Strain path dependence of {1 0 -12}twinning activity in a polycrystalline magnesium alloy

Strain path dependence of {10À12}twinning activityin a polycrystalline magnesium alloySeong-Gu Hong,a ,⇑Sung Hyuk Park b and Chong Soo Lee b ,⇑aDivision of Industrial Metrology,Korea Research Institute of Standards and Science,Daejeon 305-340,Republic of Korea bDepartment of Materials Science and Engineering,Pohang University of Science and Technology,Pohang 790-784,Republic of KoreaReceived 24August 2010;revised 17September 2010;accepted 20September 2010Available online 25September 2010The {10À12}twinning activity in plastic deformation of a polycrystalline magnesium alloy was investigated using the in situ electron backscatter diffraction technique in combination with Schmid factor analysis.The activation of different twin variants depending on the strain path introduced a significant difference in the intersection characteristics between twin bands,causing a totally different twinning contribution to the deformation.The intersection between different twin variant pairs was found to retard the twin growth and promote the nucleation of new twins.Ó2010Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.Keywords:Magnesium alloy;{10À12}twinning;Twin variant;Schmid factorDeformation twinning is an important mecha-nism for plastic deformation of wrought magnesium (Mg)alloys because the specific texture,developed dur-ing manufacturing process,makes the operation of slip systems difficult [1–7].Although several types of defor-mation twins have been reported for Mg alloys [1–7],the {10À12}twin is recognized to occur most easily and frequently,and accommodates most early plastic deformation,causing a low flow stress and strain hard-ening rate [4,7].The {10À12}twinning is generally known to occur under two strain paths (i.e.loading con-ditions):tension parallel to the c -axis of the hexagonal close-packed lattice or compression perpendicular to the c -axis [8].Recently,Hong et al.[6,7]reported that different twin variants are active depending on the strain path (their selection mechanism is governed by the Schmid law),and this influences the twinning activity in the deformation,causing a strain path dependence of flow stress and strain hardening behaviors.As the twin nucleation was governed by the Schmid law,the strain path dependence of the material yield (i.e.yield strength),which is dominated by twin nucleation,was explained successfully.It is noted,however,that the twinning activity under further deformation beyondyielding was quite different from what we was expected:(i)although a greater value of the highest Schmid factor (SF)can be achieved for the strain path of tension par-allel to the c -axis,the twinned volume fraction at a given strain was much larger for the strain path of compres-sion perpendicular to the c -axis,inducing a more signif-icant twinning contribution to the deformation;and (ii)when considering that twin growth occurs under lower stresses than those required for twin nucleation [9],the twinning process after yielding would be dominated by a twin growth mechanism.This was true for the strain path of compression perpendicular to the c -axis.For the strain path of tension parallel to the c -axis,however,twin nucleation continued to occur up to $5%,indicat-ing that there was another control factor for twin growth and it was closely related to the strain path.In this study,therefore,we explored why the {10À12}twinning activity exhibits a strain path dependence and what the control factor for twin growth is.For this purpose,quasi-static tensile and compressive tests com-bined with the in situ electron backscatter diffraction (EBSD)technique were performed on rolled Mg alloy and SF analysis was used to interpret the results.A commercial hot-rolled AZ31Mg alloy (Mg–3.6%Al–1.0%Zn–0.5%Mn)plate,50mm thick,which was homogenized at 400°C for 4h,was used.The material had a twin-free equiaxial grain structure,with an aver-age linear intercept grain size of $30l m.The initial1359-6462/$-see front matter Ó2010Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.doi:10.1016/j.scriptamat.2010.09.030⇑Corresponding authors.Tel.:+82428685868;fax:+82428685032(S.-G.Hong),tel.:+82542792141;fax:+82542792399(C.S.Lee);e-mail addresses:sghong@kriss.re.kr ;cslee@postech.ac.krScripta Materialia 64(2011)145–148/locate/scriptamattexture of the material,measured by EBSD,exhibited an intense basal texture,with a randomly oriented a-axis in the rolling plane.Tensile and compressive specimens were machined from the homogenized plate along the normal direction (ND)to the rolling plane and rolling direction(RD), respectively:the gage sections of the tensile and compres-sive specimens were10mmÂ4mmÂ2mm(lengthÂwidthÂthickness)and10mmÂ4mmÂ4mm,respec-tively.Note that the tension along the ND(T-ND)and the compression along the RD(C-RD)correspond to the strain paths of tension parallel to the c-axis and compression perpendicular to the c-axis,respectively. For EBSD examination,the specimen surface was ground on2400grit silicon carbide papers and polished using 1l m diamond paste,followed by afinal polish with colloidal silica to remove any strains and provide a high-quality surfacefinish.The specimen was loaded to the stress level required using an INSTRON8801testing machine at room tem-perature and a strain rate of10À3sÀ1,then unloaded. The unloaded specimen was then examined with EBSD installed in afield emission scanning electron micro-scope.By repeating this process at four different stress levels,in situ EBSD observation on tensile and compres-sive tests became possible.For the EBSD experiment, automated EBSD scans were performed in the stage control mode with TSL data acquisition software on an area of0.12mm2with a step size of0.3l m.Analysis of the EBSD data was accomplished with TSL OIM analysis software and the data with a confidence index of>0.1were used for twin variant analysis.Because of the intense basal texture,the crystallo-graphic lattice of the material is hardly oriented for both basal and prismatic slips for T-ND.For C-RD,basal slip is also hard to operate but prismatic slip is highly preferred[3,7,10];the minimum stress required for acti-vating prismatic slip is calculated to be110MPa(an an-gle h of0°between the a-axis and the loading axis,and a critical resolved shear stress(CRSS)of55MPa[1,3]).As shown in Figure1a,however,the experimental results show that the material yielded at$66MPa for C-RD and$58MPa for T-ND.This clearly indicates that the material yield is not dominated by dislocation slips.Figure2shows the strain path dependence of the highest SF value that can be achievable for six{10À12} twin variants;in the analysis,the material was assumed to have a perfect basal texture with a randomly oriented a-axis in the RD–TD plane(where TD is the transverse direction)[6].For T-ND,all six twin variants had an equal SF value of0.499irrespective of the angle h.For C-RD, however,only the twin variant pair adjacent to the loadingaxis had the highest SF value,which increases from0.374to0.499as the angle h increases from0to30°;note that two twin variant pairs had the highest SF value of0.374for h=0°.If the{10À12}twinning controls the materialyield,the above SF analysis results predict yield strengths of60and69MPa for T-ND and C-RD,respectively;aCRSS of30MPa was assumed for{10À12}twinning[1,3]and the average highest SF value of0.437was usedfor C-RD due to the random distribution of the a-axis in the RD–TD plane.These predicted yield strengths matchthe experimental data exactly,indicating that the materialyield is dominated by twin nucleation,which is governed by the Schmid law.However,note that,even though thematerial yielded at a lower stress for T-ND due to thegreater value of the highest SF(Fig.2),theflow stress after yielding increased more rapidly for T-ND than for C-RDand this resulted in a greaterflow stress for T-ND abovea strain of$2.6%(Fig.1a).This is contrary to the expecta-tion based on the Schmid law.Figure1b shows the strain path dependence of thetwinned volume fraction evolution with stress.Althoughtwin nucleation is governed by the Schmid law,a much larger amount of the volume was twinned for C-RDthan for T-ND.It is well known that the strain accom-modated by twinning(i.e.twinning strain e twin)is pro-portional to the twinned volume fraction f twin[11]:e twin¼f twinÁmÁc twin where m and c twin represent the aver-age highest SF value and the characteristic twinning shear,respectively.Hence,the unexpectedflow andstrain hardening behaviors beyond yielding are thoughtto result from the difference in evolution characteristicof the twinned volume fraction.It is also noted that the operation of prismatic slip above a stress of >110MPa can partly contribute to the low strain hard-ening of C-RD.Figure3presents in situ EBSD observation resultsfor T-ND.As the material yield began(66MPa),threedifferent types of twins were generated(Fig.3a).Then, as deformation progressed,the twinning process was dominated by the nucleation of new twins rather than the growth of the existing twins.This is contrary to the generally accepted idea that twin growth occurs under lower stresses than those required for nucleation146S.-G.Hong et al./Scripta Materialia64(2011)145–148[9]so that twin growth would be preferred as a twinning process rather than twin nucleation.As described earlier,for T-ND,six twin variants have an equal probability to activate because of their equal SF value(Fig.3c).The simultaneous operation of all six twin variants and the unique crystallographic relationship between the six twin variants increase the possibility of twins intersecting,which would restrict the twin growth by making high misorientation inter-section boundaries(Fig.3d);misorientations of60°explanations correspond exactly with the experimental results(Figs.1and3).For C-RD,however,the twinning process after yield-ing was dominated by the growth of existing twins (Fig.4a).Based on the SF analysis results,only one twin variant pair,T2and T5,adjacent to the loading axis had the highest SF value of$0.5(Fig.4c)and was active during deformation.The operation of such specific twin variants would facilitate the twin growth mechanism be-cause the parallel geometry between identical twin vari-EBSD observation results:(a)inverse polefigure maps of the materials tensioned to66,82,99and140relationship between the parent grain and the twin bands;(c)crystallographic orientation of the parent grain corresponding SF values of the twin variants are indicated as digits;and(d)line profiles of the misorientation angle in(a).Here,P and T i(i=1,2,3,4,5,6)represent the parent grain and the six{10À12}twin1];T2=(À1102)[1À101];T3=(10À12)[À1011];T4=(0À112)[01À11];T5=(1À102)[ÀEBSD observation results:(a)inverse polefigure maps of the materials compressed to66,82,99and140relationship between the parent grain and the twin bands;(c)crystallographic orientation of the parent grain corresponding SF values of the twin variants are indicated as digits;and(d)line profile of the misorientation angle in(a).Here,P,T2and T5represent the parent grain and two different{10À12}twin variants,respectively.existing twins,causing a rapid increase in the twinned volume fraction with stress.It is noted that the opera-tion of prismatic slip in parent grain is also thought to promote the twin growth mechanism[13].The validity of the proposed twin growth control mechanisms can also be confirmed by examining the point-to-point misorientation angle distribution with stress,which reflects the intersecting characteristics be-tween twin variants[7].In summary,although the nucleation of{10À12} twins(i.e.the selection mechanism of active twin vari-ants)was governed by the Schmid law,their growth characteristics during further deformation were con-trolled by the intersection between twin variants.The activation of different twin variants depending on the strain path introduced a significant difference in the intersection characteristics between twin bands and consequently caused a totally different twinning activity in the deformation.For tension parallel to the c-axis,the simultaneous operation of all six twin variants restricted the twin growth by increasing the possibility for twins to intersect with a high misorientation angle of$60°,and thus the twin nucleation dominated the twinning process until the late stage of deformation,causing a reduction in the contribution of twinning to the deformation. For compression perpendicular to the c-axis,however, mostly one twin variant was active in a grain and this introduced a parallel geometry of twin bands.This parallel twin geometry facilitated the twin growth by prohibiting the intersection of twin bands and thus enhanced the twinning activity in the deformation.The authors are grateful for thefinancial sup-port from POSCO and the Korea Research Council of Fundamental Science and Technology(KRCF)through the project of“Development of Advanced Materials Metrology”.[1]X.Y.Lou,M.Li,R.K.Boger,S.R.Agnew,R.H.Wagoner,Int.J.Plasticity23(2007)44.[2]Y.N.Wang,J.C.Huang,Acta Mater.55(2007)897.[3]M.R.Barnett,Z.Keshavarz,X.Ma,Metall.Mater.Trans.A37(2006)2283.[4]L.Jiang,J.J.Jonas,A.A.Luo,A.K.Sachdev,S.Godet,Mater.Sci.Eng.A445–446(2007)302.[5]L.Jiang,J.J.Jonas,R.K.Mishra, A.A.Luo, A.K.Sachdev,S.Godet,Acta Mater.55(2007)3899.[6]S.H.Park,S.G.Hong,C.S.Lee,Scripta Mater.62(2010)202.[7]S.G.Hong,S.H.Park,C.S.Lee,Acta Mater.58(2010)5873.[8]R.E.Reed-Hill,R.Abbaschian,Physical MetallurgyPrinciples,third ed.,PWS-Kent Publishing Company, Boston,MA,1994.[9]P.G.Partridge,Metall.Rev.12(1967)169.[10]S.G.Hong,S.H.Park,Y.H.Huh,C.S.Lee,J.Mater.Res.25(2010)966.[11]C.S.Roberts,Magnesium and its Alloys,John Wiley&Sons,New York,1960.[12]M.D.Nave,M.R.Barnett,Scripta Mater.51(2004)881.[13]L.Capolungo,I.J.Beyerlein,G.C.Kaschner,C.N.Tome´,Mater.Sci.Eng.A513–514(2009)42.148S.-G.Hong et al./Scripta Materialia64(2011)145–148。