Twinning system selection in a metastable β-titanium alloy by Schmid factor analysis

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<ul><li><p>aac</p><p>I.</p><p>s, 20</p><p>Februine 4</p><p>sis wstemo deton ohts r</p><p>g; Sc</p><p>make them good candidates for biomedical applications</p><p>some metastable alloys subject to a martensitic transfor-</p><p>dicted by the Schmid law for materials exhibiting hcp orfcc structures, as reported in the literature [8,9].Although it is well known that both slip and twinningoccur in bcc titanium alloys, the objective of this paper</p><p>be observed in this kind of alloy a selection parameter</p><p>structure at room temperature in its metastable state.</p><p>we observed that cyclic tensile tested specimens exhibitmore twins compared with monotonic tensile testedspecimens.</p><p>Electron backscattering diraction (EBSD) studieswere carried out in a JEOL JSM 6400 scanning elec-tron microscope equipped with a TSL EBSD system.The samples were prepared by mechanical polishing toCorresponding author. E-mail:</p><p>Available online at</p><p>1011mation, like FeNiC or FeBe [5]. In metastableb-titanium alloys both twinning systems {1 1 2}h1 1 1iand {3 3 2}h1 1 3i have been observed, depending onthe alloy composition [6,7]. Each twinning system canbe activated in 12 dierent ways, termed variants in thispaper.</p><p>The Schmid law is commonly used to predict the acti-vated slip system depending on the tensile directioncompared with the crystallographic orientation of thecrystal. Selection of the twinning variant can also be pre-</p><p>Before the recrystallization annealing at tensile testspecimens with a section of 3 0.7 mm and a gagelength of 15 mm were machined. The tensile directionwas parallel to the rolling direction. Cyclic tensile tests,including strain increments of 0.5% followed by stressrelease, were carried out up to 5% at a strain rate of104 s1. The tensile tests were followed up to rupture.This mechanical test was used to characterize the super-elastic eect due to stress-induced martensitic transfor-mation occurring in this kind of alloy [4]. In addition,[1,2]. Theses alloys possess a non-ordered bcc structureand are subject to numerous deformation mechanisms:a stress induced martensitic transformation which canlead to a superelastic eect, slip and twinning [3,4].</p><p>Twinning is a common deformation mechanism inmaterials exhibiting a low stacking fault energy in hcp,fcc or bcc structures. In bcc structures {1 1 2}h1 1 1i isa well-known twinning system, but other twinningsystems such as {3 3 2}h1 1 3i have been observed in</p><p>between these twinning systems will also be established.The metastable b-alloy composition chosen for this</p><p>study is Ti25Ta24Nb (mass%). The ingot was elabo-rated by cold crucible levitation melting (CCLM). Itunderwent homogenization annealing at 950 C for20 h, followed by a water quench. Each ingot was thencold rolled (CR = 90%), after which a recrystallizationannealing was applied at 850 C for 0.5 h, followed bya water quench in order to retain the b-phase micro-Twinning system selection inby Schmid f</p><p>E. Bertrand, P. Castany,</p><p>UMR CNRS 6226 Sciences Chimiques de Rennes, INSA Renne</p><p>Received 14 January 2011; revised 23Available onl</p><p>Electron backscattering diraction and Schmid factor analy24Nb (mass%) metastable b-titanium alloy. The two twinning sytem the Schmid factor was shown to be a relevant parameter ttwo twinning systems depends on the crystallographic orientati 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rig</p><p>Keywords: Titanium alloy; Electron backscattering diraction; Twinnin</p><p>Metastable b-titanium alloys can be elaboratedwith fully biocompatible b-stabilizer elements such asTa, Nb, Mo, etc. Their interesting mechanical properties</p><p>Scripta Materialia 64 (2011) 111359-6462/$ - see front matter 2011 Acta Materialia Inc. Published by Eldoi:10.1016/j.scriptamat.2011.02.033metastable b-titanium alloytor analysis</p><p>Peron and T. Gloriant</p><p>Avenue des Buttes de Coesmes, 35708 Rennes Cedex 7, France</p><p>ary 2011; accepted 28 February 2011March 2011</p><p>ere used to study the twinning variant selection in a Ti25Tas {1 1 2}h1 1 1i and {3 3 2}h1 1 3i were observed. For each sys-ermine the activated variant. Moreover, selection between thef the grain with respect to the tensile direction.eserved.</p><p>hmid factor</p><p>was to conrm that twinning variant selection in eachobserved system obeys the Schmid law for a metastableb-titanium alloy (bcc). As several twinning systems can</p><p>13</p><p> Ltd. All rights reserved.</p></li><li><p>a mirror nished state. In titanium alloys mechanicalpolishing is known to induce important residual defor-mation in the surface layer that has deleterious eectson the quality of EBSD patterns. Chemical etching witha solution of 5% HF, 5% HNO3 and 90% H2O (vol.%)was used to remove this surface layer.</p><p>The optical micrograph given in Figure 1a shows thatthe Ti25Ta24Nb alloy in the recrystallized state iscomposed of equiaxed grains with an average diameterof 50 lm. Figure 1b shows that most of the grains weredeformed by twinning during the tensile test. It shouldbe stated here that the grains were also deformed by slip.However, slip could not be observed by the technique ofEBSD used in this study.</p><p>Several twinned grains were characterized byEBSD and an example of the data obtained is given inFigure 2a. For each grain the orientations of the parentcrystal and twins were determined from the Euler angles.The twinning system was then characterized from thepoles belonging to the parent crystal and the twin. Toensure statistical signicance about 20 grains in severalzones of the tensile specimen were analyzed.</p><p>By way of illustration, two grains, denoted G1 andG2, and their twins, denoted T1 and T2, respectively,were located on the EBSD ma in Figure 2a. Each grainis deformed by several twins of the same variant of thesame system. The twinning system activated in G1 is{1 1 2}h1 1 1i. In G2 the other twinning system,{3 3 2}h1 1 3i, is activated. The coincidence site lattice</p><p>of 60 around h1 1 1i (Fig. 2b). For the twinning system{3 3 2}h1 1 3i the CSL boundary is R11, which corre-sponds to a misorientation of 50.57 around h1 1 0i(Fig. 2c).</p><p>Twinning can be considered as the slip of partial dis-locations, for example, in the {1 1 2}h1 1 1i twinningsystem the Burgers vector is a/6 h1 1 1i. An importantdierence between twinning and slip of perfect disloca-tions is the polarity of twinning. This means that the slipof a partial dislocation in the opposite sense to the twin-ning direction (anti-twinning direction) would notproduce a twin, since it would be energetically unfavor-able [10]. As a consequence, activated variants underuniaxial tensile stress will be dierent from those acti-vated under uniaxial compression stress in the samedirection. In order to apply the Schmid law and distin-guish the variants that can be activated during a tensile</p><p>0</p><p>10</p><p>20</p><p>30</p><p>40</p><p>50</p><p>60</p><p>0 2 4 6 8Distance (m)</p><p>Mis</p><p>orie</p><p>nta</p><p>tion</p><p> (De</p><p>gre</p><p>e</p><p>(b)</p><p>0</p><p>10</p><p>20</p><p>30</p><p>40</p><p>50</p><p>60</p><p>0 2 4 6 8 10Distance (m)</p><p>Mis</p><p>orie</p><p>nta</p><p>tion</p><p> (De</p><p>gre</p><p>es</p><p>)</p><p>(c)Figure 2. Inverse pole gure of Ti25Ta24Nb alloy (a) after tensiletesting and (b) misorientation proles between G1 and T1 and (c)between G2 and T2. Solid line, point to origin; dotted line, point topoint.</p><p>E. Bertrand et al. / Scripta Mater(CSL) of the {1 1 2}h1 1 1i twin was determined to bea R3 boundary, which corresponds to a misorientationFigure 1. Optical micrographs of the microstructure (a) before and (b)after cyclic tensile testing.70</p><p>s)</p><p>T2T2G2G2</p><p>(a)</p><p>T2T2T2T2G2G2G2G2</p><p>ialia 64 (2011) 11101113 1111test the sign of the indices of each variant must be de-ned in accordance with the usual criteria [10] in order</p></li><li><p>In G2 the activated variant is the only one possessinga positive SF higher than 0.4 (Table 3).</p><p>In the other grains studied the activated variant gen-erally possesses a SF between 0.4 and 0.5; the minimumSF value that led to the activation of twinning was 0.38.As predicted, no variant with a negative SF was ob-served. When both twinning systems exhibit a variantwith a high SF {1 1 2}h1 1 1i is the experimentally ob-served system. The {3 3 2}h1 1 3i system is generallyactivated when the SF values for {1 1 2}h1 1 1i are low-er. Occasionally, some grains with high SF values fortwinning are not deformed by twinning and are mostprobably only deformed by slip.</p><p>Table 1. The 12 variants of the {1 1 2}h1 1 1iand {3 3 2}h1 1 3i twinning systems.{1 1 2}h1 1 1itwinning system</p><p>{3 3 2}h1 1 3itwinning system</p><p>(1 1 2)111 (3 3 2)113(1 2 1)111 (3 2 3)131(2 1 1)111 (2 3 3)311112111 332113121111 323[1 3 1]211111 233311112111 332113121111 323131211111 233[3 1 1]112111 332[1 1 3]121 111 32313121111 1 233311</p><p>1112 E. Bertrand et al. / Scripta Materialia 64 (2011) 11101113to distinguish between variants leading to elongation orcompression along the applied stress direction. The setof indices used is given in Table 1.</p><p>The Schmid factor (SF) is dened similarly to slip as:</p><p>SF cos k cos /where k and / are the angles between the tensile direc-tion and the normal to the twinning plane and the twin-ning direction, respectively. The values of k and / aretaken between 0 and 180 in order to obtain SF valuesbetween 0.5 and 0.5. Using this convention a variantwhose SF is positive leads to elongation along the tensiledirection and will accommodate tensile stress. The acti-vation of a variant whose SF is negative would lead tocontraction along the tensile direction and will not beobserved during a tensile test.</p><p>The tensile direction is marked in each grain referenceframe in order to assess the value of k and /. In grainsG1 and G2 the variants possessing an absolute value ofSF higher than 0.3 are given in Tables 2 and 3. It wasconsidered that no variant whose SF is lower than 0.3can be activated, which was conrmed for every grainanalyzed. In G1 the experimentally observed varianthas the highest positive value among the variants ofthe {1 1 2}h1 1 1i system, but two variants of the twin-ning system {3 3 2}h1 1 3i have a similar SF (Table 2).Table 2. Twinning variants for which |SF| &gt; 0.3 in grain G1.</p><p>{1 1 2}h1 1 1i SF {3 3 2}h1 1 3i SF(1 2 1)111 0.43 323[1 3 1] 0.49121111 0.38 332113 0.41112111 0.40 323131 0.34211111 0.37 233311 0.40121111 0.40</p><p>The bold SF value corresponds to the experimentally activated variant.</p><p>Table 3. Twinning variants for which |SF| &gt; 0.3 in grain G2.</p><p>{1 1 2}h1 1 1i SF {3 3 2}h1 1 3i SF(1 1 2)111 0.49 (3 2 3)131 0.36112111 0.37 (3 3 2)[1 1 3] 0.48</p><p>323131 0.33The bold SF value corresponds to the experimentally activated variant.To explain this point, the highest value of SF amongthe 12 variants of the two twinning systems {1 1 2}h1 1 1i and {3 3 2}h1 1 3i is drawn in Figure 3 as a func-tion of the tensile direction. The highest SF values forthe {1 1 2}h1 1 1i twinning system were obtained whenthe tensile direction was close to the h1 0 0i directionof the parent crystal. The highest SF values for the{3 3 2}h1 1 3i system were obtained for a tensile direc-tion close to h1 1 1i. When the tensile direction was clo-ser to h1 1 1i the SF values of {1 1 2}h1 1 1i becameweak while the SF values of {3 3 2}h1 1 3i rose above0.4 and this system was then activated. In this type of al-loy crystal orientation versus tensile direction is theparameter allowing selection of the twinning system.Nevertheless, when both systems have an equivalentSF we have proved that {1 1 2}h1 1 1i is preferentiallyactivated. Thus the critical resolved shear stress (CRSS)of the {1 1 2}h1 1 1i twinning system is slightly lowerthan the CRSS of the {3 3 2}h1 1 3i twinning system.However, these values are very close. Selection of thetwinning system by CRSS only occurs for specic grainorientations for which the SF values are equivalent forboth systems. Indeed, the highest SF values of the twotwinning systems cover complementary orientation do-mains (Fig. 3). As most of the grains have only one twin-ning system with high SF values, crystallographicorientation is thus the relevant parameter selection ofthe twinning system.</p><p>As a conclusion, the Schmid factor is shown to be apertinent parameter to predict the nature of the activatedtwinning system and variant in each specic grain. Vari-ant selection in the {1 1 2}h1 1 1i and {3 3 2}h1 1 3i twin-ning systems clearly obeys Schmids law in thismetastable b-titanium alloy, i.e. for each system the acti-</p><p>010</p><p>100</p><p>SF&gt;0.45SF&gt;0.40SF&gt;0.30SF0.45SF&gt;0.40SF&gt;0.30SF0.45SF&gt;0.40SF&gt;0.30SF</p></li><li><p>vated variant is that which has the highest SF. On theother hand, selection of the twinning system is also deter-mined by the crystallographic orientation of the grainwith respect to the tensile direction, with the dierencethat when the two systems have close and high SF valuesthe {1 1 2}h1 1 1i system is activated, whereas the{3 3 2}h1 1 3i system is activated when it alone has a highSF value. As a consequence, the existence of crystallo-graphic texture in this type of alloy can lead to the pref-erential selection of one twinning system based only onthe specic crystallographic orientation of the grains.</p><p>This research was funded within the frameworkof the Eureka/MNT ERA-Net European ConsortiumProject NanoBioAll (E!4482): Advanced Metallic Bio-materials, Nano-structured, for Implantable MedicalDevices.</p><p>[1] M. Niinomi, J. Mech. Behav. Biomed. Mater. 1 (2008) 30.[2] T. Gloriant, G. Texier, F. Prima, D. Laille, D.M. Gordin,</p><p>I. Thibon, D. Ansel, Adv. Eng. Mater. 8 (2006) 961.[3] H.Y. Kim, Y. Ikehara, J.I. Kim, H. Hosoda, S. Miyazaki,</p><p>Acta Mater. 54 (2006) 2419.[4] E. Bertrand, T. Gloriant, D.M. Gordin, E. Vasilescu, P.</p><p>Drob, C. Vasilescu, S.I. Drob, J. Mech. Behav. Biomed.Mater. 3 (2010) 559.</p><p>[5] R.H. Richman, in: R.E. Reed-Hill, J.P. Hirth, H.C.Rogers (Eds.), Deformation Twinning, Gordon andBreach, New York, 1964, p. 238.</p><p>[6] M. Oka, Y. Taniguchi, Metall. Trans. 10A (1979) 651.[7] S. Hanada, O. Izumi, Metall. Trans. 17A (1986) 1409.[8] T. Sawai, A. Hishinuma, J. Phys. Chem. Solids 66 (2005)</p><p>335.[9] S. Godet, L. Jiang, A.A. Luo, J.J. Jonas, Scr. Mater. 55</p><p>(2006) 1055.[10] J.W. Christian, S. Mahajan, Prog. Mater. Sci. 38 (1995) 1.</p><p>E. Bertrand et al. / Scripta Materialia 64 (2011) 11101113 1113</p><p>Twinning system selection in a metastable -titaack2References</p></li></ul>