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Plastic deformation behavior of AZ31 magnesium alloy under multiple passes cross compression
Materials Science and Engineering A 532 (2012) 50–57
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Plastic deformation behavior of AZ31 magnesium alloy under multiple passes cross compression Yunchang Xin a,∗ , Jia Jiang b , Adrien Chapuis a , Maoyin Wang a , Qing Liu a a b
School of Materials Science and Engineering, Chongqing University, Chongqing 400030, China Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 10 June 2011 Received in revised form 10 October 2011 Accepted 15 October 2011 Available online 24 October 2011 Keywords: Magnesium alloys Texture Twinning Plane strain compression Plastic deformation behavior
a b s t r a c t Plastic deformation behavior of hot-rolled AZ31 Mg alloy under 6 passes plane strain compression along transverse direction (TD) and normal direction (ND) alternatively is systematically study in current paper. With 10% compression along TD, most grains are nearly twinned totally and extension twinning takes place during subsequent compression along ND. Yield stress rises with increased compression passes due to enhanced activation stress for extension twinning by dislocations generated in previous pass of compression. Preferred distribution of prismatic planes appears after each pass of compression besides of the rotation of basal plane poles toward compression axis, which is closely related with extension twinning. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Basal slip and {1 0 1¯ 2} extension twinning dominate the initial plastic deformation of Mg alloys at room temperature. However, basal slip can only provide two independent slip systems [1–6]. Non basal slips including prismatic slips of a dislocations and pyramidal slips of c+a dislocations cannot be initiated extensively at room temperature in coarse grained magnesium alloys due to their quite high critical resolved shear stress (CRSS) [6,7]. The main functions of twinning mainly involve the following aspects. First, twinning can reorient the grains and influence subsequent slips. {1 0 1¯ 2} extension twinning and {1 0 1¯ 1} contraction twinning can rotate the basal plane by 86◦ and 56◦ respectively [8,9]. Second, twin boundaries can serve as barrier to dislocation sliding leading to enhanced strain hardening performance [10]. In addition, twinning can refine the microstructure by subdivision of grains [11]. Increasing evidences are demonstrating that slips and twins generated by pre-loading greatly affect deformation behavior of strain path changed reloading. It has been reported that initial slips generated by pre-straining can increase the activation stress for twinning nucleation during strain path changed reloading leading to enhanced yield stress [10,12]. Recently, many publications report detwinning in which initial twins generated by pre-compression narrow or disappear during reverse tension [13–15]. Detwinning
∗ Corresponding author. Tel.: +86 23 65106407; fax: +86 23 65106407. E-mail address: [email protected] (Y. Xin). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.10.061
leads to reorientation of grains and obvious drop in yield stress compared to that in monotonic tension. Detwinning (also named untwinning) is also widely reported and studied in fatigue tests of textured Mg alloys under cyclic loading [16–18]. In fact, the influence of pre-strains on deformation of reloading involves the interaction of initial dislocation and/or twins with deformation modes in reloading. An insight understanding of pre-straining on subsequent deformation will benefit the applications of prestraining to tailor deformation of magnesium alloys. In [19], extension twinning by pre-compression along TD of hot-rolled AZ31 Mg alloy sheet is employed to vary the strong basal texture and enhanced rolling capability is obtained in subsequent rolling. Rolled Mg alloys generally have strong basal texture and extension twinning is dominated during plane strain compression along rolling direction (RD) or TD [2,3]. With increased strain, extension twins grow up quickly. It is found that most grains are nearly twinned totally below a strain of 10% [3]. In addition, slips also start and accommodate plastic deformation when the strain exceeds certain level [5]. High volume fraction of twins together with dislocations generated during pre-straining will definitely affect deformation behavior during multi-passes strain path changed reloading. However, systematical and relevant publications are rare at present. In current paper, plastic deformation behavior of hot-rolled AZ31 magnesium alloy subjected 6 passes plane strain compression along TD and ND alternately is systematically studied. The mechanical response and microstructure evolution are fully investigated. The corresponding plastic deformation mechanisms during
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(EBSD) on a FEI Nova 400 scanning electron microscope equipped with an HKL-EBSD system. A step size of 0.5 m was used. The samples for EBSD measurement were cut from central part of compressed samples and ground using waterproof diamond paper followed by electrochemical polishing in AC2 electrolyte. The orientation and the texture were analyzed using Chanel 5. 3. Results 3.1. Mechanical response As a comparison, strain–stress curves of samples only subjected monotonic compression along TD and ND respectively were also obtained and given in Fig. 2a. Under compression along TD, the strain–stress curve contains a typical yield plateau, typical feature of extension twinning [3,5]. The yield stress (about 74 MPa) of compression along TD is much lower than that of compression along ND (about 155 MPa). Such mechanical anisotropy is extensively reported in current publications [3,5,14,16]. Fig. 2b presents the strain–stress curves of sample suffered from multiple passes compression along TD and ND alternately. Yield plateau is observed in all curves. As indicated in Table 2, the yield stress rises from 74 MPa in pass 1 to 130 MPa in pass 6. The yield stress increases quickly with increased compression passes initially, while does not vary obviously since pass 5. 3.2. Microstructure evolution Fig. 1. EBSD micrographs of the as-used materials: (a) crystallographic orientation map; (b) pole figures. Inverse pole figure represents ND of the sheet.
multiple passes of compression are also discussed. This study contributes to deeper understanding in plastic deformation mechanisms of Mg alloys under strain path changed reloading and benefits the usage of extension twinning to tailor the deformation behavior of Mg alloys. 2. Experimental 2.1. Sample preparation Hot rolled AZ31 Mg alloy sheet with a thickness of 30 mm was used. Microstructure and texture of the as-used alloy were given in Fig. 1. The as-used material had a mean grain size of about 16 m (Fig. 1a) and a strong basal texture (Fig. 1b). No obvious preferred distribution of prismatic planes was noted. The as-received material was cut into blocks with a dimension of 10 mm (ND) × 9 mm (TD) × 7 mm (RD). Here, RD, TD and ND referred to the rolling direction, transverse direction and normal direction of the as-used sheet, respectively. 2.2. Plane strain compression Plane strain compression was carried out in a channel die device at room temperature using a strain rate of 10−2 s−1 . The as-polished samples were subjected 6 passes compression along TD and ND alternately with a strain of 0.1 per pass. The first pass of compression was performed along TD. Six types of samples were obtained finally. The name and corresponding deformation experience of the six samples were given in Table 1. 2.3. Microstructure characterization Microstructure of the as-received material and the as-deformed samples was studied using electron back scattered diffraction
Fig. 3 shows crystallographic orientation maps of P-1 and P2 samples. As seen in Fig. 3a, large amount of {1 0 1¯ 2} extension twin boundary is present in P-1 sample, while {1 0 1¯ 1} contraction twin boundary and {1 0 1¯ 1}–{1 0 1¯ 2} double twin boundary are nearly absent. In addition, high content of {1 0 1¯ 2}–{0 1 1¯ 2} boundary which forms due to the coalescence of different {1 0 1¯ 2} extension twinning variants is also seen in Fig. 3a. As seen in Fig. 3b, basal plane poles of most grains are nearly perpendicular to ND. The rotation of basal plane poles from ND to orientation perpendicular to ND is extensively reported to be induced by extension twinning that can rotate the basal plane by 86◦ . Therefore, it can be inferred that most grains are nearly twinned totally. Many thin lamellas with basal plane poles nearly parallel to ND are also noted. It can be inferred that these thin lamellas are the untwined matrix. {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary are also dominated in sample subjected compression along ND in pass 2, while the amount of boundary is much lower than that in previous pass of compression. The basal plane poles of most grains are nearly close to compression axis of pass 2, ND. Crystallographic orientation maps of P-3 and P-4 samples are given in Fig. 4. Similar to that of P-1 sample, only {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary appear in P-3 sample and basal plane poles of most grains are nearly perpendicular to ND again. After compression of pass 4, {1 0 1¯ 2} boundary is dominated, while the basal plane poles of most grains are close to ND. The twin boundaries in P-5 and P-6 samples (see Fig. 5) are similar to that of P-3. The orientation of grains is nearly perpendicular to ND after compression of pass 5 and rotates to ND again after compression in pass 6. As the content of twin boundaries varies greatly during the 6 passes compression, a quantitative measurement of both {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary is carried out to disclose detailed changes and the results are listed in Table 3. P-1 sample contains high amount of both {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary. The fraction of {1 0 1¯ 2}–{0 1 1¯ 2} boundary is more than half of the total boundaries. In subsequent passes of compression, the amount of the total twin boundaries drops greatly
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Y. Xin et al. / Materials Science and Engineering A 532 (2012) 50–57
Table 1 Definition of samples and their deformation experiences. Sample P-1 P-2 P-3 P-4 P-5 P-6
Pass 1 TD/ε = 0.1 √ √ √ √ √ √
Pass 2 ND/ε = 0.1
Pass 3 TD/ε = 0.1
Pass 4 ND/ε = 0.1
Pass 5 TD/ε = 0.1
Pass 6 ND/ε = 0.1
√ √ √ √ √
√ √ √ √
√ √ √
√ √
√
Table 2 Yield stress of sample in each pass of plane strain compression along TD and ND alternately.
Yield stress (MPa)
Pass 1
Pass 2
Pass 3
Pass 4
Pass 5
Pass 6
74
90
114
122
129
130
Table 3 Length of {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary in deformed samples with the same detected area. Boundaries length (mm)
P1
P2
P3
P4
P5
P6
{1 0 1¯ 2}–{0 1 1¯ 2} {1 0 1¯ 2} Total Fraction of {1 0 1¯ 2}–{0 1 1¯ 2}
17.81 16.01 33.82 53%
0.79 5.40 6.19 13%
2.88 11.54 14.42 20%
1.18 6.14 7.32 16%
1.89 6.65 8.54 22%
1.56 5.91 7.47 21%
and nearly keeps stable from pass 4. It is also noted that the fraction of {1 0 1¯ 2}–{0 1 1¯ 2} boundary in total boundaries drops greatly in pass 2 and does not change obviously with increased compression passes. Texture evolution of samples suffered from different passes of compression is given in Fig. 6. The as-received material has a strong basal texture with basal plane poles of most grains nearly parallel to ND. No preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} planes appears. After the first pass of compression along TD, basal plane poles of most grains rotate to TD. {1 0 1¯ 0} and {1 1 2¯ 0} planes both shows preferred distribution. (0 0 0 2) plane poles rotate to ND again with the presence of preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} planes after compression along ND in pass 2. It can be seen that the basal plane poles of most grains are nearly parallel to the compression axis with preferred distribution of prismatic planes after each pass of compression. 4. Discussion 4.1. Effect of initial strain on mechanical response of reloading Publications have confirmed that basal slip and {1 0 1¯ 2} extension twinning dominate initial plastic deformation of Mg alloys at room temperature. Certain amount of non-basal slips is also sus-
pected to take place at the vicinity of grains boundaries due to perturbations in local stress state by intergranular strain incompatibilities [6]. Compressed along ND of Mg alloy with basal texture, basal slip is the main mode to accommodate initial plastic strain followed by the presence of contraction twinning and double twinning. Basal slip has much lower schmid factor under compression along ND, which usually results in quite high yield stress. Twinning in magnesium alloys is polar in nature [4]. For Mg alloys with c/a ratio of about 1.623, extension twinning generally occurs under compression load perpendicular to c-axis or tensile load along caxis. Therefore, {1 0 1¯ 2} extension twinning is the main mode to accommodate initial plastic deformation under compression along TD of basal textured Mg alloy. The quite low CRSS of {1 0 1¯ 2} extension twinning (about 2–3 MPa) usually leads to quite low yield stress [6]. Some studies have reported that for basal textured AZ31 Mg alloy with pre-compression along TD, detwinning generally takes place during re-compression along ND. Detwinning does not need nucleation and the activation stress is much lower than that of extension twinning nucleation [10]. Thus, in current study, if detwinning takes place during compression along ND in pass 2, the yield stress should be lower than that in pass 1. However, in present study, the yield stress in pass 2 (about 90 MPa) is much higher than that in pass 1 (about 74 MPa). Therefore, the yield in pass 2 should not result from detwinning. In current experiment, most grains are
Fig. 2. Plane strain compression curves of samples: (a) samples subjected monotonic compression along TD and ND; (b) sample suffering from 6 passes compression along TD and ND alternately.
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Fig. 3. Crystallographic orientation maps of samples after cross plain strain compression along TD and ND alternately: (a) and (b) P-1 sample; (c) and (d) P-2 sample. Inverse pole figure represents ND direction.
nearly twinned totally after 10% compression along TD in pass 1. For these big twins, their orientations are also favorite for extension twinning again under compression load along ND. It is noted that the strain–stress curve also has yield plateau, typical feature of extension twinning. Therefore, it is suspected that the yield in pass 2 manly stems from extension twinning in these large extension twins. As the strain stress curves of pass 3, pass 4, pass 5 and pass 6 all show typical feature of extension twinning with increased yield stress in subsequent compression pass, the yield plateaus in these compression passes are considered to result from extension twinning, too. In [14], it is found that reloading along ND of hot-rolled Mg alloy with 5% pre-compression along TD definitely result in detwinning which is characterized by much lower yield stress than that of twinning in previous loading. Here, the deformation mode during reloading along ND probably involves a competition between extension twinning and detwinning in extension twins generated by pre-straining. We considered that such a competition is closely related with the size of extension twins generated in precompression. Study has verified that activation stress for extension twinning nucleation increases greatly with the drop in grain size [20]. A lower strain of pre-compression generally induces very thin extension twins in which the activation stress of extension twinning again is quite high and detwinning tends to occur preferentially during recompression along ND. However, with increased strain, extension twins grow up very fast after nucleation [4]. Most grains are nearly twinned totally after 10% compression in current study. In big extension twins or grains nearly twinned totally,
the activation stress for extension twinning drops greatly compared to that in thin twin lamellas and extension twinning probably become popular during reloading along ND. Therefore, the size of the extension twins is probably a critical parameter influencing the competition between detwinning and extension twinning in extension twins generated by pre-straining. Another issue is that why the yield stress increases with increased compression passes. Although, extension twinning is dominated during compression along TD in pass 1, slips inevitably occur when the strain exceeds certain level. Theoretical calculations demonstrate that the totally twinned structure can only generate a maximum strain of 0.065 along c-axis [7]. In current experiment, the plastic strain is about 0.08 in each compress pass. Therefore, slips also take part in the plastic deformation. We also get the evidence for dislocation sliding from microstructure of the deformed samples. In EBSD map, the dislocation in deformed materials generally appears as low angle boundary (LAB) [21]. The densities of LAB in the six deformed samples are measured and listed in Table 4. Obviously, the LAB density rises with increased passes. Previous study has demonstrated that the dislocation stored in deformed Mg alloys can enhance the activation stress for twinning nucleation, which will increase yield stress in twinning dominated deformation. Therefore, the rise of yield stress with compression passes probably results from gradually increased dislocation density. In addition, our results seem to indicate that the increasing of dislocation density does not obviously enhance the activation stress for extension twinning further when LAB density exceeds 0.196 m−1 . Some studies also find that that dislocation
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Fig. 4. Crystallographic orientation maps of samples after cross plain strain compression along TD and ND alternately: (a) and (b) P-3 sample; (c) and (d) P-4 sample. Inverse pole figure represents ND direction.
multiplication affects the twinning nucleation stress, but has little or on activation stress of detwinning [10,12]. This further confirms that the yield in each passes of recompression is due to extension twinning again in extension twins. Activation stress for twinning drops with decreased grain size. Therefore, the refinement of grains by extension twinning may also contribute to enhancement in yield stress of reloading. 4.2. Effect of initial strain on microstructure evolution in reloading Compressed along TD in pass 1, the grains are in favorite orientation for {1 0 1¯ 2} extension twinning. In fact, under compression load, nucleation and growth of {1 0 1¯ 2} extension twins are very fast. It is reported that, in hot-rolled AZ31 Mg alloy sheet under compression along RD, most twins nucleate below a strain of 2% and grow up to a strain of 6%. When strain exceeds 6%, the coalescence of growing twins appears and the materials are nearly twinned totally under strain of 8% [3]. In current study, at a compression strain of 10% in pass 1, the volume fraction of twinning reaches about 91%. As-discussed previously, extension twinning also dominates the deformation in subsequent recompressions. The nucleation and growth of extension twinning are also very fast and high volume
fraction of extension twinning can be seen in deformed samples after each compression pass. The presence of {1 0 1¯ 2}–{1 0 1¯ 2} boundary is closely related with the occurrence of different {1 0 1¯ 2} extension twinning variants in one grain. Three are three pair or 6 variants in Mg with hcp structure. The coalescence of different variants leads to the presence of {1 0 1¯ 2}–{1 0 1¯ 2} boundaries. Generally, there are three types of such boundary, (1 0 1¯ 2)–(1¯ 0 1 2), (1 0 1¯ 2)–(0 1 1¯ 2)/(1 1¯ 0 2) and (1 0 1¯ 2)–(0 1¯ 1 2)/(1¯ 1 0 2), with misorientation angle of 7.4◦ , 60◦ and 60.4◦ respectively. The selection of activated variants is thought to be closely related with their schmid factors (SF) [3,22,23]. Generally, the variant with the highest SF tends to occur preferentially. Thus, in samples under compression deformation, most grains generally contain only one type of variant [3]. Some studies also found that more than one types of variants may appear in some grains [3,23]. In [23], it is reported that more than 20% of twinned volume is provided by the second twinning variant. For sample with basal texture, while random distribution of prismatic plane, two types of variants in one grain may both have the same and the highest SF. Fig. 7 gives the calculation of SF for the three types of {1 0 1¯ 2} extension twinning variants under compression along TD. The calculation is under the assumption that the material has an ideal basal texture while random distribution
Table 4 The length of LAB per area in deformed samples.
Length of LAB per-area (m−1 )
P1
P2
P3
P4
P5
P6
0.137
0.140
0.176
0.196
0.20
0.235
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Fig. 5. Crystallographic orientation maps of samples after cross plain strain compression along TD and ND alternately: (a) and (b) P-5 sample; (c) and (d) P-6 sample. Inverse pole figure represents ND direction.
Fig. 6. Pole figures of samples subjected cross plain strain compression along TD and ND alternatively: (a) P-1 sample; (b) P-2 sample; (c) P-3 sample; (d) P-4 sample; (e) P-5 sample; (f) P-6 sample.
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Y. Xin et al. / Materials Science and Engineering A 532 (2012) 50–57
Preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} appears, too. Some previous studies also report the presence of preferred distribution of prismatic plane during extension twinning dominated deformation of Mg alloys [9]. During plastic deformation, prismatic slip of a dislocation contributes to preferred distribution of prismatic planes [24]. However, in current study, {1 0 1¯ 2} extension twinning is dominated and prismatic slips cannot be initiated extensively at room temperature. In fact, it is found that {1 0 1¯ 2} extension twinning also benefits formation of preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} planes [24]. As the basal plane of as-used materials is nearly parallel to each other and {1 0 1¯ 2} twinning rotates the basal plane by 86◦ toward compression axis along 1 0 1¯ 0. Therefore, one plane of {1 0 1¯ 0} in twinned regions is nearly parallel to each other [24]. After compression of pass 1, most grains are nearly twined totally and both the basal plane and one plane in {1 0 1¯ 0} in twinned regions are nearly parallel to each other, which definitely results in preferred distribution of (1 0 1¯ 0) plane as well as (1 1 2¯ 0) plane. 5. Conclusion In current paper, plastic deformation behavior of AZ31 Mg alloy under 6 passes plane strain compression along TD and ND alternatively are systematically investigated. The mechanical response and microstructure evolution are analyzed and the corresponding deformation mechanisms are discussed, too. The conclusions are reached as below:
Fig. 7. Schmid factor calculation of the three {1 0 1¯ 2} extension twinning variants in grains with different orientations (T1, T2 and T3 represent the three types of variants, respectively): (a) and (b); {1 0 1¯ 2}–{1 0 1¯ 2} boundary in P-1 sample: (c).
of prismatic plane. As seen in Fig. 7a, in the grain with (1 1 2¯ 0) perpendicular to TD, variant T1 and variant T2 have the same and also the highest SF and may take place at the same time. In [23], the author thought that the modified local stress by twinning strain (either from twinning in the same grain, or from neighbouring grains) is probably a reason for presence of different variants in one grain. In fact, it is reported in some publications that, during compression of textured magnesium alloy, the fraction of grains containing two or three variants is not very high, especially that of grains with three variants [23]. In current study, the strain in one pass is nearly 10% and many variants grow up and coalesce with each other, which results in high content of {1 0 1¯ 2}–{1 0 1¯ 2} boundary in compressed samples. Fig. 7c shows the three types of {1 0 1¯ 2}–{1 0 1¯ 2} boundary by lines with different colors. The green lines come from coalescence of variants from one pair, while the blue lines and purple lines originate from coalescence of variants from different pairs. Obviously, certain amount of green lines and purple lines is observed, while the blue lines are nearly absent. The inclusion of many purple lines indicates the presence of two types of variants in one grain. After compression of pass 1, preferred distribution of prismatic planes appears with [10] nearly parallel to ND. Most grains have orientation similar to that of grain in Fig. 7b. T2 variant has the highest SF and is the most popular one during compression along ND, which will reduce the chances for presence of different types of variants in one grain. Therefore, the amount of {1 0 1¯ 2}–{1 0 1¯ 2} boundary decreases after compression of pass 1. It is well known that {1 0 1¯ 2} extension twinning will reorient the basal plane by 86◦ . Therefore, basal pale poles nearly rotate to compression axis during each compression pass.
(1) The yield stress of sample enhances with increased compression passes, from 74 MPa in pass 1 to 130 MPa in pass 6. (2) With a 10% compression along TD, the grains are nearly twinned totally and extension twinning, not detwinning, takes place during recompression along ND. (3) Preferred distribution of (1 0 1¯ 0) and (1 1 2¯ 0) plane appears during each compression pass besides of the rotation of basal plane poles toward compression axis. Acknowledgements This project is supported by Fundamental Research Funds for the Central Universities (CDJZR11 13 00 01). Here I also want to give much thanks to Julian Driver in Ecole Nationale Superieure des Mines de Saint-Etienne who provides the channel die device for current study. References [1] H. Yan, S.W. Xu, R.S. Chen, S. Kamado, T. Honma, E.H. Han, Scr. Mater. 64 (2011) 141–144. [2] T. Al-Samman, X. Li, S.G. Chowdhury, Mater. Sci. Eng. A 527 (2010) 3450–3463. [3] S.G. Hong, S.H. Park, C.S. Lee, Acta Mater. 58 (2010) 5873–5885. [4] M.R. Barnett, Mater. Sci. Eng. A 464 (2007) 1–7. [5] S.R. Agnew, Ö. Duygulu, Int. J. Plast. 21 (2005) 1161–1193. [6] J. Koike, Mater. Trans. A 36A (2005) 1689–1695. [7] Q. Liu, Acta Metall. Sin. 46 (2010) 1458–1472. [8] P. Yang, Y. Yu, L. Chen, W. Mao, Scr. Mater. 50 (2004) 1163–1168. [9] M. Knezevic, A. Levinson, R. Harris, R.K. Mishra, R.D. Doherty, S.R. Kalidind, Acta Mater. 58 (2010) 6230–6242. [10] X.Y. Lou, M. Li, R.K. Boger, S.R. Agnew, R.H. Wagoner, Int. J. Plast. 23 (2007) 44–86. [11] H.Q. Sun, Y.N. Shi, M.X. Zhang, K. Lu, Acta Mater. 55 (2007) 975–982. [12] A. Jain, S.R. Agnew, Magnesium Technol. (2006) 219. [13] Y.N. Wang, J.C. Huang, Acta Mater. 55 (2007) 897–905. [14] G. Proust, C.N. Tomé, A. Jain, S.R. Agnew, Int. J. Plast. 25 (2009) 861–880. [15] L. Wu, A. Jain, D.W. Brown, G.M. Stoica, S.R. Agnew, B. Clausen, D.E. Fielden, P.K. Liaw, Acta Mater. 56 (2008) 688–695. [16] S. Kleiner, P.J. Uggowitzer, Mater. Sci. Eng. A 379 (2004) 258–263.
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Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Plastic deformation behavior of AZ31 magnesium alloy under multiple passes cross compression Yunchang Xin a,∗ , Jia Jiang b , Adrien Chapuis a , Maoyin Wang a , Qing Liu a a b
School of Materials Science and Engineering, Chongqing University, Chongqing 400030, China Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 10 June 2011 Received in revised form 10 October 2011 Accepted 15 October 2011 Available online 24 October 2011 Keywords: Magnesium alloys Texture Twinning Plane strain compression Plastic deformation behavior
a b s t r a c t Plastic deformation behavior of hot-rolled AZ31 Mg alloy under 6 passes plane strain compression along transverse direction (TD) and normal direction (ND) alternatively is systematically study in current paper. With 10% compression along TD, most grains are nearly twinned totally and extension twinning takes place during subsequent compression along ND. Yield stress rises with increased compression passes due to enhanced activation stress for extension twinning by dislocations generated in previous pass of compression. Preferred distribution of prismatic planes appears after each pass of compression besides of the rotation of basal plane poles toward compression axis, which is closely related with extension twinning. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Basal slip and {1 0 1¯ 2} extension twinning dominate the initial plastic deformation of Mg alloys at room temperature. However, basal slip can only provide two independent slip systems [1–6]. Non basal slips including prismatic slips of a dislocations and pyramidal slips of c+a dislocations cannot be initiated extensively at room temperature in coarse grained magnesium alloys due to their quite high critical resolved shear stress (CRSS) [6,7]. The main functions of twinning mainly involve the following aspects. First, twinning can reorient the grains and influence subsequent slips. {1 0 1¯ 2} extension twinning and {1 0 1¯ 1} contraction twinning can rotate the basal plane by 86◦ and 56◦ respectively [8,9]. Second, twin boundaries can serve as barrier to dislocation sliding leading to enhanced strain hardening performance [10]. In addition, twinning can refine the microstructure by subdivision of grains [11]. Increasing evidences are demonstrating that slips and twins generated by pre-loading greatly affect deformation behavior of strain path changed reloading. It has been reported that initial slips generated by pre-straining can increase the activation stress for twinning nucleation during strain path changed reloading leading to enhanced yield stress [10,12]. Recently, many publications report detwinning in which initial twins generated by pre-compression narrow or disappear during reverse tension [13–15]. Detwinning
∗ Corresponding author. Tel.: +86 23 65106407; fax: +86 23 65106407. E-mail address: [email protected] (Y. Xin). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.10.061
leads to reorientation of grains and obvious drop in yield stress compared to that in monotonic tension. Detwinning (also named untwinning) is also widely reported and studied in fatigue tests of textured Mg alloys under cyclic loading [16–18]. In fact, the influence of pre-strains on deformation of reloading involves the interaction of initial dislocation and/or twins with deformation modes in reloading. An insight understanding of pre-straining on subsequent deformation will benefit the applications of prestraining to tailor deformation of magnesium alloys. In [19], extension twinning by pre-compression along TD of hot-rolled AZ31 Mg alloy sheet is employed to vary the strong basal texture and enhanced rolling capability is obtained in subsequent rolling. Rolled Mg alloys generally have strong basal texture and extension twinning is dominated during plane strain compression along rolling direction (RD) or TD [2,3]. With increased strain, extension twins grow up quickly. It is found that most grains are nearly twinned totally below a strain of 10% [3]. In addition, slips also start and accommodate plastic deformation when the strain exceeds certain level [5]. High volume fraction of twins together with dislocations generated during pre-straining will definitely affect deformation behavior during multi-passes strain path changed reloading. However, systematical and relevant publications are rare at present. In current paper, plastic deformation behavior of hot-rolled AZ31 magnesium alloy subjected 6 passes plane strain compression along TD and ND alternately is systematically studied. The mechanical response and microstructure evolution are fully investigated. The corresponding plastic deformation mechanisms during
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(EBSD) on a FEI Nova 400 scanning electron microscope equipped with an HKL-EBSD system. A step size of 0.5 m was used. The samples for EBSD measurement were cut from central part of compressed samples and ground using waterproof diamond paper followed by electrochemical polishing in AC2 electrolyte. The orientation and the texture were analyzed using Chanel 5. 3. Results 3.1. Mechanical response As a comparison, strain–stress curves of samples only subjected monotonic compression along TD and ND respectively were also obtained and given in Fig. 2a. Under compression along TD, the strain–stress curve contains a typical yield plateau, typical feature of extension twinning [3,5]. The yield stress (about 74 MPa) of compression along TD is much lower than that of compression along ND (about 155 MPa). Such mechanical anisotropy is extensively reported in current publications [3,5,14,16]. Fig. 2b presents the strain–stress curves of sample suffered from multiple passes compression along TD and ND alternately. Yield plateau is observed in all curves. As indicated in Table 2, the yield stress rises from 74 MPa in pass 1 to 130 MPa in pass 6. The yield stress increases quickly with increased compression passes initially, while does not vary obviously since pass 5. 3.2. Microstructure evolution Fig. 1. EBSD micrographs of the as-used materials: (a) crystallographic orientation map; (b) pole figures. Inverse pole figure represents ND of the sheet.
multiple passes of compression are also discussed. This study contributes to deeper understanding in plastic deformation mechanisms of Mg alloys under strain path changed reloading and benefits the usage of extension twinning to tailor the deformation behavior of Mg alloys. 2. Experimental 2.1. Sample preparation Hot rolled AZ31 Mg alloy sheet with a thickness of 30 mm was used. Microstructure and texture of the as-used alloy were given in Fig. 1. The as-used material had a mean grain size of about 16 m (Fig. 1a) and a strong basal texture (Fig. 1b). No obvious preferred distribution of prismatic planes was noted. The as-received material was cut into blocks with a dimension of 10 mm (ND) × 9 mm (TD) × 7 mm (RD). Here, RD, TD and ND referred to the rolling direction, transverse direction and normal direction of the as-used sheet, respectively. 2.2. Plane strain compression Plane strain compression was carried out in a channel die device at room temperature using a strain rate of 10−2 s−1 . The as-polished samples were subjected 6 passes compression along TD and ND alternately with a strain of 0.1 per pass. The first pass of compression was performed along TD. Six types of samples were obtained finally. The name and corresponding deformation experience of the six samples were given in Table 1. 2.3. Microstructure characterization Microstructure of the as-received material and the as-deformed samples was studied using electron back scattered diffraction
Fig. 3 shows crystallographic orientation maps of P-1 and P2 samples. As seen in Fig. 3a, large amount of {1 0 1¯ 2} extension twin boundary is present in P-1 sample, while {1 0 1¯ 1} contraction twin boundary and {1 0 1¯ 1}–{1 0 1¯ 2} double twin boundary are nearly absent. In addition, high content of {1 0 1¯ 2}–{0 1 1¯ 2} boundary which forms due to the coalescence of different {1 0 1¯ 2} extension twinning variants is also seen in Fig. 3a. As seen in Fig. 3b, basal plane poles of most grains are nearly perpendicular to ND. The rotation of basal plane poles from ND to orientation perpendicular to ND is extensively reported to be induced by extension twinning that can rotate the basal plane by 86◦ . Therefore, it can be inferred that most grains are nearly twinned totally. Many thin lamellas with basal plane poles nearly parallel to ND are also noted. It can be inferred that these thin lamellas are the untwined matrix. {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary are also dominated in sample subjected compression along ND in pass 2, while the amount of boundary is much lower than that in previous pass of compression. The basal plane poles of most grains are nearly close to compression axis of pass 2, ND. Crystallographic orientation maps of P-3 and P-4 samples are given in Fig. 4. Similar to that of P-1 sample, only {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary appear in P-3 sample and basal plane poles of most grains are nearly perpendicular to ND again. After compression of pass 4, {1 0 1¯ 2} boundary is dominated, while the basal plane poles of most grains are close to ND. The twin boundaries in P-5 and P-6 samples (see Fig. 5) are similar to that of P-3. The orientation of grains is nearly perpendicular to ND after compression of pass 5 and rotates to ND again after compression in pass 6. As the content of twin boundaries varies greatly during the 6 passes compression, a quantitative measurement of both {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary is carried out to disclose detailed changes and the results are listed in Table 3. P-1 sample contains high amount of both {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary. The fraction of {1 0 1¯ 2}–{0 1 1¯ 2} boundary is more than half of the total boundaries. In subsequent passes of compression, the amount of the total twin boundaries drops greatly
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Table 1 Definition of samples and their deformation experiences. Sample P-1 P-2 P-3 P-4 P-5 P-6
Pass 1 TD/ε = 0.1 √ √ √ √ √ √
Pass 2 ND/ε = 0.1
Pass 3 TD/ε = 0.1
Pass 4 ND/ε = 0.1
Pass 5 TD/ε = 0.1
Pass 6 ND/ε = 0.1
√ √ √ √ √
√ √ √ √
√ √ √
√ √
√
Table 2 Yield stress of sample in each pass of plane strain compression along TD and ND alternately.
Yield stress (MPa)
Pass 1
Pass 2
Pass 3
Pass 4
Pass 5
Pass 6
74
90
114
122
129
130
Table 3 Length of {1 0 1¯ 2} boundary and {1 0 1¯ 2}–{0 1 1¯ 2} boundary in deformed samples with the same detected area. Boundaries length (mm)
P1
P2
P3
P4
P5
P6
{1 0 1¯ 2}–{0 1 1¯ 2} {1 0 1¯ 2} Total Fraction of {1 0 1¯ 2}–{0 1 1¯ 2}
17.81 16.01 33.82 53%
0.79 5.40 6.19 13%
2.88 11.54 14.42 20%
1.18 6.14 7.32 16%
1.89 6.65 8.54 22%
1.56 5.91 7.47 21%
and nearly keeps stable from pass 4. It is also noted that the fraction of {1 0 1¯ 2}–{0 1 1¯ 2} boundary in total boundaries drops greatly in pass 2 and does not change obviously with increased compression passes. Texture evolution of samples suffered from different passes of compression is given in Fig. 6. The as-received material has a strong basal texture with basal plane poles of most grains nearly parallel to ND. No preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} planes appears. After the first pass of compression along TD, basal plane poles of most grains rotate to TD. {1 0 1¯ 0} and {1 1 2¯ 0} planes both shows preferred distribution. (0 0 0 2) plane poles rotate to ND again with the presence of preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} planes after compression along ND in pass 2. It can be seen that the basal plane poles of most grains are nearly parallel to the compression axis with preferred distribution of prismatic planes after each pass of compression. 4. Discussion 4.1. Effect of initial strain on mechanical response of reloading Publications have confirmed that basal slip and {1 0 1¯ 2} extension twinning dominate initial plastic deformation of Mg alloys at room temperature. Certain amount of non-basal slips is also sus-
pected to take place at the vicinity of grains boundaries due to perturbations in local stress state by intergranular strain incompatibilities [6]. Compressed along ND of Mg alloy with basal texture, basal slip is the main mode to accommodate initial plastic strain followed by the presence of contraction twinning and double twinning. Basal slip has much lower schmid factor under compression along ND, which usually results in quite high yield stress. Twinning in magnesium alloys is polar in nature [4]. For Mg alloys with c/a ratio of about 1.623, extension twinning generally occurs under compression load perpendicular to c-axis or tensile load along caxis. Therefore, {1 0 1¯ 2} extension twinning is the main mode to accommodate initial plastic deformation under compression along TD of basal textured Mg alloy. The quite low CRSS of {1 0 1¯ 2} extension twinning (about 2–3 MPa) usually leads to quite low yield stress [6]. Some studies have reported that for basal textured AZ31 Mg alloy with pre-compression along TD, detwinning generally takes place during re-compression along ND. Detwinning does not need nucleation and the activation stress is much lower than that of extension twinning nucleation [10]. Thus, in current study, if detwinning takes place during compression along ND in pass 2, the yield stress should be lower than that in pass 1. However, in present study, the yield stress in pass 2 (about 90 MPa) is much higher than that in pass 1 (about 74 MPa). Therefore, the yield in pass 2 should not result from detwinning. In current experiment, most grains are
Fig. 2. Plane strain compression curves of samples: (a) samples subjected monotonic compression along TD and ND; (b) sample suffering from 6 passes compression along TD and ND alternately.
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Fig. 3. Crystallographic orientation maps of samples after cross plain strain compression along TD and ND alternately: (a) and (b) P-1 sample; (c) and (d) P-2 sample. Inverse pole figure represents ND direction.
nearly twinned totally after 10% compression along TD in pass 1. For these big twins, their orientations are also favorite for extension twinning again under compression load along ND. It is noted that the strain–stress curve also has yield plateau, typical feature of extension twinning. Therefore, it is suspected that the yield in pass 2 manly stems from extension twinning in these large extension twins. As the strain stress curves of pass 3, pass 4, pass 5 and pass 6 all show typical feature of extension twinning with increased yield stress in subsequent compression pass, the yield plateaus in these compression passes are considered to result from extension twinning, too. In [14], it is found that reloading along ND of hot-rolled Mg alloy with 5% pre-compression along TD definitely result in detwinning which is characterized by much lower yield stress than that of twinning in previous loading. Here, the deformation mode during reloading along ND probably involves a competition between extension twinning and detwinning in extension twins generated by pre-straining. We considered that such a competition is closely related with the size of extension twins generated in precompression. Study has verified that activation stress for extension twinning nucleation increases greatly with the drop in grain size [20]. A lower strain of pre-compression generally induces very thin extension twins in which the activation stress of extension twinning again is quite high and detwinning tends to occur preferentially during recompression along ND. However, with increased strain, extension twins grow up very fast after nucleation [4]. Most grains are nearly twinned totally after 10% compression in current study. In big extension twins or grains nearly twinned totally,
the activation stress for extension twinning drops greatly compared to that in thin twin lamellas and extension twinning probably become popular during reloading along ND. Therefore, the size of the extension twins is probably a critical parameter influencing the competition between detwinning and extension twinning in extension twins generated by pre-straining. Another issue is that why the yield stress increases with increased compression passes. Although, extension twinning is dominated during compression along TD in pass 1, slips inevitably occur when the strain exceeds certain level. Theoretical calculations demonstrate that the totally twinned structure can only generate a maximum strain of 0.065 along c-axis [7]. In current experiment, the plastic strain is about 0.08 in each compress pass. Therefore, slips also take part in the plastic deformation. We also get the evidence for dislocation sliding from microstructure of the deformed samples. In EBSD map, the dislocation in deformed materials generally appears as low angle boundary (LAB) [21]. The densities of LAB in the six deformed samples are measured and listed in Table 4. Obviously, the LAB density rises with increased passes. Previous study has demonstrated that the dislocation stored in deformed Mg alloys can enhance the activation stress for twinning nucleation, which will increase yield stress in twinning dominated deformation. Therefore, the rise of yield stress with compression passes probably results from gradually increased dislocation density. In addition, our results seem to indicate that the increasing of dislocation density does not obviously enhance the activation stress for extension twinning further when LAB density exceeds 0.196 m−1 . Some studies also find that that dislocation
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Fig. 4. Crystallographic orientation maps of samples after cross plain strain compression along TD and ND alternately: (a) and (b) P-3 sample; (c) and (d) P-4 sample. Inverse pole figure represents ND direction.
multiplication affects the twinning nucleation stress, but has little or on activation stress of detwinning [10,12]. This further confirms that the yield in each passes of recompression is due to extension twinning again in extension twins. Activation stress for twinning drops with decreased grain size. Therefore, the refinement of grains by extension twinning may also contribute to enhancement in yield stress of reloading. 4.2. Effect of initial strain on microstructure evolution in reloading Compressed along TD in pass 1, the grains are in favorite orientation for {1 0 1¯ 2} extension twinning. In fact, under compression load, nucleation and growth of {1 0 1¯ 2} extension twins are very fast. It is reported that, in hot-rolled AZ31 Mg alloy sheet under compression along RD, most twins nucleate below a strain of 2% and grow up to a strain of 6%. When strain exceeds 6%, the coalescence of growing twins appears and the materials are nearly twinned totally under strain of 8% [3]. In current study, at a compression strain of 10% in pass 1, the volume fraction of twinning reaches about 91%. As-discussed previously, extension twinning also dominates the deformation in subsequent recompressions. The nucleation and growth of extension twinning are also very fast and high volume
fraction of extension twinning can be seen in deformed samples after each compression pass. The presence of {1 0 1¯ 2}–{1 0 1¯ 2} boundary is closely related with the occurrence of different {1 0 1¯ 2} extension twinning variants in one grain. Three are three pair or 6 variants in Mg with hcp structure. The coalescence of different variants leads to the presence of {1 0 1¯ 2}–{1 0 1¯ 2} boundaries. Generally, there are three types of such boundary, (1 0 1¯ 2)–(1¯ 0 1 2), (1 0 1¯ 2)–(0 1 1¯ 2)/(1 1¯ 0 2) and (1 0 1¯ 2)–(0 1¯ 1 2)/(1¯ 1 0 2), with misorientation angle of 7.4◦ , 60◦ and 60.4◦ respectively. The selection of activated variants is thought to be closely related with their schmid factors (SF) [3,22,23]. Generally, the variant with the highest SF tends to occur preferentially. Thus, in samples under compression deformation, most grains generally contain only one type of variant [3]. Some studies also found that more than one types of variants may appear in some grains [3,23]. In [23], it is reported that more than 20% of twinned volume is provided by the second twinning variant. For sample with basal texture, while random distribution of prismatic plane, two types of variants in one grain may both have the same and the highest SF. Fig. 7 gives the calculation of SF for the three types of {1 0 1¯ 2} extension twinning variants under compression along TD. The calculation is under the assumption that the material has an ideal basal texture while random distribution
Table 4 The length of LAB per area in deformed samples.
Length of LAB per-area (m−1 )
P1
P2
P3
P4
P5
P6
0.137
0.140
0.176
0.196
0.20
0.235
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Fig. 5. Crystallographic orientation maps of samples after cross plain strain compression along TD and ND alternately: (a) and (b) P-5 sample; (c) and (d) P-6 sample. Inverse pole figure represents ND direction.
Fig. 6. Pole figures of samples subjected cross plain strain compression along TD and ND alternatively: (a) P-1 sample; (b) P-2 sample; (c) P-3 sample; (d) P-4 sample; (e) P-5 sample; (f) P-6 sample.
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Preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} appears, too. Some previous studies also report the presence of preferred distribution of prismatic plane during extension twinning dominated deformation of Mg alloys [9]. During plastic deformation, prismatic slip of a dislocation contributes to preferred distribution of prismatic planes [24]. However, in current study, {1 0 1¯ 2} extension twinning is dominated and prismatic slips cannot be initiated extensively at room temperature. In fact, it is found that {1 0 1¯ 2} extension twinning also benefits formation of preferred distribution of {1 0 1¯ 0} and {1 1 2¯ 0} planes [24]. As the basal plane of as-used materials is nearly parallel to each other and {1 0 1¯ 2} twinning rotates the basal plane by 86◦ toward compression axis along 1 0 1¯ 0. Therefore, one plane of {1 0 1¯ 0} in twinned regions is nearly parallel to each other [24]. After compression of pass 1, most grains are nearly twined totally and both the basal plane and one plane in {1 0 1¯ 0} in twinned regions are nearly parallel to each other, which definitely results in preferred distribution of (1 0 1¯ 0) plane as well as (1 1 2¯ 0) plane. 5. Conclusion In current paper, plastic deformation behavior of AZ31 Mg alloy under 6 passes plane strain compression along TD and ND alternatively are systematically investigated. The mechanical response and microstructure evolution are analyzed and the corresponding deformation mechanisms are discussed, too. The conclusions are reached as below:
Fig. 7. Schmid factor calculation of the three {1 0 1¯ 2} extension twinning variants in grains with different orientations (T1, T2 and T3 represent the three types of variants, respectively): (a) and (b); {1 0 1¯ 2}–{1 0 1¯ 2} boundary in P-1 sample: (c).
of prismatic plane. As seen in Fig. 7a, in the grain with (1 1 2¯ 0) perpendicular to TD, variant T1 and variant T2 have the same and also the highest SF and may take place at the same time. In [23], the author thought that the modified local stress by twinning strain (either from twinning in the same grain, or from neighbouring grains) is probably a reason for presence of different variants in one grain. In fact, it is reported in some publications that, during compression of textured magnesium alloy, the fraction of grains containing two or three variants is not very high, especially that of grains with three variants [23]. In current study, the strain in one pass is nearly 10% and many variants grow up and coalesce with each other, which results in high content of {1 0 1¯ 2}–{1 0 1¯ 2} boundary in compressed samples. Fig. 7c shows the three types of {1 0 1¯ 2}–{1 0 1¯ 2} boundary by lines with different colors. The green lines come from coalescence of variants from one pair, while the blue lines and purple lines originate from coalescence of variants from different pairs. Obviously, certain amount of green lines and purple lines is observed, while the blue lines are nearly absent. The inclusion of many purple lines indicates the presence of two types of variants in one grain. After compression of pass 1, preferred distribution of prismatic planes appears with [10] nearly parallel to ND. Most grains have orientation similar to that of grain in Fig. 7b. T2 variant has the highest SF and is the most popular one during compression along ND, which will reduce the chances for presence of different types of variants in one grain. Therefore, the amount of {1 0 1¯ 2}–{1 0 1¯ 2} boundary decreases after compression of pass 1. It is well known that {1 0 1¯ 2} extension twinning will reorient the basal plane by 86◦ . Therefore, basal pale poles nearly rotate to compression axis during each compression pass.
(1) The yield stress of sample enhances with increased compression passes, from 74 MPa in pass 1 to 130 MPa in pass 6. (2) With a 10% compression along TD, the grains are nearly twinned totally and extension twinning, not detwinning, takes place during recompression along ND. (3) Preferred distribution of (1 0 1¯ 0) and (1 1 2¯ 0) plane appears during each compression pass besides of the rotation of basal plane poles toward compression axis. Acknowledgements This project is supported by Fundamental Research Funds for the Central Universities (CDJZR11 13 00 01). Here I also want to give much thanks to Julian Driver in Ecole Nationale Superieure des Mines de Saint-Etienne who provides the channel die device for current study. References [1] H. Yan, S.W. Xu, R.S. Chen, S. Kamado, T. Honma, E.H. Han, Scr. Mater. 64 (2011) 141–144. [2] T. Al-Samman, X. Li, S.G. Chowdhury, Mater. Sci. Eng. A 527 (2010) 3450–3463. [3] S.G. Hong, S.H. Park, C.S. Lee, Acta Mater. 58 (2010) 5873–5885. [4] M.R. Barnett, Mater. Sci. Eng. A 464 (2007) 1–7. [5] S.R. Agnew, Ö. Duygulu, Int. J. Plast. 21 (2005) 1161–1193. [6] J. Koike, Mater. Trans. A 36A (2005) 1689–1695. [7] Q. Liu, Acta Metall. Sin. 46 (2010) 1458–1472. [8] P. Yang, Y. Yu, L. Chen, W. Mao, Scr. Mater. 50 (2004) 1163–1168. [9] M. Knezevic, A. Levinson, R. Harris, R.K. Mishra, R.D. Doherty, S.R. Kalidind, Acta Mater. 58 (2010) 6230–6242. [10] X.Y. Lou, M. Li, R.K. Boger, S.R. Agnew, R.H. Wagoner, Int. J. Plast. 23 (2007) 44–86. [11] H.Q. Sun, Y.N. Shi, M.X. Zhang, K. Lu, Acta Mater. 55 (2007) 975–982. [12] A. Jain, S.R. Agnew, Magnesium Technol. (2006) 219. [13] Y.N. Wang, J.C. Huang, Acta Mater. 55 (2007) 897–905. [14] G. Proust, C.N. Tomé, A. Jain, S.R. Agnew, Int. J. Plast. 25 (2009) 861–880. [15] L. Wu, A. Jain, D.W. Brown, G.M. Stoica, S.R. Agnew, B. Clausen, D.E. Fielden, P.K. Liaw, Acta Mater. 56 (2008) 688–695. [16] S. Kleiner, P.J. Uggowitzer, Mater. Sci. Eng. A 379 (2004) 258–263.
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