On the role of twinning and stacking faults on the crystal plasticity and grain refinement in magnesium alloys

Accepted Manuscript On the role of twinning and stacking faults on the crystal plasticity and grain refinement in magnesium alloys S.Q. Zhu, Simon P. Ringer PII:

S1359-6454(17)30947-3

DOI:

10.1016/j.actamat.2017.11.004

Reference:

AM 14175

To appear in:

Acta Materialia

Please cite this article as: S.Q. Zhu, Simon P. Ringer, On the role of twinning and stacking faults on the crystal plasticity and grain refinement in magnesium alloys, Acta Materialia (2017), doi: 10.1016/ j.actamat.2017.11.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

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ACCEPTED MANUSCRIPT

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ACCEPTED MANUSCRIPT On the role of twinning and stacking faults on the crystal plasticity and grain refinement in magnesium alloys S.Q. Zhu and Simon P. Ringer

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The University of Sydney, NSW 2006, Australia, School of Aerospace, Mechanical and Mechatronic Engineering, and Australian Centre for Microscopy & Microanalysis

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Corresponding authors: E: [email protected] T: +61 2 93517547

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and E: [email protected] T: +61 2 93512353

Abstract

We have investigated the detailed microstructural mechanisms associated with the improved strength, excellent crystal plasticity and ultra-fine grain refinement observed

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under high strain-rate deformation of Mg alloys, focusing on ZK60. Firstly, we have identified the clear formation of stacking faults in deformation-induced twinned crystal segments. Specifically, we have found that intrinsic I1 and I2 stacking faults bounded by

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1ൗ <2ത 023> and 1ൗ <101ത 0> partial dislocations, respectively, were found to occur in 6 3 very high number densities within the twins. This was due to the high Schmid factor for

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stacking fault shearing in twins and the critical role that twin boundaries played in emitting partial dislocations. Secondly, we have clarified the interplay between twinning and stacking faults on the enhanced crystal plasticity. Apart from the strain accommodated by the extensive twinning itself, we propose that the improved plasticity തതത23>{112ത 2} during high strain-rate deformation is mainly due to the nucleation of 1ൗ3<11 dislocation within twins, which provides enough independent slip systems to achieve a homogeneous deformation in the material. Finally, we have demonstrated the interplay

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ACCEPTED MANUSCRIPT between twinning and stacking fault formation on the nucleation of new grains via dynamic recrystallisation. The twin boundaries and stacking faults, especially those of the I1 type, facilitate the formation of low-angle grain boundaries that can subsequently

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transition into high-angle grain boundaries, and form ultra-fine dynamically recrystallised grains.

Keywords: Magnesium alloys; Plasticity; Stacking faults; Twinning; Dynamic

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recrystallisation

1.1.

Background and aims

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1. Introduction

Magnesium (Mg) and its alloys represent one of the lightest structural engineering platform materials and exhibit high strength-to-weight ratios ranging typically around 150 kN·m/kg. However, the difficulties in processing Mg alloys limit their applications.

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Fundamentally, these difficulties are well known and arise from low crystal plasticity arising from their hexagonal close-packed (hcp) crystal structure [1-3]. Conventionally,

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Mg alloys are deformed under the condition of low strain-rate, low strain and high temperature to prevent catastrophic cracking. A recent breakthrough in the processing of

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Mg has been the finding that deformation under a relatively high strain-rate (10~100 s-1) such as can be achieved by rolling or forging significantly eases the plastic processing of Mg alloys [4-10]. This high strain-rate deformation process has proven to be robust, and has now been applied to a variety of Mg alloys with different starting microstructures. Ultra-fine grained (UFG) microstructures with average grain sizes ~500 nm, along with high yield strengths > 280 MPa and high ductility, with total elongations exceeding 25 % have been successfully obtained in bulk Mg products,

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ACCEPTED MANUSCRIPT suggesting that this processing method has great potential to be scaled up for highperformance industrial applications [4-10]. Fig. 1 summarises the metallurgical phenomena observed to date surrounding

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crystal plasticity in Mg alloys during high strain-rate deformation, and also represents the main subjects to be addressed in this study. The situation is complex and dynamic. The improved plasticity during high strain-rate deformation is attributed to the extensive

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deformation twinning, and the subsequent dynamic recrystallisation (DRX), both of

which dissipate the deformation energy and prevent the nucleation of microcracks [4-

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10]. Indeed, twin-induced DRX has been demonstrated as the origin of the grain refinement effect, leading to the final UFG microstructures observed [4-10]. However, the fundamental mechanisms of the enhanced plasticity and the pathway to these grain refinement effects during high strain-rate deformation remain unclear. Moreover, as

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illustrated in Fig. 1f, the role of stacking faults is unstudied. Therefore, with reference to Fig. 1, this study focusses on three questions: (1) what is the influence of twinning on the formation of stacking faults; (2) what is the role of twinning and stacking faults on

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the enhanced plasticity; and (3) how do twinning and stacking faults influence the nucleation of the DRX? These questions are now discussed in more detail both for the

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purposes of setting out the context of the present work, and to serve as a self-consistent basis for the discussion of our results. 1.2.

Plastic deformation mechanisms of Mg

1.2.1. Hcp unit cell

In order to conveniently present the deformation mechanisms in Mg, the hcp crystal structure and its Thompson hexahedron [11-14] are illustrated in Fig. 2. Vectors AB, BC, CA, BA, CB and AC represent prefect dislocations (Burgers vector b =

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ACCEPTED MANUSCRIPT 1ൗ <112ത 0>); vectors ST and TS are perfect dislocations (b = <0001>); perfect dislocations (b = 1ൗ3<112ത 3> represented by symbols such as SA/TB, which means either the sum of the vectors ST and AB or, geometrically, a vector equal to twice the

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join of the mid-points of SA and TB. Glissile Shockley partial dislocations (b = 1ൗ <1ത 100>) and sessile Frank partial dislocations (b = 1ൗ <0001>) are represented by 2 3 vectors such as Aσ and σS; Sessile partial dislocations b = 1ൗ6<2ത 203> are represented

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by vectors such as AS, which is a combination of the Aσ and σS.

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1.2.2. Dislocation slip systems

During conventional deformation processing, the low plasticity of Mg and its alloys is caused by the limited number of dislocation slip systems in the hcp unit cell [15]. To achieve a general homogenous plastic deformation, five independent deformation modes need to be activated to satisfy the von Mises criteria. Dislocation gliding on the

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close-packed (0002) basal plane, with Burgers vector b = = 1ൗ3<112ത 0>, is the main slip system of Mg, providing only two independent deformation modes that operate

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only for strain along the axis [12]. Deformation along the axis is primarily accomplished by = 1ൗ3<112ത 3> dislocation gliding on the pyramidal {112ത 2}

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planes. This provides five independent deformation modes [12, 16-18]. However, the critical resolved shear stress (CRSS) of these non-basal slip systems at room temperature is approximately 100 times that of the basal slip system [19, 20]. In addition, Wu and Curtin [17] recently suggested that the dislocation is metastable on the easy-glide {112ത 2} pyramidal planes. Their simulation work using molecular dynamics shows that the edge dislocation intrinsically tends to transit to lower-energy basal-dissociated immobile dislocation structures. These dissociated

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ACCEPTED MANUSCRIPT sessile dislocations cannot contribute to deformation and also obstruct the motion of other dislocations. Similar points of view were discussed by other researchers [18, 2022]. Therefore, Mg and its alloys generally possess low levels of ductility.

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1.2.3. Deformation twinning Deformation twinning is often observed in Mg and is another mechanism that accommodates the plastic straining along the axis, in addition to the

dislocation gliding [12]. The twinning process re-orientates the crystals, and the most

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frequently observed modes include (i) {101ത 2} extension twinning, which rotates the

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crystal 86° along <12ത 10> axis; (ii) {101ത 1} (56° <12ത 10>) and (iii) {101ത 3} (64° <12ത 10>) contraction twinning, and (iv) {101ത 1}–{101ത 2} (38° <12ത 10>) and (v) {101ത 3}–{101ത 2}(22° <12ത 10>) double twinning [23, 24].

Twinning has been observed to play an important role in hcp materials, especially

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under deformation conditions involving high strain-rate and low temperatures, where dislocation gliding becomes difficult [25]. In our previous studies [4-10], twinning was significantly promoted during high strain-rate deformation. Twinning accommodates

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plastic strain; apart from this, the re-orientation of grains due to twinning has been proposed to favour dislocation gliding and thus plastic straining [15, 25, 26].

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Conventionally, twinning processes are thought to quickly saturate with strain [27], especially under high strain-rates [4], suggesting that dislocation slip should then become the main deformation mechanism for further deformation. There is a suggestion that other reactions are possible such as twin-facilitated dislocation gliding [28]. This interesting proposal is controversial, and has not been demonstrated experimentally. Therefore, it emerges that an understanding of the phenomenon of dislocation motion

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ACCEPTED MANUSCRIPT within twins may be important in order to explain the influence of twinning on the crystal plasticity of Mg alloys. 1.2.4. Stacking faults

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In perfect crystals, the closed-packed (0002) planes of the Mg lattice possess an …ABABAB… stacking sequence. It is generally accepted that three types of basalplane stacking faults exist in Mg, including two intrinsic faults, I1 and I2, and one

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extrinsic fault E [11, 12]. The intrinsic fault I1, also known as a growth fault, can be

formed by the removal of a basal plane followed by slip of 1ൗ3<101ത 0> in the crystal,

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yielding the sequence of I1 ···ABABABCBCBCB···

(1)

The intrinsic fault I2, or deformation fault, results from direct shearing of 1ൗ3<101ത 0> of the perfect crystal, yielding

(2)

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I2 ···ABABABCACACA···

The extrinsic fault E is produced by inserting an extra plane, E ···ABABABCABABAB···

(3)

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The stacking fault energies (SFE), γ, of these three faults follows γE ≈ 3ൗ2γI2 ≈ 3γI1

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[11, 12, 29, 30], yielding values of 21, 44 and 69 mJ·m-2 for I1, I2 and E, respectively, as calculated by Chetty and Weinert [29]. The stacking fault characteristics in deformed Mg and its alloys have not been well

elucidated. This is surprising considering that it is generally recognised that pure Mg possesses a relatively low SFE of around 5–125 mJ·m-2 according to experimental measurements and first-principles calculations [13, 18, 29-37]. In some reports [13, 21, 22, 28, 31-35, 38-43], stacking faults were observed in deformed or annealed Mg and Mg alloys, in the matrix grains or in twins. Interestingly, the effect of stacking faults on

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ACCEPTED MANUSCRIPT on the plastic deformation is controversial, with some researchers claiming that they enhance plasticity[32], whilst other claim that they reduce the capacity for plastic deformation [17, 28]. Critically, the effect of twinning on the formation of these

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stacking faults has not been systematically investigated. 2. Experimental

The as-received material used in this study was a commercial ZK60 (Mg–6Zn–0.5Zr,

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in wt. %) as-cast Mg alloy. A two-step homogenisation (330 °C for 24 h, and 420 °C for 4 h) was conducted, resulting in an average grain size of ~150 µm with random grain

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orientations. The as-homogenised alloy was machined into a rectangular slab with the size of 100 × 100 × 10 mm, which was heated to 300 °C followed by one pass rolling with a 30% thickness reduction (from 10 to 7 mm). As reported by the authors [4-7], uniform ultra-fine grained alloys can be obtained once the rolling reduction achieves a

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threshold value of ~80%. The 30% thickness reduction was selected for study here in order to allow us to investigate the microstructural evolution leading up to this threshold reduction. The diameter of the rolls was 350 mm, and the circumferential speed was 842

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mm·s-1, which gives an average rolling strain rate of ~11 s-1, calculated via the method described in [4]. This strain-rate value is close to that previously used during high

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strain-rate rolling (~10 s-1) [4-6]. The microstructure of the as-rolled material was observed by electron backscatter

diffraction (EBSD), transmission Kikuchi diffraction (TKD) and transmission electron microscopy (TEM). EBSD was applied to observe the overall microstructure and grain orientations. TKD and TEM were used to characterise the more local crystal orientation, twinning and stacking faults. In order to simplify the description hereafter, the geometrical directions and planes of the rolled material are denoted as RD (rolling

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ACCEPTED MANUSCRIPT direction), TD (transverse direction), ND (direction normal to rolling plane), ND plane (plane normal to ND direction, or the rolling plane) and TD plane (plane normal to the TD direction). The EBSD maps were acquired from the ND plane, while the TKD maps

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were acquired from the TD plane. The EBSD and TKD experiments were conducted on a Zeiss Ultra field emission SEM using AZtec and Channel 5 software to acquire and analyse data. The TEM was performed on a JEOL JEM–3000F field emission

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microscope, and the TEM data was analysed using the Gatan Microscopy Suite. The

EBSD sample was prepared by mechanical polishing and light etching in a polishing

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suspension during the last polishing step. The TEM and TKD experiments were conducted on the same sample, which was prepared using standard thin foil techniques [44]. Gentle argon ion beam scanning using a low voltage and low incident angle was performed to further polish and clean the sample surfaces.

3.1.

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3. Results EBSD Observations

Fig. 3 provides large area EBSD data from the as-rolled ZK60 alloy. In Fig. 3a,

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coarse grains >100 µm remained in the alloy, since the rolling reduction was low relative to the previously determined 80% threshold (i.e. ~30%). From the colour

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distribution of the inverse pole figure (IPF) map, most of the {0001} basal planes were normal to the ND, and therefore a basal texture was observed (see online version for the colour legends). Low-angle grain boundaries (LAGBs, 2-10°), high-angle grain boundaries (HAGBs, >10°), and five commonly observed twin boundaries are highlighted in different colours. The angular deviation to identify the twin boundaries was within 5° of the ideal values.

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ACCEPTED MANUSCRIPT Fig. 3b provides the frequency distribution of the corresponding misorientation angles. It is seen that there are three peaks around 38°, 56° and 86°, and their rotation axes concentrate around the <12ത 10> axis, indicating that the peaks were caused by the

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{101ത 1}–{101ത 2}, {101ത 1} and {101ത 2} twinning, respectively. It is seen that {101ത 1}– {101ത 2} double twinning was the predominant twinning under this condition, which is consistent with previous observations [7]. Additionally, DRX grains were observed

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within the twinned regions and at grain boundaries (GBs). Fig. 3c reveals details of the DRX grains within individual twin lamellae. Consistent with previous studies [4-7],

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DRX within twins plays a key role in the microstructural grain refinement due to the high density of deformation twins forming at high strain-rates. 3.2.

TKD Observations

Fig. 4a provides a local TKD map of the as-rolled ZK60 alloy. Two variants of the

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{101ത 1}–{101ത 2} 38° double twinning were observed. In particular, twins A and C are very close in orientation, indicating they belong to the same variant; and twin B possesses an alternate variant. These two variants geometrically rotate the crystal -38°

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and 38° around the same <12ത 10> axis, respectively, as shown in Fig. 4b and c. In fact, these two variants of the double twinning formed from a secondary 86° {101ത 2}

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twinning rotation in two different {101ത 1} primary twinning variants, equivalent to the variants of the twins D and E, respectively. In addition, some LAGBs were observed within the twinned segments. These LAGBs are known to have the potential to transition into HAGBs and form fine-scale DRX grains with further strain [5-7]. {0001} and {101ത 0} pole figures are provided in Fig. 4d, in which the projections of the matrix and twin B are marked.

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ACCEPTED MANUSCRIPT 3.3.

Conventional TEM Observations

All the following TEM images were viewed along directions parallel to vectors AC or CA, (i.e.) such that the zone axis was the <12ത 10> direction, which is parallel to the

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rotation axis as indicated in Fig. 4b. Fig. 5 provides the bright-field TEM images and the corresponding selected area

electron diffraction (SAED) patterns recorded from an {101ത 1} primary twin (PT) and a

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{101ത 1}–{101ത 2} double twin (DT), and these correspond exactly to the twins D and B, respectively, identified in Fig. 4a, respectively. In addition, “In addition, lines of

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contrast were observed within both the twins and the matrix, such as are typical of stacking faults [41]. These were observed to lie on the basal plane and we identify them as basal-plane stacking faults. To our knowledge, no previous observations of stacking faults within the Mg-based {101ത 1}–{101ത 2} double twin have been reported. Other

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studies have reported stacking faults within {101ത 2} twins [38-43], and Wang et al. [28] observed stacking faults in the {101ത 1} twin. In fact, we also observed stacking faults in {101ത 2} twins (not shown). In addition, the density of stacking faults in the matrix is

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much lower than that in the twins and they could only be observed at higher magnification, such as the insert in Fig. 5a. Similar phenomena was observed in an in-

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situ compression test on a single-crystal Mg pillar, reported by Liu et al. [38]. 3.4.

High-resolution TEM Observations

3.4.1. Stacking faults in matrix Fig. 6a is a high-resolution TEM (HRTEM) image recorded from the matrix region

indicated in Fig. 4. Defects lying on the {0001} planes were observed. The fast Fourier transform (FFT) pattern reveals streaks along the <0001> directions, consistent with the diffraction shape effect of stacking faults on the basal plane [41]. HRTEM images such

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ACCEPTED MANUSCRIPT as those in Fig. 6b and c were used to determine the types of stacking faults and their bounding dislocations. The partial dislocations forming stacking faults were determined by drawing Burgers circuits around the dislocation cores, where the sense vectors of the

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dislocations were arbitrarily determined to point into the page and the directions of the Burgers circuits were drawn clockwise following the start–finish/right-handed

convention [12]. The closure failure of the Burgers circuit in Fig. 6b indicates that it is a

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1ൗ <2ത 203> partial dislocation, (i.e.) vector SB drawn in Fig. 2. The stacking sequence 6 shows that this partial dislocation induces an I1 stacking fault. Using the same method,

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an I2 stacking sequence formed by a 30° 1ൗ3<101ത 0> partial dislocation (vector σA or σC in Fig. 2) may be identified in Fig. 6c. In the case of this partial dislocation, the Burgers vector cannot be explicitly determined since σA and σC overlap in the only TEM projection available. On the basis of many analyses such as this, we determined that

samples.

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intrinsic I1 and I2 stacking faults were the most frequently observed in these alloy

3.4.2. Stacking faults within {101ത 1}–{101ത 2} double twin segment

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The following HRTEM observations were focused on stacking faults in the {101ത 1}– {101ത 2} double twin, since it appears to be the dominant twinning during the

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deformation process, as seen in Fig. 3. Fig. 7 is a HRTEM image of a {101ത 1}–{101ത 2} double twin segment. This corresponds precisely to the twin B identified in Fig. 4. The twin boundary with the matrix is identified at the top left of the image. The FFT pattern converted from the twinned area is provided, and the streaks are again consistent with diffraction shape effects for basal-plane stacking faults. These were identified in the manner above as intrinsic I1 and I2 stacking faults. The Burgers circuits for the faults labelled I1 and I2 in Fig. 7 identify their bounding partial dislocations as 1ൗ6<2ത 203> and 11

ACCEPTED MANUSCRIPT 30° 1ൗ3<101ത 0>, corresponding to vectors SA (or SC) and Aσ (or Cσ) (Fig. 2), respectively. These two I1 and I2 stacking faults are only a few lattice spacings, a, apart from each other, imparting an elastic stress on the crystal lattice in between, and

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inducing a slight shift of atoms from their ideal positions. Now, since the number density of stacking faults within the twinned segments was observed to be much higher than in the matrix, we expect that the lattice distortion caused by the faults themselves

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and the interaction of this stress field to play a significant role in the crystal plasticity. 3.4.3. Formation of stacking faults

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Fig. 8a and b are HRTEM images of I1 stacking faults bounded by two kinds of 1ൗ <202ത 3> Frank partial dislocations. Fig. 8a reveals the formation process of an I1 6 stacking fault. It takes two steps to form this I1 stacking fault:

(1) A vacancy platelet formed on a basal plane (i.e.) a layer of the basal planes with

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the A stacking removed and the lattice locally collapsed, in which the resultant stacking sequence was …ABABAB|BABAB… forming a Frank dislocation loop of b = 1ൗ <0001> (vector Sσ in Fig. 2) bounding a stacking fault. The removed basal plane is 2

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seen on the left side of the “﬩” sign in Fig. 8a.

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(2) To avoid ball-on-ball stacking, a 90° 1ൗ3<101ത 0> Shockley partial dislocation (as seen from the top Burgers circuit shown in Fig. 8a), (i.e.) vector σB in Fig. 2, swept over the vacancy platelet, which process formed a 1ൗ6<202ത 3> Frank partial dislocation (as seen from the bottom Burgers circuit shown in Fig. 8a) and changed the stacking sequence to …ABABABCBCBCB…. The related dislocation reaction of this process is 1ൗ <0001> + 1ൗ <101ത 0> → 1ൗ <202ത 3> 2 3 6 (i.e.)

Sσ + σB → SB.

(4) (5)

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ACCEPTED MANUSCRIPT As discussed above, this I1 stacking fault formation process is related to the convergence of vacancies on the basal plane (i.e.) removal of a basal layer. We shall refer to it as a vacancy-type I1 fault hereafter. This process should be intrinsic to Mg,

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driven by the SFE reduction, as the γE is about 3 times of γI1 [11, 12, 29, 30]. Since the 1ൗ3<101ത 0> Shockley partial dislocation only requires a simple shear, it

should propagate faster than the vacancy platelet, which emerged an I2 stacking fault on

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the same basal plane, the stacking sequence of which was…ABABABCACACA…, as seen in Fig. 8a.

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Fig. 8b reveals the formation process of another type of I1 stacking fault. A 1ൗ <0001> (vector Sσ in Fig. 2) partial loop appears to have resulted from the 2 precipitation of an interstitial disc, (i.e.) the insertion of a basal plane B, resulting in a stacking sequence of …ABABAB|BABABAB… (an extrinsic fault E). Similarly to the

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case above in Fig. 8a, once the 1ൗ2<0001> partial met a 30° 1ൗ3<101ത 0> partial that bounded an I2 fault (i.e. vector σA or σC in Fig. 2), a 1ൗ6<202ത 3> partial formed,

reaction is:

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resulting in a stacking sequence of …ABABABCBCBCB….The resultant dislocation

(6)

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Sσ + σA ( or σC) → SA ( or SC).

As this formation process evolves the insertion of a basal plane, we shall refer to it as an interstitial-type I1 fault, hereafter. The faster propagation of I2 fault also resulted in a …ABABABCACACA…stacking, as seen in Fig. 8b. In fact, the I1 stacking faults shown in Fig. 6b and Fig. 7 are the vacancy-type and interstitial-type faults, respectively. From Fig. 8a and b, it is concluded that the formation of I1 stacking faults requires climb via short-range vacancy or interstitial assisted diffusion. Twin boundaries can act as the source emitting vacancies and interstitials. Examples are seen in Fig. 8c as two I1 13

ACCEPTED MANUSCRIPT stacking faults appear near the {101ത 1}–{101ത 2} twin boundary, the bounding dislocations of which are vacancy-type (bottom) and interstitial-type (top) 1ൗ6<202ത 3> partial dislocations. In addition, as seen in Fig. 8c, atoms near the twin boundary are

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offset from their ideal positions, indicating a concentration of stress at the twin boundaries. 3.4.4. Low Angle Grain Boundaries (LAGB)

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Fig. 9a presents TEM images at the vicinity of a LAGB in twin B indicated in Fig. 4. The SAED pattern across the LAGB splits into two sets of spots with a 6°

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misorientation, as highlighted within the inset circle. The LAGB is formed by arrays of dislocations, as seen in Fig. 9b. Some of the dislocations are sessile geometrically necessary dislocations (GNDs) that contribute to the curvature and misorientation of the crystal lattice [45]. Fig. 9c is an example of the GNDs, revealing an extra basal plane.

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This implies that the GNDs contain the 1ൗ2<0001> sessile segments. As discussed in section 3.4.3, the 1ൗ2<0001> forms from the aggregation of a vacancy/ interstitial disc via atom climb. In addition, a stacking fault ended at the LAGB, as revealed in Fig. 9b.

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In fact, almost all of the stacking faults observed in our TEM experiments did not

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penetrate the LAGBs. 4. Discussion 4.1.

Factors affecting the formation of stacking faults

4.1.1. Grain orientation Table 1 lists the Schmid factors, m, for each of the six variants of the 1ൗ <101ത 0>{0002} slip system in the matrix, and twin B shown in Fig. 4. The Schmid 3 factors were calculated from the equation m = cosφ·cosλ

(7) 14

ACCEPTED MANUSCRIPT where, φ is the angle between the loading direction and the slip plane normal [0001], and λ is the angle between the loading direction and the slip direction. The loading direction of rolling was along ND. The slip direction and the normal to the slip plane

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were <101ത 0> and <0001>, respectively. The values of φ and λ were measured from the (0001) and {101ത 0} pole figures (Fig. 4d), respectively. It is seen that the highest and second highest Schmid factors calculated for twin B were 50% and 74% higher than

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those in the matrix, respectively. Fig. 10 illustrates the distribution of the values of the highest Schmid factor of 1ൗ3<101ത 0>(0002) under the rolling load in the area observed

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by TKD in Fig. 4. It demonstrates that the Schmid factors in the {101ത 1} primary and {101ത 1}–{101ത 2} double twins are always higher than that in the matrix. This is caused by the basal texture formation in the matrix, and grain rotation induced by the twinning process, as seen in Fig. 4. Therefore, the 1ൗ3<101ത 0>(0002) partial dislocation slip is

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more favoured in these twins, consistent with Schmid law. Since 1ൗ3<101ത 0> shearing is essential for the formation of both I1 and I2 stacking faults as expressed by equations 1

observed.

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and 4–6, higher frequency of stacking faults in these twins than in the matrix was

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4.1.2. Twin boundaries

As discussed in Fig. 8c in section 3.4.3, twin boundaries can act as a source for

partial dislocations and stresses can concentrate at these boundaries. This stress concentration would very likely contribute to the emission of vacancies and interstitials, and also favour the 1ൗ3<101ത 0> shearing. Therefore, we suppose that twin boundaries stimulate the formation of both I1 and I2 stacking faults, and it is understandable that a higher frequency of stacking faults is observed within twinned segments than in the

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ACCEPTED MANUSCRIPT matrix. As reported above in sections 4.1.1 and 4.1.2, twinning stimulates the formation of stacking faults mainly by (1) re-orientating the crystal and thus favouring 1ൗ3<101ത 0> shearing, and (2) emitting vacancies and interstitials at the twin boundaries. Effect of stacking faults and twinning on plasticity

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4.2.

4.2.1. Nucleation of dislocation

The aforementioned simulations by Wu and Curtin [17] suggest that the low

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ductility of Mg is due in significant part to the dissociation of the glissile perfect

1ൗ <11 തതത23>{112ത 2} dislocation into two sessile 1ൗ <202ത 3> partials bounding a ribbon of 3 6

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I1 stacking fault in between. This has the following dislocation reaction, as described in [22].

1ൗ <11 തതത23> → 1ൗ <2ത 023> + 1ൗ <02ത 23>, 3 6 6 (i.e.)

BD (i.e., TB/SC) → BS + SD.

(8) (9)

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The sessile BS and SD partials cannot easily contribute to further deformation since the movement of this kind of dislocation requires climb. Moreover, the sessile dislocation loops act as obstacles for other dislocation motion. Therefore, Mg single crystals exhibit

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high strain-hardening and low ductility at temperatures up to 500 K [17, 22]. However,

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under the deformation conditions investigated here, instead of forming from the തതത23> perfect dislocation, the 1ൗ <202ത 3> partials are more likely to dissociation of 1ൗ3<11 6 form directly from reaction of the 1ൗ3<101ത 0> and 1ൗ2<0001> partials, as seen in Fig. 8 and equations 4–6.

As discussed in sections 3.4.3 and 4.1.2, twin boundaries act as an effective emission source for stacking faults, resulting in a high density of stacking faults within twins. Within these highly constrained twinned volume segments, there is a high

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ACCEPTED MANUSCRIPT probability that two partial dislocations will interact with each other, and form a perfect dislocation. For two 1ൗ6<2ത 023> partials bounding I1 stacking faults, the dislocation reaction equivalent to the following occurs

(i.e.)

BS + SD → BD.

(10)

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1ൗ <2ത 023> + 1ൗ <02ത 23> → 1ൗ <11 തതത23>, 6 3 6

(11)

This reaction nucleates a perfect dislocation which can then glide away,

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such that this reaction converges two sessile partials into a perfect glissile dislocation. Therefore, this reaction increases the ductility of magnesium alloys by increasing the

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nucleation of dislocation gliding. A similar phenomenon was reported in Mg-Y alloys, which show higher room-temperature ductility than pure Mg [32]. The addition of Y lowered the I1 SFE and increased the amount of I1 stacking faults. The authors [32] proposed that the I1 stacking faults actually act as a heterogeneous nucleation source for

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the perfect dislocations, and thus improves the ductility of the alloys due to the lower I1 SFE and higher amount of dislocations observed. Overall, the partial dislocation reactions set out in equations 10 and 11 have opposing effects on ductility to

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the dissociation reactions represented by equations 8 and 9. The former reactions increase ductility as discussed above; the latter reactions are expected to deteriorate the

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ductility, since they turn glissile dislocations into sessile partials [17]. Yoo et al. [16, 18] pointed out that the deformation behaviour of Mg alloys is

expected to be strongly affected by the relative difficulty in nucleating dislocations, and that this is a more dominant factor that the mobility of these dislocations. They proposed several possible sources for the nucleation of dislocations, including (1) the formation of an attractive junction between glissile and sessile dislocations from a prismatic plane into a pyramidal plane via cross slip

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ACCEPTED MANUSCRIPT [16, 18]. (2) nucleation as perfect dislocations at grain boundaries or twin boundaries, which probably occurs in alloys with high SFE [18]. (3) in contrast to mechanism (2), a partial dislocation with a strip of staking fault may form first, and subsequently another

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partial dislocation is generated and forms a perfect dislocation. In the present study, we have observed the nucleation of the dislocations follows this latter case (3), and it may be closely related to the relatively low SFE of Mg alloys.

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We further propose a nucleation mechanism for a dislocation on the pyramidal system. Fig. 11 provides a schematic representation of the nucleation of

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1ൗ <11 തതത23>{112ത 2} pyramidal dislocations. In Fig. 11a, a 1ൗ <0001> sessile partial 3 2 dislocation loop (σS) containing a stacking fault forms on a basal plane. In Fig. 11b, a 1ൗ <101ത 0> glissile partial dislocation loop (σC) sweeps and reacts with the fault 3 bounded by σS, generating a 1ൗ6<2ത 023> partial (SD) bounding an I1 stacking fault

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ribbon. This reaction is equivalent to the reactions presented in equations 4 and 5. The 1ൗ <0001> partial loop lies on the non-glide basal plane, which makes it sessile so that 2 it can only climb during deformation [14, 17, 46, 47]. As the σC sweeps through the

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faulted region bounded by σS, a single faulted SD partial loop forms on the basal plane

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(Fig. 11c). These types of dislocation loops were observed in refs. [14, 22, 31]. This is still a sessile partial dislocation since the Burgers vector is out of the plane of the loop [22].

Another 1ൗ6<2ത 023> partial (BS) is formed by the reaction of a 1ൗ2<0001> partial

(σS) and a 1ൗ3<101ത 0> partial (Bσ) (Fig. 11d-f). When the BS partial sweeps the faulted region that the SD partial has already passed, the region is unfaulted (Fig. 11g). The rate of this sweeping process is limited by climb on the basal plane [46]. Once the two

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ACCEPTED MANUSCRIPT തതത23> perfect partials meet each other, the reaction between them forms a sessile 1ൗ3<11 dislocation (BD) lying on basal plane (Fig. 11h). Obara et al. [20] and Price [46, 48] observed dislocations bounded on the basal plane in hcp metals such as Mg, Zn

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and Cd. Obara et al. [20] have also observed that many of these dislocations lie along the <101ത 0> directions, intersecting the (0001) and {112ത 2} planes, and that these dislocations therefore moves onto the easy-glide {112ത 2} pyramidal planes from the

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basal plane, as shown in Fig. 11i. This process nucleates a glissile dislocation on a {112ത 2} pyramid plane, which contributes positively to the capacity for plastic flow of

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the crystal. 4.2.2. Twinning, stacking faults and plasticity

തതത23>{112ത 2} pyramidal From the discussion above, the nucleation of a 1ൗ3<11 dislocation requires climbing, which is the slowest step, and restricts the nucleation rate.

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Under the high strain-rate deformation condition, twinning is significantly promoted and the twin boundaries can emit vacancies or interstitials that facilitate climb (Fig. 8). In addition, the higher density of stacking faults within the twins compared to that in the

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matrix, especially the I1 stacking faults formed by the sessile 1ൗ6<2ത 023> partials, causes

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higher local strain energy in the material (as discussed in Fig. 7). This can also facilitate climb. Moreover, the high strain-rate deformation was conducted at relatively high temperature (300 °C), and the fast deformation can also induce adiabatic heating [4], both of which facilitate climb processes. On the other hand, Price and Kroupa [46, 48, 49] observed conservative climb in hcp metals, (i.e.) the total area enclosed by a dislocation was found be conserved during its movement. They suggested that the material inside the sessile dislocation loops lying on basal plane was redistributed by pipe diffusion around the periphery of the loops. This type of diffusion 19

ACCEPTED MANUSCRIPT requires lower activation energy than that for volume self-diffusion and ordinary climb. As a summary, the dislocation climb is facilitated during the high strain-rate തതത23>{112ത 2} is increased, which deformation and therefore the nucleation rate of 1ൗ3<11

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provides enough independent deformation modes for Mg alloys, and significantly improve their ductility.

Similarly, for the I2 stacking fault, once its bounding partial 1ൗ3<101ത 0>, Aσ, meets

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another partial σB, a perfect dislocation forms. The dislocation reaction is as follows:

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1ൗ <101ത 0> + 1ൗ <011ത 0> = 1ൗ <112ത 0> 3 3 3 Aσ + σB → AB.

(12) (13)

Both the 1ൗ3<101ത 0> partial and 1ൗ3<112ത 0> perfect dislocations are glissile on the basal plane and thus contribute to slip on the basal plane. Since the 1ൗ3<101ത 0> partials are

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more easily activated within the twins as discussed in Table 1 and Fig. 10, twinning and the subsequent stacking faults facilitate the deformation processes on the basal planes.

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Overall, apart from the strain accommodated by the extensive twinning itself, we attribute the enhanced plasticity of Mg alloys deformed via high strain rate rolling

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തതത23>{112ത 2} dislocations within deformation-induced mainly to the nucleation of 1ൗ3<11 twins. 4.3.

Effect of stacking faults and twinning on grain refinement

As seen in Fig. 3 and Fig. 4, grain refinement was mainly caused by DRX within

twins during the high strain-rate deformation, and the formation of LAGBs plays an important role in the nucleation of DRX grains. On the basis of the character of the LAGB observed in Fig. 9, a model for the formation process of a LAGB is drawn

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ACCEPTED MANUSCRIPT schematically in Fig. 12. In Fig. 12a, a high frequency of stacking faults form within a twin. In Fig. 12b, the twin boundaries emit partial dislocations, and the newly formed stacking fault loops may sweep through a part of the pre-existing faulted loops. The

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dislocation reactions for this process were described in equations 10–13, and Fig. 11. This results in perfect dislocations that may glide away and leave a residual segment

from these partial dislocations (Fig. 12c). The residual segments and the existing twin

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boundary cause high stress concentrations (Fig. 7). This is particularly so for the sessile partials bounding I1 stacking faults. The resultant effect is the pinning of other

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dislocations to form a new LAGB bounding against the twin boundary (Fig. 12d). The LAGB then acts as a sink for the partial dislocations formed subsequently (Fig. 12e). Therefore, any local stacking faults cannot penetrate the LAGB, as evidenced experimentally in Fig. 9b. These LAGBs can transition into HAGBs, and form fine

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DRX grains with further strain [5-7]. In summary, twinning is promoted by the highstrain rate deformation [4-7] and stacking faults are facilitated by the twinning as discussed in section 4.1. This results in the formation of a high density of LAGBs,

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facilitating the nucleation of DRX. Therefore, the high-strain-rate deformation can produce a uniform ultra-fine grained microstructure once the strain reaches a certain

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threshold value, such as ~80% rolling reduction [4-7]. 5. Conclusions

This paper provides a detailed microstructural characterisation of the early stages of

high strain-rate rolling on a ZK60 Mg alloy so as to investigate the underlying mechanisms of the improved plasticity and grain refinement observed via this processing. Three specific and inter-related topics were investigated: the influence of twinning on the formation of stacking faults; the role of twinning and stacking faults on

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ACCEPTED MANUSCRIPT the enhanced crystal plasticity; and the role of twinning and stacking faults on the nucleation of the DRX. We conclude the following: (1)

The intrinsic I1 and I2 stacking faults bounded by 1ൗ6<2ത 023> and 1ൗ3<101ത 0>

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partial dislocations, respectively, were observed in both the matrix and the twins. The frequency of these stacking faults in the twins was much higher, since the twin

boundaries played a critical role by emitting partials, and the Schmid factor for stacking

(2)

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fault shearing was higher in twins.

Apart from the strain accommodated by the extensive twinning itself, the

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improved plasticity during high strain-rate deformation is mainly due to the nucleation തതത23>{112ത 2} dislocation within twins, which provides enough independent slip of 1ൗ3<11 systems to achieve a homogeneous deformation in the material. The nucleation of 1ൗ <11 തതത23>{112ത 2} dislocation takes place from the dislocation reaction 1ൗ <2ത 023> + 3 6

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1ൗ <02ത 23> → 1ൗ <11 തതത23>, which then moves from the basal plane onto the {112ത 2} 6 3 pyramidal plane. This process turns the sessile partials into glissile perfect dislocations and this dramatically improves the capacity for crystal plasticity. The

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തതത23>{112ത 2} dislocation is controlled by the dislocation nucleation rate of the 1ൗ3<11

(3)

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climbing rate, and this is accelerated by the high strain-rate deformation. The nucleation of fine DRX grains is prone to occur in twins. The twin

boundaries and stacking faults, especially those of the I1 type, facilitate the formation of LAGBs that can subsequently transition into HAGBs, and form ultra-fine DRX grains with further strain. Overall, the combined effect of deformation twinning and stacking fault formation plays a critical role in enhancing the crystal plasticity of Mg alloys during high strain-

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ACCEPTED MANUSCRIPT rate deformation, making this deformation process feasible. The combined effects facilitate the nucleation of DRX, which enables the formation of the observed UFG microstructure.

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Acknowledgments The authors are grateful for research funding from the Australian Research Council, and the University of Sydney, including support under the aegis of the Faculty of

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Engineering & Information Technology's 'Materials and Structures Research Cluster'.

The authors acknowledge the facilities, and the scientific and technical assistance of the

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Australian Microscopy & Microanalysis Research Facility at the Sydney Microscopy & Microanalysis, The University of Sydney. The authors greatly acknowledge the assistance in conducting the rolling work from Mr. Zemin Wang, and the School of Materials Science and Engineering, Shanghai Institute of Technology. The authors also

References

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appreciate the suggestions from Dr. Anna V. Ceguerra and Mr Steven J. Moody.

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[8] Y.Z. Wu, H.G. Yan, J.H. Chen, Y.G. Du, S.Q. Zhu, B. Su, Microstructure and mechanical properties of ZK21 magnesium alloy fabricated by multiple forging at different strain rates, Mater. Sci. Eng. A 556 (2012) 164-169. [9] Y.Z. Wu, H.G. Yan, J.H. Chen, S.Q. Zhu, B. Su, P.L. Zeng, Hot deformation behavior and microstructure evolution of ZK21 magnesium alloy, Mater. Sci. Eng. A 527 (2010) 3670-3675. [10] Y.Z. Wu, H.G. Yan, J.H. Chen, S.Q. Zhu, B. Su, P.L. Zeng, Microstructure and mechanical properties of ZK60 magnesium alloy fabricated by high strain rate multiple forging, Mater. Sci. Technol. 29 (2013) 54-59. [11] D. Hull, D.J. Bacon, Introduction to Dislocations. fifth ed., ButterworthHeinemann, Oxford, 2011. [12] J.P. Hirth, J. Lothe, Theory of dislocations, John Wiley & Sons, United States of America, 1982. [13] Z. Yang, M.F. Chisholm, G. Duscher, X. Ma, S.J. Pennycook, Direct observation of dislocation dissociation and Suzuki segregation in a Mg-Zn-Y alloy by aberration-corrected scanning transmission electron microscopy, Acta Mater. 61 (2013) 350-359. [14] A. Berghezan, A. Fourdeux, S. Amelinckx, Transmission electron microscopy studies of dislocations and stacking faults in a hexagonal metal: zinc Acta Metall. 9 (1961) 464-490. [15] M.H. Yoo, Slip, twinning, and fracture in hexagonal close-packed metals, Metall. Trans. A 12A (1981) 409-418. [16] M.H. Yoo, S.R. Agnew, J.R. Morris, K.M. Ho, Non-basal slip systems in HCP metals and alloys: source mechanisms, Mater. Sci. Eng. A 319 (2001) 87-92. [17] Z. Wu, W.A. Curtin, The origins of high hardening and low ductility in magnesium, Nature 526 (2015) 62-+. [18] M.H. Yoo, J.R. Morris, K.M. Ho, S.R. Agnew, Nonbasal deformation modes of HCP metals and alloys: Role of dislocation source and mobility, Metall. Mater. Trans. A 33 (2002) 813-822. [19] J. Koike, T. Kobayashi, T. Mukai, H. Watanabe, M. Suzukia, K. Maruyama, K. Higashi, The activity of non-basal slip systems and dynamic recovery at room temperature in fine-grained AZ31B magnesium alloys Acta Mater. 51 (2003) 20552065. [20] T. Obara, H. Yoshinga, S. Morozumi, {11-22} <-1-123> slip system in magnesium, Acta Metall. 21 (1973) 845-853. [21] J.F. Stohr, J.P. Poirier, Electron-microscope study of pyramidal slip {11-22} <11-23> in magnesium, Phil. Mag. 25 (1972) 1313-&. [22] J. Geng, M.F. Chisholm, R.K. Mishra, K.S. Kumar, The structure of < c + a > type dislocation loops in magnesium, Phi.l Mag. Lett. 94 (2014) 377-386. [23] M.D. Nave, M.R. Barnett, Microstructures and textures of pure magnesium deformed in plane-strain compression, Scripta Mater. 51 (2004) 881-885. [24] L. Jiang, J.J. Jonas, A.A. Luo, A.K. Sachdev, S. Godet, Twinning-induced softening in polycrystalline AM30 Mg alloy at moderate temperatures, Scripta Mater. 54 (2006) 771-775. [25] J.W. Christian, S. Mahajan, Deformation twinning, Prog. Mater. Sci. 39 (1995) 1-157. [26] W.H. Hartt, R.E. Reed-Hill, Internal deformation and fracture of second-order {10-11}-{10-12} twins in magnesium, Trans. Metall. Soc. AIME 242 (1968) 1127-1133.

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[27] W.W. Wei, E. Povoden-Karadeniz, E. Kozeschnik, Saturation of Deformation Twinning in Magnesium Alloys. In: Sommitsch C, Ionescu M, Mishra B, E. K, T. C, (Eds.). THERMEC 2016, vol. 879, 2016. [28] X. Wang, L. Jiang, A. Luo, J. Song, Z. Liu, F. Yin, Q. Han, S. Yue, J.J. Jonas, Deformation of twins in a magnesium alloy under tension at room temperature, J. Alloys Compd. 594 (2014) 44-47. [29] N. Chetty, M. Weinert, Stacking faults in magnesium, Phys. Rev. B 56 (1997) 10844-10851. [30] Z. Ding, S. Li, W. Liu, Y. Zhao, Modeling of Stacking Fault Energy in Hexagonal-Close-Packed Metals, Adv. Mater. Sci. Eng. (2015). [31] R.E. Smallman, P.S. Dobson, Stacking fault energy measurement from diffusion, Metall. Trans. 1 (1970) 2383-2389. [32] S. Sandlöbes, M. Friák, S. Zaefferer, A. Dick, S. Yi, D. Letzig, Z. Pei, L.F. Zhu, J. Neugebauer, D. Raabe, The relation between ductility and stacking fault energies in Mg and Mg-Y alloys, Acta Mater. 60 (2012) 3011-3021. [33] Y.M. Zhu, A.J. Morton, M. Weyland, J.F. Nie, Characterization of planar features in Mg-Y-Zn alloys, Acta Mater. 58 (2010) 464-475. [34] D.K. Sastry, Y.V.R.K. Prasad, K.I. Vasu, On the stacking fault energies of some close-packed hexagonal metals, Scripta Metall. 3 (1969) 927-930. [35] A. Couret, D. Caillard, An in situ study of prismatic glide in magnesium-II. microscopic activation parameters, Acta Metall. 33 (1985) 1455-1462. [36] A. Datta, U.V. Waghmare, U. Ramamurty, Structure and stacking faults in layered Mg-Zn-Y alloys: A first-principles study, Acta Mater. 56 (2008) 2531-2539. [37] A.E. Smith, Surface interface and stacking fault energies of magnesium from first principles calculations, Surf. Sci. 601 (2007) 5762-5765. [38] B.-Y. Liu, J. Wang, B. Li, L. Lu, X.-Y. Zhang, Z.-W. Shan, J. Li, C.-L. Jia, J. Sun, E. Ma, Twinning-like lattice reorientation without a crystallographic twinning plane, Nat. Commun. 5 (2014). [39] S. Morozumi, M. Kikuchi, H. Yoshinaga, Electron-microscope observation in and around {1-102} twins in magnesium, Trans. JIM 17 (1976) 158-164. [40] H.Q. Sun, Y.N. Shi, M.A. Zhang, K. Lu, Plastic strain-induced grain refinement in the nanometer scale in a Mg alloy, Acta Mater. 55 (2007) 975-982. [41] B. Li, P.F. Yan, M.L. Sui, E. Ma, Transmission electron microscopy study of stacking faults and their interaction with pyramidal dislocations in deformed Mg, Acta Mater. 58 (2010) 173-179. [42] D. Zhang, B. Zheng, Y. Zhou, S. Mahajan, E.J. Lavernia, Prism stacking faults observed contiguous to a {10-12} twin in a Mg-Y alloy, Scripta Mater. 76 (2014) 61-64. [43] H.W. Pickering, S.P. R., Electron metallography of chemical attack upon some alloys susceptible to stress corrosion cracking, Corrosion 19 (1963) 373t-389t. [44] D.B. Williams, C.B. Carter, Transmission Electron Microscopy, Springer Science+Business Media, New York, 1996. [45] W. Gu, J.Y. Li, Y.D. Wang, Effect of dislocation structure evolution on lowangle grain boundary formation in 7050 aluminum alloy during aging, Int. J. Miner. Metall. Mater. 22 (2015) 721-728. [46] P.B. Price, Nonbasal glide in dislocation-free cadmium cystals. II. the (11-22)[1-123] system, J. Appl. Phys. 32 (1961) 1750-1757.

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[47] P. Yang, Y. Yu, L. Chen, W. Mao, Experimental determination and theoretical prediction of twin orientations in magnesium alloy AZ31, Scripta Mater. 50 (2004) 1163-1168. [48] P.B. Price, Pyramidal glide and the formation and climb of dislocation loops in nearly perfect zinc crystals, Phil. Mag. 5 (1960) 873-&. [49] F. Kroupa, P.B. Price, Conservative climb of a dislocation loop due to its intereaction with an edge dislocation, Phil. Mag. 6 (1961) 243-&.

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Fig. 1. A synthesis of the metallurgical phenomena observed to date surrounding crystal

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plasticity in Mg alloys during high strain-rate deformation: (a) initial coarse grain; (b) extensive twinning in coarse grains; (c) nucleation of DRX in twins and at grain boundaries; (d) refined microstructure. (b) ─ (d) occur during the high strain-rate

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deformation (e) and this process may take place repeatedly to achieve the final ultra-fine

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grained microstructure. It has been reported in refs. [4-10]. (f) stacking fault observed in twins and matrix, which will be presented in this work. The “?” marks represent the main fundamental mechanisms to be investigated in this study, including (1) the effect of twinning on the formation of stacking faults; (2) the influence of twinning and stacking faults on the enhanced plasticity; and (3) their co-effect on the nucleation of DRX.

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Fig. 2. (a) Illustration of the hcp crystal structure; (b) Thompson hexahedron for

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identifying dislocation Burgers vectors in hcp structure. a and c are the two lattice

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തതത23>{112ത 2} slip system is indicated. parameters. The 1ൗ3<11

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Fig. 3. (a) EBSD map of the as-rolled ZK60 alloy viewing on the ND plane, showing as an inverse pole figure (IPF) colouring map along the ND direction with the scanning step size of 0.5 µm; (b) misorientation angle distribution in (a); and (c) enlargement of the rectangular region denoted in (a). The insert in (a) denotes the colour legends of the

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IPF map and the boundaries. The inserts in (b) indicate the distribution of

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misorientation rotation axes for the circled peaks.

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Fig. 4. (a) TKD map of the as-rolled ZK60 alloy viewing on the TD plane, showing as

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an IPF image along the ND direction with a scanning step size of 15 nm; (b) and (c)

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indicate the crystallographic rotations of two different variants of {101ത 1}–{101ത 2} double twinning from matrix to the twins marked as A, B and C in (a), of which the two {101ത 1} primary twinning variants are marked as D, E, respectively. Twins A and C share the same twinning variant, which rotate the crystal -38° from the matrix along a <12ത 10> axis; and twin B rotates the crystal 38° from the matrix along the same <12ത 10>

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marked.

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axis. (d) {0001} and {101ത 0} pole figures. The projections of the matrix and twin B are

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Fig. 5. <12ത 10> bright-field TEM images and corresponding selected area electron

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diffraction patterns of (a) a {101ത 1} primary twin (PT), and (b) a {101ത 1}–{101ത 2} double twin (DT). The images are viewed parallel to the vector CA indicated in Fig. 2. These

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two twins are the twins D and B showing in Fig. 4a. The orientation of (0001) planes of twins and matrix (M) are indicated with straight lines. Stacking fault streaks on basal

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plane appear in both the twins and in the matrix.

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Fig. 6. (a) HRTEM image of the matrix marked in Fig. 4, showing basal intrinsic

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stacking faults I1 and I2; (b) and (c) enlargements of the rectangular regions denoted in (a). The viewing direction is parallel to the vector AC shown in Fig. 2. Insert in (a) is

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the fast Fourier transform (FFT) pattern of the HRTEM image. Insert in (c) is the enlarged image of the square region surrounding by the dash lines. The Burgers vectors b of the partial dislocations forming I1 and I2 stacking faults are determined by the Burgers circuits drawing in (b) and (c), respectively. Letters S and F denote the start and

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finish of the Burgers circuits. The Burgers vectors are shown by arrow heads in (b) and (c). The stacking sequences of the perfect crystal and the stacking faults are also shown

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in (b) and (c).

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Fig. 7. HRTEM image showing the stacking faults in a {101ത 1}–{101ത 2} double twin (twin B marked in Fig. 4). The viewing direction is parallel to the vector CA shown in Fig. 2. Inserts are the FFT pattern from the twinned area, and the enlarged image of the square region surrounding by dash lines, respectively. The Burgers circuit and stacking

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sequence for I1 and I2 are indicated, and the Burgers vectors are shown by arrow heads.

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Fig. 8. HRTEM images showing (a) a Frank partial dislocation forming from the

combination of the aggregation and collapse of a vacancy disc and a Shockley partial

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dislocation. Image was recorded from the matrix; (b) a Frank partial dislocation forming from the combination of the precipitation of an interstitial disc (extrinsic fault E) and a Shockley partial dislocation. Image was recorded from twin B identified in Fig. 4; (c) the two types of Frank partial dislocation forming in twin B at the vicinity of the twin

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boundary. (a) is viewed along the axis parallel to the vector AC shown in Fig. 2; (b) and (c) are viewed along the axis parallel to the vector CA. The orientation difference between (b) and (c) is caused by the different positioning of the TEM foil on the TEM

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holder at different observing sessions.

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Fig. 9. TEM images showing (a) a LAGB with a 6° misorientation in twin B marked in

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Fig. 4; (b) dislocation arrays at the LAGB and a stacking fault (SF) ends at the LAGB;

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indicate the extra half planes.

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(c) dislocations at the LAGB. Insert in (a) is the FFT pattern and the “﬩” symbols in (c)

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Fig. 10. Distribution of value of the highest Schmid factor of 1ൗ3<101ത 0>(0002) under

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the load along ND in the area observed by TKD in Fig. 4.

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തതത23>{112ത 2} pyramidal Fig. 11. Schematic diagram of the nucleation of a 1ൗ3<11 dislocation: (a) a sessile 1ൗ2<0001> partial (σS) bounding a faulted region on basal plane; (b) a glissile 1ൗ3<101ത 0> partial (σC) sweeping the faulted region bounded by σS partial and forming a sessile 1ൗ6<2ത 023> partial (SD); (c) the newly formed SD partial

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lying on basal plane; (d)-(f) formation of another 1ൗ6<2ത 023> partial (BS) by the reaction of a 1ൗ2<0001> partial (σS) and a 1ൗ3<101ത 0> partial (Bσ); (g) BS partial

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sweeping the faulted region SD partial has passed and unfaulting the region; (h) തതത23> perfect dislocation (BD) lying on basal plane by formation of a sessile 1ൗ3<11

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convergence of SD and BS partials; and (h) BD dislocation moving onto a {112ത 2} pyramidal plane, making the dislocation glissile. Please see Fig. 2 for the crystal directions denoted by letters/symbol here. Filled areas are faulted.

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Fig. 12. Schematic diagram of the formation process of a LAGB: (a) Stacking faults (SF) marked with numbers 1–5 form in a twin (twin boundaries are denoted as “TB”); (b)

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and (c) stacking faults 6–8 are emitted from either TB and sweep a part of the preexisting stacking faults 2–4, which process forms perfect dislocations and leave a

M AN U

residual segment from these partial dislocations, marked with “﬩”; (d) the residual segments and the existing TB cause stress concentration at their vicinities and pins other dislocations, resulting in the formation of a new LAGB, marked with an array of “﬩”, bounding against the TB; (e) the LAGB acts as a sink for the partial dislocations

AC C

EP

TE D

bounding the stacking faults 9–11 formed subsequently.

38

ACCEPTED MANUSCRIPT Table 1 Schmid factors of six variants of 1ൗ3<101ത 0>(0002) slip system in the matrix and twin B shown in Fig. 4.

m

λ σA/ Aσ

σB/ Bσ

σC/ Cσ

19.53°

86.14°

71.40°

75.94°

Twin B

48.76°

46.95°

52.17°

86.05°

σA/ Aσ σB/ Bσ σC/ Cσ 0.06

0.30

0.23

0.45

0.40

0.05

SC

Matrix

RI PT

φ

m — Schmid factor;

M AN U

φ — angle between the loading direction (ND) and the slip plane normal [0001];

AC C

EP

TE D

λ — angle between the loading direction (ND) and the slip direction <101ത 0>.

39