Sequential activation of deformation modes in textured alloy AZ31B during tensile deformation

Journal Pre-proof Sequential activation of deformation modes in textured alloy AZ31B during tensile deformation Linghui Song, Baolin Wu, Xinghao Du, Yinong Wang, Claude Esling, Marie-Jeanne Philippe PII:

S0921-5093(20)30013-7

DOI:

https://doi.org/10.1016/j.msea.2020.138921

Reference:

MSA 138921

To appear in:

Materials Science & Engineering A

Received Date: 21 October 2019 Revised Date:

26 December 2019

Accepted Date: 3 January 2020

Please cite this article as: L. Song, B. Wu, X. Du, Y. Wang, C. Esling, M.-J. Philippe, Sequential activation of deformation modes in textured alloy AZ31B during tensile deformation, Materials Science & Engineering A (2020), doi: https://doi.org/10.1016/j.msea.2020.138921. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Credit Author Statement

This article has been finished by authors: Linghui Song, Baolin Wu, Xinghao Du,Yinong Wang, Claude Esling, Marie-Jeanne Philippe.

Linghui Song is doctoral student directed by Baolin Wu and Yinong Wang, finished experimental investigation, data curation, etc; Baolin Wu played a role in formal analysis, research scheme design, methodology, experiment supervision, etc;

Xinghao Du took part in EBSD analysis, data

curation and calculation;

Yinong Wang took part in research scheme design, deformation mechanisms discussion and manuscript writing;

Claude Esling took part in orientation analysis and manuscript writing.

Marie-Jeanne Philippe discussed methodology, deformation mechanisms and smoothed English writing.

Baolin Wu

School of Materials Science and Engineering, Shenyang Aerospace University, South Avenue of Daoyi, 110136, Shenyang, China Email: [email protected] tel./fax numbers: 86-24-89728701/86-24-89728729

Sequential activation of deformation modes in textured alloy AZ31B during tensile deformation Linghui Songb, Baolin Wua,∗,Xinghao Dua,Yinong Wangb,∗,Claude Eslingc,d, Marie-Jeanne Philippee a

School of Materials Science and Engineering, Shenyang Aerospace University, Shenyang 110136, China b

School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China cUniversité de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, F-57000, Metz, France

d Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures (DAMAS), Université de Lorraine, 57073 Metz, France eCheminen Paradis, F-71390 Granges, France

Abstract Sequential activation of deformation modes in a fiber-textured magnesium alloy AZ31B during tensile deformation was investigated through in-situ observation of microstructure evolution under EBSD. The results showed that initiation of deformation modes is asynchonous, texture has little effect on the activation sequence. Basal slip is the mode activated first, and then{10-12} extension twinning and {10-11} contraction twinning. It is concluded that prismatic and pyramidal slips could be activated subsequently with basal slip. Kernal average misorientation (KAM) varies within individual grains indicating the inhomogeneity of the deformation. Slips are activated early inside small grains at the grain boundaries. The activation of most twin variants is SF-related. The activation of some non-SF-related twin variants can be explained in terms of strain accommodation parameter.

Keywords： Magnesium alloy; deformation mode; slip; twinning; twin variant selection

∗ Corresponding author. E-mail address: [email protected]; [email protected]

1

1. Introduction

Slip and twinning are two important kinds of deformation modes in magnesium alloys[1–4]. Including basal slip ({0001}<11-20>), prismatic slip ({10-10}<11-20>), pyramidal slip ({11-22} <11-23>), {10-12} extension twinning and {10-11} contraction twinning[5–10], magnesium alloys exhibit multiple deformation modes that is possibly propitious to improving ductility. However, the activation of these deformation modes is usually asynchronous at room temperature because of the difference between their critical resolved shear stresses (CRSSs). In addition, Schmid factor (SF) plays an important role in the selection of deformation modes. For instance, it is well known that contraction twinning is favored in fiber textured magneisum alloys during tensile deformation due to its high SF in most grains . Good coordination between SF and CRSS can effectively promote the initiation of multivariate modes. Deformation mode selection is of significance investigating for revealing the deformation process to find a way promoting the formability of polycrystalline magnesium alloys. However, in addition to CRSS and crystal orientation, strain accommodation between neighboring grains plays an important role in deformation mode and deformation system selection. This makes the deformation process quite complicated. Recently, many researches have focused on twin variant selection with several approaches[11–26]. The previous works indicated that the selection of {10-12} extension twin variant is closely related to SF[16, 19, 25, 26]. However, some activated variants were found with low or even negative SFs in the following investigations[11, 14, 17]. This kind of non-schmid related behavior was also found in {10-11} contraction twin variant selection[18]. Jonas et. al[18] proposed a strain accommodation model to explain the occurrence of the variant with low SF, and indicted that these activated variants are easily accommodated by slip in the neighboring grains. Similarly, a geometric compatibility parameter was proposed to evaluate the effect of the twinning-slip interaction on twin variant selection[27, 28]. These models are rational in accordance with the regulation of plastic deformation coordination between grains in polycrystalline magnesium alloys. Considering strain accommodation, a misorientation factor and a strain accommodation parameter were proposed in our previous 2

work[29], which allowed to evaluate the potential deformation systems for strain accommodation and to predict the activated {10-12} extension twin variants. It is known that texture always forms in polycrystalline magnesium alloys, which strongly affects deformation mode selection in most grains. Texture weakening is an effective way to reduce the strong anisotropy[30–32]. Grains in weak-textured magnesium alloys are more randomly orientated, but not necessarily favorable for multiple modes activation because of different CRSS. To investigate the sequential activation of deformation modes in differently orientated grains is helpful for understanding the criterion of synchronous modes activation. In the present work, a textured magnesium alloy AZ31B was prepared, and the sequential activation of deformation modes was investigated through in-situ observation during tensile deformation under EBSD. The deformation mode selection and deformation system selection, especially twin variant selection, were discussed.

2. Experimental The magnesium alloy AZ31B (with chemical compositions of 2.70wt.%Al, 0.96wt.% Zn, 0.21wt.%Mn and Mg as balance) was received in the form of an extruded rod with size of Φ70mm×80mm. A round bar with size of Φ16×50mm was cut out of the rod with its axis along the extrusion direction (ED). To reduce residual stress and eliminate deformation microstructure, the bar was annealed at 520oC for 100min. After annealing, complete recrystallization took place, the grains were equiaxed with a broad grain size distribution and a weak fiber texture (Fig. 1(a)). The tensile sample was prepared from the annealed bar with the tensile direction parallel to ED (Fig.1(b)). The small area colored in grey on the surface of the sample was observed in-situ under EBSD. For EBSD measurement, the sample surface was mechanically ground, followed by mechanical polishing. Then electrolytic polishing was carried out in a solution of 10% perchloric acid (HClO4) and 90% ethyl alcohol at -30 ºC. To remove the Beilby layer of the surface completely, an argon ion beam was applied onto the selected area for 2 hours. EBSD pattern indexing rate reached to 99.8% for the un-tensioned sample. 3

(a)

(b)

Fig.1 EBSD orientation map of the annealed bar (a) and schematic showing of the tensile sample preparation for in-situ observation under SEM-EBSD (b).

The microstructure evolution was observed in-situ during tensile deformation at ambient temperature under Oxford Aztec EBSD system quipped with the micro-test tensile instrument on a Zeiss-Sigma scanning electron microscope (SEM). The micro-test tensile instrument in the SEM is Gatan Mtest 2000 ES. HKL Channel 5 software was used for data post-processing. The SEM scanning step size was 2µm and the voltage was 20kV. The tensile test was performed at a strain rate of 3×10-4/s. The tension was interrupted at engineering strain levels of 2.8%, 8.2% and 17.7%, respectively, for EBSD in-situ observation.

3. Results 3.1 Mechanical behavior and microstructure evolution Fig.2 (a) presents a tensile stress-strain curve of the alloy. It exhibits a typical concave-down shape that corresponds to magnesium alloys with fiber texture [6, 33]. In Fig.2 (a), the stress-strain curve is labeled with letters A, B and C corresponding to the interrupted points with the strains of 2.8%, 8.2% and 17.7%, respectively. It is seen that the stress at point A is just slightly higher than the yield stress. With increasing of strain, stress at points B and C raises evidently. Figs.2 (b)-(f) show the development of surface morphology of the sample with the increase of strain. Visibly, the original smooth surface (Fig.2 (b)) becomes rough at the strain of 2.8% (Fig.2(c)), and a few dislocation slip trace lines can be observed. Based on slip trace analysis, 4

the slip mode was determined as basal slip. Since no additional types of slip traces were found, only basal slip can be evidenced in this study. However, only two independent basal slip systems cannot satisfy homogenous plastic deformation, there would exist other slips to accommodate strain between grains. This will be discussed in the subsequent section of this paper. As the strain increases to 8.2%, flaky-shaped crystallites appear in some grains (Fig.2(d)). These crystallites should be inferred to be twins. At the strain of 17.7%, more twins can be found (Fig.2 (e)). Fig.2 (f) presents the surface morphology of the sample after fracture. The deformation microstructure changes little as compared with that shown in Fig.2 (e) because of the small strain increment. It should be noted that stress relaxation happened when the tensile tests were interrupted for EBSD measurement, which made the stress drop abruptly at the points A, B and C on the curve (Fig.2 (a)).

5

Fig.2 Tensile stress-strain curve of the sample (a) and the correspondent morphologies of the sample surface at different tensile stages: initial (b), 2.8% strain (c), 8.2%strain(d), 17.7%strain(e) and fractured (f).

Fig.3 Orientation maps (A) and band contrast maps (B) of the tensile sample at different tensile stages: (a)initial; (b) 2.8% strain; (c) 8.2% strain; (d) 17.7% strain. 6

Fig.3 shows orientation maps (Fig.3 A) and band contrast maps (Fig.3 B) of the original microstructure and deformation microstructures at different strain levels. In total, Euler angles of 121 grains labeled with a sequence number were recorded for analysis of the relationship between deformation mechanism and orientation (see Fig.3B (a)). The deformation twins generated are named as N-i, where N and i are respectively the sequence numbers of the parent grain and twin crystallite. In Fig.3A (a), no twin is spotted in the original microstructure. Most grains are in green color, indicating that the c-axis direction is around <11-20>. In Fig.3 A (b) or Fig.3 B (b), several twins (indicated with blue line in Fig.3B (b)) can be seen in grains 16, 32, 45, 58, 61 and 89. These twins were identified as {10-12} extension twins according to the misorientation of <11-20>86.4° to the parent grains. This result indicates that extension twinning activates accompanying basal slip at the same tensile stress. By comparison, it was found that their resolved shear stresses, obtained via SFs and the tensile stress at point A on the stress-strain curve, are both around 51.0MPa. However, it is known that the critical resolved shear stress is respectively 0.45-0.81MPa for basal slip and 2.0-2.8 MPa for extension twinning, so it is suggested that extension twinning activates after basal slip as tensile stress elevated further. The surface morphology in Fig.2 (c) presenting more evident slip traces illustrates this sequence. The number of {10-12} extension twins in Fig.3 A (c) or Fig.3 B (c) has increased as compared to that in Fig.3 A (b) or Fig.3 B (b). Meanwhile, one {10-11} contraction twin (indicated by the red line in Fig.3 B (c)) appears in grain 24. In contrast to the former maps, it can be seen that when the strain reaches 17.7%, the number of twins increases further and some twins grow up (Fig.3B (d)). On the top left corner of Fig.3B (d), it can be found that several {10-11} contraction twins penetrate the grain boundary between the adjacent grains. Such penetrating twins can be observed between grains 24 and 39, 78 and 80. Based on the above results, it is summarized that {10-12} extension twinning and {10-11} contraction twinning are both activated and increase in number with increasing stress/strain. However, the 7

activation of {10-12} extension twinning occurs prior to {10-11} contraction twinning. The above results suggests that the initiation of basal slip, extension twinning and contraction is asynchronous in different grains, but as tensile stress elevated, the activation of slip and twinning can be synchronous in different grains.

3.2 Twin variants According to the Euler angles of the parent grains and twins, twin variant was identified with orthogonal coordinate transformation matrix T between the parent and the twin. The transformation matrix T is defined as follow [22, 34]: Tij=2ninj−δij; δij=0 if i ≠ j; δij=1

(1)

where n represents the unit vector of the twin plane normal. The six equivalent variants for {10-12}<-1011> extension twinning are respectively E1(10-12)[-1011], E2(01-12)[0-111], E3(-1102)[1-101], {10-11}<10-1-2> C2(01-11)[01-1-2],

E4(-1012)[10-11], contraction

E5(0-112)[01-11]

twinning

C3(-1101)[-110-2],

they

are

and

E6(1-102)[-1101];

respectively

C4(-1011)[-101-2],

C1(10-11)[10-1-2],

C5(0-111)[0-11-2]

C6(1-101)[1-10-2]. Table 1 Twins, twin variants, SFs and SF ranks in the grains tensioned at 2.8%strain Grain

Twin

Variant

SF

SF rank

SF-related

16

16-1

E6

0.3893

2

No

16-2

E5

0.3850

3

No

16-3

E2

0.4036

1

Yes

32

32-1

E6

0.2140

1

Yes

45

45-1

E2

0.0110

1

Yes

58

58-1

E3

0.2244

1

Yes

61

61-1

E3

0.1439

1

Yes

89

89-1

E3

0.1809

1

Yes

8

for

and

Table 1 lists the identified extension twin variants in the twinned grains in Fig3A (b) or Fig.3B (b). SF and SF rank of the grains for these twin variants are also listed in the table. It is can be seen that the SF value distributes in a wide range from 0.0110 to 0.4036. Of these eight twin variants, six have SF ranking 1, others ranking 2 and 3. Hence, most {10-12} extension twin variants follow Schmid law (i.e. are SF-related) here, but some variants suffer exception. These non-SF-related variants should be accommodated by deformation systems in the neighboring grains as suggested in previous studies[11, 18, 35].

Table 2 Twins, twin variants, SFs and SF ranks in the grains tensioned to 8.2% strain Grain

Twin

Variant

SF

SF-rank

SF-related

61

61-2

E3

0.1439

1

Yes

61-3

E6

0.1423

2

No

83

83-1

E5

0.0860

2

No

24

24-1

C1

0.3380

1

Yes

Table 2 lists additional twins activated in the grains 24 (C1), 61 (E3 and E6)and 83 (E5) when the strain reaches 8.2%. Obviously, SF values of the new {10-12} extension twin variants are lower. The SF value of twin 83-1 (variant E5) is the lowest. It should be noted that the resolved shear stress is increased due to the increment of loading stress. The twins with lower SF could be activated. Twin 24-1 (C1) is the first {10-11} contraction twin spotted in the observation area during the tensile test. The corresponding SF value of 0.3380 is ranking 1, suggesting that the variant selection is SF-related. In table 3, five contraction twin variants are listed with their SF values. Twins 24-2 (C6) and 39-1 (C6) can be spotted in the two neighboring grains, as if they were connected to each other across the grain boundary (Fig.3B (d)). The pair of twins 1-1 (C4) and 115-1 (C4) is in similar relationship. It should be noted that these two pairs of twins respectively belong to the same variants.

9

Table 3Twins, twin variants, SFs and SF ranks in the grains tensioned at 17.7% strain Grain

Twin

Variant

SF

SF-rank

SF-related

1

1-1

C4

0.2783

3

No

24

24-2

C6

0.2608

3

No

39

39-1

C6

0.3773

1

Yes

80

80-1

C1

0.3988

1

Yes

115

115-1

C4

0.1947

3

No

4. Discussion

4.1 The analysis of activation sequence of slips and twinning Synchronous activation of deformation modes, as well as multiple slip systems and twin variants, are necessary to ensure a homogenous deformation. However, the above results show that although the deformation modes can be activated at the same time in different grains as stress increases, the initiation of these modes is asynchronous. The activation of the various deformation modes exhibits a seriation. Basal slip activates first, and then {10-12} extension twinning and {10-11} contraction twining. In the observation, traces of prismatic and pyramidal slips were not found, nevertheless, the highest Schmid factor among the slip systems of 121 grains for basal , prismatic and pyramidal slips was calculated, respectively, for the analysis of activation sequence of the slips in the present work. The calculation result is presented in Fig.4 (a). It can be seen that the maximum SFs of prismatic and pyramidal slips concentrate in the range of 0.4-0.5, while, that of basal slip distributes homogeneously in the whole range of 0-0.5. With the lowest CRSS, basal slip could be activated easily, although its SF may be very low. So basal slip initiates first and would act as the main mode. In contrast, CRSSs of prismatic and pyramidal slips are much higher. However, they could be also activated according to the calculated tensile stress based on the SF values of 0.4-0.5. The calculated tensile stress is respectively 78.4-98.0MPa for prismatic slip and 90.0-202.5MPa for pyramidal slip (where the critical resolved shear stress of 10

prismatic slip was taken as 39.2MPa[36], and that of pyramidal slip was taken as 45.0-81.0MPa[36]). The calculated tensile stress for prismatic is much lower than 131.3MPa under which basal slip activates as shown in Fig.2 (c), so it can be deduced that prismatic slip should be activated because of their narrow and much higher SF value range. SF for basal slip of the grain in Fig.2 (c) is 0.3945, the calculated tensile stress is merely 1.1-2.1MPa (where the critical resolved shear stress was taken as 0.45-0.81MPa[37]). This means that when prismatic slip activated, basal slip should have been already activated heavily, its traces are easy to be observed. The tensile stress for pyramidal slip is higher, by maximum, it is round the stress of point B on the stress-strain curve, at which contraction twinning has been already activated.

(a)

(b)

Fig. 4 The distribution of the highest SF of 121 observed grains for slip (a) and twinning (b).

Fig.4 (b) presents respectively the highest SF for extension and contraction twining among all active winning systems. Obviously, the maximum SF for the two modes distributes differently. For extension twinning, it concentrates in a low range from -0.1 to 0.2. It concentrates in a higher range from 0.3 to 0.5 for contraction twinning. From the experimental results, it is found that {10-12} extension twinning is activated at the early stage of deformation, but {10-11} contraction twinning later, although the alloy has the fiber texture more favorable for contraction twinning. However, extension twinning is easy to activate in some deviated-fiber orientation grains due to its low CRSS [2], despite the average SF for {10-11} contraction twinning is much higher than that for {10-12} extension twinning. 11

Based on the results and the analysis above, it is suggested that although the deformation modes are able to activate synchronously in various grains, the initiation of them is sequential, the sequence refers to basal slip, extension twinning, prismatic slip, pyramidal slip and contraction twinning. It is seen that the activation sequence is highly related to CRSS, the texture affects it little. However, as the texture decide the grain orientation distribution, most fiber-orientated grains have high SF for prismatic slip, pyramidal slip and contraction twinning as seen in Figs.4. This would result in a rapid increment of these modes in the individual grains as tensile stress elevated. As an example, our previous work [38] demonstrates that the number of contraction twins increases more rapidly than that of extension twins in fiber-textured alloy AZ31B.

4.2 Strain accommodation for twin variant selection

Occurrence of multiple deformation systems in the same grain is crucial to accommodate plastic strain between neighboring grains for homogenous deformation according to Von Mises criterion [39]. In the present study, the activation of multiple slip systems in the same grain is unable to be determined, but twin variants are easily observed. When a grain twinned, its plastic strain should be accommodated by slips or twinning in neighboring grains. Accommodation dislocations are often named as “Geometrically necessary” dislocations (GNDs) [40]. In the present work, three regions in the deformed microstructure (Fig.3A) have been selected to analyze the strain accommodation for twin variant selection. As described in ref.[29], strain accommodation parameter A is defined as:

A = τ cp (mt ⋅ ml ⋅τ ct ) + 1 mt

(1)

where, mt is Schmid factor of twin variant in the deformed grain, ml is misorientation factor, τcp is CRSS of the accommodative deformation system and τct is the CRSS of the twinning system. The higher values of mt and ml are, the easier for strain accommodation activating is. On the contrary, the higher value of τcp will be more difficult for the strain accommodation system to be activated. Misorientation factor ml is defined as: 12

ml = cos λ ⋅ sin α

(2)

where, λ is the angle between twinning shear direction and accommodative shear direction, α is the angle between twinning shear direction and accommodative shear plane normal direction.

Fig.6 EBSD maps showing microstructure evolution in region 1 (a), (0001) pole figure of parent grain 16 and the twins in it (b) and schematic showing of crystallographic orientation relationship between the parent grain and the twins(c).

Table 4 Strain accommodation parameter of slip systems for extension twins in grain 16. Twin

Neighbor

Slip system

E1

E2

E3

E4

E5

E6

16-1

8

Basal

4.1502

3.1729

3.9658

4.4748

3.3563

4.4181

prismatic

65.4811

47.9485

62.3122

64.4727

49.0387

74.6945

pyramidal

92.4900

169.2888

86.4362

131.8155

126.0481

71.6626

Basal

3.7721

3.8415

5.2379

4.3845

3.3954

3.4755

prismatic

61.2962

65.4340

88.2018

62.8914

49.2011

51.4158

pyramidal

234.3222

72.8593

76.3164

159.1436

108.8162

89.3496

Basal

3.8239

3.2519

4.3969

4.4009

3.4458

4.2788

prismatic

56.9080

47.8161

78.2827

64.5199

51.3160

76.2914

pyramidal

126.1675

102.1553

82.0560

157.4733

100.5176

74.0580

16-2

16-3

17

15

13

Note: The activated variant is highlighted in bold.

Fig.6 (a) shows the twins evolution in grain 16 (region 1 in Fig.3A) orientated favorably for extension twinning. It can be seen that three twins (16-1, 16-2, 16-3) generate in the parent grain when strained to 2.8%. With increasing strain, twins gradually swallow the parent grain. As shown in Figs.6 (b) and (c), the three activated twins belong to different variants (E6, E5 and E2, respectively). The misorientation between E5 and E2 is <11-20>7.4°. Accroding to equation (1), strain accommodation parameters for the variants were calculated (see table 4). It was found that among six potential variants, the activated twin 16-1 (E6) has the lowest strain accommodation parameter by pyramidal slip in grain 8. Meanwhile, its parameters by basal and prismatic slips are higher than those for other variants. Consequently, E6 is easier to activate under strain accommodation by pyramidal slip than other variants, although its SF is not the highest. For twins 16-2 (E5) and 16-3 (E2), their strain accommodation parameters by basal and prismatic slips are respectively the lowest among all variants, which suggests that the selection of the two activated twin variants benefits more from strain accommodation by basal and prismatic slips of the neighboring grains.

Fig.7 EBSD maps showing microstructure evolution in region 2 (a), (0001) pole figure of parent grain 14

61 and the twins in it (b) and schematic showing of crystallographic orientation relationship between the parent grain and the twins(c).

Fig.7 (a) shows the twins evolution in grain 61 (region 2 in Fig.3A). Parent grain 61 orientates with its c-axis more perpendicular to tensile direction than parent grain 16 (see Figs.7 (b) and (c)). SF for extension twinning is not high (see table1 and table2), but extension twins 61-1(E3), 61-2(E3) and 61-3(E6) are still activated due to the lower CRSS. SF for variant E3 (0.1439) is the highest among the six variants, that is reasonable for its activation from the point of view of Schmid law. However, E6 appears and grows up with Schmid factor (0.1423) ranking in the second order when strain increased. Consulting with the strain accommodation parameter for variant E6 (table 5), it can be found that accommodated by basal and prismatic slips, it is the lowest.

Table 5 Strain accommodation parameter of slip systems for extension twins in grain 61. Twin

Neighbor

Slip system

E1

E2

E3

E4

E5

E6

61-1

48

Basal

-8.4940

-9.3722

10.6904

12.0417

14.6718

12.5754

Prismatic

-128.8808

-136.7808

193.2938

174.1443

220.1993

231.0294

Pyramidal

-245.5357

-338.8387

212.1443

431.9158

428.6959

201.1240

Basal

-8.8718

-9.2180

8.9925

-12.1721

-25.6034

36.0777

Prismatic

-136.7952

-135.0574

149.2364

-174.3413

-455.0230

468.5418

Pyramidal

-208.6621

-546.3847

567.5465

-380.6879

-312.4685

209.2743

Basal

-8.3895

-9.4621

11.3931

-12.5721

-14.4115

10.5145

Prismatic

-126.7572

-138.9904

185.7496

-201.7224

-224.4782

164.8421

Pyramidal

-267.1825

-307.7772

193.9683

-349.4891

-532.5442

204.9347

61-2

61-3

63

80

Note: The activated variant is highlighted in bold.

15

Fig. 8 EBSD maps showing microstructure evolution in region 3 (a), (0001) pole figure of parent grains24 and 39 and the twins in it (b) and schematic showing of crystallographic orientation relationships between the parent grain and the twins(c).

Fig.8 (a) presents the evolution of the contraction twins in grains 24 and 39 (region 3 in Fig.3A). When strained at 8.2%, thin contraction twin 24-1 (variant C1) appears. Another contraction twin 24-2 (variant C6) forms when strained to 17.7%. At this stage, contraction twin 39-1 (variant C6) also appears in grain 39. From the band contrast map (Fig.3B), it can be seen that twins 24-2 and 39-1 are in fact connected across the grain boundary, as if twin 24-2 penetrates the grain boundary into grain 39, or twin 39-1 penetrates the grain boundary into grain 24. Table 6 presents the strain accommodation parameters for these contraction twin variants. In the table, strain accommodation parameters for twin 24-1 (C1) by the three slip systems are the lowest among the six variants, but for twin 24-2 (C6), the accommodation parameters are not the lowest. Considering that the parameters for twin 39-1 (C6) are the lowest, it may be deduced that it nucleates at the grain boundary and induces accommodation slips, and these slips trigger the contraction twin variant 24-2. However, this hypothesis suggests a question that whether slips can induce twinning, in terms of passive strain accommodation for twinning. It should be further investigated. 16

Table 6 Strain accommodation parameter of slip systems for contraction twins in grain 24 and 39. Twin

Neighbor

Slip system

C1

C2

C3

C4

C5

C6

24-1

23

Basal

2.9989

421.7385

3.5983

3.0891

561.4690

3.6236

Prismatic

4.5601

654.2531

5.5238

5.5045

1458.1569

6.4518

Pyramidal

4.6145

665.9141

5.5411

4.6571

780.4115

5.4676

Basal

2.6751

72.9255

4.6137

2.9703

136.6722

3.8878

Prismatic

4.9153

179.4055

8.2487

4.7465

203.6820

5.9273

Pyramidal

4.0468

103.0259

6.9647

4.6029

213.9246

5.9721

Basal

3.2701

-297.5101

3.4382

4.4278

248.0950

2.7217

Prismatic

4.8884

-448.7858

5.4618

8.3794

593.9267

4.7244

Pyramidal

5.0549

-467.4638

5.2873

6.6531

352.6162

4.1293

24-2

39

39

24

Note: The activated variant is highlighted in bold.

4.3 Plastic strain accumulation Kernel average misorientation (KAM) or local misorientation (a terminology used in Channel 5 software) resulted from orientation gradient represents the distribution of local plastic strain induced by slips[41]. To discuss the magnitude of plastic strain in the surface grains, KAM dealt with 3×3 grids was applied in this work.

17

Fig. 5 Kernel average misorientation maps of the grains at a strain of (a) 0 %, (b) 2.8%, (c) 8.2% and (d) 17.7%.

Fig. 5 shows KAM distribution in the surface grains at original state (Fig.5(a)) and different strain levels (Figs.5(b), (c) and (d)). KAM values vary within individual grains, indicating inhomogeneity of the plastic deformation. It is seen that in addition to twinning, local strain induced by slips at the early stage of deformation (2.8%) is mainly concentrated at the boundaries of several small grains (Fig.5 (b)). This indicates that slips are easily activated in the small grains. SF distributions of these small grains for basal, prismatic and pyramidal slips are similar to those of grains as a whole, as seen in Fig.4 (a). Since SF for prismatic and pyramidal slips is much higher, these two slips should be able to activate concomitantly with basal slip. With increasing strain, the local strain accumulates and expands into the grains interior (Fig.5(c)). As deformation continues, local strain also accumulates at boundaries of some large grains and also expands into the grains interior (Fig.5(c) and (d)).The un-indexed black regions in Fig.5(d) have the largest lattice distortion, thus have higher KAM in these regions[31]. The above results demonstrate that plastic deformation induced by slips behaves 18

sequentially and non-uniformly in different grains.

5. Summary and Conclusions Activation sequence of deformation modes was investigated by means of in-situ observation of the microstructure evolution under EBSD. It is summarized as following: Both slip and twinning modes play important roles in a fiber-textured magnesium alloy AZ31B during tensile plastic deformation. With the lowest CRSS, basal slip initiates first, and then {10-12} extension twinning occurs. Although CRSS for prismatic and pyramidal slips is much higher, they could be activated subsequently in the grains with high SF with tensile stress increasing, or could be activated as strain accommodation mechanisms. The activation of {10-11} contraction is the latest due to the highest CRSS, even the alloy exhibits fiber texture. KAM value varies within individual grains, indicating slips behave sequentially and non-uniformly in orientated grains. Slips are activated first in small grains. Local plastic strain induced by slips is mainly concentrated at the grain boundaries. The activation of most twin variants is SF-related. The activation of some non-SF-related twin variants can be explained in terms of strain accommodation. The accommodation parameters are generally the lowest for the activated twin variants not having the highest SF rank.

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: