Bioio Yng,Chenying Shi,Siyu Zhng,Jingjing Hu,Jinwei Teng,Yujie Cui,Yunping Li,?,Akihiko Chi

a State Key Lab for Powder Metallurgy,Central South University,Changsha 410083,China

b Institute for Materials Research,Tohoku University,Sendai 980-8577,Japan

Abstract Twinning-detwinning(TDT)behavior in a strongly basal-textured Mg-Li alloy during two-step compression(RD)-compression(ND)process was investigated using quasi-in-situ EBSD.TDT behavior and TDT variants selection were statistically discussed with the loading path for the first time.Non-Schmid twinning behavior was observed in the first step compression,owing to the local stress fluctuations by neighboring twins;in contrast,Schmid’s law well predicted the detwinning variants selection.This asymmetrical TDT behavior was first investigated to date related with the strong basal texture and loading path.Besides,with the progress of compression,Schmid factors for twinning demonstrated a decreasing tendency;however,those for detwinning during the second step displayed an abnormally increasing trend,fundamentally stemming from prior twinning behavior.

Keywords:Twinning-detwinning;Mg-Li alloy;Quasi-in-situ;Biaxial loading.

1.Introduction

Owing to the high strength-to-weight ratio,exceptional machinability and relatively low cost,Mg alloys have drawn extensive interests in recent decades as potential structural material candidates[1–7].However,poor plasticity of Mg alloys at ambient temperature greatly limits their wide applications due to the underlying hexagonal close-packed(HCP)lattice structure[8,9].As an important deformation mode of Mg,{10-12}extension twinning features a 86.3° lattice reorientation and accommodates the deformation along c-axis with a shear strain of 0.126[10,11].It has been also indicated that pre-twinning is a potential avenue to improve plasticity,strength,etc.by tailoring the texture of Mg alloys[12–16].

Ascribed to the critical role of twinning in deformation of Mg,twinning-detwinning(TDT)behavior has been investigated using a variety of experimental methods and simulations[17–21].Schmid factor(m)was extensively adopted to explain and predict the twinning(detwinning)variants selection behavior,given the macroscopic mechanical response of bulk materials could be regarded as the superposition of each individual grain[22,23];the appearance of non-Schmid twinning variants implies that other factors need to be taken into consideration[24].To be specific,when local stress/strain dominates,geometric compatibility factor(m’)from Luster and Morris is capable of clarifying the non-Schmid twinning variants selection phenomenon[25–27].It has to be noted that the aforementioned studies on TDT behavior mostly rely on the uniaxial loading by means of either cyclic loading and/or reverse loading.In this situation,both variants of twinning and detwinning share the comparable value ofm.

Nevertheless,actual stress state for general structural components of Mg alloy in service is not the abovementioneduniaxial loading state,but tends to be more complex like multiaxial loading[28–30].Previous studies under biaxial or multiaxial loading conditions revealed the quite different TDT behaviors and mechanical responses compared to the uniaxial loading condition[31–35].A two-step loading on rolled AZ31 alloy with initial compression along rolling direction(RD)and subsequent tension along various directions indicated the more sigmoidal shape of the tensile stress-strain curve in the tension along RD than that along transverse direction(TD);yield strength,hardening parameters and twinning(detwinning)activities were also closely dependent on the loading path of second step[33].Multiaxial loading via radial compression perpendicular to extruded direction(ED)and further compression along ED of as-extruded AZ31 alloy were studied by Li et al.[34].Non-lenticular residual twins and twin traces with misorientation of 5–7° were observed,uncovering an alternate detwinning mode through{10-12}-{10-12}re-twinning.Similar researches on biaxial or multiaxial loading of Mg alloys were also performed mostly via analyzing the macroscopic stress-strain behavior and texture evolution[36–39].

To date,a few studies on deformation of Mg alloys under biaxial or multiaxial loading were reported but still lacked a deep understanding on the TDT behavior especially the relationship between twinning and detwinning under the complex loading condition[40–42].For instance,deformation and fracture behaviors of a basal-textured AZ31 alloy sheet were investigated under uniaxial tension and biaxial stretching by electron backscatter diffraction(EBSD)andin-situdigital image correlation(DIC)techniques[40].TDT and mechanical behaviors of rolled AZ31 sheet during various tension-tension loading paths were investigated byin-situacoustic emission technique while no detailed analysis on the relationship between loading paths and TDT behavior like TDT variants selection was performed[41].Likewise,although the influence of loading paths on reversible{10-12}twinning under compressive loading along RD and normal direction(ND)was investigated byquasi-in situEBSD on a rolled AZ31 sheet,the correlation between the twinning and detwinning behavior is still not clarified clearly[42].Considering the abovementioned conditions,comprehensive understandings on TDT behavior especially the correlation between twinning and detwinning of Mg alloys in biaxial or multiaxial loading condition are imperative and meaningful to aid in optimizing the microstructures and the corresponding properties of Mg alloys in service.

Mg-Li alloys are more lightweight and more ductile than the other Mg alloys with wide applications in aerospace and aircrafts[43,44].The non-basal slips are more active in Mg-Li alloys ascribed to the increased critical resolved shear stress(CRSS)of basal slip by Li addition,resulting in higher ductility compared to other Mg alloys[44–46];although several studies have also exhibited the important role of TDT in deformation of Mg-Li alloys,TDT behavior,especially detwinning,in Mg-Li alloys has not been paid much attention due to the lower twinning activity in plastic deformation[47–49].For instance,extension twinning was reported to contribute greatly to the ductility of Mg-5Li alloy during stretching along transverse direction(TD),while the correlation between TDT behavior and Mg-Li alloy didn’t get thorough analysis[50].Therefore,in the present work,TDT behavior of rolled Mg-0.3Li(at.%)alloy during two-step compression(RD)-compression(ND)process was investigated in detail byquasi-in-situEBSD.Schmid factor evolution behaviors for twinning(detwinning)variants were unraveled using MTEX codes[51].For the twinning variants not following the Schmid’s law,geometric compatibility factor(m’)was introduced to explore the potential twinning variants selection mechanisms.A schematic diagram for TDT behavior of rolled Mg-Li alloys under biaxial loading condition is presented for the first time,to unmask the detailed TDT behavior under complex loading condition.

2.Material and methods

Ingot of Mg-0.3Li(at.%)alloy was prepared by vacuum melting,followed with a solution treatment at 400°C for 2h and air cooling.Then,the alloy was hot rolled at 300°C with a thickness reduction of 67% and was subsequently annealed at 400°C for 2h with air cooling.

Rectangular specimen with dimensions of 10(RD)×9(TD)×6.5(ND)mm3was prepared using wire electrical discharge machining(EDM)for the two-step compression(RD)-compression(ND)process.This was performed using MTS landmark materials testing system(MTS Systems Corporation,Eden Prairie,MN,USA)with a displacement speed of 0.05mm/min at room temperature.“First step”compression was performed along RD to an engineering strain of approx.3.50%,and then the sample was subjected to a“second step”compression along ND.Interrupted microstructural characterization was conducted at engineering strains of 0.77%(Stage A),1.82%(Stage B),2.34%(Stage C),2.86%(Stage D),3.50%(Stage E)during the“first step”compression and 0.97%(Stage F),4.50%(Stage G),8.12%(Stage H)during the“second step”compression.For comparison,uniaxial compressions along RD and ND were also performed independently.

Before EBSD observation,the sample was sequentially polished using SiC paper,0.5μm alumina suspension,and 40nm oxide polishing suspensions(OPS).EBSD measurements were carried out using a field emission scanning electron microscope(FESEM,FEI XL30S,FEI Company,Portland,OR,USA)with a voltage of 30kV and a spot size of 3.5.To fathom out the initial texture of Mg-0.3Li(at.%)alloy before compression tests,an area of 600×600 μm2was selected for EBSD observation with a step size of 1.3μm.Forquasi-in-situEBSD observations during the interrupted two-step compression(RD)-compression(ND)test,an area of 200×200 μm2and a step size of 0.5μm were chosen.Note that for avoiding the potential stress concentration,area forquasi-in-situEBSD observation was selected in the plane of RD×ND but noncentral[52].EBSD data were analyzed using HKL Channel 5.0 software.The detailed TDT behaviors were analyzed by MATLAB with MTEX codes[51].Todistinguish the twinning variants,6 possible twinning systems(-1102)[1-101]variant with rotation axis of[11–20],(-1012)[10,11]variant with rotation axis of[-12-10],(0-112)[01-11]variant with rotation axis of[-2110],(01-12)[0-111]variant with rotation axis of[2-1-10],(10-12)[-1011]variant with rotation axis of[1-210]),and(1-102)[-1101]variant with rotation axis of[-1-120]),were signed as R1-R6,respectively.

Fig.1.(a)The EBSD results in terms of inverse pole figure(IPF)shaded by grain boundaries(GB),(b)grain size distributions,and(c)pole figures of hot rolled Mg-0.3Li(at.%)alloy after aging at 400°C for 2h.

3.Results

3.1.Initial microstructure

Fig.1(a)depicts with the initial microstructure of the extruded Mg-0.3Li(at.%)alloy in terms of inverse pole figurenormal direction(IPF-ND)with grain boundaries(GB),characterized with most grains along＜0001＞direction.The grain size distribution is shown in Fig.1(b),revealing the peak grain size and average grain size of 14.90 and 23.04μm,respectively.Further analysis using pole figures shown in Fig.1(c)indicates a strong basal plane texture(＜0001＞//ND),which is in accordance with the result of Fig.1(a).

3.2.Compressive stress-strain curves

Fig.2 presents the compressive stress-strain curves of Mg-0.3Li(at.%)alloy under various loading paths.It’s obvious to notice the sigmoidal and convex parabolic stress-strain curves during the uniaxial compression along RD and ND,respectively,which were ascribed to the strong basal texture of Mg alloy after rolling[53,54].However,for the biaxial compression,stress-strain curve along ND in the second step is much different to that of the uniaxial compression along ND.The slope of“elastic stage”during the second step is distinctly lower than that during the first step.This phenomenon has been closely linked with detwinning behavior during the second step[42].

Fig.2.The compressive stress-strain curves of Mg-0.3Li(at.%)alloy under various loading paths.

3.3.Microstructural evolution during biaxial loading

As shown in Figs.3 and 4 in terms of IPF-ND and image quality(IQ)map,respectively,microstructural characteristic during the two-step compression(RD)-compression(ND)process can be clearly classified into twinning in the first step(Figs.3 and 4(a–e))and detwinning in the second step(Figs.3 and 4(f–h)).With the progress of compression along RD in the first step,twinning number increases,and twinning lamella widens gradually through the migration of twin boundaries(TBs).On the contrary,large numbers of twins become narrower,shorter,and then vanish finally in the second step.Moreover,under stage H,some traces of prior TBs are still visible as shown in IQ map(Fig.4(h)),albeit they are not visible in IPF map(Fig.3(h)).

Fig.3.The EBSD results regarding inverse pole figure(IPF)shaded by grain boundaries(GB)of Mg-0.3Li(at.%)alloy under different stages:(a-h)A-H.

Fig.4.The EBSD results regarding image quality(IQ)maps shaded by grain boundaries(GB)of Mg-0.3Li(at.%)alloy under different stages:(a-h)A-H.

The misorientation angle distributions under various stages are presented in Fig.5(a).Obviously,except stages A and H,all the other stages exhibit a misorientation angle peak of around 83.5–89.5° with a rotation axis of＜2-1-10＞,revealing the existence of{10-12}extension twin.In addition,the intensity of low-angle boundaries(LABs)roughly increases with the progress of biaxial compression,implying that the potential slip is also activated throughout the process.As quantitatively given in Fig.5(b),twinning boundary length fractions are increasing during the first step(stages A to E)and decreasing during the second step(stages F to H).This tendency is closely in accordance with the microstructural evolution behavior shown in Figs.3 and 4.Note that the slight increase in the twinning boundary length fraction from stages E to F should be related with the deviations of observed regions duringquasi-in-situexperiments.

Fig.5.(a)Misorientation angle distributions and(b)boundary length fractions of{10-12}extension twins of Mg-0.3Li(at.%)alloy under different stages:A-H.

Fig.6.{0001},{11-20},and{10-10}pole figures in RD under various stages:(a)A,(b)G,and(c)J.

To further ascertain the orientation distribution of twins,{0001},{11-20}and{10-10}pole figures are drawn by Channel 5.0 software under stages A,E,H and shown in Fig.6.Clearly,twins exhibit a strong basal texture(＜0001＞//RD);intensity of initial basal plane texture(＜0001＞//ND)is weakened in the first step owing to twinning yet recovered in the second step thanks to detwinning.

3.4.Analysis of m for TDT

Fig.7(a)gives EBSD IPF-ND and IQ map as well as the correlated illustrations regarding crystal-lattice orientations ofthe twinning variants and parent grains in the region of interest(ROI)1 in Fig.3.Fig.7(b)provides{0001}pole figures of parent grains G1,G2,and their potential extension twinning variants.According to Fig.7(a)and(b),two twins T1 and T4 with twinning systems of R3 and R4 in parent grain G1,as well as the other two twins T2 and T3 with twinning systems of R6 and R3 in parent grain G2,are observed,respectively.Twinning(detwinning)Schmid factor were calculated using following formula:

Fig.7.(a)Microstructural evolutions of grain 1(G1),grain 2(G2)during biaxial compression.(b){0001}pole figures of G1,G2 and their potential twinning variants.(c){0001}pole figures of T1,T2,T3,T4 and their potential re-twinning variants.

whereφrepresents the angle between the{10-12}extension twinning plane normal direction and the loading force,andλis the angle between the{10-12}extension twinning shear direction and the loading force.Obviously,in G1,T1 and T4 have 1st and 2nd ranks of Schmid factor(m);T2 and T3 have 1st and 3rd ranks ofmin G2.To further analyze the detwinning behavior of the abovementioned 4 twins,the positions in{0001}pole figure of T1,T2,T3,T4 and their potential{10-12}re-twinning variants are summarized in Fig.7(c).It’s quite remarkable that detwinning will occur if an opposite rotation axis of re-twinning is selected with that of previous twinning.This detwinning phenomenon is observed to occur for all twinning variants.

With twinning(detwinning)mof 60 twins being collected,statistical analysis was performed in four different views as shown in Fig.8:(a)scatter diagram of twinningmand detwinningmfor each twin,(b)variation of twinning(detwinning)munder different stages,contributions of(c)6 potential rotation axes,and(d)6mrankings for all active twinning(detwinning)variants.

From Fig.8(a),most twins exhibit higher detwinningmthan the corresponding twinningm.To quantitatively describe this,the ratio(k)of detwinningm(mdet)to the corresponding twinningm(mt)is introduced and calculated for each twin:

Fig.8.(a)Scattering diagram of all twins regarding twinning and detwinning Schmid factors.Statistics on(b)appeared twinning or detwinning variants Schmid factors under various compressive stages,the contributions of(c)chosen rotation axis and(d)macroscopic Schmid factor ranks during twinning(detwinning)processes.34 grains and 60 twins were used for the statistical analysis.

From Fig.8(a),kcan be classified into three regions:only 8% twins locate in the region ofklowering than 0.91,and 42% twins exhibit a comparablemvalue for both detwinning and twinning(kranging from 0.91 to 1.10);however,the number fraction of twins exhibitingkhigher than 1.10 is 50%.In this condition,mdettends to display higher value thanmtfor a twin.Thismt-mdetasymmetric phenomenon will be later discussed in detail.

From Fig.8(b),mtdecreases with the progress of compression along RD during the first step.This is reasonable considering that larger strain(stress)will assist lowermtwinning variant nucleation according to Schmid’s law.However,it is astonished to find thatmdetincreases with the progress of compression along ND during the second step,implying that twins with lowermdettend to disappear earlier whilst twins with highermdetprefer to vanish later.This is contrary to Schmid’s law,that’s twin(slip)with highermis prone to nucleate and move earlier.This abnormal phenomenon will be also analyzed in subsequent discussion.

Fig.8(c)depicts with the contributions of 6 potential rotation axes for twinning and detwinning throughout the two-step compression(RD)-compression(ND)process.Given all the twins finally disappear by detwinning,a symmetrical distribution for the contributions of twinning and detwinning rotation axes is observed.Four rotation axes of R2 to R5 occupy a large proportion.Only one twin,T2 with twinning rotation axis of R6 and detwinning rotation axis of R1 is observed in Fig.8(c).The area fraction of T2 as shown in Fig.7(a)varies little as compressive progress moves from stages of B to E,though T2 nucleates very early.This suggests a latent influence of rotation axis on the growth of twins.

Fig.8(d)statistically presents themrankings of both twinning and detwinning throughout the two-step compression(RD)-compression(ND)process.All detwinning variants exhibit either 1st or 2ndmranking.However,only 70% of twinning variants have the 1st and 2nd ranks ofm;lowmt(especially 3rd and 4thmrankings)twinning variants occupy a considerable number fraction(i.e.30%)of total twins.This discrepancy reveals an inconsistency between twinning and detwinning variant selection behaviors,desiring a further discussion.

Fig.9.(a)Microstructural evolution of grain 3(G3)and grain 4(G4).(b){0001}pole figures of G3,G4 and appeared twinning variants.Schmid factors of potential twinning variants in G3 and G4 as well as geometrical compatibility parameter(m’)between T5 and 6 potential extension twinning variants in G4 are also tabulated in Fig.9(b).(c)Statistics regarding m’and Schmid factors of 15 twin bands emerged in this work.

4.Discussion

4.1.Anomalous twinning variant selection

The abnormal twinning variant selection behavior shown in Fig.8(d)has been discussed in a variety of researches[25,55–59].Jonas et al.used a local strain accommodation theory to explain the lowmcontraction twinning formation,indicating that lowmcontraction twinning with less or no prismatic strain accommodation prefers to be activated than highmcontraction twinning[60].In their theory,either＜c+a＞pyramidal glide or twinning component in the neighboring strain accommodation zones is necessary for nucleation of a new twin.{10-12}extension twinning with lowmin AZ31 alloy was also analyzed using local strain compatibility model by Shi et al.[61].The nucleation of lowmtwinning near GB is ascribed to the accommodated strain generated by basal or pyramidal slip in neighboring grains.Guan et al.supposed a different viewpoint that basal slip rather than non-basal slip or extension twinning in the neighboring strain accommodation zones dominates twinning variant selection in WE43 alloy[25].Despite the inconsistency in clarifying the lowmtwinning variant formation,geometrical compatibility parameter(m’)introduced for the first time by Luster and Morris was adopted in above studies[26]:

whereαrepresents the angle between the plane normal directions of primary twinning(slipping)and induced twinning,βrepresents the angle between the shear directions of primary twinning and induced twinning.

Following above theory,lowmtwin(T6)in the ROI 2 of Fig.3(a)is selected for further analysis as shown in Fig.9.T5 appears earlier than T6,and an obvious T5-T6 twin band across GB is observed from Fig.9(a).Fig.9(b)indicates that both twins share a same twinning system(i.e.R5)and have the 4thmranking(m=0.08,for T6).m’between T5 and T6 is calculated by using Eq.(3)exhibiting with the highest value of 0.91.In this situation,m’is proved to be more effective thanmin predicting the twinning variant selection behavior.Statistical evidence is presented in Fig.9(c)with more twin bands being considered,demonstrating such twin bands are of prime importance in non-Schmid twinning behavior(Fig.8(d)).Besides,twin bands with similar rotation axes or twinning systems exhibit a large proportion(i.e.80%)during neighboring twin-induced twin nucleation in this work.

3rd and 4th rankings ofmaccount for the considerable number fraction of approx.26.67%(Fig.8(d)),which can be further explained by combiningm’with crystal orientations of parent grains.Theoretically,when the“first step”compression is parallel to＜11-20＞crystal direction of parent grains,1st,2nd,3rd,and 4th highestmextension twinning will share a comparablemof approx.0.37.Slight deviations of＜11-20＞crystal direction from the compression direction probably altermlittle,while actual twinning variant selection varies easily from 1st to 4thmranking.In this condition,other factors like local stress fluctuation and/or accommodated strain from neighboring grains will make more difference.A typical example can be found in G2 of the ROI 1,which has twinning variants with 1st to 4thmrankings of 0.37(T3),0.35,0.33(T2),and 0.31,respectively(cf.Fig.7(b)).Clearly,there’s little difference ofmamong these twinning variants;however,the geometrical compatibility parameter(m’)between T1 in G1 and six potential twinning variants in G2 are shown in decreasing order:0.90(T3),0.72,0.18,0.07,0.06(T2)and 0.01.These indicate that local stress condition probably exerts stronger impacts on the twinning variant selection behav-ior especially when various twinning variants exhibit comparablemvalue.Besides,unlike detwinning process with the nearly uniform shrinking of twin which may be less sensitive to local stress fluctuation,twin nucleation mostly emerges at grain boundary and especially near triple points(Figs.3 and 4)where the local stress state is necessarily multi-axial due to the different crystal orientations of grains.The different mechanisms may be another reason of the inconsistency regarding Schmid factor behavior for twinning and detwinning.

Fig.10.(a)Evolution of detwinning Schmid factor during biaxial compression.(b)Microstructural evolution of grain 5(G5)and sub-grain 5(G5sub).Orientation gradient measured by the line i-iii is also presented in Fig.10(b).

4.2.Non-Schmid evolution of detwinning process

To date,detailed investigations on detwinning behavior of Mg alloys were scarcely performed regarding various loading paths.The non-Schmid evolution ofmdetduring the second step,that twin with lowmdettends to vanish earlier(cf.Fig.8(b)),is reported for the first time in the present research.

To comprehensively understand the evolution behavior ofmdetin the“second step”compression,statistics on hypotheticalmdetof twins during the“first step”compression are conducted.The hypotheticalmdetin the“first step”compression is obtained by imposing a hypothetical compression along ND at stages of A to E,assuming all twins in each stage will undergo detwinning process during the hypothetical compression.The hypotheticalmdetin the first step together with actualmdetin the second step are summarized in Fig.10(a).Twomdetevolution trends are observed in the“first step”and“second step”compressions,respectively:for one thing,with the process of first step,the hypotheticalmdetroughly decreases(actual twinning process);for another,themdetabnormally increases during the second step(actual detwinning process).It seems that the“first step”twinning process plays an important influence on the“second step”detwinning process.An explanation regarding the non-Schmidmdetevolution behavior(cf.Fig.8(b)and Fig.10(a))is that twin with highermdetwill nucleate and grow earlier during the first step,finally resulting in a higher probability to lock or interact with boundaries(e.g.GB)and more difficult for the reversible motion of TBs(detwinning behavior)compared to lowermdettwin with posterior nucleation.

To prove the above explanation,the ROI 3(cf.Fig.3(a))with differentmdetof twins is selected and re-presented in Fig.10(b).T7(R4)and T8(R3)are observed in G5;Meanwhile,T9(R3)is observed in G5sub.T7 has a lowermdet(0.39)while both T8 and T9 have a higher and comparablemdetof 0.48.From Fig.10(b),T7 nucleates much latter during the first step and vanishes much earlier than T8 and T9 in stage G.In fact,the close interactions of T8(T9)with neighboring TBs,sub-grain boundaries and GBs are speculated to retard the reverse motion of TBs.Similar phenomenon has been reported in other works[62–65].These are greatly consistent with our proposed explanation.

4.3.Impact of loading paths on asymmetrical mt-mdet behavior

From Fig.8(a),it has been indicated that,for about 50%twins,mdetis 1.10 times higher than correspondingmt;however,only 8% twins exhibitmt1.10 times higher than correspondingmdet.This asymmetricalmt-mdetbehavior is first reported in this work,which is supposed to be ascribed to two following reasons.For one thing,a few twins exhibit non-Schmid behavior regarding twinning whilst detwinning variants well obey Schmid’s law,contributing to the asymmetricalmt-mdetbehavior.For another,mtdepends greatly on the orientation of＜11-20＞crystal direction of parent grains during the first step,implyingmt(loading path:RD)proba-bly varies in a large range.Regarding detwinning behavior,given the strong basal texture(＜0001＞//ND)and{10-12}extension twinning characteristics,it’s expected that ND has intersection angles of approx.43° and 47° with the potential detwinning shear direction and the potential detwinning planes normal direction,respectively.Unlike undulatorymt(loading path:RD),a highmdet(loading path:ND)in the range of 0.49–0.50 can be expected theoretically considering the detwinning shear direction,the detwinning plane normal direction and ND exactly locate in the same plane.Thus,strong basal texture and various loading paths should be the other reason responsible for the asymmetricalmt-mdetbehavior.

Fig.11.Schematic illustrations of twinning and detwinning processes regarding different loading paths(RD and ND).

Given above analysis is fulfilled qualitatively,quantitative calculations onmtand mdetare expected to be useful in understanding themt-mdetasymmetrical behavior(cf.Fig.8(a)).Before twinning,＜0001＞directions of most parent grains are supposed to be parallel to ND(,unit vector);specific crystal-lattice direction along RD(,unit vector)is analyzed locally between＜1-210＞and＜1-100＞given the symmetrical characteristic of hexagon[11–20](twinning)and[-1-120](detwinning)rotation axes are selected for this calculation,considering both rotation axes correspond to the highestmin present condition,as illustrated in Fig.11.The intersection angle between RD(,unit vector)and＜10-10＞is defined asθ.mtcan be obtained as the product of two projections of loading path()on twinning plane normal direction(,unit vector)and twinning shear direction(unit vector)by:

After calculations,mtcan be further rewritten as:

Further substations of A and B in Eqs.(6)and(7)into Eq.(9),mtcan be obtained as a function ofθ:

Obviously,mtranges from 0.37 to 0.50;on the contrary,mdetis determined to be in the range of 0.49–0.50 from previous analysis.These are in accordance with the asymmetrical TDT behavior as shown in Fig.8(a).Note that both qualitative and quantitative analysis are still limited to the specific condition(＜0001＞//ND),thus actualmdetandmtshould have larger ranges,owing to the deviation between actual and ideal crystal-lattice orientations as well as non-Schmid behavior ofmt.In brief,the initial strong basal texture of Mg-0.3Li(at.%)alloy and different loading paths render lowermtthanmdet;non-Schmid twinning variants with lowmtduring the first step should have also aggravated the asymmetricalmt-mdetphenomenon.

5.Conclusion

Twinning(detwinning)evolution behaviors of a strongly textured Mg-0.3Li(at.%)alloy were thoroughly and statistically investigated byquasi-in-situEBSD during the interrupted two-step compression(RD)-compression(ND)measurement.The main conclusions are drawn as:

(1)Non-Schmid twinning variant nucleation behaviors are observed,ascribed to local stress fluctuations by neighboring twins.On the contrary,Schmid’s law shows a good prediction on detwinning variant selection behavior with all detwinning variants belonging to either 1st or 2ndmranking.

(2)With strain increasing during the first step,both twinning and detwinning Schmid factors show decreasing tendency;while detwinning Schmid factor during second step exhibits abnormally opposite evolution trend,which is fundamentally ascribed to prior twinning behavior,initially strong basal texture and different loading paths.

(3)Statistical results also reveal that detwinning variants not only exhibit highermranking,but also show highermvalue than twinning variants.This asymmetrical phenomenon of Schmid factors for twinning and detwinning is first reported,which could be ascribed to the strong basal texture and different loading paths(RD and ND);non-Schmid twinning variant selection behavior during twinning should have also intensified this asymmetricalmt-mdetphenomenon.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This investigation is supported by the grant from the Natural Science Foundation of China(51871244),the Hunan Provincial Innovation Foundation for Postgraduate(CX20200172)and the Fundamental Research Funds for the Central Universities of Central South University(1053320190103).