Variant selection of primary, secondary and tertiary twins in a ...

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2046 S. Mu et al. / Acta Materialia 60 (2012) 2043–2053 Fig. 2. (a) EBSD map measured at a strain of e = 0.11 (the grain outlined in red is of interest)—the regions separated by high-angle boundaries are identified by colors related to their orientations (Euler angles); (b) the most frequently observed twin types in Mg alloys are listed together with the corresponding disorientations with respect to the matrix given in minimum angle-axis pairs; (c) disorientation distribution; (d) (0002) PF for the e = 0.11 sample; (e) the Euler angle color code. these are boundaries between: (i) ETWs and the matrix (ETW–MAT with a characteristic disorientation of 86° h 12 10i), and (ii) two ETWs of different types (ETW– ETW with a characteristic disorientation of 60 h10 10i), respectively. The high frequency of ETW–MAT and ETW–ETW boundaries indicates that there was massive activation and growth of primary ETWs up to the strain level employed. The formation of such ETW–ETW boundaries can be understood as follows. Although a grain can theoretically twin on any of the six f1 0 12g planes, those twins can be assumed to nucleate where the resolved shear stress on the twinning plane and in the shear direction exceeds the critical value s c . When two or three ETW variants form in a particular matrix grain, one twin will generally nucleate first, after which the second (and third) ETWs nucleate at slightly larger strains and applied stresses. According to this view, the ETWs grow into the matrix continuously until straining ceases or their boundaries collide with the other twins or the grain boundary. Another slight peak in the disorientation distribution appears at 30–45° about the h 12 10i rotation axis. These disorientations can be classified as boundaries between the matrix and f1 0 11g–f1 0 12g double twins. This set of frequently detected boundaries indicates that a second generation of CTWs formed within the first-generation ETWs. As most grains initially had their c-axes aligned with LD, the conditions were not favorable for the formation of first-generation CTWs. Once ETWs formed and reoriented the twinned part of a grain by rotating the c-axis about the h 12 10i by 86°, aligning it with CD, contraction twinning could take place during further compression. In this way, the first generation ETWs became the “matrix” for the secondgeneration CTWs. Meanwhile, a still smaller peak with much lower frequency appears in the range 50–65° about the h 12 10i axis, which corresponds to f1 0 11g CTWs. To differentiate among the three generations of twins, they are labeled here as primary ETWs, secondary CTWs, and tertiary ETWs. The macrotexture measured on the surface perpendicular to CD at e = 0.11 is presented in the form of a (0002) PF in Fig. 2d. On comparison with the initial texture shown in Fig. 1b, it can be seen that the original LD texture component (c-axes parallel to LD) has disappeared and been replaced with three texture components: the newly generated CD basal component (c-axes parallel to CD with an
S. Mu et al. / Acta Materialia 60 (2012) 2043–2053 2047 intensity peak in the center of the (0002) PF), and the two minor texture components located symmetrically between LD and CD. The newly formed CD texture component can be attributed to f1 0 12g extension twinning, which rotates the crystal by 86°. The two texture components between LD and CD can be produced either by dislocation slip, which rotates the LD orientation toward CD gradually, or by contraction twinning, which rotates the newly formed CD orientation back towards LD again by rotating the c-axis about the h 12 10i axis by 56°. In order to investigate the formation of these three generations of twins and to determine a possible criterion for the variant selections observed, a grain in which all three kinds of twins were detected by the EBSD technique was chosen for further investigation, as identified by the red ellipse in Fig. 2a. One further matter should be mentioned. There is a low-angle (2°) boundary within the selected grain. Since the two parts within the grain are of similar orientation, they will be considered to belong to the same matrix grain and the low-angle boundary to have formed by the operation of slightly different sets of slip systems in the two parts of the grain. 3.2. Identification of the three generations of twins The selected grain is shown at higher magnification in Fig. 3a. The different regions separated by boundaries with >10° disorientations (between twins and matrix) are identified with the same colors according to their orientations (Fig. 2e) as before and are now denoted by letters from a to h. Their orientations are listed in Euler angle form in Table 1 and shown schematically in Fig. 3b on a (0002) Table 1 Euler angles of all the detected orientations in the “red” grain outlined in Fig. 2a. (The (0°,0°,0°) orientation has one of its ½11 20Š directions parallel to the y-axis and the basal plane is perpendicular to the z-axis.) a 98844.7 b 1662711 c 1711384.7 d 1701557 e 106630.2 f 52.513947 g 1498322 h 11316655 PF. All the internal high-angle boundaries are black and numbered from 1 to 10. The corresponding disorientation angles and rotation axes are listed in Table 2. The orientations of all the adjacent neighboring grains (identified using roman numerals from I to XI) are listed in Table 3. In what follows, the order of the various twin generations is deduced by analyzing the orientation relationships, i.e. the disorientations, between pairs of adjacent orientations within the selected “red” grain. Then the orientations and SFs of all six potential twin variants pertaining to each generation were calculated. These are represented in Fig. 4a–e in terms of (0002) and f1 1 20g PFs, which will now be employed to identify the twin variants that were actually selected. As listed in Table 2, boundary 2 separating regions a and b exhibits a disorientation of 76° about the h1 210i axis. According to Fig. 2b, the closest disorientation is that Fig. 3. (a) EBSD map of the grain outlined in Fig. 2a that contains tertiary twins: the matrix and twins are denoted by letters from a to h, the twin boundaries by numbers from 1 to 10, the neighboring grains by roman numerals from I to XI, and the matrices and twins in certain neighboring grains are denoted by M and T, respectively; (b) the orientations of the matrix and the twins are illustrated on (0002) stereographic projections.
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