CommunicationGrain Size Effects on Primary,Secondary, and Tertiary TwinDevelopment in Mg-4 wt pct Li(-1 wt pct Al) Alloys

MARTIN LENTZ, ANDREAS BEHRINGER,CHRISTOPH FAHRENSON,IRENE J. BEYERLEIN, and WALTER REIMERS

Grain size effects on three generations of twins wereinvestigated in extruded Mg-4 wt pct Li (-1 wt pct Al)alloys using electron-backscatter diffraction. Sampleswith three distinct grains sizes, yet the same texture andapplied strain were analyzed. With these variables fixed,we show that compression and double twinning decreasesubstantially with decreasing grain size. We find thatcompression twinning exhibits a stronger grain sizeeffect than tension twinning, whereas the compressiontwinning to double twinning transition is independent ofgrain size.

DOI: 10.1007/s11661-014-2491-y� The Minerals, Metals & Materials Society and ASMInternational 2014

Deformation twinning significantly impacts thestrength and ductility of magnesium and its alloys.[1–7]

For instance, when a tensile load is applied parallel tothe c-axis of a Mg crystal, tension twinning (TTW-ing) isreadily activated, which usually results in a low flowstress and work hardening.[1,2,8] Additionally,f10�11g 10�1�2

� �compression twinning (CTW-ing) can

be observed, if compression is applied parallel to thec-axis.[3] Deformation twinning in Mg can also undergoa complex sequence of twinning, where an internal twinforms within a primary twin (secondary twinning), andwithin the internal twin, another twin can form (tertiarytwinning). Such internal twinning is often observed invarious Mg alloys[3,9–13] as well as other hcp metals likeZr[14] and Ti.[15] For Mg, the most frequent example ofinternal twinning is f10�11g - f10�12g double twinning(DTW-ing), where a TTW is formed within a preexistingCTW. DTW-ing was observed in Mg single crystals,[9]

pure polycrystalline Mg,[16] and a variety of Mg alloys

such as AZ31,[3,10–12] AM30,[13] and ZK60.[3] The mostcommon DTW variant (type 1) has been correlated tothe onset of flow localization, void formation, andfracture, as the activity of hai basal slip is significantlyenhanced within the narrow DTW.[3,9,10] Therefore, it isimportant to identify ways to suppress the activation ofDTW-ing.Grain size reduction is known to hinder twinning in

many classes of metals.[17–29] It is, therefore, a promisingapproach to minimize DTW-ing activity. Severalauthors observed grain size effects on the activation ofTTW-ing in Mg alloys, where TTW-ing is promoted, ifthe grain size increases.[23–26] It was found that TTW-ingobeys the Hall–Petch effect and that the Hall–Petchslope for twinning is greater than the slope correspond-ing to deformation controlled by slip.[23,25] However,recent studies performing statistical analyses on hcpmetals indicate that this trend may not always be thecase.[30,31] Using EBSD to study TTW-ing in pure Mg, itwas found that grain size had little influence on whetheror not a grain had formed at least one twin, while it hadan undeniably strong effect on the number of twins pergrain. The number of twins per grain increased as thegrain area increased, while the twin thickness was notaffected by the grain area.[30] Later using opticalmicroscopy, Tsai et al.[32] confirmed this result onTTW-ing in another Mg alloy. Interestingly, it was alsosuggested that CTW-ing had a different relationshipwith grain size than TTW-ing. For CTW-ing, a reduc-tion in its frequency with reduction in grain sizes wasobserved unlike in TTW-ing. Thus, it may be that eachhcp twin type has its own dependency with grain size. Tothe authors’ knowledge, no detailed investigation on therelative grain size dependence of CTW-ing and TTW-inghas been conducted. In this regard, the grain size effectin internal twinning has not been explored. Does theinternal twin adopt the same grain size effect as theparent twin or does it possess its own dependency?Twinning is well recognized as being sensitive to grain

orientation (texture), applied stress, and strain.[17,18,33]

Ideally, the Hall–Petch effect should be analyzedthrough modifications of the grain size only, whilekeeping other variables constant. Unfortunately, this isextremely challenging to achieve. In many studies,changes in the grain size are accompanied by changesin other influential microstructural variables. Further-more, a large number of twinned grains are required toenable a statistically meaningful analysis of grain sizeeffects. The latter can be achieved relatively easy in thecase of TTW-ing, while CTWs and especially DTWs areusually observed in small quantities complicating astatistical analysis.[13]

The present study investigates grain size effects onthree generations of twins (primary TTW-ing, secondaryCTW-ing, and tertiary DTW-ing) in Mg-4 wt pct Li(-1 wt pct Al) alloys. By adjusting the extrusion param-eters, we obtained material featuring different grain sizesand very similar textures, which only differ mildly inintensity. All samples were compressed to �15 pctengineering strain and analyzed using EBSD. Thisenables the analysis of grain size effects, decoupledfrom strain, strain rate, and texture effects.

MARTIN LENTZ, Research Associate, ANDREAS BEHRINGER,Student, and WALTER REIMERS, Chair, are with the MetallischeWerkstoffe, Technische Universitat Berlin, Ernst-Reuter-Platz 1, 10587Berlin, Germany. Contact e-mail: martin.lentz@tu-berlin.deCHRISTOPH FAHRENSON, Scientist, is with the ZentraleinrichtungElektronenmikroskopie, Technische Universitat Berlin, Straße des 17.Juni 135, 10623 Berlin, Germany. IRENE J. BEYERLEIN, Scientist, iswith Theoretical Division, Los Alamos National Laboratory, LosAlamos, NM 87545.

Manuscript submitted May 21, 2014.Article published online August 6, 2014

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, OCTOBER 2014—4737

With this approach, we show that at �15 pct strain,the initial microstructure of the coarse grained (CG) andmedium grained (MG) samples is completely overtakenby primary TTW-ing. Additionally, secondary CTWsand a large amount of tertiary DTWs were observedwithin the primary TTWs. In contrast, the fine grained(FG) samples contain several grains that have not beenovertaken by TTW-ing completely or have not twinnedat all indicating a grain size effect in TTW-ing. Evenmore important, the amount of CTWs and DTWs issignificantly reduced in the FG samples. Thereby, weshow that CTW-ing and subsequent DTW-ing can beeffectively suppressed by reducing the grain size.

To synthesize material with different grain sizes, weused different extrusion ratios (R), product speeds (v),and billet temperatures (TB). These parameters werechosen to maximize the difference of the grain size of theextruded materials. The Mg-4 wt pct Li (-1 wt pct Al)billets (Ø = 123 mm, l = 150 mm) were obtained fromthe Leibniz Universitat Hannover (Institut fur Werkst-offkunde). The indirect extrusion process was carried outat the Extrusion Research and Development Center atTechnische Universitat Berlin. The sample denominationand the extrusion parameters are given in Table I.

To form deformation twins, compression samples(Ø = 10 mm, l0 = 20 mm) were machined from theextruded round bars, with the load axis being parallel tothe extrusion direction. The samples were compressedup to engineering strains (e) of �15 pct. Afterward, thecompression samples were cut in the middle and theircross-sections were prepared by standard metallo-graphic methods including grinding, mechanical, andchemical polishing. Here, a solution of 12 mL hydro-chloric acid (37 pct), 8 mL nitric acid (65 pct), and100 mL ethanol was applied. A Zeiss DSM 982 GEM-INI SEM equipped with an EDAX Hikari camera wasused for the EBSD data acquisition.

After etching the samples in a solution of 5 g citricacid in 95 mL distilled water, the grain size was obtainedfrom optical micrographs using the software ImageJ.[34]

The average grain size of the samples (FG1 ~5 lm, FG2~5 lm, MG ~21 lm, CG ~30 lm), the as-extrudedtextures parallel to extrusion direction, and the flowcurves are given in Figure 1. While the grain sizes of theFG, MG, and CG samples are significantly different, thetextures differ only slightly in the sharpness. Based onthe initial texture, CTWs and DTWs are expected toform in tensile tests. However, the use of compressiontests has the advantage that primary TTWs are formedallowing a comparison of three generations of twins. Muet al.[12] used plane strain compression tests to investi-

gate variant selection of primary, secondary, andtertiary twins. We adopt this approach to investigategrain size effects on primary TTW-ing, secondary CTW-ing, and tertiary DTW-ing. Additionally, the reorienta-tion through primary TTW-ing equalizes the texture ofthe extruded bars and hence minimizes texture effects onsecondary CTWs and tertiary DTWs.The as-extruded texture indicates that the grains are

favorably oriented for the activation TTW-ing in com-pression. Even though minor differences in the sharpnessof the texture are present, these do not affect the activityof TTW-ing significantly as the grains either belong to the10�10� �

or the 11�20� �

texture component. Both orienta-tions feature a high Schmid factor for TTW-ing and haiprismatic slip and a low Schmid factor for hai basal slip.Hence, a sigmoidal shape flow curve is observed for allsamples indicating a high TTW-ing activity at low strains,which is caused by the initial texture and the low criticalresolved shear stress (CRSS) of TTW-ing.[1,8,11]

In Reference 35, we show that a sequence of primaryTTW-ing, secondary CTW, and tertiary DTW occurswithin CG sample, where TTW-ing dominates the initialdeformation up to �10 pct strain and a significantamount of DTWs is formed within the strain range from�12 to �18 pct. Therefore, �15 pct strain samples wereselected to investigate the influence of the grain size onCTW-ing and DTW-ing. Figure 2 shows the EBSDmaps of the samples compressed to the same strain(maps at higher magnification in Figure 2 show moredetail). As can be seen by the red color, the analysisindicates that almost all parent grains are completelyovertaken by TTWs in case of the CG and the MGsamples. Here, it should be noted that the parent grainsare overtaken by one primary twin variant causing anequal grain size of the parent and the TTW. In contrast,the FG samples, particularly FG1, contain severalgrains that have not been overtaken by TTW-ingcompletely or have not twinned. The volume fractionof the primary TTWs was determined from the EBSDdata by evaluating the fiber volume of the h0002i texturecomponent. Therefore, the intervals from W = 60 to 90deg and u = 0 to 360 deg were assigned to primaryTTW-ing. The twin volume fractions are 81 pct (CG),76 pct (MG), 65 pct (FG), and 73 pct (FG2), confirmingthe Hall–Petch effect of TTW-ing.Nevertheless, the compression test has further equal-

ized the texture eliminating its effects on the generationof CTWs and DTWs. The misorientation distributionfunctions computed from the entire maps (MDF,Figure 3) reveal a higher relative frequency of TTWboundaries (~86 deg) in case of the FG samples. These

Table I. Sample Denotation and Extrusion Parameters

Sample AlloyExtrusionRatio

BilletTemperature

[K (�C)]Product Speed

(m/min)CoolingCondition

CG (coarse grained) Mg-4 wt pct Li (L4) 25:1 573 (300) 1.7 airMG (medium grained) Mg-4 wt pct Li-1 wt pct Al (LA41) 41:1 573 (300) 1.7 airFG1 (fine grained) Mg-4 wt pct Li (L4) 71:1 473 (200) 1.7 waterFG2 (fine grained) Mg-4 wt pct Li-1 wt pct Al (LA41) 25:1 473 (200) 1.7 water

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Fig. 1—Flow curves of the extruded bars; (a) L4, (b) LA41. The insets represent the initial texture parallel to the extrusion direction (=loaddirection) and the average grain size (equivalent diameter) of the samples.

Fig. 2—EBSD maps highlighting CTW (yellow) and type 1 1TW (green); (a) CG, (b) FG1, (c) MG, (d) FG2. (a), (c) are details of 8809 720 lm2

maps. (b) and (d) are details of 2489 248 lm2 maps. White arrows mark DTWs in the FG samples (Color figure online).

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, OCTOBER 2014—4739

results are consistent with the previously reported Hall–Petch effect in TTW-ing.[23–26]

Even more importantly, we found that the amounts ofCTWs and DTWs are significantly reduced in the FGsamples. While the CG and MG samples (Figures 2(a)and (c)) contain numerous DTWs (green) and occa-sional CTWs (yellow), these twin modes are effectivelysuppressed in the FG samples (Figures 2(b) and (d)),particularly in sample FG1. In this sample, the com-bined number of CTWs and DTWs is less than 5 in theentire 2489 248 lm2 map (not shown).

The comparison of the MDF (Figures 3 (a) and (b))confirms these results. In CG, three maxima are visible.By plotting the distribution of the rotation axis distribu-tions (see insets), these maxima can be correlated to theactivity of twin modes. Within the angular range from 35to 40 deg, the most common rotation axis is 2�1�10

� �

corresponding to type 1 DTW-ing. Within 54 to 58 deg,the rotation is most common about the 10�10

� �axes and

less common about the 2�1�10� �

axes. The former men-tioned angle-axis pair is caused by the intersection ofdifferent TTW variants,[12,16] while the latter correspondsto CTW boundaries. Within the angular range 84 to 86deg, the most frequent rotation axis is 2�1�10

� �corre-

sponding to TTW boundaries. Figure 3(a) indicates that

DTWs are dominant in the CG sample, while CTWs andDTWs are absent in case of the FG1 sample. Hence, weconclude that CTW-ing and DTW-ing can be almosteliminated by reducing the mean grain size from ~30 to~5 lm in the case of the L4 alloy. Similar grain size effectswere observed by Tsai and Chang[32] in an AZ31 alloy,indicating that the fraction of twinned grains increasesfrom 1.6 pct in the case of fine grains (3 to 7 lm) to28.5 pct in the case of coarse grains (35 to 39 lm). Theirstudy employs optical microscopy, however, and hencedoes not distinguish between CTWs and DTWs.Figures 2(c) and 3(c) show that CTW-ing andDTW-ing

are activated to a high extent in the case of theMGsample.The activity of both twin modes is comparable to the CGsample indicating a negligible effect of the Al addition onthe activity of CTW-ing and DTW-ing. Again, thereduction of the average grain size reduces the amount ofCTWs and DTWs as can be seen in Figures 2(d) and 3(d).However, the FG2 sample features an inhomogeneousgrain size (Figure 2(d)) enabling the investigation of grainsize effects on CTWs and DTWs within one sample.Several DTWs were observed, but only within the largergrains. The fine grain fraction does not contain significantamounts of CTWs or DTWs confirming a pronouncedHall–Petch effect on these deformation modes.

Fig. 3—Correlated misorientation distribution function: (a) CG (�30 lm), (b) FG1 (�5 lm), (c) MG (�21 lm), (d) FG2 (�5 lm). The insetsshow the texture and the distribution of the rotation axis for characteristic angular ranges. 86 deg 11�20

� �= red, 56 deg 11�20

� �= yellow, 38

deg 11�20� �

= green.

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With three generations of twins in the same set ofmaterials, we have the unique opportunity to examinetheir relative dependencies on grain size. Although grainrefinement hinders primary TTW-ing, significant primaryTTW volume fractions (between ~65 and ~81 pct) wereobserved regardless of the grain size, while at 5 lmCTW-ing and DTW-ing are considerably hindered particularlyin the L4 alloy. This indicates that CTW-ing has a morepronounced grain size dependence than TTW-ing.

In References 35, we show that the CTW is nucleatedand quickly transformed into DTWs within the strainrange from 10 to 18 pct in the CG sample. In the presentstudy, the observed contraction twins correspond almostexclusively to DTWs in both the CG and the FGsamples regardless of the alloy, although the number oftwins and hence the statistic dataset are very limited inthe FG samples. Combining these results indicates thatthe transition from CTWs to DTWs occurs readilyregardless of the grain size.

MD simulations by Serra and Bacon[36] indicate thatf10�12g twinning dislocations, responsible for formingthe DTW, are much more mobile than the f10�11gtwinning dislocations needed to advance the CTWboundary. In Reference 11, it has been proposed thatthe CRSS of CTW-ing is significantly higher than theCRSS of TTW-ing. Hence, we conclude that reductionin DTW-ing with grain size is a consequence ofreduction in the parent CTW-ing with grain size.

In summary, we found that reducing the grain size is aviablewayof suppressingCTW-ingand subsequentDTW-ing. The results also indicate that CTW-ing has a strongergrain size effect than TTW-ing. We studied materials withdifferent average grain sizes deformed to the same strain.On this basis, the propensity to transition from the CTWinto a DTW is found to be insensitive to grain size. Thus,the grain sizedoesnot hinder orpromoteDTW-ingand thegrain size effect on DTW-ing is a consequence of the grainsize effect on the parent CTW-ing.

The authors are grateful for the financial supportof the Deutsche Forschungsgemeinschaft (DFG) underthe contract number RE 688/67-1. IJ Beyerlein wouldlike to acknowledge support by a Laboratory DirectedResearch and Development program Award Number20140348ER.

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