Role of {101‾2} twinning in the anisotropy and asymmetry of AZ31 magnesium alloy under high strain rate deformation

Materials Science & Engineering A 772 (2020) 138814

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Role of f1012g twinning in the anisotropy and asymmetry of AZ31 magnesium alloy under high strain rate deformation Xiaoxia Wang a, b, Pingli Mao a, b, *, Ruifeng Wang a, b, Zheng Liu a, b, Zhi Wang a, b, Feng Wang a, b, Le Zhou a, b, Ziqi Wei a, b a b

School of Materials Science and Engineering, Shenyang University of Technology, 110870, PR China Key Laboratory of Magnesium Alloys and the Processing Technology of Liaoning Province, 110870, PR China

A R T I C L E I N F O

A B S T R A C T

Keywords: 1012extension twinning AZ31 magnesium alloy Schmid factor Anisotropy Asymmetry

In order to investigate the role of f1012g extension twinning in anisotropy and asymmetry of highly textured magnesium alloy under high strain rate deformation, tensile and compression deformation were conducted by Split Hopkinson Tension and Pressure Bar under the strain rate of 1800s 1. With the help of theoretical calcu­ lated Schmid Factors (SFs), the dynamic tensile and compression behavior and deformation mechanism of extruded AZ31 magnesium alloy along extrusion direction (ED) and transverse direction (TD) were analyzed in the present paper. The results demonstrated that extruded AZ31 magnesium alloy shows obvious anisotropic and asymmetric behaviors under high strain rate deformation and the anisotropic and asymmetric behaviors are arisen from the different role of f1012g extension twinning. The Schmid Factor calculation results of six extension twinning variants revealed that the six variants have the same opportunity to activate under tensile loading along TD, while for compression along ED, only two variants have the opportunity of operating due to the highest SF among the six variants. When high strain rate tensile loading was applied along ED and compression loading along TD, f1012g extension twinning is not favored.

1. Introduction Magnesium and its alloys have been attracted extensive research interesting in recent years due to their potential usage in automobile industry as a candidate to reduce the weight and save energy. Owing to the polarity of f1012g extension twinning, pure magnesium and its al­ loys exhibit specific phenomenon, such as anisotropy and tensilecompression asymmetry during deformation, especially in the highly textured extrusion or rolling sheet [1,2]. Additionally, the limited slip systems due to the close-packed crystal structure have their contribution in the anisotropy and asymmetry in Mg alloys. Generally, there are four frequently observed slip systems operate in Mg alloys, those are basal slip, prismatic slip and first pyramidal slip and secondary pyra­ midal slip. According to Von misses criterion that at least five independent slip systems are needed to satisfy the homogeneous deformation [3]. For Mg alloys, both of basal and prismatic slip only have two independent slip systems, pyramidal slip has 4 inde­ pendent slip systems, while pyramidal slip supply 5 independent

slip systems [2]. Then it is reasonable to assume that the activation of pyramidal slip might increase the plasticity of Mg alloys. However, it was known that {1122}<1123> () pyramidal slip is hard to activate at room temperature due to its relatively high critical resolved shear stress (CRSS). Several types of deformation twinning have been observed and played a very important role in Mg alloys deformation, such as f1012g, f1011g, f1013g, f3034g and f1014g [4]. Due to the low CRSS of activation, f1012g extension twinning has been paid much attention [5–8]. f1012g extension twinning can active under two loading conditions: tension parallel to the c-axis of the hexagonal close-packed lattice and compression perpendicular to the c-axis. Be­ sides causing extension along the c-axis, f1012g twinning can rotate the twined area by 86.3� about an < 1120 >axis. Due to the reorientation of the crystal within the twined region, slip systems that were not favored to activate prior to twinning may be activated. f1012g extension twin­ ning in Mg alloys have six equivalent variants, those are ET1 (1012) [1011], ET2 (0112)[0111], ET3 (1102)[1101], ET4 (1012)[1011], ET5

* Corresponding author. School of Materials Science and Engineering, Shenyang University of Technology, 110870, PR China. E-mail addresses: [email protected] (X. Wang), [email protected] (P. Mao), [email protected] (R. Wang), [email protected] (Z. Liu), [email protected] (Z. Wang), [email protected] (F. Wang), [email protected] (L. Zhou), [email protected] (Z. Wei). https://doi.org/10.1016/j.msea.2019.138814 Received 26 November 2019; Accepted 10 December 2019 Available online 18 December 2019 0921-5093/© 2019 Elsevier B.V. All rights reserved.

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anisotropy under high strain rate deformation, tensile and compression testing were conducted along ED (ED-T and ED-C, here, T refer to tensile and C refer to compression, hereafter) and TD (TD-T and TD-C, here­ after). The tensile and compression testing were performed at a strain rate of 1800s 1 and at room temperature. Macro-texture testing was carried out by X-ray diffraction method, Co target, Ka radiation, Fe filter, voltage of 35 kV, current of 40 mA. The microstructure and micro-texture analysis were performed on a field emission MERLIN Compact (ZEISS) scanning electronic microscope (SEM) equipped with an electron back-scattering diffraction (EBSD) detector system (Oxford HKL), the scanning step size is 0.6 μm, binning band is 2 � 2 and the voltage is 20 KV. EBSD data analysis was carried out using the Channel 5 software. The samples for EBSD mapping were mechanically ground and electrochemically polished in an electrolyte of 10% perchloric acid and 90% ethanol at 15 V and 30 � C for 120s.

(0112)[0111] and ET6 (1102)[1101], respectively. The relationship between the applied stress and the activation of the twinning variant is depended on Schmid Law, which is the twinning variant, which has the highest SF, will have the highest probability to activate. Several works have been done to understand the anisotropic behavior in pure Mg. It was found that during the plane-strain compression along rolling di­ rection (RD) and normal direction (ND) of a hot rolled pure Mg plate, the obvious anisotropic behavior was arisen from massive activation of f1012g extension twins in RD samples, in which the majority of the c-axis reoriented from perpendicular to the RD prior to deformation to align with RD. While for ND compression, the c-axis alignment with ND was strengthened during plain-strain compression, which was caused by f1011g-f1012g double twinning [9]. As for Mg alloys, the anisotropic phenomenon is still persisted and it is further strengthened by the po­ larity of the f1012g twinning. When a highly textured AZ31 Mg alloy sheet was compressed along ND, the dominant deformation mode was non-basal slip and f1011g compression twinning, while when the alloy sheet subject to tensile along RD, the author emphasized the contribu­ tion of non-basal slip [10]. Some researchers studied the texture distri­ bution of AZ31 Mg alloy extrusion bar. They reported that the distribution of {0002} texture affects the twinning behavior in the alloy, which is the main reason of tensile-compression asymmetry and anisotropy [11–13]. Up to date, several works have concerned with the high strain rates deformation behavior and deformation mechanisms of Mg alloys. However, the role of f1012g extension twinning on the anisotropy and asymmetry of highly textured Mg alloy under high strain rate deformation were still not thoroughly understood. The aim of this work is to explore the anisotropic and asymmetric behavior of highly textured AZ31 extrusion under high strain rate deformation and to reveal the role of f1012gextension twinning in behind.

3. Results 3.1. Initial microstructure and texture The initial microstructure of as-extruded AZ31 Mg alloy displays in Fig. 2 (a), and it shows that the equiaxed grains are somewhat hetero­ geneous, scattered twins can be observed in large grains. The average grain size is 6.95 μm and the standard deviation of grain size is 67, indicating that the initial microstructure are quite heterogeneous. The EBSD orientation map in Fig. 2 (a) shows a very strong texture presents in the microstructure, it is confirmed by the micro- and macro-texture (Fig.2 (b) and Fig.2 (c)). The (0002) pole in Fig.2 (b) and Fig.2 (c) in­ dicates that the majority of the grains c-axes are essentially perpendic­ ular to ED and the basal planes are parallel to ED, it is a typical extrusion texture that the basal planes of the grains rotate to parallel to ED during extrusion. It also can be seen from Fig. 2b that many c-axes slightly rotate from ED toward ND.

2. Materials and experiments The samples were cut from a commercially hot extruded AZ31 (Mg3.1Al-1.05Zn-0.54Mn) magnesium alloy plate, which was fabricated at Timminco, Denver Co., USA with an extrusion ratio of ~6 and the extrusion temperature of 360–382 � C. Four sets of samples were cut from the plate using a wire electrical discharge machine (Fig. 1). Among them, two sets have the dimension of 10 mm in diameter and 6 mm in height, and they are designed for compression test. Two sets have the dimension of gauge length of 8 mm and gauge diameter of 4 mm, they are designed for tensile test. One set of compression samples was ori­ ented such that the compression occurred in extrusion direction (ED) and the other set compression occurred in transverse direction (TD) (Fig. 1). One set of tensile samples was oriented such that the tensile occurred along ED and the other set tensile occurred along TD (Fig. 1). The high strain rate tests were carried out by Split Hopkinson Pressure Bar (SHPB) and Split Hopkinson Tension Bar (SHPT). The reader is referred to Mao et al. [14] for a more detailed description of the testing procedures. In order to reveal the dynamic deformation behavior and the relevant deformation mechanisms of highly textured AZ31 Mg alloy, in particular, to explore the tensile-compression asymmetry and

3.2. Deformation characterization 3.2.1. Compression behavior of extruded AZ31 magnesium alloy at 1800s 1 The compression true stress-strain curves along ED (ED-C) and TD (TD-C) are present in Fig. 3 (a). It is shown that the compression be­ haviors along ED and TD are quite different. The stress-strain curve of ED-C exhibited a “S” shape in the early stage of deformation, which is known as a typical feature off1012g extension twinning dominated deformation [15–20]. While the stress-strain curves of TD-C show a traditional work hardening shape, implying the predominant activation of slip and/or f1011g-f1012g double twinning [9]. This distinction of deformation behaviors between ED-C and TD-C can be clearly reflected in the strain hardening rate vs true strain curve, as shown in Fig. 3b. The strain softening caused by extension twinning in ED-C in the early stage of deformation is apparently revealed, while for TD-C the strain hard­ ening displays a continues decreasing tendency. After ED-C, cracks formed in the sample, the yield stress (σ0.005) is 89.17 MPa, and the strain to fracture is 2.74%. After TD-C, the sample is broken, and the yield stress is 123.99 MPa, the strain to fracture is 2.24%. 3.2.2. Tensile behavior of extruded AZ31 magnesium alloy at 1800s 1 The tensile true stress-strain curves along ED (ED-T) and TD (TD-T) are present in Fig. 4. It shows apparently that the tensile behavior along two different directions has large distinguish in two aspects: (1) the yield strength of ED-T (407.38 MPa) is about three times larger than that of TD-T; (2) strain hardening is apparently visible after the material yield for TD-T (128.1 MPa), but show a slight strain softening after yield for ED-T (Fig. 4). The difference of deformation behavior of ED-T and TD-T is arisen from the different loading direction, further it is attributed to the different deformation mechanism. It can be seen from Fig. 4 that the

Fig. 1. Orientation of the tensile and compression samples relative to the loading direction and the plate coordination. 2

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Fig. 2. Initial microstructure and texture of extruded AZ31 Mg alloy: (a) EBSD orientation map, grain boundaries with misorientation greater than 10� are outlined in black and f1012g extension twin boundaries are outlined in red, (b) (0002) micro pole figure, (c) (0002) and （1010）macro pole figures. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3. The compression true stress-strain curves along ED and TD (1800s 1) in (a) and the strain hardening rate - true strain curve in (b).

TD-T curve also featured with “S” type shape in the early stage of deformation, implying that the activation off1012gextension twinning is also responsible for the early stage deformation. As for ED-T, the strain softening after yielding was believed to cause by dynamic recrystalli­ zation [21]. Both ED and TD samples are broken after high strain rate tensile of 1800s 1, the elongation to fracture of ED-T and TD-T are 2% and 2.5%, respectively.

subject to tension loading due to the strong initial texture, resulting in the activation of f1012g extension twinning to accommodate the applied tension strain; the other is c-axis contraction, including ED-T and TD-C (Table 1, the third row, the second column and the second row, the third column), in which the c-axis of the most of the grains subject to compress, resulting in the activation of f1011g contraction twinning, non-basal slip and/or f1011g-f1012g double twinning to accommodate the compressive strain along c-axis. The true stress-strain curves of c-axis extension and c-axis compression are comparably dis­ played in Fig. 5. It can be seen from Fig. 5 (b) that the yield strength of TD-C is obviously lower than that of ED-T, which is mainly related to the pre-existing twins in the original material. Wang et al. [22] found that when AZ31 magnesium alloy was compressed along the c-axis, the twins will detwin at first, this would greatly reduce the yield strength of the samples.

4. Discussion According to the orientation relationship between loading direction and extruded plate coordination, the four deformation conditions can be classified into two categories, one is c-axis extension, including ED-C and TD-T (Table 1, the second row, the second column and the third row, the third column), in which the c-axis of the most of the grains 3

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4.1. C-axis extension 4.1.1. Activation of f1012g extension twinning For ED-C and TD-T (Fig. 5a), it is noted that although the early stage deformation behavior under both loading directions are quite similar and are dominant by the f1012g extension twinning [23]. However, in the later stage of deformation they are apparently different, especially in strain hardening behavior. These differences featured in ED-C and TD-T deformation behaviors seems to result from the different loading path, i. e. compressive loading perpendicular to the c-axis of Mg crystal and tensile loading parallel to the c-axis of the crystal. SF has been suc­ cessfully used to predict the deformation behavior of magnesium alloys [24]. SF can be calculated by following equation: (1)

m ¼ cos ϕ cos λ

Fig. 4. The tensile true stress-strain curves along ED and TD (1800s

1

whereϕ is the angle between the loading direction and the slip (twin­ ning) plane normal, λ is the angle between the loading direction and slip (twinning) direction. For twinning (slip) system, which is in the MillerBravais indices as {hkil}, the twinning (slip) plane normal [uvtw] of (hkil) is calculated by the following equation: � � 3 � c�2 ​ ½u; v; t; m� ¼ h; k; i; l (2) 2 a

).

Table 1 Loading direction with respect to the c-axis orientation under different defor­ mation conditions. Sample axis direction (ED)

where c/a is the axial ratio of magnesium, 1.624. For two fourdimensional Miller-Bravais indices directions, V1[u1 v1 t1 w1] and V2[u2 v2 t2 w2], the angleϕ (λ) between them is given by the standard equation [25].

Sample axis direction (TD)

Compressive loading

cos ϕðλÞ ¼

V1 ⋅V2 jV1 j⋅jV2 j

� �2 u1 u2 þ v1 v2 þ 12 ðu1 v2 þ u2 v1 Þ þ 13w1 w2 ac ffiffiffiffiffi�ffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� ffiffiffiffiffi�ffiffiffiffi ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� u1 2 þ v1 2 þ u1 v1 þ w31 Tensile loading

2

c a

2

�

u2 2 þ v2 2 þ u2 v2 þ w32

2

c a

(3)

2

V1 [u1 v1 t1 w1] is the twinning (slip) plane normal or the twinning (slip) direction, V2 [u2 v2 t2 w2] is the loading direction. Theoretically, f1012g extension twinning has six equivalent twin variants: ET1 (1012) [1011], ET2 (0112)[0111], ET3 (1102)[1101], ET4 (1012)[1011], ET5 (0112)[0111], ET6 (1102)[1101], as shown in Table 2. For the conve­ nience of calculation of the SF, two angles are assigned to represent the loading direction and the axis in a magnesium unit cell, θ and α. Where θ is the angle between c-axis and the loading direction, α is the angle between a-axis and the projection of loading direction on the basal plane. θ is changed within 0–90� , α is change from 0 to 30� due to the asymmetry of magnesium unit cell. The SF calculation results of six f1012gextension twinning variants

Fig. 5. Comparison of true stress-strain curves of c-axis extension in (a) and c-axis contraction in (b). 4

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¼ 0� to 0.499 at α ¼ 30� (Figs. 7 and 8) are obtained at θ being 90� (the loading direction is perpendicular to the c-axis, θ ¼ 90� in Figs. 7 and 8) for a f1012g twin variant pair of ET1 and ET4. The SF for the two loading conditions of ED-C and TD-T are summarized in the (0001) pole figure, as shown in Fig. 9. It has been proved by several researchers [23,26–28] that the acti­ vation of f1012g twin variants or variant pair follow the Schmid low, which is the twin variants with the highest SF will activate and dominant the twinning behavior. It can be seen from Fig. 9 that in the loading condition of ED-C, the twin variant pair of ET1 and ET4 with the highest SF is aligned with ED, implying that the activation of this twin variant pair results in the reorientation of the c-axis of the twined area toward ED, i.e. the loading direction. Further compression along ED causes c-axis of twined area subject to compressive loading, which is favor for the f1011g contraction twinning or slip rather than detwinning, as is suggested by some researchers [9,27]. When a twin variant or a twin variant pair activate in a grain, there are two possible misorientation relationship formed [9]: 0� or 7.4� < 1210 >, it means that the f1012g extension twin formed in ED-C samples will parallel to each other within a grain in most of the grains. As for TD-T, i.e. tensile along transverse direction, it is corresponding to θ ¼ 0� in Fig. 6. Based on the above SF calculation results, as shown in Fig. 9, all six twin variants have an equal SF value of 0.499, which means that six twin variants have the equal opportunity to activate in a grain, implying that in the deformation condition of TD-T, there will be more than one twin appeared in a grain. There are three possible misorientation relationships between different twins generated from six twin variants, those are 7.4� between Para-position (a twin variant pair) (T1 and T4, T2 and T5, T3 and T6), 60� between ortho-position (T2 and T1, T2 and T3), 60.4� between Meta-position (T1 and T3, T1 and T5) [29], as is shown in Table 3 [9]. The twin variants grow to twin bands. As a result, the different twin

Table 2 6 equivalent twin variants.

for tensile loading parallel to the c-axis (TD-T) and compressive loading perpendicular to the c-axis (ED-C) are shown in Fig. 6 through Fig. 7. It is indicated from Fig. 6 that when the c-axis is subject to tensile loading (TD-T) the highest SF value of 0.499 are obtained at θ being 0� (the loading direction is parallel to the c-axis, θ ¼ 0� in Fig. 6) for the six f1012g twinning variants and the SF values decrease with the increasing of the tilting angle between the c-axis and loading direction regardless of the α variation. While when the basal plane is subject to compressive loading (ED-C) the SF values of six f1012g twinning variants increase with the tilting angle between the c-axis and the loading direction increasing and the highest SF value, which is increased from 0.374 at α

Fig. 6. SF values of six f1012g twinning variants under c-axis tensile loading (TD-T), the angle between a-axis and the projection of loading direction (α) are 0� (a), 10� (b), 20� (c)and 30� (d). 5

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Fig. 7. SF values of six f1012g twinning variants under basal plane compression loading (ED-C), the angle between a-axis and the projection of loading direction(α) are 0� (a), 10� (b), 20� (c) and 30� (d).

deformation mode but basal slip has an equal possibility to activate. Whether a deformation mode can be activated not only depends on its SF but also depends on its CRSS. According to the estimated result by Barnett [30], Wan [31] and Gong [32] that the CRSS for the 5 defor­ mation modes in room temperature was in the following sequence: CRSS basal < CRSS extension twinning < CRSS prismatic slip < CRSS pyramidal slip < CRSS pyramidal slip. From the above analysis, it can be deduced that f1012g extension twinning is the only operating deformation sys­ tem at the early stage of ED-C condition. While for TD-T deformation, the SF of slip (0.446, Table 4) is close to that of twinning (0.499, Table 4), however, the τCRSS of pyramidal slip is higher than that of twinning, like in ED-C, f1012g extension twinning is also the only operate deformation system at the early stage of TD-T condition. It was proved by acoustic emission (AE) combined with digital image corre­ lation (DIC) method [33] that f1012g extension twinning play a domi­ nant role in the early stage of deformation and responsible for the relatively softening regime after yielding when c-axis subject to tension stress. 4.1.2. Slip induced by f1012g extension twinning Twinning in a grain can cause a change in the deformation mecha­ nisms due to the following two reasons:(1) twinning introduce twin boundaries, which can serve as barriers to certain slip systems, give rise to the Hall-Petch effect and twinning-slip interaction; (2) twinning form reoriented regions that can promote more slip or twin modes within the twinned domains than in the parent grain under the same imposed stress state. In the deformation condition of ED-C, the presence of f1012g twins will reorient the c-axis of the twinned region by 86� and aligns close to the imposed compression axis. Consequently, the twinned re­ gion can deform by slip and/or contraction twinning for accommodating the compression strain in further deformation. Reorientation of 86� of

Fig. 8. Variation of SF values of six f1012g twinning variants with the angle between a-axis and the projection of loading direction on the basal plane (α) (loading direction is parallel to the basal plane (θ ¼ 90� , ED-C).

bands formed in a grain under the TD-T condition have the misorien­ tation angle about 60� . In magnesium alloy, twinning is a very important deformation mode. However, dislocation slip also plays an important role during the deformation. In order to weight the relative contribution of slip and twinning to the deformation, the highest SFs of basal slip and non-basal slip, as well as f1012gtwinning for the loading condition of ED-C and TD-T are shown in Table 4. It can be seen that for ED-C, any 6

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Fig. 9. (0001) pole figures of the SF for six twinning variants at the stress state of ED-C and TD-T. Table 3 Misorientation generated between f1012gtwin variants.

Table 5 Highest SF for slip systems within twined region.

Type of twins

Misorientation angle/axis

Slip systems

Highest SF (ED-C)

Highest SF (TD-T)

ð1012Þ -ð1012Þ

7.4� < 1210 >

ð1012Þ -ð0112Þ

60� < 1010 >a

ð1012Þ -ð0112Þ

60.4� < 8170 >b

basal slip prismatic slip pyramidal slip pyramidal slip

0 0 0.138 0.386

0 0.446 0.401 0.372

a b

Actual axis is 3.7� off.< 1010 > Actual axis is 0.2� off.< 8170 >

off1012gextension twinning. This is the reason why the true stress-strain curve of ED-C is in the appearance of S shape. For TD-T sample, the prismatic and pyramidal slip have the comparable SFs (0.45 and 0.4 in Table 5) and the comparable CRSS, implying that after twinning prismatic and pyramidal slip would be the pre­ dominant deformation mechanism instead of f1012g twinning in TD-T sample. The alternation of deformation mechanism during TD-T is also responsible for the “S” shape of the true stress-strain curve.

Table 4 The highest SF of twinning and slip in c-axis extension. Deformation systems

Highest SF (ED-C)

Highest SF (TD-T)

f1012g twinning

0.499

0.499

basal slip prismatic slip pyramidal slip pyramidal slip

0 0.492 0.434 0.446

0 0 0 0.446

4.2. C-axis contraction Consider the strong initial texture, both of the loading path of ED-T and TD-C apply compression stress along c-axis of the crystal, in regardless of the loading direction of ED-T is perpendicular to the c-axis and the loading direction of TD-C is parallel to the c-axis [9]. C-axis compression with strong initial basal texture in hot rolled and hot-extruded AZ31 magnesium alloy was studied by several works [20, 34]. They all argue that when c-axis was subject to compression loading, the applied force favors the formation of f1011g contraction and f1011g-f1012g double twinning, irrespective of c-axis was applied direct compression (compress parallel to c-axis, TD-C) or indirect compression (tension perpendicular to c-axis, ED-T). Due to the char­ acteristic of polarity that once the stress is inverse, f1012g extension twins can’t activate, it is supported by the negative value of SFs of f1012g extension twins in Fig. 6 (θ ¼ 90� ) and Fig. 7 (θ ¼ 0� ). Even though there were several authors reported the evidence of f1012g

twined region relative to the matrix is the reason for initiation of the slips [18]. This point of view was also supported by other studies [17, 20]. In twined area, the operations of slip systems also follow the SF criteria. Additionally, slips in twined regions require higher stress to initiate since the dislocation movement within twins is restricted by a much shorter mean free path than in the matrix. The calculated SFs of basal slip, prismatic slip, pyramidal slip and pyramidal slip systems in twinned area for ED-C and TD-T are listed in Table 5. It can be seen from that for ED-C sample in twinned area slip systems with Burges cannot operate according to the Schmid law. Pyramidal slip, however, can operate due to its highest SF (0.386 in Table 5) among the four slip systems after twinning. For ED-C after the extension twin­ ning is exhausted, further deformation will be accommodated by pyra­ midal slip and/or contraction twinning. The CRSS of pyramidal slip and contraction twinning are far higher than that 7

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twins in c-axis compression sample [29], however, no convincible explanation was given or the author claimed that the presence of f1012g extension twins was attributed to the unloading [16]. The SFs of f1011gtwinning, basal slip and non-basal slip are displayed in Table 6 for the deformation condition of ED-T and TD-C. It is shown from Table 6 that for ED-T the highest SF is achieved by prismatic slip (0.492) and the SF for basal slip is 0, implying that basal slip has no chance to activate, however, prismatic slip has the highest possibility. In addition, pyra­ midal slip (0.434, 0.446) have the comparable SF and CRSS [34] with that of prismatic slip and then pyramidal slip act as an additional slip system other than prismatic slip. As for TD-C there are only two defor­ mation systems can be operated to accommodate the deformation ac­ cording to the SF, those are pyramidal slip and f1011gtwinning. Like the reorientation effect of f1012g extension twinning, f1011g contraction and f1011g-f1012g double twinning also have misorienta­ tion relationship with untwined region. The misorientation angle of f1011g contraction and f1011g-f1012g double twinning is 56� and 38� , respectively. Unlike the f1012g extension twins that the initial texture will rotate ~90� after twinning, the initial texture of f1011gcontraction twins only exhibited a slight change [35] and even intensified [20] after twinning due to the “narrow” fact of f1011gcontraction twins [35]. Like the f1012g extension twins that reorientation of twined area will favor some slip systems which are very hard to active prior to twinning, f1011g contraction and f1011g-f1012g double twins are also favoring some specific slip system after twinning. The SFs of basal slip, prismatic slip, pyramidal and pyramidal slip systems in f1011gcontraction twined area are calculated and listed in Table 7. It can be seen that for both deformation conditions within the twined area the pyramidal slip has a high possibility to activate.

Table 7 Highest SF for slip systems within twined region (θ ¼ 90� , α ¼ 30� ).

The microstructure (EBSD orientation map) after ED-C, TD-T, ED-T and TD-C are shown in Fig. 10. It shows that with different loading path the microstructures are quite different, implying the materials undergo different deformation mechanism. The microstructure after EDC is heterogeneous, like that of initial microstructure (Fig. 2 (a)), whereas those after TD-D, ED-T and TD-C, the microstructure are somewhat homogeneous. Comparing the micro pole figures after deformation (Fig. 11) with that of initial material (Fig. 2 (b), it shows that the texture changed obviously after deformation. It also shows that the texture of ED-C has a tendency to deflect toward ED and TD-T to­ wards ND, while for ED-T, the texture is almost unchanged and TD-C becomes scattered. The formation of twins causes the grain reor­ ientation, leading to the change of texture orientation. As shown in Table 4, for ED-C and TD-T, f1012g extension twinning has the highest SF and the lowest CRSS among the deformation modes, the activation of f1012gextension twining leads to the reorientation of the parent grain with 86.3� . Due to the fact that only one twin variant pair has the op­ portunity to activate for ED-C, and all the six twin variants have the opportunity to activate for TD-T, then the texture of ED-C is only rotated to ED, while the texture of TD-T rotate to several locations according to the location of the highest SF (Fig. 9). Additionally, in ED-C, the parent Table 6 The highest SFs of twinning and slip in c-axis contraction. Highest SF (ED-T)

Highest SF (TD-C)

f1012g twinning

Negative value

Negative value

f1011g twinning

0.403

0.415

basal slip prismatic slip pyramidal slip pyramidal slip

0 0.492 0.434 0.446

0 0 0 0.446

Highest SF (ED-T)

Highest SF (TD-C)

basal slip prismatic slip pyramidal slip pyramidal slip

0.365 0.105 0.269 0.462

0.365 0.314 0.461 0.401

grains are consumed completely by extension twins (Fig. 10 (a)), while the volume of extension twins in TD-T is 11.96% (Fig. 10 (b)), resulting in the high degree of texture change in ED-C than that of TD-T. Further, it shows that there are some pre-existing twins in the initial material (Fig. 2 (a)) and the orientation of these twins is mostly toward ND (Fig. 2b). The pre-existing twins have high SF, and then they have the high opportunity to grow during the deformation [36]. When the pre-existing twins grow to grain boundaries, the shear stress from those twins induces the twins nucleated in the neighboring grains, and the new twins always have similar orientation with the pre-existing twins [37]. It is the reason why the texture after TD-T is toward ND. From Table 6 it can be seen that for ED-T, f1011gcontraction twinning and non-basal slip all have high SF and they have the comparable higher CRSS [27]. Then the activation of f1011gcontraction twinning and non-basal slip give rise to not only the much high yield strength (Fig. 4) but also the unchanged texture. For TD-C, only f1011gcontraction twinning and pyramidal slip have high SF and they have similar CRSS at room temperature, then both of them have an equal opportunity to activate. The formation of contraction twinning deflects the c-axis of a parent grain about 56� . If the newly formed contraction twins are treated as a parent grain, with the deformation continuing, there are at least two twin variants have positive SFs (Fig. 7d) when θ � 56� (the deflection angle of the contraction twin). As a result, f1012g extension twins have the opportunity to nucleate inside the contraction twin, forming f1011g-f1012g double twin, which leads to a misorientation of 38� between the secondary f1012g extension twin and the parent grain. The CRSS of extension twin is much smaller than that of contraction twins, so the contraction twin can easily be transformed into secondary twin. Furthermore, the formation of contraction twins and double twins provides favorable conditions for the activation of dynamic recrystalli­ zation, which resulting in the scattered texture. The above texture analysis can be further supported by the variation of misorientation angles of the material prior to and after the high strain rate deformations. For the clarity, the local enlargement of the selected area in each figure of Fig. 12 is shown in the center. It is displayed that after deformation there are some specific misorientation angles can be observed in the misorientation angles spectrum. 38� is the angle be­ tween f1011g-f1012g double twin and the parent grain; 56� is the angle between f1011g contraction twin and the parent grain; 60� is the angle between two extension twins; 86� is the angle between f1012g extension twin and the parent grain. The small peak in Fig. 12 (a) is the evidence of pre-exsiting extension twins. From Fig. 12 (b) through Fig. 12 (e) it can be seen that the extension twin is the main deformation mode for TD-T (Fig. 12c), and f1011g-f1012g double twin for TD-C (Fig. 12e). For ED-T (Fig. 12d), the distribution of misorientation angles is similar to that of initial sample (Fig. 12a), implying that the deformation mode for ED-T is mainly slip. However, for ED-C, due to the twins are full of the whole grain, only a few twin boundaries remain. According to that, although the extension twin is the main deformation mode, few misorientation angles are concentrating around 86� . Besides, in the extension twins where the compress stress is parallel to the c-axis, some secondary f1011g contraction twins are activated.

4.3. Microstructure and texture evolution

Deformation systems

Slip systems

4.4. Dynamic recrystallization The dynamic recrystallization in Mg alloys can be divided into two 8

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Materials Science & Engineering A 772 (2020) 138814

Fig. 10. The EBSD orientation map of (a) ED-C, (b) TD-T, (c) ED-T and (d) TD-C. Grain boundaries with a misorientation greater than 10� are outlined in black and extension twinning are outlined in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 11. The micro pole of (a) ED-C, (b) TD-T, (c) ED-T and (d) TD-C.

categories: twin-induced dynamic recrystallization (TDRX), and continuous dynamic recrystallization (CDRX) [38]. In TDRX, twins can induce the formation of dynamic recrystallization (DRX) by three ways: (1) mutual intersection of primary twins, (2) occurrence of secondary twinning and (3) subdivide into nuclei by development of transverse low angle grain boundaries inside coarse twin lamellae into high angle grain boundaries upon further straining. For continuous dynamic recrystalli­ zation (CDRX), the most common mechanism in Mg alloys is rotational dynamic recrystallization (RDRX) [39], in which local lattice rotation induced by dislocation accumulation leads to the transformation of grain boundary from low angle grain boundary to high angle grain boundary. In order to analyze the DRX of the samples after different stress state under high strain rate deformation, the kernel average misorientation maps, the distribution maps of the recrystallized grains, substructure grains and deformed grains (2� is the standard angle of recrystallized grain and 10� is the standard angle of deformed grain) are shown in Fig. 13. It is shown from Fig. 13 (a) that for ED-C, there are many strain concentration regions in the microstructure (Fig. 13 (a), implying that the chance of recrystallization is very low, it is verified by Fig. 13 (e) that the volume fraction of recrystallized grain is only 1.6%,

which can be almost ignored. As for TD-T the degree of strained regions is much smaller than that of ED-C and their distribution are more uni­ form (Fig. 13 (b). It is consistent with the distribution maps of the recrystallized grains shown in Fig. 13 (f), in which the volume fraction of recrystallized grains is 11%. From the above analysis we can know that in the later stage of deformation for TD-T the deformation mechanism is transformed from extension twinning to non-basal slip, then the recrystallization mechanism is dedicate to the RDRX. It is shown from Fig. 13 (g) that for ED-T, the volume fraction of recrystallized grains is 29.1%, and the volume faction of substructured is 55.7%. The corre­ sponding strained regions shown in Fig. 13c are reduced further. The mechanism of the recrystallization of ED-T is RDRX, in which the for­ mation of recrystallized grains is caused by the increased activity of dislocations caused by intergranular incompatibility [39]. The degree of freedom of the recrystallized grains formed by the RDRX mechanism is significantly less than that of the recrystallized grains formed by the TDRX mechanism, and a large number of subgrain that are being con­ verted to recrystallization can be seen in Fig. 13 (c) and (g). Comparing with nucleation in the primary f1012g extension twins, the formation of TDRX induced byf1011g-f1012gdouble twin are much easier, duo to the 9

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Materials Science & Engineering A 772 (2020) 138814

Fig. 12. The misorientation angles of the samples of (a) initial microstructure, (b) ED-C, (c) TD-T, (d) ED-T and (e) TD-C.

anisotropy and asymmetry of extruded AZ31 magnesium under high strain rate deformation was investigated by the SHTB and SHPB. The deformation mechanism is analyzed based on the SF calculation and microstructure observation. The main conclusions of the studies are as follows:

higher strain energy stored inhomogeneously in f1011g-f1012gdouble twin [40], this is the case in TD-C and it is confirmed by free stained region shown in Fig. 13 (d) and the high volume fraction of recrystal­ lized grains (88.8%) shown in Fig. 13 (h). 5. Conclusion

(1) AZ31 extruded magnesium alloy shows obvious anisotropic and asymmetric behavior under high strain rate deformation. When

In the current paper, the role of f1012g extension twinning in 10

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Materials Science & Engineering A 772 (2020) 138814

Fig. 13. Kernel average misorientation map of (a) ED-C, (b) TD-T, (c) ED-T, (d) TD-C, and distribution maps of the recrystallized, substructured and deformed grains: (e) ED-C, (f) TD-T, (g) ED-T, (h) TD-C.

the c-axis is subject to the tensile stress (ED-C, TD-T), in the early stage, the deformation is dominated by f1012g extension twin­ ning; when the c-axis is subject to the compression stress (ED-T, TD-C), the deformation is dominated by non-basal slip and/or f1011g-f1012g double twinning. (2) The activation of the deformation mode is closely related to the SF. According to the calculation result, for ED-C and TD-T, f1012g extension twinning has high and positive SF. For ED-T and TD-C, f1012g extension twinning has negative SF. (3) The SF of extension twinning variants revealed that the six vari­ ants have the same opportunity to activate under tension loading along TD. While for compression along ED, only two variants have the opportunity of operating due to the highest SF among the six variants. It is responsible for the texture variation: texture of ED-C deflects towards ED and TD-T towards ND.

[8] B. Song, R. Xin, X. Zheng, G. Chen, Q. Liu, Activation of multiple twins by pretension and compression to enhance the strength of Mg-3Al-1Zn alloy plates, Mater. Sci. Eng. A 621 (2015) 100–104. [9] M.D. Nave, M.R. Barnett, Microstructures and textures of pure magnesium deformed in plane-strain compression, Scr. Mater. 51 (2004) 881–885. [10] S.R. Agnew, O. Duygulu, Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B, Int. J. Plast. 21 (2005) 1161–1193. [11] Y. Chino, K. Kimura, M. Hakamada, M. Mabuchi, Mechanical anisotropy due to twinning in an extruded AZ31 Mg alloy, Mater. Sci. Eng. A 485 (2008) 311–317. [12] J.J. He, Y. Mao, Y.P. Gao, K. Xiong, B. Jiang, F. Pan, Effect of rolling paths and pass reductions on the microstructure and texture evolutions of AZ31 sheet with an initial asymmetrical texture distribution, J. Alloy. Comp. 786 (2019) 394–408. [13] H.C. Chen, T.M. Liu, D.W. Hou, D.F. Shi, Improving the mechanical properties of a hot-extruded AZ31 alloy by {101‾2}twinning lamella, J. Alloy. Comp. 680 (2016) 191–197. [14] P.L. Mao, Z. Liu, C. Wang, Texture effect on high strain rates tension and compression deformation behavior of extruded AM30 alloy, Mater. Sci. Eng. A 539 (2012) 13–21. [15] E.W. Kelley, W.F. Hosford, Plane-strain compression of magnesium and magnesium alloy crystals, Trans. AIME 242 (1968) 5–13. [16] L. Wu, A. Tain, D.W. Brown, G.W. Stoica, S.R. Agnew, B. Clausen, D.E. Fielden DE, P.K. Liaw, Twinning-detwinning behavior during the strain-controlled low-cycle fatigue testing of a wrought magnesium alloy, ZK60A, Acta Mater. 56 (2008) 688–695. [17] Y.N. Wang, J.C. Huang, The role of twinning and untwinning in yielding behavior in hot-extruded Mg-Al-Zn alloy, Acta Mater. 55 (2007) 897–905. [18] M.R. Barnett, Z. Keshavarz, A.G. Beer, D. Atwell, Influence of grain size on the compressive deformation of wrought Mg-3Al-1Zn, Acta Mater. 52 (2004) 5093–5103. [19] M.R. Barnett, Z. Keshavarz, X. Ma, A semianalytical sachs model for the flow stress of a magnesium alloy, Met. Mater. Trans. A 37 (2006) 2283–2293. [20] L. Jiang L, J.J. Jonas, A.A. Luo, A.K. Sachdev, S. Godet, Influence of{101‾2} extension twinning on the flow behavior of AZ31 Mg alloy, Mater. Sci. Eng. A 445–446 (2007) 302–309. [21] J.R. Xu, J.A. Su, J.J. Cui, Y. Liu, X. Zhang, G.Y. Sun, Tensile behavior and microstructural evolution for AZ31 magnesium alloys sheet at high strain rate, Int. J. Mater. Res. 108 (2017) 560–570. [22] R.F. Wang, P.L. Mao, Y.Y. Liu, Y. Chen, Z. Zhi, F. Wang, L. Zhou, Z. Liu, Influence of pre-twinning on high strain rate compressive behavior of AZ31 Mg-alloys, Mater. Sci. Eng. A 742 (2019) 309–317. [23] S.G. Hong, S.H. Park, C.S. Lee, Role of {10–12} twinning characteristics in the deformation behavior of a polycrystalline magnesium alloy, Acta Mater. 58 (2010) 5873–5885. [24] X.L. Nan, H.Y. Wang, L. Zhang, J.B. Li, Q.C. Jiang, Calculation of Schmid factors in magnesium: analysis of deformation behaviors, Scr. Mater. 67 (2012) 443–446. [25] F.C. Franic, On Miller-Bravais indices and four-dimensional vectors, ActaCryst 18 (1965) 862–866. [26] R.L. Xin, Y.C. Liang, C.H. Ding, C.F. Guo, B.S. Wang, Q. Liu, Geometrical accommodation factor analysis of paired extension twins in extruded Mg–3Al–1Zn alloys, Mater. Des. 86 (2015) 656–663. [27] B.S. Wang, R.L. Xin, G.J. Huang, Q. Liu, Strain rate and texture effects on microstructural characteristics of Mg-3Al-1Zn alloy during compression, Scr. Mater. 66 (2012) 239–242. [28] S. Mu, J.J. Jonas, G. Gottstein G, Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy, Acta Mater. 60 (2012) 2043–2053. [29] C.F. Guo, R.L. Xin RL, J.B. Xu, B. Song B, Q. Liu, Strain compatibility effect on the variant selection of connected twins in magnesium, Mater. Des. 76 (2015) 71–76. [30] M.R. Barnett, A taylor model based description of the proof stress of magnesium AZ31 during hot working, Metall. Mater. Trans. A 34 (2003) 1799–1806.

Declaration of competing interest No potential conflict of interest was reported by the authors. Acknowledgement The authors would like to acknowledgement of the financial support of the National Natural Science Foundation of China (No.51571145), the Innovation Talent Program in Sciences and Technologies for Young and Middle-aged Scientists of Shenyang (No.RC180111) and the Doctoral Scientific Research Foundation of Liaoning Province (No.20170520033). References [1] J.B. Jordon, J.B. Gibson, M.F. Horstemeyer, H. El Kadiri, J.C. Baird, A.A. Luo, Effect of twinning, slip, and inclusions on the fatigue anisotropy of extrusiontextured AZ61 magnesium alloy, Mater. Sci. Eng. A 528 (2011) 6860–6871. [2] M.H. Yoo, Twinning, and fracture in hexagonal close-packed metals, Met. Trans. A 12 (1981) 409–418. [3] E. Goo, K.T. Park, Application of the von mises criterion to deformation twinning, Scr. Metall. 23 (1989) 1053–1056. [4] J.W. Christian, Deformation twinning, Prog. Mater. Sci. 39 (1995) 1–157. [5] I.J. Beyerlein, L. Capolungo, P.E. Marshall, Statistical analyses of deformation twinning in magnesium, Philos. Mag. A 90 (2010) 2161–2190. [6] Z.Z. Shi, Y.D. Zhang, F. Wanger, P.A. Juan, S. Berbenni, L. Capolungo, J. S. Lecomte, T. Richeton, On the selection of extension twin variants with low Schmid factors in a deformed Mg alloy, Acta Mater. 83 (2015) 17–28. [7] H. El Kadiri, J.C. Baird, J. Kapil, Flow asymmetry and nucleation stresses of {101‾2}twinning and non-basal slip in magnesium, Int. J. Plast. 44 (2013) 111–120.

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X. Wang et al.

Materials Science & Engineering A 772 (2020) 138814

[31] G. Wan, B.L. Wu, Y.D. Zhang, G.Y. Sha, C. Esling, Anisotropy of dynamic behavior of extruded AZ31 magnesium alloy, Mater. Sci. Eng. A 527 (2010) 2915–2924. [32] J.C. Gong, T.B. Britton, M.A. Cuddihy, F.P.E. Dunne, A.J. Wilkinson, a> Prismatic, basal, and slip strengths of commercially pure Zr by micro-cantilever tests, Acta Mater. 96 (2015) 249–257. [33] K. Hazeli, J. Cuadra, P.A. Vanniamparambil, A. Kontsos, In situ identification of twin-related bands near yielding in a magnesium alloy, Scr. Mater. 68 (2013) 83–86. [34] Z. Keshavarz, M.R. Barnett, EBSD analysis of deformation modes in Mg-3Al-1Zn, Scr. Mater. 55 (2006) 915–918. [35] L. Jiang, J.J. Jonas, R.K. Mishra, A.A. Luo, A.K. Sachdev, S. Godet, Twinning and texture development in two Mg alloys subjected to loading along three different strain paths, Acta Mater. 55 (2007) 3899–3910.

[36] L. Capolungo, P.E. Marshall, R.J. McCabe, I.J. Beyerlein, C.N. Tom�e, Nucleation and growth of twins in Zr: a statistical study, Acta Mater. 57 (2009) 6047–6056. [37] Z. Z Shi, Compound cross-grain boundary extension twin structure and its related twin variant selection in a deformed Mg alloy, J. Alloy. Comp. 716 (2017) 128–136. [38] O. Sitdikov, R. Kaibyshev, Dynamic recrystallization in pure magnesium, Mater. Trans. 42 (2001) 1928–1937. [39] I. Ulacia, N.V. Dudamel, F. G� alvez, S. Yi, M.T. P� erez-Prado, I. Hurtado, Mechanical behavior and microstructural evolution of a Mg AZ31sheet at dynamic strain rates, Acta Mater. 58 (2010) 2988–2998. [40] H.L. Kim, J.-H. Lee, C.S. Lee, W. Bang, S.H. Ahn, Y.W. Chang, Shear band formation during hot compression of AZ31 Mg alloy sheets, Mater. Sci. Eng. A 558 (2012) 431–438.

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