Research Article Inverse Slip Accompanying Twinning and...
Transcript of Research Article Inverse Slip Accompanying Twinning and...
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Hindawi Publishing CorporationJournal of MaterialsVolume 2013, Article ID 903786, 8 pageshttp://dx.doi.org/10.1155/2013/903786
Research ArticleInverse Slip Accompanying Twinning and Detwinning duringCyclic Loading of Magnesium Single Crystal
Qin Yu,1,2 Jian Wang,2 and Yanyao Jiang1
1 Department of Mechanical Engineering, University of Nevada, Reno, NV 89557, USA2Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Correspondence should be addressed to Jian Wang; [email protected] and Yanyao Jiang; [email protected]
Received 5 May 2013; Revised 18 July 2013; Accepted 19 July 2013
Academic Editor: Xiaozhou Liao
Copyright ยฉ 2013 Qin Yu et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In situ, observation of twinning and detwinning in magnesium single crystals during tension-compression cyclic loading wasmade using optical microscopy. A quantitative analysis of plastic strain indicates that twinning and detwinning experience twostages, low and high work hardening de-twinning, and pure re-twinning and fresh twinning combined with retwinning. Slip isalways activated. For the first time, inverse slip accompanying with pure retwinning and high work hardening detwinning wasexperimentally identified, which provides insights in better understanding of the activity of twining, detwinning, and slips.
1. Introduction
Plastic deformation in materials with hexagonal-close-packed (HCP) structure is accommodated by both slip andtwinning (or detwinning) [1, 2]. For magnesium (Mg) alloys,twinning ismainly related to the extension twin {1012}โจ1011โฉwith six variants that can be activated by an equivalent tensionalong the c-axis. Due to its polar nature, detwinning leadsto the reorientation of the basal pole from the twin backto the matrix [1โ4]. Under cyclic loading and strain pathchanges, twinning and detwinning appear alternately [5โ9]. Experimental studies have been focusing on the role oftwinning and detwinning in cyclic deformation and fatigue[5โ9]. In addition to twinning, slips are necessary to accom-modate arbitrary plastic deformation. However, the activityof twinning and slip is different in terms of nucleation andglide (or growth). For instance, nucleation of lattice glidedislocations is relatively easier than twins, but the mobilityof a {1012} twinning dislocation is greater than that of alattice dislocation [10โ14]. As a consequence, the plasticdeformation in the twinned crystal resulted from twinningshear can be greater than that in the matrix resulted fromdislocation slip. The incompatibility of plastic deformationbetween the twin and the matrix can generate a change in thestress state in the matrix surrounding the growing twin. To
be specific, the shear stress in the matrix near the growingtwin can have an opposite sign to the shear stress in thematrix far away from the twin. The opposite signed stresssurrounding the twin is often referred to as โbackstress.โ Thegrowth of twin can be slowed down and even stopped if thelocal backstress keeps increasing. To sustain the growth oftwin, the magnitude of the backstress must be reduced or thedirection of the backstress should reorient to align with thatof the external load. Such changes can be achieved througheither increasing the external load or initiating slips in thedirection opposite to the twinning shear (or the externalload). Note that at any moment, the total plastic strain rate( ฬ๐Exp๐(๐๐)
) with respect to time is equal to the summation ofthe twinning-induced plastic strain rate ( ฬ๐Tw
๐(๐๐)) and the slip-
induced plastic strain rate ( ฬ๐๐๐(๐๐)
); that is, ฬ๐Exp๐(๐๐)= ฬ๐
Tw๐(๐๐)+ ฬ๐๐
๐(๐๐),
where the subscripts ๐ and ๐ denote the coordinates. If aslip flows in the direction opposite to that of the twinningshear, we define such a slip as โinverse slip.โ To validate theexistence of inverse slips, it is essential to experimentally andquantitatively separate the plastic deformation contributed bytwinning/detwinning and slips.
In the current study, a tension-compression cyclic loadingexperiment of a [0001]-orientated Mg single crystal wasconducted at room temperature. In situ, optical microscopy
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2 Journal of Materials
was employed to directly observe the evolution of twins.Optical microscopy (OM) was chosen for the study due tothe large observation area and high frame rate [5]. A largeobservation area is extremely crucial for the determinationof macrostrain that is equal to the strain measured by usingan extensometer in the tension-compression experiment ofa single crystal. In addition, twins are generally larger thanmicrometers in size and grow very fast. Therefore, an opticalmicroscope equipped with a fast digital camera can properlycapture the twin growth. To this end, in situ high/low reso-lution transmission electron microscopy (TEM) or scanningelectron microscope or electron backscatter diffraction is notsuitable to study the cyclic tension-compression deformationdue to the geometry limit of the testing samples and due tothe small observation region and the low frame rate [15โ19].For example, the buckling could occur for a TEM sample thatis subjected to a cyclic loading with a total strain magnitudeof 0.5%.
2. Material, Experiment, and Analysis Method
Mg single crystal was grown by the Bridgman method [20].Small plate dog-bone testing specimen is cut by chemicalcorrosion technique [5] and has a gage length of 5.0mmand a square cross-section of 3.0mm by 3.0mm.The loadingdirection was aligned with the c-axis. The specimen surface,that is, the (1010) prismatic plane, was carefully polisheddown to 1๐m using polycrystalline diamond suspension,followed by chemical polishing using a solution of 1 partof nitric acid, 2 parts of hydrochloric acid, and 7 parts ofethanol as described in [21]. The well-prepared specimenwas characterized using OM, and no mechanical twins weredetected before the testing. A servohydraulic load framewith a load capacity of ยฑ25 kN was employed to performthe cyclic loading experiment. A grip system was speciallydesigned to ensure the accurate alignment of the loadingaxis with the testing specimen. A strain-gaged extensometerwith a range of ยฑ9.15% was attached to the specimen todirectlymeasure the engineering strainwithin the gage lengthof the testing sample. The load was measured by the loadcell and recorded by a computer. A long-distance opticalmicroscope was employed to trace the twins in the middle ofthe specimen observation surface during testing. The imageframe covers an area of 1.4mm ร 1.0mm on the specimensurface with a resolution of approximate 1 ๐m per pixel. Thevideo recording rate was 42 frames perminute. Fully reversedstrain-controlled tension-compression was applied at a totalstrain amplitude of 0.5% at a frequency of 0.01Hz in ambientair.
The plastic strain, ๐๐(๐ก), is determined by subtracting the
elastic strain, ๐๐(๐ก), from the total applied strain ๐Exp(๐ก). The
elastic strain ๐๐(๐ก) is calculated using theHookeโs Law employ-
ing a constant Youngโsmodulus of 44.7GPa.The plastic strainconsists of two parts: twinning-induced and slip-inducedplastic strains. The twinning-induced plastic strain, ๐Tw
๐(๐ก), is
determined according to the measured twin volume fractionthat is identified in optical micrographs through an imageanalysis. With the given crystallography and the observation
direction under investigation, there are six {1012} extensiontwin variants that could be equally activated due to identicalSchmid factors of the variants (Figure 1(a)). For each twinvariant, the twin volume fraction is calculated from the twinarea fraction by multiplying a geometrical factor ๐ฝ
๐(๐ = 1, 2,
3, . . ., 6, denoting the six variants) that accounts for the truetwin thickness. ๐ฝ is equal to 0.73 for two variants and 0.94for the other four variants. Due to a technique difficulty tonumerically distinguish the type of twin variants, an averagegeometry factor ๐ฝ = (1/6)โ6
๐=1๐ฝ๐was adopted in this study
(to avoid an overestimation of the contribution to the plasticdeformation by twins, we also performed an analysis byusing a low geometry factor of 0.73, in Figure S1. The resultsfrom both low and averaged geometry factors are similar).The total twin area fraction ๐ด is equal to the ratio of thetotal number of dark contrasted pixels (representing twins)over the total number of pixels within the observed region.The plastic strain accommodated by twinning/detwinning iscalculated according to the volume average plastic strain [22],๐Tw๐(๐๐)= (๐พ๐ก๐ค๐ฝ๐ด/2)(๐ โ ๐ + ๐ โ ๐), where ๐Tw
๐(๐๐)is the plastic
strain accommodated by twinning, ๐พ๐ก๐ค
is the twinning sheardefined as โ3/(๐/๐) โ (๐/๐)/โ3, which is equal to 0.129 as๐/๐ =1.624 for Mg, and ๐ and ๐ are the normal vectors ofthe twin plane and the twinning direction corresponding tothe specimenโs coordinates, respectively. Slip-induced strainis the difference between the measured plastic strain and thetwinning-induced plastic strain, that is, ๐๐
๐(๐๐)= ๐
Exp๐(๐๐)โ ๐
Tw๐(๐๐)
.The subscripts ๐ and ๐ represent the specimen coordinates๐ฅ, ๐ฆ, and ๐ง. Since the experiment was conducted with thecontrolled strain along the ๐ง-axis (see Figure 1), only thestrain components in the ๐ง direction (๐Exp
๐(๐ง๐ง), ๐Tw๐(๐ง๐ง)
, and ๐๐๐(๐ง๐ง)
)are analyzed and discussed. A parabolic curve is used tofit a successive set of five data points in the experimentallyobtained relationship between the plastic strain (๐Exp
๐(๐ง๐ง), ๐Tw๐(๐ง๐ง)
,or ๐๐๐(๐ง๐ง)
) and the time. The first-order derivative of theobtained fitting curve at the middle point in the successivefive-point data set is reported as the plastic strain rates ( ฬ๐Exp
๐(๐ง๐ง),
ฬ๐Tw๐(๐ง๐ง)
, and ฬ๐๐๐(๐ง๐ง)
).With the increasing number of loading cycles after the
tenth loading cycle, residual twins are found to accumulatesignificantly. Large amounts of crossing-like twin-twin junc-tions are developed severely at local areas, for example, asshown in the optical micrographs at the tensile peak strainand compressive peak strain in the 40th, 400th, and 1610thloading cycle in Figure 2. To ensure the reliability of theanalysis, we only report the plastic strains (total, twinninginduced, and slip induced) during the first ten loading cycles,where much fewer crossing-like twin-twin junctions wereobserved (see Figure 1 and Supplementary Material MOVIEavailable online at http://dx.doi.org/10.1155/2013/903786).
3. Results and Discussion
Figure 3(a) illustrates a typical stress-plastic strain hysteresisloop for the ๐th loading cycle with four featured segmentsdivided by critical points from ๐ด
๐, ๐ต๐, ๐ถ๐, ๐ท๐, ๐ธ๐, and ๐ด
๐+1.
These four featured segments are related to slips and three
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Journal of Materials 3
โa3 โa3โa3๐ = 30โ๐ = 30โ ๐ = 30
โ
twin twin twin twin twinTop
Right
Axial
Front
or (1102) (0112) (0112)(1012) (0001)(1012)
(1012)
(1102)
[1011]
[1101]
(1102)
[1011]
(1012)
[1101] [0111]
(0112)
(1102)
[0111]
(0112)
(1010)
[0001]
(1210)
Z [0001]
YO
X
XXX
[1210][1010]
โ39.22โโ39.22โ 39.22โ39.22โ
a1a1a1
C (Z) C (Z)C (Z)
a2 (Y)a2 (Y) a2 (Y)
(a)
200 ๐m
Tensile peak
1st cycle (1010)
(b)
200 ๐m
Tensile peak
10th cycle (1010)
(c)
200 ๐m 1st cycle (1010)
Compressive peak
(d)
200 ๐m 10th cycle (1010)
Compressive peak
(e)
Figure 1: (a) Schematics showing six {1012} twin variants and their projections on the (1010) prismatic plane. In situ optical micrographsshowing twins at the tensile peak strain ((b) and (c)) and compressive peak strain ((d) and (e)) at the first loading cycle and the tenth loadingcycle.
distinctive twinning mechanisms: fresh twinning, detwin-ning, and retwinning. Fresh twinning refers to the nucleationand propagation of new twins from the virgin, material andretwinning corresponds to the repeated growth of a residualtwin that is not fully detwinned [5]. ๐ด
๐and ๐ถ
๐are defined as
points at the tensile and compressive peak strain, respectively.Stage from ๐ด
๐and ๐ถ
๐refers to the unloading including
the tensile unloading and the compressive reloading. Weintroduced a critical point ๐ต
๐, from ๐ด
๐to ๐ต๐, and plastic
deformation ismainly accommodated by the easy detwinning(corresponding to a low work hardening). From ๐ต
๐to ๐ถ๐,
detwinning and slips both accommodate plastic deformation,causing a high work hardening. Due to the dislocation-twininteraction, detwinning becomes difficult, thus referred to
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0.6
0.4
0.2
0.0
โ0.2
โ0.4
10โ1 100 101 102 103 104
400 1610
400 1610
Cycle 40 comp peak
Cycle 40 tensile peak
Twin
vol
ume f
ract
ion
Number of loading cycles
Mg single crystalT-C along [0001]ฮ๐/2 = 0.5%, RT
Figure 2: Variation of twin volume fraction with respect to the loading cycles together with the optical micrographs showing twins at tensileand compressive peak strains in the 40th, 400th, and 1610th loading cycle.
as the high work hardening detwinning. The critical point๐ต๐is defined as the point where the plastic strain rate
induced by slip inverses its sign from negative to positive inFigure 3(c). The critical point ๐ท
๐is defined as the end of the
elastic segment following the compressive strain peak ๐ถ๐in
Figure 3(d), duringwhich no plastic flow exists. Similar to thecase of ๐ต
๐, the transition point ๐ธ
๐from pure retwinning to re-
and fresh-twinning is defined as the point at which the slip-induced plastic strain rate inverses its sign from negative topositive in Figure 3(c).
Figure 4(a) presents the stress-plastic strain hysteresisloops for the first and second loading cycles. Six snapshotsfrom in situ optical micrographs show morphology changeof twins at critical points (๐ด
1, ๐ต1, ๐ถ1, ๐ท1, ๐ธ1, and ๐ด
2). The
variations of plastic strain, plastic strain rates, and the abso-lute activities of twinning and slip with respect to the timeare also quantified, as shown in Figure 4(b)โFigure 4(e). Theactivity of twin or slip is a normalized factor that is used toindicate the percentage of plastic deformation in associationwith twinning or slip during a deformation segment. Forexample, ๐๐ด๐๐ต๐Tw = (ฮ๐
Tw๐(๐ง๐ง))๐ด๐๐ต๐/(ฮ๐
Tw๐(๐ง๐ง)+ ฮ๐๐
๐(๐ง๐ง))๐ด๐๐ต๐
is fortwin activity during deformation from ๐ด
๐to ๐ต๐, and ๐๐ด๐๐ต๐
๐=
(ฮ๐Tw๐(๐ง๐ง))๐ด๐๐ต๐/(ฮ๐
Tw๐(๐ง๐ง)+ ฮ๐๐
๐(๐ง๐ง))๐ด๐๐ต๐
corresponds to the slipactivity, where ฮ denotes the plastic strain (twinning or slip)range between๐ด
๐and ๐ต
๐. In Figure 4(d), the absolute value of
the normalized activity factor is shown.During initial tension (๐ to๐ด
1), the six variants of {1012}
tensile twins are easily activated due to the same Schmidfactor of 0.499 (see Figure 1). As observed in in situ opticalmicroscopy (see SupplementaryMOVIE), deformation twinsnucleate instantaneously and grow very rapidly, forming freshtwins [5]. In Figures 4(c) and 4(d), it is noticed that the twin-induced strain rate has the same sign as the applied total strainrate, but the slip-induced strain rate has an opposite sign once
twinning is activated. At the tensile peak strain (๐ด1), all the
deformation twins are fully expanded (see micrograph ๐ด1in
Figure 4(a)). From ๐ด1to ๐ต1in Figure 4(c), the slip-induced
plastic strain rate is initially greater than the detwinning-induced plastic strain rate, but later approximately equals tozero, implying that detwinning mainly accommodates theapplied strain. Comparing the optical micrographs ๐ด
1and
๐ต1in Figure 4(a), detwinning of the fully expanded twins at๐ด1is clearly observed. As revealed in Figures 4(d) and 4(e),
both detwinning and slip-induced strain rates have the samesign as the applied strain rate. During tensile unloading andthe early stage of compressive reloading, slip has a higheractivity than detwinning (Figure 4(d)) and the magnitude ofthe stress quickly decreases, indicating recovery of slips (orreversible slip). Subsequently until point ๐ต
1, the stress-plastic
strain curve shows slight strain hardening where detwinninghas the higher activity than slip (Figure 4(d)). From ๐ต
1to
๐ถ1in Figure 4(c), detwinning-induced strain rate has the
same sign as the applied strain rate, but slip-induced strainrate has an opposite sign, clearly showing the occurrence ofinverse slip. Detwinning during this segment has a higheractivity than the slip activity (Figure 4(d)). Differing fromdetwinning from๐ด
1to๐ต1, themagnitude of the stress quickly
increases from ๐ต1to ๐ถ1. It is noted that ๐ต
1in Figure 4 is a
critical point corresponding to the transition from low workhardening detwinning to high work hardening detwinning,at which the plastic strain rate induced by slip inverses itssign from negative to positive (Figure 3(c)). From ๐ถ
1to ๐ท1,
deformation is elastic, and๐ท1corresponds to the yield point.
No morphology change is observed by comparing opticalmicrographs at๐ถ
1and๐ท
1. From๐ท
1to๐ด2, retwinning occurs
at a compressive stress of โ50MPa at the early stage (๐ท1to
๐ธ1) of reversed loading. As revealed in opticalmicrograph๐ธ
1,
pure retwinning is terminated at ๐ธ1with the appearance of
two fresh twins (see Arrows ๐1and ๐
2in Figure 4). During
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Journal of Materials 5
โ100
โ80
โ60
โ40
โ20
0
20
40
0.0060.0040.0020.000โ0.002โ0.004Plastic strain
Stre
ss (M
Pa)
Ei
Bi
Di
Ci
Ai+1
Ai
Cycle i (Ai Ai+1): detwinning: detwinning
: elastic: retwinning
: re- and fresh twinning
0.3
0.0
โ0.3
0.0
0.3
0.6
0.6
Ai
Bi
Bi
Ci
Ci
Di
Di
Ei
Ei
Ai+1
โ0.6โ0.3
(b)
(c) (d) (e)
TotalTwinningSlip
TotalTwinningSlip
TotalTwinningSlip
Plas
tic st
rain
Plas
tic st
rain
rate
(10โ
3/s
)
BiAi toBi to Ci
Ci to DiDi toEiEi to Ai+1
to
rate
(10โ
3/s
)
(a)
Figure 3: Stress-plastic strain hysteresis loop with critical points (๐ด๐to ๐ด๐+1) for the ๐th loading cycle (a) and variation of plastic strain rates
(b) with the focused areas near critical point ๐ต๐(c),๐ท
๐(d), and ๐ธ
๐(e).
A1
A2
A3
โ100
โ80
โ60
โ40
โ20
0
20
40
0.0060.0040.0020.000โ0.002โ0.004
Stre
ss (M
Pa)
Plastic strain
Cycle 1Cycle 2
: fresh twinning
: detwinning: elastic: retwinning
: re- and fresh twinning: detwinningO Bi
BiAi to
BiAi to
toCi toDi
200 ๐m
E2
E1
B1B2
D2
D1
C2 C1
A1
A2
B1 C1
D1 E1
P1 P2
โ80โ40
040
2252001751501251007550250
1.00.50.0
โ0.70.00.71.4
โ0.60.00.61.2
โ1.4
โ1.2
Time (s)
Activ
itySt
ress
(MPa
)Pl
astic
stra
inPl
astic
stra
inra
te(10โ
3/s
)
(b)
(c)
(d)
(e)
(a)
TotalTwinningSlip
A1 B1 C1D1 E1 A2 B2 C2D2E2 A3ร10โ2
O
Di to EiEi toAi+1
Figure 4: (a) Stress-plastic strain hysteresis loops at the critical points of the first and second loading cycles. In situ, optical micrographs atcritical points (๐ด
1, ๐ต1,๐ถ1,๐ท1, ๐ธ1, and๐ด
2) show the morphology change of twins. from (b) to (e) illustrate the variations of (b) plastic strains,
(c) plastic strain rates, (d) absolute activity of twinning and slip which indicates the percentage of plastic deformation by twinning or slipduring a deformation segment in the stress-plastic strain hysteresis loop, and (e) the stress with respect to the time for the first and secondloading cycles.
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โ0.7
0.0
0.7
1.4
Number of loading cycles0 1 2 3 4 5 6 7 8 9 10
TotalTwinning
Slipโ1.4
Plas
tic st
rain
ร10โ2
(a)
โ80
โ40
0
40
Stre
ss (M
Pa)
0.0030.000โ0.003
Plastic strain
Cycles 1 to 10ฮ๐/2 = 0.5% in [0001]
(b)
30
15
0
Stre
ss (M
Pa)
10987654321
Number of loading cycles๐D โC๐๐
๐A๐|๐B๐|
(c)
10987654321
Number of loading cycles
โ6
0
โ3
Normal detwinning
Plas
tic st
rain
ร10โ3
Ai to Bi
(d)
10987654321
Number of loading cycles
0
6
โ6
โ12Hard detwinning
Plas
tic st
rain
Bi to Ciร10โ3
(e)
10987654321
Number of loading cycles
0
โ3
3
6
โ6 Easy twinning
Plas
tic st
rain
Di to Ei
ร10โ3
SlipTwining
(f)
10987654321
Number of loading cycles
3
0
6
Normal twinning
Plas
tic st
rain
Ei to Ai+1
ร10โ3
SlipTwining
(g)
Figure 5: Dependence of plastic strains and other physical quantities associated with deformation mechanisms on the loading cycles. (a)Variations of twin-induced and slip-induced strains, (b) stress-plastic strain hysteresis loops, (c) the stresses at๐ด
๐and ๐ต
๐and the stress range
between ๐ท๐and ๐ถ
๐. (d)โ(g) Variation of twin-induced and slip-induced strains during (d) low work hardening detwinning, (e) high work
hardening detwinning, (f) pure retwinning, and (g) retwinning and fresh twinning together.
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Journal of Materials 7
pure retwinning from ๐ท1to ๐ธ1, the slip-induced strain
rate has an opposite sign to the applied plastic strain rate,indicating that inverse slip appears. After๐ธ
1, twinning during
๐ธ1to ๐ด2is mainly associated with fresh twinning combined
with retwinning, and the stress magnitude is approximatelyconstant. As observed in optical micrograph ๐ด
2, several new
twins are nucleated.The second loading cycle (๐ด
2to๐ด3) experiences a similar
deformation process as the first loading cycle (๐ด1to ๐ด2,
see Figure 4). Deformation mechanism corresponding to thesegment from ๐ด
2to ๐ต2is the same as that from ๐ด
1to
๐ต1. The slip-induced plastic strain rate is initially greater
than that associated with detwinning but later approachesapproximately zero where detwinningmainly accommodatesplastic deformation. From ๐ต
2to ๐ถ2, detwinning-induced
strain has the same sign as that of the applied strain, but slip-induced strain rate has an opposite sign. Deformation from๐ถ2to ๐ท2is elastic. From ๐ท
2to ๐ด3, the single crystal initially
experiences re-twinning and subsequently fresh twinning.Inverse slip only accompanies with retwining and ends upat ๐ธ2, at which the sign of slip-induced rate changes from
negative to positive.Similar features were observed for the subsequent loading
cycles (Figure 5) with typical four featured segments: (i)twinning from ๐ท
๐โ1to ๐ด๐, including pure retwinning (๐ท
๐โ1
to ๐ธ๐โ1
) and fresh twinning combined with retwinning (๐ธ๐โ1
to ๐ด๐), (ii) low work hardening detwinning from ๐ด
๐to ๐ต๐,
(iii) high work hardening detwinning from ๐ต๐to ๐ถ๐, and
(iv) elastic deformation from ๐ถ๐to ๐ท๐. To visualize the
dependence of the deformation characteristics on loadingcycle, Figure 5(a) plots the variations of twin-induced strainand slip-induced strain for the first ten loading cycles. Acomprehensive analysis was performed for all loading cycles,and the results indicate that inverse slip always accompanieswith pure retwinning (๐ท
๐to ๐ธ๐) and high work hardening
detwinning (๐ต๐to ๐ถ๐).
The variation of the stresses at ๐ด๐and ๐ต
๐and the
stress range between ๐ท๐and ๐ถ
๐are plotted in Figure 5(c)
with respect to the loading cycles. The stress magnitude ๐ต๐
increases with loading cycles, which can be ascribed to strainhardening due to the dislocation-twin boundary interactions[23, 24]. Accompanying with cyclic loading, more slips areactivated and interact with the twin boundaries. Atomisticsimulations combining with dislocation theory show thatlattice glide dislocations can transmit across twin boundaryor dissociate on twin boundary while the residual and sessiledislocations are left at twin boundary and further pin thetwin boundaries [10, 23โ26]. However, the elastic stressrange between ๐ท
๐and ๐ถ
๐decreases with increasing loading
cycles, which could be mainly due to the accumulation ofresidual twins and the increase in the backstress resultedfrom detwinning. The peak stress at ๐ด
๐increases with
loading cycles, indicating that strain hardening is the resultof both dislocation-dislocation and dislocation-twin inter-actions [24]. The variation of twin activity and slip activitywith respect to the four segments during cyclic loadingare plotted in Figures 5(d)โ5(g). The ratio of detwinning-induced strain over slip-induced strain is approximately 1.60during low work hardening detwinning and is 1.20 during
fresh twinning, while both accommodate the applied strain.However, during high work hardening detwinning and pureretwinning, the ratio is approximately โ1.80 in average whereinverse slips take place.
In summary, plastic deformation of [0001]-oriented Mgsingle crystals during cyclic loading can be featured withfour segments that correspond to distinctive deformationmechanisms. Both slip and twin are always activated duringplastic deformation, but twinning (or detwinning) is moreactive and contributes more to the total plastic strain. Forthe first time, inverse slip is found to be always accompanyingwith pure retwinning and high work hardening detwinning.This implies that twinning dislocation experiences a smallerPeierls stress than the lattice glide dislocation, which isin agreement with atomistic simulations [11]. In addition,retwinning can take place at macroscale compression accom-panying with inverse slip, indicating that the local stress(which can be ascribed to the backstress resulted from thedetwinning) has a significant effect on deformation mecha-nisms. The observed high work hardening detwinning asso-ciated with inverse slip and the increase of stress magnitudemight be an indicator of strain hardening aroused from thedislocation-twin interaction. The current findings provide anew insight in understanding plastic deformation and willbenefit the development of polycrystalline plastic models forhexagonal-close-packed crystals [27โ29].
Acknowledgments
Jiang and Yu acknowledge support by the US Departmentof Energy, Office of Basic Energy Sciences under Grantno. DE-SC0002144. Wang and Yu gratefully acknowledgesupport from Office of Basic Energy Sciences, Project FWP06SCPE401, under US DOE Contract no. W-7405-ENG-36.The authors acknowledge the valuable discussion with Dr.Carlos N Tome at Los Alamos National Laboratory andProfessor Peidong Wu at McMaster University.
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