Twinning-detwinning behavior of E-form Mg alloy sheets during in-plane reverse loading

Journal Pre-proof Twinning-detwinning behavior of E-form Mg alloy sheets during in-plane reverse loading Jaiveer Singh, Min-Seong Kim, Lalit Kaushik, Joo-Hee Kang, Daeyong Kim, Etienne Martin, Shi-Hoon Choi PII:

S0749-6419(19)30529-7

DOI:

https://doi.org/10.1016/j.ijplas.2019.11.016

Reference:

INTPLA 2637

To appear in:

International Journal of Plasticity

Received Date: 20 July 2019 Revised Date:

26 October 2019

Accepted Date: 28 November 2019

Please cite this article as: Singh, J., Kim, M.-S., Kaushik, L., Kang, J.-H., Kim, D., Martin, E., Choi, S.-H., Twinning-detwinning behavior of E-form Mg alloy sheets during in-plane reverse loading, International Journal of Plasticity (2020), doi: https://doi.org/10.1016/j.ijplas.2019.11.016. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

1

Twinning-detwinning behavior of E-form Mg alloy sheets during in-plane

2

reverse loading

3

Jaiveer Singh,1 Min-Seong Kim,1 Lalit Kaushik,1 Joo-Hee Kang,2 Daeyong Kim,2

4

Etienne Martin,3 and Shi-Hoon Choi1,*

5 6 7 8 9 10 11 12

1

Department of Printed Electronics Engineering, Sunchon National University, 255 Jungang-ro, Suncheon, Jeonnam, 57922, Republic of Korea 2 Korea Institute of Materials Science, 797 Changwondaero, Changwon, Gyeongnam, 51508, Republic of Korea 3 Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West Waterloo, Ontario, N2L 3G1, Canada *Corresponding author: [email protected] (Shi-Hoon Choi)

Abstract

13

In the present work, we studied the twinning-detwinning (TDT) behavior of E-form Mg

14

alloy (EFMA) sheets during cyclic loading-unloading via in-plane compression and in-situ

15

tensile tests, respectively. An in-plane compression test was conducted to induce pre-twinning

16

in order to tailor the initial texture of an EFMA sheet. Detwinning kinetics of EFMA was

17

linked to both crystallographic orientations and the morphology of twin bands. EBSD results

18

indicated that most of the pre-twins were removed at lower tensile strains (0.04~0.06) during

19

the in-situ tensile test. The thickness direction strains were effectively accommodated via the

20

detwinning of twin bands in the pre-twinned EFMA sheet under lower tensile strains. Under

21

higher tensile strains (0.08~0.12), however, the deformations were accommodated via the

22

dislocation accumulation in localized deformation regions, which resulted in relatively higher

23

average KAM (kernel average misorientation) and GOS (grain orientation spread) values at the

24

grain and twin boundaries (TBs) during in-situ tensile testing. Resolved shear stress (RSS)

25

analysis and a crystal plasticity finite element method (CPFEM) were used to investigate the

26

detwinning behavior during in-situ tensile testing. The rate of detwinning showed a linear

27

relationship with both the average RSS for twin bands and the average accumulated detwinning

28

fraction when multiplied by the real average twin width.

29

Keywords: Magnesium, Twinning, Detwinning, RSS, CPFEM 1

1

1.

Introduction

2

Magnesium (Mg) alloys are an excellent choice for structural parts in the automotive

3

and aviation industries due to superior physical properties that include low density, good

4

machinability, and high specific strength (Aslam et al., 2014; Polmear, 1994). In addition to

5

their low ductility and stretch formability at room temperature (RT), Mg alloys have the

6

potential to reduce an automobile's weight, which imparts fuel efficiency and is crucial for

7

reductions in carbon dioxide emissions (Stalmann et al., 2001). Activation of non-basal slip

8

systems is generally difficult to accomplish at RT (Huang et al., 2009) due to the inferior

9

formability of Mg alloys at RT, which limits their widespread usage. Therefore, several

10

researchers have attempted to promote non-basal systems via suitable texture and

11

microstructure modifications in Mg alloys (He et al., 2016; Song et al., 2010). Furthermore,

12

deformation twinning also plays a significant role in low-symmetry materials with hexagonal

13

close-packed (hcp) crystal structures. Addition of rare-earth elements (Farzadfar et al., 2012;

14

Wenwen et al., 2003) as well as Ca and Sn (Kim et al., 2009; Suh et al., 2017), is an available

15

method for improving the formability of Mg alloys at RT. Ca is one of the most promising

16

additions for this purpose because it is a relatively inexpensive alloying element with low

17

solubility in Mg (Kim et al., 2016). Grain refinement through thermo-mechanical processing

18

based on severe deformation has also been used to establish routes for altering the

19

crystallographic texture, which improves the strength and ductility in Mg alloys (Biswas et al.,

20

2010; Kim et al., 2012; Suwas et al., 2007). Essentially, these techniques effectively activate

21

non-basal slip by tailoring the crystallographic texture in Mg alloys.

22

Recent studies have shown that altering the basal fiber texture via the activation of pre-

23

twins ( 1012 tension twins (TTs)) through in-plane compression (He et al., 2016; Jiang et al.,

24

2007a; Park et al., 2013) and cyclic bending-unbending testing (Habibnejad-Korayem et al.,

25

2015) has many advantages over other techniques for the tailoring of texture. Pre-twins can 2

1

effectively modify the crystallographic texture which greatly improves stretch formability at

2

RT (He et al., 2016; Park et al., 2013; Wang et al., 2015). Therefore, a significant amount of

3

pre-twins are generated via different pre-twinning techniques such as in-plane compression,

4

pre-stretching, and cyclic bending-unbending (Habibnejad-Korayem et al., 2015; Jiang et al.,

5

2007a; Xin et al., 2012). Pre-twinning also enhances the strength and mechanical anisotropy

6

through texture hardening, which is generally exhibited by grain reorientation or nucleation

7

and growth of twin lamellae during pre-twinning (Knezevic et al., 2010; Song et al., 2014).

8

In recent years, many studies have elucidated the twinning-detwinning (TDT) behavior

9

under cyclic loading in Mg alloys (Culbertson et al., 2017; Dong et al., 2015; Guillemer et al.,

10

2011; Hama et al., 2013, 2016; Li et al., 2014; Wu et al., 2016; Yin et al., 2008a, 2008b). Yin

11

et al. (Yin et al., 2008a) have shown crack initiation and propagation mechanisms to be the

12

main results of deformation twinning while dimple structures are formed by the slip in AZ31

13

Mg alloy. Furthermore, Dong et al. (Dong et al., 2015) investigated the evolution of TDT

14

structures during cyclic deformation in an extruded ZK60 Mg alloy. The investigators observed

15

an increase in twin nucleation sites whereas twin growth/shrinkage was inhibited due to

16

repeated TDT. Moreover, the increased twin nucleation sites were responsible for the observed

17

increase in the twin lamellae and volume fractions with loading cycles. Therefore, TDT

18

enhances the formation of 1011 compression twins (CTs) and 1011 − 1012 double

19

twins (DTs), which can be attributed to delays in the fracture of the material. (Rev2-3)

20

Moreover, Wu et al. (Wu et al., 2016) investigated the TDT behavior within a particular grain

21

inside a polycrystalline AZ31B via in-situ 3D synchrotron X-ray microbeam diffraction.

22

Investigation has shown that the macroscopic cyclic loading contributed to the TDT and

23

twinning-like lattice reorientation process which were captured within an individual grain

24

inside a bulk material during the strain reversal. (Rev2-4) Recently, Culbertson et al.

25

(Culbertson et al., 2017) investigated the microstructure evolution in pure Mg under cyclic 3

1

loading-unloading in ambient air. That study showed that subsequently reversed loading led to

2

a combination of low Schmid factor (SF) twinning, detwinning, and secondary twinning.

3

Deformation twinning in low symmetry hcp materials has been widely studied using

4

electron back-scattered diffraction (EBSD) (Beyerlein et al., 2010; Choi et al., 2007; Jiang et

5

al., 2007b; Martin et al., 2010; Nave and Barnett, 2004; Shin et al., 2013; Singh et al., 2019a,

6

2019b). Texture evolution due to the rotation of crystals during the activation of twin variants

7

(TVs) can affect the shear localized deformation regions near the grain boundaries (GBs), as

8

well as the work-hardening behavior (Choi et al., 2010a; Lou et al., 2007; Nave and Barnett,

9

2004). The macroscopic response of bulk materials indicates the combined behavior of

10

individual grains. Schmid factor (SF) analysis mostly explains the activation of TVs in

11

individual grains, so it is unnecessary to state that the activation of TVs always corresponds to

12

high SF grains (Beyerlein et al., 2010; Jiang et al., 2007b; Jin et al., 2015; Martin et al., 2010).

13

Jin et al. (Jin et al., 2015) used SF analysis to investigate the influence of crystallographic

14

orientations on twin nucleation and twin growth for TTs in AM30 and AZ31 under the uniaxial

15

stress state. However, the interactions among neighboring grains play a crucial role in the local

16

stress state that activates the TVs in Mg alloys.

17

This study was also focused on microstructure input-based polycrystal plasticity

18

modeling to explain the role that neighboring grains play in the orientation sensitivity of

19

detwinning and non-detwinning grains. Extensive studies based on crystal plasticity

20

simulations have been conducted for hcp single and polycrystalline bulk materials to simulate

21

the deformation mechanisms and texture evolution (Abdolvand et al., 2015; Abdolvand and

22

Daymond, 2013; Ardeljan et al., 2016; Cheng and Ghosh, 2015; Choi et al., 2010a, 2010b,

23

2011; Graff et al., 2007; Izadbakhsh et al., 2011; Qiao et al., 2016; Staroselsky and Anand,

24

2003; Wu et al., 2007). In earlier studies, crystal plasticity finite element method (CPFEM)

25

models considering the interaction among neighboring grains have simulated the spatial 4

1

distribution of stress heterogeneity under in-plane compression (Choi et al., 2010a) and the

2

type of TVs activated in deformed specimens under uniaxial compression (Shin et al., 2012). In

3

another study, a complete 3D CPFEM model considered both slip and deformation twinning to

4

simulate the texture evolution and twin volume fraction under in-plane compression in an

5

AZ31 Mg alloy (Choi et al., 2011). In this approach, however, EBSD data such as grain size

6

and microtexture were used to create a 3D synthetic microstructure for the initial configuration

7

(Choi et al., 2011; Erieau and Rey, 2004; Héripré et al., 2007). Ardeljan et al. (Ardeljan et al.,

8

2016) proposed a 3D CPFEM model that could successfully encapsulate the effect of

9

deformation twins and simulate the macroscopic response, texture evolution, and twin volume

10

fraction under different deformation paths for AZ31 Mg alloy.

11

Furthermore, recent studies have used polycrystal crystal plasticity models to predict

12

twin nucleation, propagation, and growth (Liu et al., 2018) and TDT mechanisms during

13

monotonic and cyclic loading (Guillemer et al., 2011; Hama et al., 2018; Hou et al., 2018; Li et

14

al., 2010; Murphy-Leonard et al., 2019; Qiao et al., 2015; Song et al., 2019; Wang et al., 2013,

15

2018; Zhang et al., 2019) in hcp materials. (Rev2-1) Recently, Liu et al. (Liu et al., 2018) used

16

a dislocation density-based crystal plasticity model to successfully simulate the heterogeneous

17

distribution of macroscopic stress-strain dislocation activity. These numerical simulations

18

predicted the experimentally observed twin nucleation at the GBs, followed by propagation in

19

the grain interior and the subsequent transverse twin thickening of TTs. Tensile twinning leads

20

to a reorientation of the basal poles by about 86°, whereas detwinning occurs when the load is

21

subsequently reversed, which is generally relevant to cyclic loading and fatigue. (Rev2-6) As

22

earlier discussed, many twinning models have been developed and implemented while

23

detwinning behavior is opposite with respect to twinning, but is rarely integrated into crystal

24

plasticity models. Wang et al. (Wang et al., 2013) proposed a physics-based TDT model that

25

was implemented as an Elasto-Visco-Plastic Self-Consistent model. TDT models have dealt 5

1

with, and been characterized by, four deformation mechanisms: twin nucleation, growth,

2

shrinkage, and re-twinning. Li et al. (Li et al., 2010) developed a phenomenological method for

3

modeling both twinning and detwinning under cyclic loading of AZ31B Mg alloy sheets. The

4

model used a von Mises yield surface that accounted for plastic that yields an asymmetry

5

induced by isotropic and nonlinear kinematic hardening. Furthermore, Qiao et al. (Qiao et al.,

6

2015) also developed a crystal plasticity model for simulating TDT behavior during monotonic

7

and cyclic loading of extruded ZK60A Mg alloy. Their model accounted for the initial texture

8

and differentiated between the stress required for twin initiation and the thickening of

9

previously initiated twins, and also predicted the evolution of lattice strain during cyclic

10

loading. Recently Hama et al. (Hama et al., 2018) used CPFEM to quantitatively discuss the

11

effect of detwinning on thickness strain. The simulation results indicated that the thickness

12

strain was composed of both slip and detwinning activities in the first stage of work-hardening,

13

while only slip activities contributed the second stage. (Rev1-5)

14

In this work, an in-plane compression test was used to generate pre-twinning in

15

advance to modify the initial basal fiber texture in E-form Mg alloy (EFMA). This method is

16

very effective for improving the formability of Mg alloys at RT (Song et al., 2014). The

17

influence of the crystallographic orientation of a twin band on the detwinning kinetics as a

18

function of strain is still not completely understood. First, an experimental study was

19

conducted to elucidate the TDT behavior under in-plane reverse loading and the orientation

20

sensitivity on detwinning kinetics in EFMA. An EBSD system installed with an in-situ stage

21

for tensile testing was used to study the evolution of microstructure and microtexture under

22

different levels of strain. Second, we focused on a theoretical prediction and explanation of the

23

orientation sensitivity of detwinning kinetics during the in-situ tensile testing using TT trace,

24

RSS analysis, and CPFEM.

25 6

1

2.

Experimental Methods

2

2.1.

Mechanical testing

3

The chemical composition of the hot-rolled sheet of EFMA that was used is given in

4

Table 1. The EFMA sheets with an initial thickness of 1.3 mm were produced by POSCO Mg

5

Inc. Fig. 1 shows the initial microstructure and corresponding (0002) pole figure of the EFMA

6

sheet used in the present study. (Rev2-2) Pre-twinning was induced to tailor the initial

7

crystallographic texture via an in-plane tension-compression tester that was recently developed

8

using an anti-buckling clamp (Kim et al., 2018). For the in-plane compression test, a specimen

9

was fabricated by wire electrical discharge machining (EDM), as shown in the schematic

10

drawing in Fig. 2(a). The compression axis (CA) was maintained along the rolling direction

11

(RD) during the in-plane compression test. A 4% strain at a strain rate of 1×10−3/s was applied

12

to accomplish a proper volume fraction of deformation twins. An in-situ tensile test specimen,

13

as shown by the schematic drawing in Fig. 2(b), was machined out of the gauge length region

14

(see Fig. 2(a)) of the in-plane compression specimen. The strain rate and tensile axis for the in-

15

situ tensile test were the same as those for the in-situ compression test.

16 17

2.2.

EBSD measurement and analysis

18

Microstructure measurements under different levels of strain were obtained using an

19

electron backscattered diffraction (EBSD) technique. A position of the EBSD measurement

20

under in-situ tensile testing is marked in Fig. 2(b). The specimen was polished through

21

standard metallography using SiC abrasive papers, ethanol-based diamond, and colloidal silica

22

suspensions. A field emission scanning electron microscope (FE-SEM) JEOL JSM-7001F

23

system equipped with an Oxford NordlysNano (sensitive camera) and 5 forescatter detectors

24

(FSD) (Kamaya et al., 2016) and an in-situ tensile test set-up (TSL Solutions, Japan) were used

25

in the present study. EBSD measurements during in-situ tension were performed in the ND 7

1

(normal direction) section and were measured at 0, 0.005, 0.01, 0.02, 0.04, 0.06, 0.08 and 0.12

2

tensile strains during the in-situ tensile testing. The scanning area and step size for EBSD

3

analysis were fixed at 140 × 105 µm2 and 0.3 µm, respectively, under all tensile strain

4

conditions, which covered about 80 grains/map. TSL orientation imaging microscopy (OIM)

5

analysis software version 7.3 was used to characterize the EBSD data and an average

6

confidence index of 0.87 ± 0.04 was obtained. EBSD data points with a confidence index (CI)

7

value below 0.1 were removed due to uncertain indexing. For clean-up procedures, a grain CI

8

standardization with a grain tolerance angle of 5° and a minimum grain size of 2 µm were

9

applied along with a neighbor orientation correlation with a grain tolerance angle of 5°, a

10

minimum confidence of 0, and a clean-up level of 4 (Kim et al., 2013). (Rev2) Other than using

11

the grain maps for detwinning kinetics, the EBSD data were also used for microtexture, twin

12

area fractions, measurement of twin band widths, and in-grain misorientation estimates. For

13

estimations of the kernel average misorientation (KAM) and grain orientation spread (GOS), a

14

grain definition is important. KAM is defined as the average misorientation between each

15

measurement point and all immediate neighbors. In this work, the 3rd nearest neighbors were

16

considered to calculate the KAM at a specific point inside a grain, and misorientations

17

exceeding a critical value of 5° were excluded in the calculation. GOS, on the other hand,

18

represents the misorientation between all measurement points of a grain and the average

19

orientation of the grain.

20 21 22

3.

Simulation Details RSS analysis and CPFEM were conducted to explain the detwinning kinetics. The first

23

method (RSS analysis) was based on the Schmid tensor (

24

predict the maximum RSS of the TVs for the TT of each grain, as defined in Eq. (1): =

∙

⨂

8

=

). RSS analysis was used to

− − − − − − − − − −(1)

1

In Eq. (1),

is the stress component in the sample coordinate (SC) system, the Schmid tensor

2

(=

3

vector

4

SC by the tensor transformation. The vectors

5

deformation is ignored. In this study, we used the uniaxial tension stress tensor for RSS

6

analysis, which is presented as the following tensor:

) is defined by the unit vector,

, which is parallel to the twin direction of the twin system, .

1 σ = 0 0

7

8 9

, which is normal to the twin plane and the unit

and

was also used in the

are orthogonal when the elastic

0 0 0 0! − − − − − − − − − − − − − − − (2) 0 0

This study considered six twin systems for TT as follows: (TT1: (1012)"1011# , TT2: (0112)"0111# , TT3: (1102)"1101# , TT4: (1012)"1011# , TT5: (0112)"0111# , and TT6:

10

(1102)"1101# . However, since a constant stress state in RSS analysis was assumed, the

11

interactions with neighboring grains could not be considered.

12

Furthermore, the crystal plasticity finite element method (CPFEM) was used for the

13

second method. In order to simulate the micromechanical deformation and detwinning

14

phenomenon, the experimentally obtained EBSD data were used in the finite element analysis

15

with the polycrystalline material model. This section contains a brief description of the crystal

16

plasticity model. For a more detailed explanation, readers are encouraged to refer to the

17

previous papers (Choi et al., 2010a, 2010b, 2011).

18

% $

A suitable evolution of CRSS values,

in microscopic hardening law (Choi, 2003;

19

Kalidindi et al., 1992) is required. This work used a simple phenomenological form for a

20

hardening matrix as follows. &

%'

=(

%'

ℎ$ *1 −

% $

sat

/

. − − − − − − − − − − − − − (3)

21

In Eq. (3), & %' is a hardening matrix and was introduced to consider the interaction between

22

the slip and deformation twinning systems. The CRSS values ( 9

% $)

and microscopic hardening

sat , ℎ$ , 2)

1

parameters (

2

curves and the twin fraction. In the present work, 4 slip and 2 twin systems were accounted for:

3

basal 〈2〉 ( 0001 〈1120〉 ), prismatic 〈2〉 ( 1100 〈1120〉 ), pyramidal 〈2〉 ( 1101 〈1120〉 ),

4

for deformation modes should be fitted using macroscopic stress-strain

pyramidal 〈5 + 2〉 ( 1122 〈1123〉), TT ( 1012 〈1011〉), and CT ( 1011 〈1012〉).

5

A 3D mesh (20 × 20 × 10 = 4000 elements) was used to evaluate the material

6

parameters for an EFMA. Initial size of the 3-D polycrystalline model was 140.1 µm (RD) ×

7

105 µm (TD) × 0.9 µm (ND). The total number of elements was 496,616, and the element type

8

was C3D8R. To consider the effect of deformation twinning on the micromechanical behavior

9

of Mg alloys, the original predominant twin reorientation (PTR) scheme (Tomé et al., 1991)

10

was modified for implementation in the CPFEM (Choi et al., 2010a, 2010b, 2011). This

11

approach required a tracking of both the shear strain, 7

12 13 14

and the associated volume fraction 9

,8

=7

,8 ⁄

,8

, contributed by each twin system, ,

: (: <=. = 0.129 is the characteristic twin

shear) within each orientation, ? . Summation of all twin systems in each element, the accumulated twin fraction, 9 /@@ , in each orientation was determined, as shown in Eq. (4).

9 /@@ = A BC |7E | ,8 ⁄: F G − − − − − − − − − − − −(4) $

15

Reorientation by twinning was applied only to the CPFEM for the determination of the

16

material parameters and was not applied to the microstructure-based CPFEM, which directly

17

used EBSD data for the purpose of evaluating the driving force for the detwinning under a low

18

level of strain. The activity fractions of the deformation modes within the twin bands help to

19

explain the contribution of dislocation modes within the twin band during detwinning. The

20

activity fraction (A.F.% ) of each deformation mode, α , among slip and twin systems, (K =

21

KL + K ), was calculated by the addition of shear strain in the elements (M), as shown by Eq.

22

(5).

10

A.F. = %

1

OP ∑
P ',< ∑O ∑O
− − − − − − − − − − − − − (5)

In Eq. (5), K< is the total number of elements in the analysis.

2

An indicator was used to express the degree of strain accumulation induced by

3

dislocation slip. The plastic velocity gradient, TU , can be evaluated from the slip rates, 7E % , on

4

slip/twin systems with a normal, V% , and slip/twin directions, W % , as given in Eq. (6) (Choi et

5

al., 2013, 2014). O

T = C 7E % W % ⊗ V% − − − − − − − − − − − − − −(6) U

%QR

6

The indicator defined by accumulated plastic strain due to slip, ZUL , can be evaluated for an

7

integration point in each element, as given in Eq. (7). (Rev2-7) ZUL

2 \ \ R/` = A [ T : T ^ G − − − − − − − − − − − − − (7) $ 3

8 9

4.

Results and Discussion

10

4.1.

Macroscopic stress-strain behavior

11

Macroscopic stress-strain responses under in-plane reverse loading corresponded to the

12

characteristics of TDT behavior in the EFMA sheet, as shown in Fig. 2(c). The main objective

13

for in-plane reverse loading tests at different tensile strains was to obtain the precise twin area

14

fractions that could then be further used to determine the material parameters required for the

15

CPFEM to explain the detwinning kinetics. Specimens with tensile axes (TA) and compression

16

axes (CA) parallel to the RD are denoted as TA//RD and CA//RD, respectively. Characteristics

17

of TDT behavior under in-plane reverse loading were attributed to the formation of the 1012

18

TTs during the in-plane compression and detwinning behaviors during the subsequently

19

reversed tension. When the specimens were further loaded during reverse tension, a rapid 11

1

increase in strain hardening was attributed to the dislocation accumulation, which was followed

2

by the detection of a steady stress-strain response.

3

4.2.

Microstructure evolution via in-situ tension testing

4

An in-situ tensile test specimen was prepared from the gauge length region of the in-

5

plane compressed specimen to explain the detwinning behaviors. In Fig. 3, the microstructural

6

evolution during the in-situ tensile test is depicted in the inverse pole figure (ND-IPF) maps.

7

The microstructure of the in-plane compressed specimen showed that most of the grains were

8

twinned under the in-plane compression test. Furthermore, this microstructure was served as

9

the starting state (b = 0) for the in-situ tensile test to explain the detwinning kinetics. Two

10

grains (G1: detwinning and G2: non-detwinning) are highlighted with black and white circles

11

in Fig. 3 to emphasize the different detwinning behaviors during in-situ tensile testing. Grains

12

G1 and G2 show distinct detwinning behavior, and it should be noted that most of the grains

13

exhibited different detwinning kinetics during the in-situ tensile test. This result seems to be

14

caused by the orientation relationships between twin systems and the external loading direction

15

and is also strongly influenced by the local stress states inside the twin bands. Corresponding

16

(0002) pole figures (PFs) measured under different tensile strains are also shown in Fig. 3. The

17

in-plane compressed specimen had a large TVF of TTs, which indicates that many of the 5-

18

axes of grains were aligned along the RD due to twin orientations. The reorientation of twin

19

bands to their parent orientations (5-axis aligned with ND) is also marked schematically in the

20

in-plane compressed specimens (0002), as PF. The detwinning behavior led to the evolution of

21

the typical texture of an EFMA (Singh et al., 2018) under a strain of 0.12. The maximum

22

intensities of (0002) PFs in Fig. 3 for EFMA under different tensile strains ranged from

23

9.23~11.95. The detwinning behavior seemed to be attributed to the maximum intensity of

24

(0002) PF that reached 10.75 under a strain of 0.12. (Rev2-8) Moreover, the in-situ tensile test

25

deformation led to an enhancement of the basal texture. 12

1

Image quality (IQ) maps showing the evolution of twin boundaries (TBs) and the

2

KAM maps of the EFMA under different levels of strain under in-situ tensile testing are shown

3

in Figs. 4(a) and (b), respectively. TBs, which were described as 86°〈1210〉 ± 5° for TTs

4

using the misorientation angle and the rotation axis, are plotted and highlighted in red in Fig.

5

4(a). The in-plane compressed specimen (b = 0) of an EFMA showed a significant amount of

6

TT boundaries, which corresponded to the misorientation across the boundaries of TTs.

7

However, under higher tensile strains, the TT boundaries were diminished due to the

8

detwinning phenomenon. A significant amount of detwinning started to occur at low tensile

9

strains (>0.005). At a very low tensile strain ~0.005, however, no significant contribution to the

10

reduction in twin width could be observed. Furthermore, the twin boundary fraction was

11

decreased from 0.611 to 0.168 under a tensile strain of 0.12. Therefore, the evolution in the

12

microtexture was attributed mostly to the rotation of the 5-axis from the RD to the ND plane

13

during the in-situ tensile test, which was caused by the detwinning behavior. Reduction in the

14

twin area fraction was attributed to the detwinning phenomenon where dislocations present in

15

the matrix reacted with the TT boundaries that resulted in shrinkage of the twin band (Sarker

16

and Chen, 2012; Singh et al., 2018). KAM maps showing the evolution of the misorientation

17

distribution are also shown in Fig. 4(b). The KAM maps show the localized deformation zones,

18

which mostly exhibit the non-detwinning grains and the accumulation of dislocations near the

19

grain boundary (GB) regions under a higher tensile strain of 0.12. Under lower tensile strains

20

of ~0.04, the thickness direction strains were accompanied by a detwinning of the twin bands,

21

but a higher KAM at a later stage was attributed to an accumulation of dislocations in the

22

localized deformation regions. It should be noted that the significant increase in average KAM

23

under a higher tensile strain of 0.12 resulted in the initiation of microcracks and localized

24

deformation regions. Fig. 4(b) clearly shows that the grains under a tensile strain of 0.12 that

25

do not undergo detwinning (G1 and G4), as marked with red circles, have a higher level of 13

1

KAM (and in-grain misorientation developments) compared with the detwinning grains.

2

(Rev1-6)

3

Developments in average KAM and GOS values for all grains (average), separately for

4

matrix and twin bands are shown in Fig. 5(a) and (b), respectively. Average KAM and GOS

5

values were separated for matrix and twin bands to understand the strain accommodation by

6

the detwinning of twin bands and dislocation. The specimens show that the twin bands

7

exhibited relatively higher average KAM values compared with the matrix. The relatively low

8

average KAM and GOS values in the matrix prior to a tensile strain of 0.08 were attributed to

9

strain accommodation via the detwinning of twin bands whereas the higher average KAM

10

values at a later stage seemed closely related to the dislocation accumulation in the localized

11

deformation regions. (Rev3-1)

12

4.3.

Detwinning kinetics and twin trace analysis

13

In order to explain the effect that crystallographic orientation exerts on detwinning

14

kinetics, we randomly selected 12 grains (G1 to G12), which accounted for almost all different

15

types of grain orientations, including detwinning and non-detwinning, in the ND-IPF map of

16

the in-plane compressed specimens, as shown in Fig. 6(a). To avoid confusion, we marked the

17

multiple twins in a single matrix as 1 and 2, which represents the twins that were identified for

18

further observation under different levels of strain. Fig. 6(b) shows the corresponding

19

experimentally observed matrix and twin bands along with theoretically possible TVs as a

20

discrete pole figure (DPF) for previously identified grains (G1 to G12). The matrix (M) and

21

twin (T) orientations are included in the DPF for each grain separately. The observations in

22

Fig. 6(b) clearly show that grains such as G1, G4, G5, and G10 have more than 1 variant.

23

Furthermore, the evolution of detwinning is shown in Fig. 7(a) for identified grains (G1 to

24

G12). It is important to note that grains such as G1-T1, G4-T1, G10-T2, and G11-T1

25

corresponded to non-detwinning orientations during an in-situ tensile test, whereas other grains 14

1

showed detwinning behaviors. Interestingly, one grain (G10) showed simultaneous detwinning

2

(G10-T1) and non-detwinning (G10-T2) behaviors. It seemed that the effect of neighboring

3

grains/orientations, as well as the initial twin width, also played a significant role in detwinning

4

kinetics, which is analyzed in more detail in the last section. Furthermore, corresponding TT

5

trace analysis for the ND direction (RD-TD plane) is also included in Fig. 7(a) for previously

6

identified grains (G1 to G12). A detailed explanation and plotting of traces of the twin planes

7

for all six TVs of TT are given in Appendix A. ND-IPF maps of grains combined with the TT

8

traces for the RD-TD plane effectively show the active TVs that occurred in the EFMA. Fig.

9

7(b) schematically shows the method used in the present study to measure the average twin

10

band widths from ND-IPF maps. However, because we know that twins are three-dimensional

11

(3D) structures, what is seen on the ND-IPF map might not be representative of the entire twin

12

volume. Therefore, it is impossible to obtain the real average twin band width (f gh ) from two-

13

dimensional (2D) ND-IPF maps. To calculate the initial f gh , the inclination of the 3D twin

14

structure in the grains must be found in order to correct the measured average twin band width

15

(f gi ). Therefore, we traced the twin planes for TT to obtain the inclination of the twin plane to

16

a reference plane in order to calculate the f gh from f gi , as explained in Fig. 7(b). The method

17

used to obtain the inclination of the twin plane to the reference plane is detailed in Appendix B.

18

4.4.

Defining the rate of detwinning

19

Furthermore, Fig. 8(a) shows the evolution of the real average twin band width (f gh ) in

20

identified grains (G1 to G12) under different levels of strain under the in-situ tensile test. It

21

should be noted that most of the detwinning behavior was completed within 0.04~0.06 tensile

22

strains, and these twin widths were corrected using TT trace analysis, as explained in Appendix

23

B. The rate of detwinning was different, however, in all twin bands in the identified grains. In

24

order to more clearly and quantitatively explain the different rates of detwinning in different

25

grains, the rate of detwinning is defined as shown in Eq. (8). 15

Rate of detwinning =

Change in average twin band width ∆f gh =r r − − − − − −(8) Change in tensile strain ∆b

1

Fig. 8(b) shows the rate of detwinning versus tensile strains for identified grains (G1 to

2

G12). However, the rates of detwinning were highest under lower tensile strains (from 0.005 to

3

0.01), and these rates gradually decreased up to a tensile strain of 0.06, at which point they

4

became negligible. The low rate of detwinning under a tensile strain of 0.005 was mainly

5

attributed to an insufficient amount of tensile strain at the initial stage of the in-situ tensile test.

6

Based on the different rates of detwinning for different grains, as shown in Fig. 8(b), and to

7

elucidate the effect of crystallographic orientation on detwinning kinetics, these grains were

8

grouped into fast, slow, and no-change (non-detwinning) orientations for further analysis. The

9

average KAM and GOS for the three groups of grains (fast, slow and no change) depended on

10

their rate of detwinning, as shown in Figs. 8(c) and (d), respectively. Figs. 8(c) and (d) clearly

11

show that non-detwinning (no-change) grains possessed higher averages for KAM and GOS

12

compared with the fast and slowly detwinning grains at larger strains. (Rev1-8) This result

13

implies that detwinning was useful for strain accommodation during the in-situ tensile test.

14

Therefore, the increase in orientation gradients was fastest for the cases where the detwinning

15

was negligible, as shown in Figs. 8(c) and (d). (Rev2-13)

16

In order to further explain the detwinning kinetics through in-grain misorientation

17

analysis, Fig. 9(a) and (b) shows the evolution of the average KAM analysis of matrix and twin

18

bands, respectively, for fast (G2), slow (G9), and no-change (G1) grains under different levels

19

of strain during the in-situ tensile test. Fast (G2) and slow (G9) grains had lower levels of

20

KAM development compared with the no-change (G1) grains, which was further attributed to

21

the strain accommodation due to the detwinning phenomenon during the in-situ tensile test.

22

The KAM for relatively fast (G2) and no-change (G1) grains matrices and twin bands

23

gradually increased, while the slow (G9) grains showed no significant change in the KAM

16

1

matrix value, but these did maintain a relatively high KAM from the initial stage of the in-situ

2

tensile test.

3

4.5.

4

In order to explain why different grains in EFMA showed different detwinning

5

behaviors, RSS analysis was used to simulate the effect of the stress state on the detwinning

6

phenomenon during in-situ tensile testing. RSS analysis indicates that the twin mode with the

7

highest RSS at a specific point can be activated for deformation twinning. Spatial distributions

8

of the highest RSS in each grain of an EFMA sheet under a uniaxial tension stress state are

9

shown in Fig. 10(a). The average RSS for the twin bands in identified grains (G1 to G12)

10

appears in Fig. 10(b). If a value corresponding to 80% (=0.4) of the maximum RSS is set as the

11

threshold for the twin bands, RSS analysis shows a clear difference between detwinning and

12

non-detwinning grains, with the exception of grains G10 and G12 (see Fig. 10(b)). RSS

13

analysis showed that twin bands with low RSS values (less than 80% of the maximum RSS for

14

twin bands) exist in non-detwinning orientations. Grain G10, however, has an average RSS

15

higher than 0.4 in the twin bands and simultaneously showed both detwinning and non-

16

detwinning behaviors. Hence, it seemed that the effect of either neighboring grains or the

17

initial twin band width also played a critical role in determining the detwinning kinetics. RSS

18

neglects the effect of the size of twin bands and neighboring grains. Furthermore, the

19

relationship between the average RSS and the rate of detwinning during in-plane reverse

20

loading was established and is shown in Figs. 10(c) and (d). It is evident from Figs. 10(c) and

21

(d) that these randomly selected grains (G1 to G12) show three different categories of the

22

detwinning phenomenon and the difference between fast and slow detwinning orientations can

23

be clearly observed. The detwinning rate of the twin bands did not show a linear relationship

24

with the average RSS for twin bands (see Fig. 10(c)), whereas the rate of detwinning showed a

25

linear relationship with the average RSS multiplied by the initial twin width (f g h tu vQ$ ) for twin

RSS analysis and relationship with the rate of detwinning

17

1

bands (see Fig. 10(d)). Fig. 10(d) establishes how the initial twin width plays a significant role

2

in deciding the detwinning kinetics and phenomenon. Therefore, higher values for RSS and

3

thicker twins are more favorable for easy detwinning because a higher RSS helps with the

4

activation of shearing along the twin direction. Moreover, thicker twins show a greater

5

probability for the nucleation of a detwinning nuclei due to the relatively high accumulation of

6

pseudo-slip on twin systems compared with thinner twins.

7

4.6.

CPFEM simulation

8

Furthermore, the experimentally obtained and simulated flow curves of EFMA are

9

shown in Fig. 11(a). Since the present experiment was conducted during in-plane compression

10

and tensile testing, a compression of 4% and a tension of 8% were applied in the RD as a

11

displacement boundary condition. Fitting of an experimentally obtained flow curve using

12

CPFEM simulation was carried out by obtaining the material parameters shown in Table 2.

13

Fig. 11(b) is a schematic that explains the mapping method of the EBSD data, which was used

14

as the starting microstructure for CPFEM simulation. Quasi-3D finite element mesh was based

15

on data obtained from the EBSD data of in-plane compressed EFMA. Furthermore, a buffer

16

layer with anisotropic properties surrounded the polycrystalline aggregates to diminish the

17

stress concentration that could be occurred on the edge of the polycrystalline aggregates. Hill's

18

yield function (Hill, 1948) was used to simulate the anisotropic nature of the buffer layer. The

19

coefficients of the yield function were determined on the basis of the plastic strain ratios

20

obtained from uniaxial tension.

21

Figs. 12(a)-(c) show the spatial distribution maps of effective stress, accumulated

22

plastic strains (ZUL ), and accumulated detwinning fractions, respectively, developed in the

23

EFMA under tensile strains of 0.005 and 0.01. Grains with relatively higher effective stress,

24

accumulated plastic strain (ZUL ), and accumulated detwinning fractions seemed favorable for

25

the detwinning phenomenon. This result is consistent with the RSS results listed in Fig. 10 18

1

where RSS analysis describes the detwinning phenomenon. However, the contribution of

2

accumulated plastic strain (ZUL ) attributed to a relatively higher level of localized deformation

3

regions in the matrix compared with that of the twin bands. The non-uniformity in the

4

detwinning kinetics in different grains seemed closely related to the non-uniformity of the

5

crystallographic orientation of the matrix and twin bands. A comparison between the RSS

6

analysis and the CPFEM results shows equivalent detwinning kinetics for previously identified

7

grains (G1 to G12), which was mainly governed by a higher average RSS and an accumulating

8

detwinning fraction. In particular, since the accumulated detwinning fraction had a high value

9

in the region near the GB, the region was expected to have a greater probability for the

10

nucleation of a detwinning nuclei. It seems that the accumulated detwinning fraction

11

successfully predicted the detwinning kinetics whereas the accumulated plastic strain (ZUL )

12

could not explain the deformation heterogeneities during the in-situ tensile test because

13

reorientation by detwinning was not considered in the simulation.

14

Fig. 13 shows the spatial distributions of the activity fractions of basal ⟨a⟩, prismatic

15

⟨a⟩, pyramidal ⟨a⟩, pyramidal ⟨c + a⟩, and TT developed in the EFMA under a tensile strain of

16

0.01. A quantitative comparison of the average activity fractions of different deformation

17

modes is also shown in Fig. 13. Plastic deformation in EFMA was achieved via the activation

18

of basal ⟨a⟩ slip as the primary deformation mode while TT acted as a secondary deformation

19

mode. Relatively low levels of prismatic ⟨a⟩, pyramidal ⟨a⟩, and pyramidal ⟨c + a⟩ slips were

20

also observed in the limited number of grains. Moreover, the basal ⟨a⟩ slip and TT activities

21

were concentrated in the matrix and twin bands, respectively. However, the macroscopic

22

stress-strain response of the EFMA specimen during in-plane reverse loading exhibited a

23

sigmoidal hardening behavior, as shown in Fig. 11(a), which is a well known typical TDT

24

dominated deformation behavior. It is noteworthy that the activation of TT during the in-plane

25

compression and detwinning behaviors during the subsequently reversed tension contributed to 19

1

the high hardening rates. (Rev3-3) Therefore, it was apparent that the higher TT activities in

2

the twin bands seemed to contribute to the detwinning kinetics.

3

Furthermore, the average accumulated detwinning fraction for twin bands in identified

4

grains (G1 to G12) is shown in Fig. 14(a). Unlike the RSS analysis described in Fig. 14, a

5

value corresponding to 80% (=0.1832) of the maximum average accumulated detwinning

6

fraction (0.229) was not an appropriate tolerance for distinguishing between detwinning and

7

non-detwinning behaviors in grains. A value corresponding to 70% (=0.1603) of the maximum

8

average accumulated detwinning fraction is an appropriate tolerance for that purpose.

9

However, non-detwinning grains such as G10-T2 and G12 were not accurately predicted when

10

only the average accumulated detwinning fraction was considered. Therefore, the relationship

11

between the rate of detwinning and the average accumulated detwinning fraction was

12

determined by multiplying the average accumulated detwinning fraction by the real average

13

twin width in the pre-strained specimen after the in-plane compression test, and the results

14

appear in Figs. 14(b) and (c), respectively. It is apparent in Figs. 14(b) and (c) that these

15

randomly selected grains (G1 to G12) show three different categories (similarly shown during

16

RSS analysis in Fig. 10) of the detwinning phenomenon and can also be clearly observed here.

17

Therefore, the effect of the initial twin band widths is an important factor and worth

18

considering in order to accurately predict the detwinning kinetics during the in-situ tensile test.

19

4.7.

Role of initial twin width on detwinning kinetics

20

In order to further understand the inconsistent detwinning and non-detwinning

21

behaviors of different twins (T1 and T2) in grain G10, a trace of twin planes for TT was

22

performed to explain the detwinning kinetics. Fig. 15(a) shows the ND-IPF map, the average

23

orientation of T1 and T2 twins, and the experimentally observed matrix and twin bands along

24

with the theoretically possible TVs shown in DPF for G10. The trace of twin planes for TT

25

occurring in the ND, RD and TD sections during the in-situ tensile test is shown in Fig. 15(b). 20

1

The average orientation of T1 and T2 twins in DPF shown in Fig. 15(a) clearly shows that T1

2

and T2 are two different TVs that can be further identified and confirmed as TT1 and TT4,

3

respectively, from the TT trace analysis of the ND section shown in Fig. 15(b). The stress state

4

in hcp materials is very different in the center of the grain compared with that of the GB area

5

(Gong et al., 2018; Wang et al., 2014). Moreover, the KAM maps shown in Fig. 4(b) also

6

display a higher concentration of strain that existed along the grain and GB. Hence, T1 is in the

7

middle of the grain, so less geometric strain accommodation for the neighboring grains is

8

required whereas T2 is at the GB, which requires more geometric strain accommodation for the

9

neighboring grains. However, the stress state approximates that of the external stress

10

conditions (uniaxial tensile stress along the RD) for T1, while for T2 the stress state then

11

depends on the orientations of the neighboring grains and how they deform. Therefore, more

12

dislocation must be activated to preserve the strain compatibility at the GBs near T2.

13

Detwinning behavior of the twin bands during the in-situ tension occurs mainly in the

14

region below the free surface, which is the polished surface. Therefore, in order to understand

15

the difference in the detwinning rate of each of the twin bands, information on the 3-D

16

morphology of twin bands is required. A schematic of the 3-D morphology of the T1 and T2

17

twins of G10 on the TD section is shown in Fig. 16. The reconstruction of T1 and T2 (twin

18

variants (TVs): TT1 and TT4) was based on the trace analysis for TT on three orthogonal

19

sections, as shown in Fig. 15(b). The procedure can provide the exact initial twin band width

20

and inclination of the twin plane with a reference plane. Therefore, as either Case-1 or Case-2

21

makes clear in Fig. 16, the initial width of T1 was much larger than that of T2, which was the

22

main factor for the different detwinning kinetics.

23 24

5.

Conclusions

21

1

TDT behavior in an EFMA sheet was studied under in-plane reverse loading. Pre-

2

twinning was successfully induced via in-plane compression testing to modify the initial

3

texture of the EFMA sheet. Evolutions of both the microstructure and microtexture under

4

different levels of strain were examined via an EBSD system installed with an in-situ tensile

5

test at RT. The in-situ tensile test showed that both detwinning of twin bands at lower tensile

6

strains (0.04~0.06) and dislocation by slip at higher tensile strains (0.08~0.12) are the main

7

deformation mechanisms in EFMA. Under higher tensile strains (0.08~0.12), the highest KAM

8

distribution was confined mostly to the detwinned regions and GBs during an in-situ tensile

9

test. Detwinning kinetics in EFMA was linked to both the effect of the initial orientation and

10

the initial twin band width. EBSD results indicate that the thickness-direction strains were

11

effectively accommodated via the detwinning of twin bands in the in-plane compressed EFMA

12

sheet under lower tensile strains (0.04~0.06) during the in-situ tensile test. In order to explain

13

the effect of crystallographic orientation on detwinning kinetics, 12 grains (G1 to G12) were

14

randomly selected and grouped into fast, slow and no-change (non-detwinning) orientations

15

depending on the different rates of detwinning.

16

Furthermore, the rate of detwinning of the previously identified twin bands did not

17

show a linear relationship with either the average RSS or the average accumulated detwinning

18

fraction obtained by CPFEM. However, the detwinning rates of twin bands showed a linear

19

relationship with the average RSS and average accumulated detwinning fraction multiplied by

20

the initial twin band width, which precisely explained the experimentally observed detwinning

21

kinetics. Therefore, a higher RSS, a higher average accumulated detwinning fraction, and

22

thicker twins, all are more favorable to an enhancement of detwinning.

23 24

Acknowledgements

22

1

This research was supported by the National Research Foundation of Korea (NRF)

2

funded by the Ministry of Science, ICT (NRF-2016M3C1B5906955), and the Basic Science

3

Research Program through the National Research Foundation of Korea (NRF) funded by the

4

Ministry of Education (NRF-2014R1A6A1030419). J.-H. Kang was supported by the

5

Fundamental Research Program of the Korea Institute of Materials Science (PNK6410).

23

1

Appendix A

2

A line that traces the twin planes on a reference plane is the intersection of the two

3

planes. However, a line that intersects both planes will be perpendicular to their respective

4

normal vectors. Therefore, the cross product of the normal vectors of the planes will give a

5

trace of the twin planes.

6

The normal vector of the twin planes is represented by Eq. (A.1). y = ℎẑ + |}̂ + ~|• − − − − − − − − − − − − − (€. 1)

7

The normal vector of the reference plane for the RD-TD plane, as shown in Fig. A.1(a), is

8

represented by Eq. (A.2). • = 0ẑ + 0}̂ + 1|• − − − − − − − − − − − − − (€. 2)

9

Therefore, the twin trace is given by Eq. (A.3). ẑ ‚= ℎ 0

}̂ | 0

|• ~ ! = |ẑ − ℎ}̂ − − − − − − − − − − − (€. 3) 1

10

In a similar manner, the twin traces of other reference planes, viz., ND-TD and ND-RD

11

planes

as

shown

in

Figs.

A.1(b)

and

24

A.1(c),

can

also

be

determined.

1

Appendix B

2

The angle between the twin plane and the reference plane is known to be equal to the

3

angle between their respective normal vectors. However, the Miller indices of any plane will

4

give its normal direction. Therefore, a plane with Miller indices (ℎ|~) will show the normal

5

direction of the vector, as given in Eq. (B.1).

6

y = ℎẑ + |}̂ + ~|• − − − − − − − − − − − − − −(ƒ. 1)

7

The angle between the normal vectors of a twin plane and a reference plane (RD-TD

8

plane), as shown in Fig. B.1(a), can be calculated using the dot product of both the normal

9

vectors, as given in Eqs. (B.2-B.6). y„ = ℎR ẑ + |R 1}̂ + ~R |• ≡ 0† + 0‡ + 1| − − − − − − − − − (ƒ. 2) yˆ = ℎ` ẑ + |` 1}̂ + ~` |• − − − − − − − − − − − −(ƒ. 3) cos ‹ = cos ‹ =

y„. yˆ − − − − − − − − − − − − − (ƒ. 4) | 1|| 2| ~`

√0` + 0` + 1` •ℎ`` + |`` + ~``

− − − − − − − − − (ƒ. 5)

~` ‹ = cosŽR * . − − − − − − − − − − − (ƒ. 6) •ℎ`` + |`` + ~``

10 11

Therefore, the measured twin band width (fi ) from the top can be corrected to the

real twin band width (fh ) by accounting for the inclination of the twin plane away from the

12

RD-TD plane. Hence, the fh can be calculated according to the inset of section A-A, as

13

shown in Fig. B.1(b) and Eq. (B.7). fh = fi sin θ − − − − − − − − − − − − − (ƒ. 7)

25

1

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12

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13

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33

1

Table 1. The chemical composition of the EFMA used in the present study. Elements (wt %)

Al

Zn

Ca

Mg

3

1

1

Balance

2 3

Table 2. The hardening parameters used in the fitting simulation. Material

E-form

•‘

’‘

•“”‚

”

Pyramidal 〈2〉

30

100

60

1.1

112

400

190

0.8

Pyramidal 〈5

112

400

190

0.8

112

400

190

0.8

24

50

50

1.1

200

100

300

1.1

Mode

Basal 〈2〉

Prismatic 〈2〉 TW CT

+ 2〉

4

34

1

Figure Captions

2

Fig. 1: ND-IPF (normal direction - inverse pole figure) and corresponding (0002) pole figure

3

(PF) map of the as-received rolled sheet of EFMA used in the present study. (Rev1-2)

4

Fig. 2: (a) Schematic drawing of the specimen used for an in-plane compression test to

5

modify the texture through pre-twinning. (b) Schematic drawing of the specimen used for the

6

in-situ tensile testing of an EFMA sheet. The specimen was fabricated from the gauge length

7

region of an in-plane compressed EFMA specimen shown in (a); the position for the

8

measurement of the electron backscattered diffraction (EBSD) map is also marked in (b). All

9

dimensions are given in mm. (c) The macroscopic response under in-plane reverse loading

10

and the corresponding strain levels for the characteristics of twinning and detwinning in an

11

EFMA sheet.

12

Fig. 3: ND-IPF and corresponding (0002) PFs map of an EFMA sheet under different levels

13

of strain during the in-situ tensile test. The black and white circles mark the detwinning and

14

non-detwinning grains, respectively.

15

Fig. 4: (a) Image quality (IQ) and (b) kernel average misorientation (KAM) maps showing

16

the evolution of twin boundaries (TBs) and misorientation distributions in an EFMA sheet

17

under different levels of strain during the in-situ tensile test.

18

Fig. 5: (a) Area fractions of the low-angle grain boundaries (LAGBs), high-angle grain

19

boundaries (HAGBs), twin boundaries (TBs), and evolution of the twin boundary lengths.

20

Evolution of (b) the average KAM for whole grains, matrix orientations, and twin bands, and

21

(c) the average GOS for whole grains, matrix orientations and twin bands in an EFMA under

22

different levels of strain during the in-situ tensile test.

23

Fig. 6: (a) The grains (G1 to G12) are marked on an EBSD map to explain the detwinning

24

kinetics and (b) corresponding experimentally observed matrix and twin bands along with

25

theoretically possible twin variants (TVs) shown as a discrete pole figure (DPF). The DPF is 35

1

used to plot the 3D orientation of a given pole (with respect to the sample reference frame) as

2

discrete points in a 2D projection. (Rev2-12)

3

Fig. 7: (a) Evolution of detwinning kinetics in previously identified grains (G1 to G12) under

4

different levels of strain during the in-situ tensile test. (b) The schematic shows the method

5

used in the present study to measure the real average twin band widths under different levels

6

of strain.

7

Fig. 8: (a) Evolution of the real average twin band widths for identified grains (G1 to G12)

8

under different levels of strain during the in-situ tensile test. (b) Rate of detwinning versus

9

change in tensile strains, (c) average KAM and (d) average GOS as divided into three groups

10

(fast, slow and no-change) depending on their rate of detwinning. The increase in orientation

11

gradients is fastest for the cases where the detwinning is negligible. (Rev2-13)

12

Fig. 9: Evolution of the average KAM during in-grain misorientation analysis for (a) the

13

matrix and (b) twin bands for fast (G2), slow (G9), and no-change (G1) grains under different

14

levels of strain during the in-situ tensile test.

15

Fig. 10: (a) Spatial distribution of the highest RSS in each grain of an EFMA sheet under a

16

uniaxial tension stress state and (b) the average RSS for twin bands in identified grains (G1 to

17

G12). The relationship of the rate of detwinning with (c) average RSS and (d) average RSS

18

multiplied by the real average twin width in the in-plane compressed specimen after the in-

19

plane compression test.

20

Fig. 11: (a) Experimentally measured and simulated macroscopic response under in-plane

21

reverse loading for an EFMA sheet. (b) A schematic diagram explaining the second method

22

based on direct mapping of EBSD data onto a quasi-3-D finite element mesh. The in-plane

23

compressed microstructure of EFMA is included as the inverse pole figure (IPF) map utilized

24

in the simulation as input.

36

1

Fig. 12: Spatial distributions of (a) effective stress, (b) accumulated plastic strains (ZUL ), and

2

(c) accumulated detwinning fraction developed in the EFMA under tensile strains of 0.005

3

and 0.01.

4

Fig. 13: Spatial distributions of the activity fractions of different deformation modes basal

5

⟨a⟩, prismatic ⟨a⟩, pyramidal ⟨a⟩, pyramidal ⟨c + a⟩, and TT developed in the EFMA under a

6

tensile strain of 0.01. Quantitative comparison of the average activity fractions of different

7

deformation modes is also included.

8

Fig. 14: (a) The average accumulated detwinning fraction for twin bands in identified grains

9

(G1 to G12). The relationship of the rate of detwinning with (b) average accumulated

10

detwinning fraction and (c) average accumulated detwinning fraction multiplied by the real

11

average twin width in the pre-strained specimen after an in-plane compression test.

12

Fig. 15: (a) EBSD IPF map, the average orientation of T1 and T2 twins, and experimentally

13

observed matrix and twin bands along with theoretically possible twin variants (TVs) shown

14

in discrete pole figures (DPF) for G10 to explain the detwinning kinetics. (b) TT traces

15

occurring in the ND, RD and TD directions during the in-situ tensile test.

16

Fig. 16: Schematic showing the three-dimensional reconstruction of T1 and T2 twins of G10

17

in the TD direction.

18

Fig. A.1: Trace of twin planes with (a) RD-TD, (b) ND-TD and (c) ND-RD planes.

19

Fig. B.1: Schematics showing the inclination of a (a) twin plane with a reference plane and

20

gh ). (b) inset of section A-A for measurement of the real average twin band width (f

37

100 µm

Fig. 1

(a)

(b)

Grain boundaries Twin boundaries

Fig. 2

(c)

?? ??

?? ??.??????

?? ??.????

?? ??.????

G2 G1

9.29

9.23

10.65

11.10

TD

RD

?? ??.????

?? ??.????

11.95

?? ??.????

11.67

?? ??.????

11.74

Fig. 3

10.75

?? ??

?? ??.??????

?? ??.????

?? ??.????

G2 G1

?? ??.????

? ? ? ? . ? ?6

? ? ? ? . ? ?8

(a)

Fig. 4

?? ??.????

Grain boundaries Twin boundaries

?? ??

?? ??.??????

?? ??.????

?? ??.????

G2 G1 Avg. KAM = 0.55

?? ??.????

Avg. KAM = 0.55

? ? ? ? . ? ?6

Avg. KAM = 0.56

? ? ? ? . ? ?8

Avg. KAM = 0.57

?? ??.????

G1

G4

Avg. KAM = 0.59

Avg. KAM = 0.63

(b)

Fig. 4 (Contd.)

Avg. KAM = 0.67

Avg. KAM = 0.92

(b)

(a)

Fig. 5

As pre-compressed (? ? ? ?)

(a)

: Matrix : Twin variants : Experimental

(b)

Fig. 6

? ???, ? ???, ? ???,

? ??? ? ?

? ???,

? ???, 3 ? ??? sin? ?

0 ? ???

? ???,

;

? ??? , ? ??? , ? ??? ,

? ??? ? ?

? ??? ,

0 ? ???

? ??? , 3 ? ??? sin? ?

(b) (a)

Fig. 7

? ??? ,

;

(a)

(b)

(c)

(d)

Fig. 8

(a)

(b)

Fig. 9

G7

G2

G8 G1 G9

G12 G11

G10

G3 G4

G5

G6

(a)

(b)

(c)

(d)

Fig. 10

ND RD TD

(b)

(a)

Fig. 11

Grain boundaries Twin boundaries

?? ??.??????

Max. 277.16

Max. 0.028

Max. 0.293

Max. 298.83

Max. 0.063

Max. 0.696

?? ??.????

(a)

(b)

Fig. 12

(c)

Basal ? ?

Prismatic ? ?

70µ µm

Pyramidal ? ? ? ?

TT

Fig. 13

Pyramidal ? ?

(a)

(c)

(b)

Fig. 14

IPF Map

T1

DPF

Twin Variants

T2

TT1 TT4 : Matrix : Twin variants : Experimental

(a) ND

RD

(b)

Fig. 15

TD

Case-2

Case-1

T1

T2

TT1

TT4

Top view of the grain (along ND direction)

T1

T2

Polishing plane

Side views of the grain (along TD direction)

Fig. 16

T1

T2

(a)

(b)

(c)

Fig. A.1

Measured twin width ? ??? from the top

(a)

(b)

Fig. B.1

Highlights •

The twinning-detwinning behavior in an E-form Mg alloy sheet was studied under inplane reverse loading.

•

The evolutions of both the microstructure and microtexture were examined via an EBSD system equipped with an in-situ tensile test.

•

The detwinning kinetics in E-form Mg alloy was linked to both the effect of the initial orientation and the initial twin band width.

•

Randomly selected grains were grouped into fast, slow and no-change orientations depending on the different rates of detwinning.

•

A higher RSS, a higher average accumulated detwinning fraction, and thicker twins, all are more favorable to an enhancement of detwinning.

Conflict to interest I confirm that there is no conflict of interest.