The influence of a secondary twin on the detwinning deformation of a primary twin in Mg–3Al–1Zn alloy

Materials Science & Engineering A 606 (2014) 81–91

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The influence of a secondary twin on the detwinning deformation of a primary twin in Mg–3Al–1Zn alloy Yunchang Xin n, Xiaojun Zhou, Liangchen Lv, Qing Liu School of Materials Science and Engineering, Chongqing University, Chongqing 400030, PR China

art ic l e i nf o

a b s t r a c t

Article history: Received 18 September 2013 Received in revised form 17 March 2014 Accepted 20 March 2014 Available online 28 March 2014

In the present paper, the influence of a f1012g–f1012g secondary twin on detwinning of a f1012g primary twin is systematically investigated by compression along the normal direction (ND) of pre-strained samples at room temperature. Samples containing both a f1012g primary twin and a f1012g–f1012g secondary twin are prepared by pre-compression along the transverse direction (TD) and subsequent re-compression along the rolling direction (RD) of a hot-rolled AZ31 Mg alloy plate at room temperature. Our results show that the introduction of a f1012g–f1012g secondary twin into the primary twin can enhance the compression yield strength along the ND. During compression along the ND, the f1012g–f1012g secondary twin mainly deforms by f1012g twinning, forming a f1012g–f1012g–f1012g ternary twin, while detwinning of the f101  2g primary twin also takes place. When a f1012g–f1012g secondary twin happens to totally separate a f1012g primary twin from the matrix, it can serve as a barrier to impede detwinning of this f1012g primary twin. The f1012g twinning in a f1012g–f1012g secondary twin can induce a preferred distribution of prismatic planes in twinned regions, which is closely related to the activation of preferential twin variants. & 2014 Elsevier B.V. All rights reserved.

Keywords: Mg alloy Strengthening Twinning Detwinning

1. Introduction Mg alloys are desirable candidates as structure components with a need of weight reduction. However, Mg and its alloys can only initiate limited slip systems at room temperature, which leads to a poor cold working capability. The start of non-basal slip systems in a large amount generally happens at a temperature over 220 1C [1–3]. Therefore, twinning plays an important role in plastic deformation of Mg alloys at room temperature [4–6]. For Mg alloy with a c/a ratio of about 1.623, f1012g twinning generally takes place under a compressive stress perpendicular to the c-axis or a tensile load along the c-axis of a grain. Therefore, for a hotrolled Mg alloy with a basal texture, f1012g twinning dominates compression along the RD (or the TD) or tension along the ND at room temperature [4–10]. Compression along the extrusion direction of the extruded Mg alloy with a prismatic fiber texture is mainly controlled by f1012g twinning, too. The f1012g twins generated by pre-straining can narrow or disappear during a reverse reloading, which is termed as detwinning. The above twinning–detwinning process frequently occurs during fatigue tests of textured Mg alloys that are subjected to a cyclic loading

n

Corresponding author. Tel./fax: þ 86 23 65106407. E-mail address: [email protected] (Y. Xin).

http://dx.doi.org/10.1016/j.msea.2014.03.068 0921-5093/& 2014 Elsevier B.V. All rights reserved.

[11–17]. Detwinning also happens in a strain path changed reloading, e.g. recompression along the ND of a hot-rolled Mg alloy plate that is pre-compressed along the TD [10]. Detwinning greatly affects the deformation characteristics and mechanical behavior of Mg alloys. The twinning–detwinning process often generates an asymmetric sigmoidal-shaped hysteresis loop in the strain–stress curve of cyclic loading [18]. The asymmetry between the compression stress and the tension stress is more pronounced with a higher strain or a higher stress amplitude [11,14,18]. Detwinning does not need nucleation and, thus, its activation stress is considered to be lower than that for twinning [17,19,20]. Generally, the experimentally measured yield stress in detwinning dominated deformation is often much lower than that associated with deformation that is dominated by f1012g twinning [10,20]. However, Park et al. found that a higher prestrain level would result in a higher yield stress of detwinning dominated deformation [16]. Recently, several publications reported the application of twins to tailor the mechanical properties of Mg alloys [21–25]. It was found that grain refinement by f1012g twins obtained by a precompression along the RD of an AZ31 Mg alloy plate effectively enhanced both tension and compression yield strengths along the TD without any compromise in ductility [21,24]. However, detwinning constitutes one of the main deformation modes of a Mg alloy containing twins, and greatly affects mechanical behavior [18–20].

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In our previous publication [24], it was found that appropriate loading can induce f1012g twinning in the f1012g primary twin, forming a f1012g–f1012g secondary twin. Detwinning behavior of a f1012g primary twin has been extensively studied and reported [18–20]. However, the deformation behavior of a Mg alloy that contains both a f1012g primary twin and a f1012g–f1012g secondary twin is hardly studied. The f1012g–f1012g secondary twin and the f1012g primary twin have different orientations and they may deform by different modes.

Therefore, the presence of f1012g–f1012g secondary twin may greatly affect the deformation behavior of a f1012g primary twin and mechanical properties of samples. A deep understanding about these topics will greatly benefit the application of secondary twins to tailor deformation and mechanical properties of Mg alloys. In the present paper, AZ31Mg alloy that contains both a f1012g primary twin and a f1012g–f1012g secondary twin is prepared. Mechanical properties and deformation behavior of the as-prepared samples at room temperature are fully addressed.

2. Experiments and methods

Fig. 1. (a) Inverse pole figure map and (b) pole figures of the hot-rolled AZ31 Mg alloy plate. The pole figures were acquired by XRD. (Inverse pole figure represents ND.)

Table 1 The pre-straining experience and the designation of samples. Sample

PRT1 PRT2 PRT3 PRT1R1 PRT2R2 PRT3R3

Pre-compression along TD (plastic strain, %) Recompression along RD (plastic strain, %)

2.6

4.7

6.7

2.6

4.7

6.7

―

―

―

2.4

2.4

3.0

AZ31 Mg alloy is a commercially available alloy and widely used in studies of plastic deformation behavior. It hardly contains any precipitates, which allows studying the deformation behavior without the influence of precipitates. A thick, hot-rolled AZ31 Mg alloy plate with fully recrystallized grains and a typical basal texture (see Fig. 1) was used. Blocks of 10  10  8 mm3 were cut from the as-received plate for compression test that was conducted at room temperature at a strain rate of 10  3 s  1. The samples containing only a f1012g primary twin were prepared by pre-compression along the TD of the as-received plate. Different pre-strains, 2.6%, 4.7% and 6.7% (designated as PRT1 sample, PRT2 sample and PRT3 sample, respectively), were used to prepare samples with different volume fractions of the f1012g primary twin. The samples that contain both a f1012g primary twin and a f1012g–f1012g secondary twin were prepared by a recompression of PRT1 sample, PRT2 sample and PRT3 sample along the RD by 2.4%, 2.4% and 3.0%, respectively, (defined as PRT1R1 sample, PRT2R2 sample and PRT3R3 sample, respectively). The designations of pre-strained samples are listed in Table 1. Annealing treatment of the pre-strained samples at 160 1C for 12 h was carried out to remove the dislocations as much as possible; meanwhile, it did not damage the twin structure. The electron backscattered diffraction analysis (EBSD) shows that the twin structure was well retained after the annealing. Mechanical properties (yield strength, ultimate compressive strength and elongations to fracture) of the pre-strained and annealed samples were measured by compression along the ND. For comparison, the compression strain–stress curves along the TD and the ND of the as-received plate were also measured (designated as ART sample and ARN sample, respectively). To disclose the deformation behavior during plastic deformation, EBSD mappings at the same area were conducted before and after loading. The sample was measured first followed by reloading outside SEM chamber and re-mapping at the same region

Fig. 2. Strain–stress curves under compression along ND of the pre-strained sample at room temperature. ARN and ART are the strain–stress curves of the hot-rolled plate under compression along ND and TD, respectively. PRT1 – the sample with 2.6% pre-compression along TD; PRT1R1 – the sample with 2.6% pre-compression along TD and 2.4% recompression along RD; PRT2 – the sample with 4.7% pre-compression along TD; PRT2R2 – the sample with 4.7% pre-compression along TD and 2.4% recompression along RD; PRT3 – the sample with 6.7% pre-compression along TD; PRT3R3 – the sample with 6.7% pre-compression along TD and 3.0% recompression along RD.

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again. Pole figures of samples were determined using X-ray diffraction (XRD, Rigaku D/max-2500PC) analysis.

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to a longer “Stage 2”. In fact, both f1012g twinning and detwinning can generate a peak in strain hardening rate curve [18,26]. Thus, to judge what causes the peaks in strain hardening rate curves, it is required to disclose the main deformation modes in these samples.

3. Results 3.2. Deformation behavior of samples containing only primary twin 3.1. Mechanical properties Fig. 2 presents the strain–stress curves of pre-strained samples under compression along the ND. Mechanical properties derived from the strain–strain curves are listed in Table 2. Compression along the TD, ART sample is characterized by a plateau shape, the typical feature of f1012g twinning dominated deformation [4]. A plateau shape also appears in all the curves of pre-strained samples under compression along the ND. Yield strengths of PRT1R1 sample (111 MPa), PRT2R2 sample (125 MPa) and PRT3R3 sample (141 MPa) are all much higher than that of PRT1 sample (71 MPa), PRT2 sample (80 MPa) and PRT3 sample (87 MPa). Compared to the hot-rolled plate, the elongations of pre-strained samples do not drop obviously. Strain hardening performance of the curves in Fig. 2 is analyzed by the working hardening rate as a function of strain (Fig. 3). The work hardening rate was calculated by the differentiation of strain–strain curves. The plot of ARN sample has a continuously decreasing strain hardening rate, which has been extensively reported for a slip dominated deformation [8]. The curve of the ART sample contains three distinct stages: Stage 1, a fast drop in hardening rate; Stage 2, a quick increase in hardening rate; Stage 3, a fast drop in hardening rate again. In previous publications [26–28], it was reported that the strain hardening behavior of “Stage 2” mainly results from the rotation from “soft orientation” (favorable for f1012g twinning) to “hard orientation” (unfavorable for f1012g twinning) by f1012g twinning. Length of "Stage 2" is mainly determined by the volume fraction of the regions favorable for f1012g twinning [26]. Obviously, all the strain hardening curves of pre-strained samples are composed of similar three stages, too. Length of “Stage 2” in pre-strained samples highly depends on the pre-strain level. A higher pre-strain level leads Table 2 The mechanical properties derived from the strain–stress curves in Fig. 2. Sample Yield stress (MPa) Peak stress (MPa) Elongation (%)

ART

ARN

PRT1

68

126

71

80

87

111

125

141

282

266

265

270

276

294

308

323

14.5

15.1

14.4

PRT2 PRT3 PRT1R1 PRT2R2 PRT3R3

12.8

14.2

13.9

14.7

14.5

EBSD mappings at the same area were carried out before and after compression along the ND of the PRT1 sample are shown in Fig. 4. Many lamellas discerned as the f1012g twin are seen in Fig. 4(a). Volume fraction of the f1012g twin drops from 42.1% in Fig. 4(a) to 6.2% in Fig. 4(b) after 3.2% compression along the ND. Deformation characteristics of several selected grains in Fig. 4 (a) are further analyzed in Fig. 4(c) and (d). In Fig. 4(c), some f1012g primary twins, e.g. regions 3 and 4, disappear after compression along the ND, the typical feature of detwinning. For the grain with large f1012gtwin (see Fig. 4(d)), besides the contraction of twins, new f1012g twins, e.g. regions 3 and 4, that have different orientations with the matrix also appear in f1012g primary twin (region 2) after compression along the ND. Therefore, regions 3 and 4 are f1012g twins in f1012g primary twin and they are f1012g–f1012g secondary twin. In the present study, the identification of a f1012g–f1012g secondary twin is mainly judged by the presence of a f1012g twin in a f1012g primary twin. In Fig. 5 (EBSD mapping at the same area of PRT2 sample before and after compression along the ND), many twin lamellas narrow or disappear after 3.7% compression along the ND, too. As seen in Fig. 5(c), detwinning also occurs through growing up of the matrix. However, in Fig. 5(d), new f1012g twins, e.g. regions 5 and 6, that share a f1012g twin boundary with the f1012g primary twin (region 1) also appear. Although regions 5 and 6 have the same orientation as the matrix (region 3), they are f1012g–f1012g secondary twin. The EBSD analysis at the same area of PRT3 sample before and after compression along the ND is shown in Fig. 6. As seen in Fig. 6(a), many grains of the PRT3 sample are totally twinned. In the grain that contains small matrix, detwinning also occurs by contraction of twins during compression along the ND. In the totally twinned grain in Fig. 6(c), detwinning cannot happen due to the absence of matrix and f1012g twinning (regions 3 and 4) is the only deformation mode. In the grains containing both a large f1012g primary twin (the size of twins is similar to the average grain size) and matrix (Fig. 6(d)), new f1012g twins (regions 6, 7 and 8) appear after compression along the ND, besides detwinning. The above results shows that, under compression along the ND, detwinning deformation in the pre-strained samples that contains only the f1012g primary twin is highly dependent on grain structure. For the grains that are not totally twinned, detwinning of f1012g primary twin will happen. However, if the f1012g

Fig. 3. Strain hardening curves of the pre-strained sample under compression along ND at room temperature. ARN and ART are strain hardening curves of the hot-rolled plate under compression along ND and TD, respectively. PRT1 – the sample with 2.6% pre-compression along TD; PRT1R1 – the sample with 2.6% pre-compression along TD and 2.4% recompression along RD; PRT2 – the sample with 4.7% pre-compression along TD; PRT2R2 – the sample with 4.7% pre-compression along TD and 2.4% recompression along RD; PRT3 – the sample with 6.76% pre-compression along TD; PRT3R3 – the sample with 6.7% pre-compression along TD and 3.0% recompression along RD.

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Fig. 4. EBSD analysis at the same area of PRT1 sample before and after 3.2% compression along the ND: (a), inverse pole figure map before compression along the ND; (b), inverse pole figure map after compression along ND; (c, d), inverse pole figure maps, misorientation analysis and pole figures of selected grains in (a, b). Detwinning often takes place in the small primary twins, while new extension twins tend to form in the large primary twins under compression along the ND.

Fig. 5. EBSD analysis at the same area of PRT2 sample before and after 3.7% compression along the ND: (a), inverse pole figure map before compression along the ND; (b), inverse pole figure map after compression along ND; (c, d), inverse pole figure maps, misorientation analysis and pole figures of selected grains in (a, b). It can be seen that the deformation behavior of PRT2 sample during compression along the ND is similar to that of the PRT1 sample (Fig. 4).

primary twin is quite large (similar to the average grain size), f1012g twinning can also take place in the primary twin. For the totally twinned grains, only f1012g–f1012g secondary twinning takes place in the primary twins. 3.3. Deformation behavior of samples containing both a primary twin and a secondary twin EBSD analysis about the same area of the PRT1R1 sample before and after compression along the ND is given in Fig. 7. Many

intersections of twins are present in the sample containing both a primary twin and a secondary twin. A pre-compression along TD generates many primary twins with basal plane poles close to TD. During recompression along RD, many new primary twins with basal plane poles near RD and secondary twins appear. These new twins easily intersect with the primary twins generated during pre-compression along TD. A recent study has shown that the intersections of twins can stimulate the nucleation of twins [29]. Volume fractions of the matrix, f1012g primary twin, f1012g–f1012g secondary twin and f1012g–f1012g–f1012g ternary

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Fig. 6. EBSD analysis at the same area of PRT3 sample before and after 3.2% compression along the ND: (a), inverse pole figure map before compression along ND; (b), inverse pole figure map after compression along the ND; (c, d), inverse pole figure maps, misorientation analysis and pole figures of selected grains in (a, b). For the totally twined grains or the grain with a small size of matrix, nucleation of new extension twins is the main deformation mode during compression along the ND.

Fig. 7. EBSD analysis at the same area of PRT1R1 sample before and after 4.6% compression along the ND: (a), inverse pole figure map before compression along the ND; (b), inverse pole figure map after compression along ND; (c, d), inverse pole figure maps, misorientation analysis and pole figures of selected grains in (a, b). It can be seen that f1012g twinning is the main deformation mode in f1012g–f1012g secondary twin.

twin in Fig. 7(a) and (b) are measured and listed in Table 3. The twin volume fractions were measured by the area fraction of twin regions in the inverse pole figure maps. After compression along the ND, volume fraction of the f1012g primary twin drops from 45.4% to 16.3%, while volume fraction of the f1012g–f1012g secondary twin only decreases slightly. The f1012g–f1012g–f1012g ternary twin in Fig. 7(b) only accounts for 1.1% volume fraction. As seen in Fig. 7(c), region 1, a f1012g primary twin, totally disappears after compression along the ND, while region 4, a f1012g–f1012g secondary twin, is

well retained. In Fig. 7(d), region 5 discerned as a f1012g–f1012g secondary twin turns into a new f1012g twin (region 6) after the ND compression. The f1012g twin in f1012g–f1012g secondary twin generally forms a f1012g–f1012g–f1012g ternary twin (region 6). EBSD micrographs at the same area and volume fractions of different microstructure in PRT2R2 sample before and after 4.9% compression along the ND are shown in Fig. 8 and Table 4, respectively. After compression along the ND, volume fraction of the f1012g primary twin varies from 48.9% in Fig. 8(a) to 26.4% in

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Table 3 The volume fractions of different structures in Fig. 7(a) and (b).

Before compression After compression

The untwined matrix (%)

f1012g Primary twin (%)

f1012g–f1012g Secondary twin (%)

f1012g–f1012g–f1012g Ternary twin (%)

47.5 87.7

45.4 16.3

7.1 4.9

– 1.1

Fig. 8. EBSD analysis at the same area of PRT2R2 sample before and after 4.9% compression along the ND: (a), inverse pole figure map before compression along the ND; (b), inverse pole figure map after compression along the ND; (c, d), inverse pole figure maps, misorientation analysis and pole figures of selected grains in (a, b). Some f1012g–f1012g secondary twins (e.g. region 5) with appropriate distribution can serve as a barrier to impede detwinning.

Table 4 The volume fractions of different structures in Fig. 8(a) and (b).

Before compression After compression

The untwined matrix (%)

f1012g Primary twin (%)

f1012g–f1012g Secondary twin (%)

f1012g–f1012g–f1012g Ternary twin (%)

32.9 54.4

48.9 26.4

18.1 18.6

– 0.6

Fig. 8(b). The content of f1012g–f1012g secondary twin does not change obviously. Quite low volume fraction of the f1012g– f1012g–f1012g ternary twin (0.6%) is detected in Fig. 8(b). In Fig. 8(c), new f1012g twins, e.g. regions 7 and 8, appear in the f1012g–f1012g secondary twin (region 4) after compression along the ND, forming f1012g–f1012g–f1012g ternary twin. In addition, some new f1012g twins (regions 9 and 10) also appear in the f1012g primary twin (e.g. region 5) after compression along the ND, generating f1012g–f1012g secondary twins. In Fig. 8(d), region 5 effectively separates region 1 (matrix) from region 3 (a f1012g

primary twin). It can be inferred that region 5 may serve as a barrier to impede detwinning of the f1012g primary twin. The EBSD analysis about the same area of PRT3R3 sample before and after compression along the ND is shown in Fig. 9. As seen in Table 5, volume fraction of the f1012g primary twin decreases dramatically, while volume fraction of the f1012g–f1012g secondary twin hardly changes. Volume fraction of f1012g–f1012g– f1012g ternary twin in Fig. 9(b) is quite low, too. In Fig. 9(c), region 4, the f1012g–f1012g secondary twin, effectively separates the f1012g primary twins of regions 2 and 3 from the matrix. After

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Fig. 9. EBSD analysis at the same area of PRT3R3 sample before and after 5.3% compression along the ND: (a), inverse pole figure map before compression along the ND; (b), inverse pole figure map after compression along ND; (c, d), inverse pole figure maps, misorientation analysis and pole figures of selected grains in (a, b). If a primary twin is totally separated from its matrix by secondary twins, detwinning will not take place in this primary twin and f1012g twinning is the deformation mode during compression along the ND.

Table 5 The volume fractions of different structures in Fig. 9(a) and (b).

Before compression After compression

The untwined matrix (%)

f1012g Primary twin (%)

f1012g–f1012g Secondary twin (%)

f1012g–f1012g–f1012g Ternary twin (%)

15.9 45.3

61.4 31.0

22.7 22.2

– 1.5

compression along the ND, f1012g twinning takes place in both regions 2 and 3, forming f1012g–f1012g secondary twins. For the totally twinned grain in Fig. 9(d), no detwinning takes place and a new f1012g–f1012g secondary twin (region 5) appears in the f1012g primary twin of region 1. The above results show that, during compression along the ND of samples containing both a f1012g primary twin and a f1012g– f1012g secondary twin, the detwinning of f1012g primary twins also happens in grains that contain the matrix. The main deformation mode in f1012g–f1012g secondary twins is f1012g twinning. The distribution of secondary twins affects detwinning of f1012g primary twin. When f1012g–f1012g secondary twin happens to separate a f1012g primary twin from its matrix, it can impede detwinning of this f1012g primary twin. 3.4. Texture evolution Pole figures of the samples that are subjected to different loading conditions are given in Fig. 10. The detailed loading conditions are listed in the table below pole figures. Compression along the TD results in a rotation of (0002) plane poles toward the TD as seen in Fig. 10(a), (c), and (e), which has been extensively reported to result from f1012g twinning. The inclined (0002) plane poles generally fall in the range of 7301 around TD. A higher strain level along the TD generates more (0002) plane poles toward the compression axis, TD. Recompression along the RD of samples that are pre-compressed along the TD also induces a rotation of (0002) plane poles toward RD. A higher strain along the

RD also results in more (0002) plane poles around the RD. Similarly, the inclined (0002) plane poles after compression along the RD are also in the range of 7301 around the RD. For all the pre-strained samples, (0002) plane poles totally rotate to the ND again after ND compression. As seen in Fig. 1(b), prismatic planes of the hot-rolled plate distribute randomly. However, a preferred distribution of ð1010Þ planes appears after compression along the TD (Fig. 10). The samples that are subjected to both compression along TD and RD also have a preferred distribution of ð1010Þ planes. The compression along the ND of PRT1 sample, PRT2 sample and PRT3 sample generates a random distribution of ð1010Þ planes again. However, after compression along the ND, both the ð1010Þ planes of PRT2R2 sample and PRT3R3 sample are composed of two parts: a random distribution of ð1010Þ planes and a preferred distribution of ð1010Þ planes as denoted by the blue arrows.

4. Discussion 4.1. The influence of secondary twin on deformation behavior Compression along the TD of a hot-rolled AZ31 Mg alloy plate is mainly dominated by f1012g twinning. Generally, f1012g twinning rotates the (0002) plane poles by about 861 toward the compression axis [4]. Therefore, both the f1012g primary twin and the matrix after pre-compression along the TD are favorable for f1012g twinning during recompression along the RD. In the present study, the

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Fig. 10. Pole figures of the samples with different deformation experiences as listed in the table below the pole figures. The pole figures were acquired by XRD. The texture evolution shows that f1012g twinning will rotate basal plane poles of twinned regions toward the compression axis and induce the presence preferred distribution of prismatic planes (the regions denoted by blue arrows). Detwinning of primary twins also rotates the basal plane poles toward the compression axis, while does not generate preferred distribution of prismatic planes. (For interpretation of references to color in this figure legend, the reader is referred to the web version of this article)

samples only pre-compressed along the TD mainly contain f1012g primary twin and the matrix, while the samples that are subjected to cross-compression along the TD and the RD are generally composed of f1012g–f1012g secondary twins, f1012g primary twins and the matrix. Theoretically, under compression along the ND, the orientation of f1012g primary twins generated by pre-compression along the TD is favorable for both detwinning and f1012g twinning. The competition between the detwinning and the f1012g twinning should be determined by their activation stress. As extensively reported, detwinning has much a lower activation stress than that for twinning nucleation [19,30,31]. The activation stress for f1012g twinning increases with grain size drop [9,22]. It can be inferred that the activation stress for f1012g twinning in a thin f1012g primary twin should be much higher than that for detwinning of a

f1012g primary twin. Therefore, in a grain with very thin f1012g primary twin, detwinning dominates compression along the ND. However, f1012g primary twin can broaden quickly under a higher pre-strain and the activation stress for f1012g twinning in a large twin drops dramatically [21]. Thus, in a grain with quite large f1012g primary twin, f1012g twinning may take place, too. However, when a grain is totally twinned, detwinning cannot take place and f1012g twinning is the predominant deformation mode during compression along the ND. The above discussion shows that the size of f1012g primary twins plays an important role in its deformation behavior. Volume fractions and distribution of f1012g primary twin and f1012g–f1012g secondary twin are highly dependent on the prestrain levels along the TD and the RD. According to their distribution, the influence of a f1012g–f1012g secondary twin on the

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Fig. 11. Schematic illustration about the influence of secondary twin on detwinning of the primary twin. M, T, ST and TT represent the matrix, the primary twin, the secondary twin and the ternary twin, respectively. The distribution of secondary twins and primary twins in a grain greatly affect the deformation mode in it.

detwinning of a f1012g primary twin during compression along the ND can be classified into 5 types, which are schematically illustrated in Fig. 11. In “Type 1”, the f1012g–f1012g secondary twin (ST) is small and cannot effectively impede the detwinning. The f1012g primary twin will completely revert into the matrix. M1 and M2 can coalesce with each other finally. As seen in “Type 2”, the grains are divided into two separated regions by a f1012g– f1012g secondary twin. Although detwinning can proceed, M1 and M2 cannot merge with each other. When a secondary twin happens to separate a f1012g primary twin from its matrix of M1 ("Type 3"), detwinning only takes place between the f1012g primary twin and the matrix of M2. M1 will deform as an independent grain. Generally, basal slip is considered to dominate the deformation of M1 during compression along the ND [10]. In “Type 4”, a f1012g–f1012g secondary twin divides a f1012g primary twin into two separated regions, T1 and T2. Detwinning only happens between M1 and T1. Under compression along the ND, f1012g twinning generally occurs in the f1012g primary twin of T2. In “Type 5”, a f1012g–f1012g secondary twin happens to separate the f1012g primary twin from the matrix. Detwinning would not take place in the whole grain during compression along the ND. Generally, f1012g twinning will happen in T and basal slip mainly dominates the deformation of M. Under compression along the ND, the main deformation mode in f1012g–f1012g secondary twins is f1012g twinning, forming f1012g–f1012g–f1012g ternary twins (TT). In fact, when the deformation temperature increases to 200 1C, slips, especially non-basal slip, have higher activity. Generally, the activity of twinning will be suppressed. However, detwinning at room temperature is widely studied, while detwinning at high temperature is seldom reported. This needs to be clarified in future studies. 4.2. The influence of secondary twin on mechanical properties The low activation stress for detwinning often results in low yield stress in detwinning dominated deformation [19,20]. Compression along the ND of samples containing both a f1012g primary twin and a f1012g–f1012g secondary twin is mainly controlled by detwinning of the f1012g primary twins and f1012g twinning in f1012g–f1012g secondary twins. Therefore, the compression yield strength along the ND should be determined by both the activation stresses for detwinning and the activation stress for f1012g twinning in f1012g–f1012g secondary

twin. The thickness of twin lamella plays a similar role as that of grain size. Due to the small size of f1012g–f1012g secondary twins, the activation stress for f1012g twinning in them should be much higher that for detwinning of f1012g primary twins. Therefore, a higher volume fraction of a f1012g–f1012g secondary twin contributes to a higher compression yield strength along ND. However, enhancing the pre-strain level increases volume fraction of f1012g–f1012g secondary twins; meanwhile, it may also result in thickening of the f1012g–f1012g secondary twins. A higher volume fraction of secondary twin benefits a higher yield strength, while the larger f1012g–f1012g secondary twins will decrease the activation stress for f1012g twinning in them, reducing the yield stress. Therefore, the contribution of f1012g–f1012g secondary twins to compression yield strength along the ND is determined by both the volume fraction and the size of f1012g–f1012g secondary twins. As detwinning is a process of twin boundary migration, the volume fraction of regions that deform by detwinning should hardly influence the activation stress for detwinning. 4.3. The influence of twinning and detwinning on texture Under compression load, f1012g twinning rotates the basal plane poles by 861 toward the compression axis [4]. The texture change induced by f1012g twinning is closely related with the activation of f1012g twin variants. The f1012g twin has six variants: ð1012Þ½1011, ð0112Þ½0111, ð1102Þ½1101, ð1012Þ½1011, ð0112Þ½0111 and ð1102Þ½1101. Increasing evidences have demonstrated that the variant with the highest Schmid factor (SF) tends to start and grow up preferentially [8]. To disclose the influence of f1012g twin variant activation on texture evolution, SFs of f1012g twin variants under compression along the TD with an ideal basal texture and randomly distributed prismatic planes are calculated. SFs of the six f1012g twin variants (T1, T2, T3, T4, T5 and T6) and their basal plane pole distribution are given in Fig. 12. Under compression along the TD, SFs of the six variants vary with the angle (θ) between the TD and the a-axis. Due to a symmetrical distribution of the three a-axes, θ all falls in the range from 01 to 601 and the SFs for θ in 01–301 are identical with that in 601  θ. Therefore, the SF calculation is only performed under three representative θ (301, 151 and 01). When θ drops from 301 to 01, the highest SF also decreases from 0.499 to 0.374. As seen in Fig. 12(d), the (0002) plane poles of these variants with the highest SF in the three types of grains all fall in the range of

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Fig. 12. (a–c) Schematic showing the Schmid factor analysis on the six f1012g twin variants and the (0002) poles distribution of these variants. (d) The distribution of (0002) poles and ð1010Þ poles of f1012g twin variants with the highest Schmidt factor in (a–c). The preferred start of f1012g twin variant with the highest Schmid factor will result in inclination basal plane poles of twinned regions toward compression axis as well as the presence of preferred distribution of prismatic planes.

7301 around the TD. Therefore, it can be inferred that, in the asreceived sample, (0002) plane poles of the f1012g twin variants with the highest SF in all the grains are also in the range of 7301 around the compression axis, too. As seen in Fig. 12(d), a preferred distribution of the basal plane consequently results in a preferred distribution of ð1010Þ planes. Similarly, both f1012g–f1012g secondary twinning and f1012g–f1012g–f1012g ternary twinning in the present study can also induce a preferred distribution of prismatic planes. Although prismatic slip of an 〈a〉 dislocation in Mg alloy can also result in a preferred distribution of prismatic planes, the prismatic slip cannot be extensively initiated at room temperature and, thus, hardly contributes to the preferred distribution of prismatic plane in the present study. Generally, the detwinning of a f1012g primary twin would rotate the orientation of twins to that of the matrix [12,17,19]. For the sample only containing f1012g primary twins, detwinning is dominated during compression along the ND and the texture of samples that are compressed along ND by a large strain should be similar to that of the hot-rolled plate (a basal texture with a random distribution of prismatic planes). However, for the samples containing both f1012g primary twins and f1012g–f1012g secondary twins, both detwinning of f1012g primary twins and f1012g twinning in the f1012g–f1012g secondary twins take place during compression along the ND. As stated above, f1012g twinning can generate a preferred distribution of prismatic planes of the twinned regions. Therefore, after compression along the ND, the prismatic planes with a preferred distribution in the PRT2R2 sample and the PRT3R3 sample mainly come from the f1012g– f1012g–f1012g ternary twins.

5. Conclusions In the present study, samples that contain both a f1012g primary twin and a f1012g–f1012g secondary twin are prepared by a pre-compression along the TD and a subsequent recompression along the RD of a hot-rolled AZ31 Mg alloy plate. The effects of f1012g–f1012g secondary twin on the detwinning of f1012g

primary twins is systematically studied. Several conclusions can be reached as follows: (1) The f1012g–f1012g secondary twin can increase the compression yield strengths along the ND by about 40–50 MPa. (2) Under compression along the ND, f1012g–f1012g secondary twins mainly deform by f1012g twinning, forming f1012g– f1012g–f1012g ternary twins, while the detwinning of f1012g primary twins also takes place. The distribution of f1012g– f1012g secondary twins affects the detwinning of f1012g primary twins. When a f1012g–f1012g secondary twin happens to separate a f1012g primary twin from the matrix, it can sever as a barrier to suppress the detwinning of this f1012g primary twin. (3) Both the f1012g twinning in matrix and f1012g–f1012g secondary twins can generate a preferred distribution of prismatic planes of the twinned regions. The presence of a preferred distribution of prismatic planes is closely related to the activation of twin variants.

Acknowledgment The current study was co-supported by the National Natural Science Foundation of China (51371203, 51101175 and 51131009), the National Key Basic Research Program of China (2013CB632205) and the Research Fund for the Doctoral Program of Higher Education of China (20110191120016). References [1] [2] [3] [4] [5] [6]

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