3. Results and Discussions
Figure 2a shows the grain orientation (GO) maps of 316 ASS specimens at several plastic strain conditions in a similar viewing area. In the origin specimen, the dots in the Inverse Pole Figure (IPF) map represent a distinct, concentrated distribution. For instance, within the mark of the red-dotted circle, the distance between each dot is small, and these dots are found principally for Grain 1 and Grain 2. By contrast, the orientation dots in the IPF map of 316 ASS show much dispersion after tensile point 2, and a number of new orientations emerged, revealing that the lattice rotation occurred after the plastic deformation. Chen and Mao et al. [
7] reported that the lattice rotation behavior in an Al–Mg–Si alloy was related to the activation of slip systems and the Schmid factors (SFs). Zhang and Lu et al. [
12] suggested that the orientation of softer grains with large SF slips more easily. Here, the change of SF of 316 ASS during tensile was shown in
Figure 2c; the SF was computed using the {111}<110> slip systems of the FCC lattice, and its variation rules were investigated in the way of global grain statistics and individual grain analysis, respectively.
Figure 2d first shows the average value of SF for all pixels within the scanning area. The average SF was highest at the original state (0.43718) but decreased monotonically with the increase in deformation degree, even at the end of the plastic stage. The reduction in average SF also indicates that the lattice slip of 316 ASS becomes more difficult with increasing plastic strain. The relative frequency histogram of SF distribution clearly shows that after the plastic tensile, the proportion of SF in the range of 0.40–0.5 decreased and transformed into the range of 0.30–0.4. Generally, the SF can be the parameter to evaluate the ease of slip system activation since a slip system with a larger SF could be easier to move due to the higher magnitude of shear stress. Thus, further studies on the internal relations between lattice orientation, rotation behavior, and SF variation at the level of individual grains are needed.
Figure 3a shows the GO map and SF map of a subset region inside the origin specimen, which contains the grains from ID-3 to ID-8. This region is significant in that Grains 3–5 have larger SF values, which stand in sharp contrast to other grains since the SF levels of Grains 6–8 are relatively low. The average lattice orientation (LO) maps of Grains 3, 5, 7, and 8 are shown in
Figure 3b, and their specific Euler angle values are also given here. The Miller indices of Grain 3 are (9, 30, 95) [−6.86, −95.01, 30.43], and its activated slip system is (1–11)[110]. Numerical computation showed that the angle
φ between loading direction
X1 and the slip plane normal was 46.79°, and the angle
λ between
X1 and slip direction was approximately 43.92°; thus, Grain 3 has a SF value as high as 0.492. For Grain 5, the
φ and
λ were 41.17° and 49.24°, and its SF value was 0.491. In contrast to that, it was found that the
φ,
λ of Grain 7 and Grain 8 were 57.71°, 41.95° and 63.07°, 32.84°, and the SF values of them were 0.397 and 0.378, respectively. Compared with the large SF of Grain 3 and 5, the high
φ angle of Grain 7 and 8 was directly responsible for their low SF values. This is most marked in Grain 8, though it has a small angle
λ; the high
φ (63.07°) results in a low cosine of 0.4529, which significantly lowers the SF value.
Figure 3c shows the component map of those grains that have an approximate orientation (<20° misorientation angle) with Grains 3, 5, 7, and 8, respectively. In the first case, Grains 9 and Grain 10 have misorientations of nearly 8.11° and 18.3° with Grain 3, and their SF values are 0.472 and 0.468. Grain 11 and Grain 12 have misorientations of 8.51° and 9.89° with Grain 5, and their SF values could go as high as 0.495 and 0.496. In the second case, the SF values of those grains that have the approximate orientation with Grain 7 and Grain 8 are shown in the components map, and it can be seen that the SF values of these grains are significantly smaller. Moreover, it can be seen that the grain number acquired in the second case is much higher than that of the first case. From a consistency perspective, the results indicate that those grains with low SF values may have a similar orientation, while those with high SF values may have an arbitrary orientation instead of a homogeneous orientation.
Figure 4 shows the evolution of the IPF map, the GO map, the LO map, the IPF single pixel (IPF-S) map, and the SF map of Grain 7 during the in situ tensile. Grain 7 is a representative grain since it took the lead in the SF reduction (see
Figure 2c). The redistribution of lattice orientation of Grain 7 can be clearly observed in the IPF map as the specimen was stretched to Point 2; multiple rotation paths appeared in this grain, and the maximum rotation angles of paths I, II, III, and IV were approximately 6.48°, 6.08°, 8.34°, and 8.06°, respectively. The occurrence of a new slip system in Grain 7 during tensile may be responsible for this multidirectional rotation since the main slip system in Grain 7 at the origin state was (1–1–1)[101], but (1–1–1)[01–1], (111)[01–1], and (1–11)[110] appeared at the Point 2 state. To figure out the specific rotation action, individual pixels (A~H) were selected for further analysis.
The Miller indices of Pixel A and Pixel B are approximately (15, 64, 75) [−67.31, 62.53, −39.48] and (15, 64, 75)[−67.50, 62.59, −39.07], and their activated slip system is (1–1–1)[101]. The calculated results revealed that the φ of Pixel A and Pixel B were approximately 58.55° and 58.30°, and their λ values were approximately 40.96° and 41.10°; thus, the SF of these two pixels were 0.394 and 0.396, respectively. After being stretched to Point 2, from Pixel C and Pixel D, it can be seen that the lattice rotation occurred as a result of plastic deformation, which can be observed in the LO map in comparison with the orientation of A-C and B-D pixels. The Miller indices of Pixel C and Pixel D are approximately (6, 68, 73) [−59.61, 61.58, −51.52] and (4.23, 69.69, 71.59) [−59.88, 59.13, −54.02]; the rotation path seems to conform to path IV (see IPF and IPF-S map); and the misorientations between A-C and B-D were approximately 5.62° and 7.63°. Since (1–1–1)[01–1] is one of the main slip systems of Grain 7 in the Point 2 state, the computed results showed that the φ values of Pixel C and Pixel D were approximately 66.28° and 67.96°, and their λ values were approximately 36.89° and 36.86°; hence, the SF of Pixel C and Pixel D were 0.322 and 0.302. Compared with Pixel A and Pixel B, the SF of Pixel C and Pixel D were relatively small, and it can be seen that the reduction in SF is principally because of the increase in φ, i.e., and . Meanwhile, the higher φ also means that the slip plane tends to be parallel to the loading direction. The higher φ, the lower its cosine, which results in a low shear stress acting on the slip plane; thus, the slip of the crystal plane became difficult.
After stretching to Point 3, the SF value of some pixels continued to slow down, and the SF of Pixel E and Pixel F were 0.291 and 0.292, and their activated slip systems were both (1–1–1)[101]. The decrease in SF was still due to the increase of φ since the calculated results showed that the and were approximately 68.95° and 68.92°, which are larger than and . Nevertheless, after stretching to Point 4, it was found that the SF of many pixels increased instead of continuing to decline, as the SF of Pixel G and Pixel H were 0.297 and 0.323, respectively. The Miller indices of Pixel G and Pixel H were approximately (67.5, 0.21, 73.78) [−59.74, −58.53, 54.82] and (0.99, 67.41, 73.86) [62.93, −57.82, 51.93], and the total slip system of Grain 7 was (1–1–1)[101], (1–1–1)[01–1], (1–1–1)[110], (111)[01–1], (111)[10–1], (1–11)[10–1], (1–11)[110]. The computed results showed that, for Pixel G, the max SF occurred on the (111)[10–1] slip system since the φ and λ values in this system were approximately 68.51° and 35.9°; thus, the SF of this system was approximately 0.296. For Pixel H, the max SF occurred on the (1–1–1)[101] slip system; the φ and λ values in this system were 66.59° and 35.9°; thus, the SF of this system was approximately 0.323.
Based on the above results and the comparison of Pixel E and Pixel G, it can be deduced that when the SF is small (i.e., 0.291 of Pixel E) and the slip in the (1–1–1)[101] system becomes harder, other systems might activate (i.e., (111)[10–1]) and the slip behavior will translate to the other system, which results in the increase in SF. From a comparison of Pixel F and Pixel H, it can be seen that the activated slip system of each is (1–1–1)[101]; however, the SF increases from Point 3 to Point 4 (i.e., 0.292→0.323) rather than continuing to decrease. The cause of this increase resultingfrom the rotation of local lattice, the φ decrease from 68.92° to 66.59°, which lead to the increase of SF.