 −1 1 0) and (2 −1 −1 0) faces yields the slip trace angles that are shown in Fig. 1. These values can be compared with experimental observations to determine the relative activity of pyramidal I and II slips. A total of four single-crystalline samples were compressed in this study (Fig. 2a). A typical true stress and strain curve (blue) and
Fig. 2. A typical engineering stress–strain curve and its strain hardening rate curve of Mg single crystal compressed along c-axis at room temperature.
corresponding true strain hardening rate curve (green) are plotted in Fig. 2b. The shape of the flow curves and the measured stress levels are similar to the observations reported by Obara et al. and Syed et al.:
Fig. 1. Summary of all the possible pyramidal slip systems and the corresponding slip traces that may be activated in single crystals Mg compressed along c-axis. Red arrows in the crystal unit cells indicate the Burger's vectors of bc + aN dislocations, colored planes indicate slip planes and bold black boxes highlight the (0 1 1 0) and (2 −1 −1 0) which the slip traces are projected on.
Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016
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no apparent yield point, high flow stress up to 300 MPa before failure and much higher strain hardening rates (~ 5–10 GPa) than pure FCC (e.g. ~ 1.5–2.5 GPa in Ir) and BCC single crystals [3,5,17]. The yield strength at 0.2% strain offset is estimated to be ~135 MPa, comparable to that reported by Syed et al. [5], and this value is used to estimate the critical resolved shear strength (CRSS) for pyramidal slip. All four compressed samples developed slip traces on both (0 −1 1 0) and (2 −1 −1 0) faces. The faces of undeformed samples are free of slip traces as expected (Fig. 3a & b). The speckles in these images are etch pits of pre-existing dislocations from the chemical polishing. After 3% deformation, a high density of inclined and smaller number of coarse horizontal slip traces were observed. Most inclined slip traces on the (0 −1 1 0) faces of all four samples were measured to be ±50° to ±55° to the basal planes (see for example Fig. 3c). This measurement is close to the calculated angle of ±58° for pyramidal I slip and quite different from the angle of ±39° that would be associated with pyramidal II slip. Only occasionally, evidence of slip traces aligned at ±39° on the (0 − 1 1 0) face was observed. The (2 − 1 − 1 0) faces of all four deformed single crystals were also imaged and numerous slip trace angles ranging from ±45° to ±60° were observed (see for example Fig. 3d). This range of inclination angles may be explained by the cross slip of bc + aN dislocations. Geometrically, pyramidal I bc + aN dislocations can cross slip onto another pyramidal I plane. For example, [−1 −1 2 − 3] dislocation can cross slip from (− 1 0 1 1) plane (first crystal in Fig. 1) to (0 −1 1 1) plane (third crystal in Fig. 1). The former produces 43° angle while the latter 62°. Depending on the likelihood and frequency of cross slip, the resultant slip trace angles can be any value between ±43° and ±62°. Comparing these measured values with the calculated angle-pair values in Fig. 1 provides further evidence for the activation of pyramidal I slip, which produce angle-pairs of: ±58° on the (0 −1 1 0) surface and ±0°, ±43°, ±62° on the (2 −1 −1 0) face.
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The coarse horizontal slip traces that occur on both faces are likely associated with basal slip. The compression samples were aligned in a way that basal and prismatic slips are restrained, but the CRSS of basal slip is extremely low (~ 0.5 MPa) [18,19] and slight misalignment or grip constraints could activate basal slip. In revisiting the work of Obara et al. [3], we note that they compressed b 0001 N oriented Mg single crystals, observed non-basal slip traces at an angle of 55° ± 5° on the (0 −1 1 0) surface, and interpreted this to be an indication of {1 1 −2 2} pyramidal II slip. However, close inspection of the geometry associated with the pyramidal I and pyramidal II planes is not consistent with Obara's conclusion; pyramidal II planes do intersect the (0 −1 1 0) face at angles of ±58° or ±39°, but as shown in Fig. 1, the Burger's vector is parallel to the face and does not create a slip step for the planes that intersect at ±58°. Thus, pyramidal II slip systems can only produce ± 39° slip traces on the (0 − 1 1 0) face. By contrast, pyramidal I slip would produce slip traces at ± 58° on this face. Thus the geometry outlined in Fig. 1 suggests that the slip traces presented in Obara's Fig. 2 [3] actually discount pyramidal II slip while leaving open the possibility of pyramidal I slip. The prevalence of pyramidal I slip could be attributed to it having a lower CRSS than pyramidal II slip. The Schmid factor for pyramidal II slip is 10% higher than for pyramidal I slip, but our experiment showed that pyramidal I slip is prevalent, which suggests that the CRSS of pyramidal I slip is lower than for pyramidal II. This interpretation is in good agreement with MD simulations; Tang et al. and Nogaret et al. reported that in their simulations bc + aN dislocations nucleated and multiplied on pyramidal I planes because the lattice friction pyramidal I glide is lower than for pyramidal II [13,20]. For all pyramidal I slip systems, the Schmid factor for c-axis loading is 0.40 and the measured yield strength of 135 MPa translates to a CRSS of 54 MPa, which is 108 times higher than the reported value for basal slip [18,19]. Taken
Fig. 3. Confocal micrographs of the (a) (0 -1 1 0) face and (b) (2 −1 −1 0) face of an undeformed Mg single crystal, (c) (0 -1 1 0) face and (d) (2 −1 −1 0) face of a 3% deformed Mg single crystal. The contrast from pyramidal slip traces is very weak and the images were purposely colored to enhance the contrast.
Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016
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friction, as suggested by MD simulations [13,20], or dislocation debris evidenced in TEM studies [5,6]. In either case, higher stresses are required to support non-basal glide, which leads to very high strain hardening rate and low strain-to-failure (Fig. 2). In conclusion, we identified {1 0 −1 1}b1 1 −2 3N pyramidal I slip as the dominant non-basal slip mode in the pure Mg single crystals compressed along the c-axis. This conclusion is at odds with the highly cited work of Obara et al. [3], but is supported by detailed slip trace analysis of the orthogonal (0 −1 1 0) and (2 −1 −1 0) surfaces and can be explained by the geometry associated with slip step formation. The CRSS for pyramidal I slip is 54 MPa. The diffuse pyramidal I slip traces, high strain rate hardening and low ductility point to limited activity of the bc + a N dislocations. These observations may be used as a benchmark for MD and discrete dislocation dynamics (DDD) simulations of Mg and help guide Mg alloying strategies to improve ductility.
Acknowledgments The authors would like to thank Drs. H.D. Fang, Y.Z. Tang, J. El-Awady and Miss. G. Valentino for extensive and fruitful discussions. This research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-20022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
Fig. 4. (a) High resolution 3-D surface profile of the (0 -1 1 0) face from a 3% deformed sample that contains some basal and pyramidal slip traces. Some slip traces are indicated by arrows. The line profiles across (b) pyramidal slip traces and (c) a basal slip trace.
altogether, these observations indicate that pyramidal I slip is the preferred non-basal deformation mode for accommodating c-axis compression in pure Mg single crystals. In addition to studying the slip trace angles, we also measured the relative height of the surface steps to provide insight on the heterogeneity of slip. A surface profile of pyramidal I and basal slip steps is shown in Fig. 4a. The pyramidal I slip traces are dense, but most of them are faint and many steps are too fine to be resolved. Drawing a line across the pyramidal I slip traces reveals steps on the order of 10 to 20 nm (Fig. 4b). This is much smaller than the ~100 nm steps produced by the unintentionally activated basal slips (Fig. 4c). We note that there are many finer pyramidal I slip traces that were visible in the confocal image but are beyond the resolution limit of the profilometry. These observations suggest that each b c + aN source generates very little plastic strain when activated, which is in contrast to the burst of activity that occurs when basal sources operate. The b c + a N glide may be limited by lattice
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Please cite this article as: K.Y. Xie, et al., Pyramidal I slip in c-axis compressed Mg single crystals, Scripta Materialia (2015), http://dx.doi.org/ 10.1016/j.scriptamat.2015.09.016