Fig. 1. Basal pole figure, IPF (inverse pole figure) map, GB (grain boundaries) map and KAM (Kernel average misorientation) map of AR sample.

Fig. 2. (a) Distribution of shear stress on the cross-section of the specimen with square section during free-end torsion. (b) Equivalent stress state between simple shear and bi-axial normal stresses. Finite element simulation of reciprocating torsion: equivalent strain contour plot of (c) AR sample; (d) the sample twisted to 108° at anticlockwise and (e) ART108 sample.

Fig. 3. Stress state of anticlockwise torsion in various typical regions.

Fig. 4. The orientation of compressive component in {0001} pole figure in some typical regions during reciprocating torsion. Red pentagram and blue pentagram are the compressive orientations when twisted at anticlockwise and clockwise, respectively. The curve in each pole figure is the trajectory of the change in the stress axis from region A to region C. (a) region A; (b) region B and (c) region C.

Fig. 5. OM images of various typical regions in the cross-section of ART108 sample.

Fig. 6. {0001} pole figures, IPF maps, GB maps and KAM maps of typical regions in ART108 sample: (a) R9 (close to torsion axis); (b) R3 (～60 μm from the upper surface); (c) R3′ (～550 μm from the lower surface).

Fig. 7. EBSD data of region R3 with maximum shear stress in ART108 sample. (a) {0001} pole figures of parent twins and twins; (b) schemes of deformation history during reciprocating torsion; (c)-(e) EBSD maps and corresponding crystallographic orientations of typical grains. Here, Pi and Tij (i, j = 1; 2; 3 …) represent the parent grain and twin lamellae, respectively. Red pentagram and blue pentagram are the compressive orientations when twisted at anticlockwise and clockwise, respectively.

Fig. 8. EBSD data of ART108 sample. (a) {0001} pole figure and EBSD maps in region R5; (b) {0001} pole figure and EBSD maps in region R7 (～75 μm from the surface); (c) Typical grains and corresponding crystallographic orientations in region R5; (b) Typical grains and corresponding crystallographic orientations in region R7; Here, Pi and Tij (i, j = 1; 2; 3 …) represent the parent grain and twin lamellae, respectively. Schmid factor values of typical grains are calculated during torsion at clockwise.

Fig. 9. The relationship between the angle between normal stress and c-axis and Schmid factor of {10-12} twinning on cross-section under torsion.

Fig. 10. (a) Various positions on the cross-section; (b) orientations of normal stress on various positions during torsion at clockwise; (c) main texture components on various positions of ART sample. The red dot is the initial orientation and the blue dot is the new orientation via torsion in the pole figure of (c).

Fig. 11. Distribution of average KAM, area fraction of twins and length of TB per area on the cross-section of ART108 sample.

Fig. 12. Misorientation angle distributions. The misorientation rotation axis distributions are shown for some of the angular ranges in the crystal coordinate system. (a) AR sample, (b) region R3 of ART108 sample, (c) region R5 of ART108 sample, (d) region R7 of ART108 sample.

Fig. 13. 2D hardness maps on cross-section with a size of 5 mm × 5 mm of various samples (a) AR sample; (b) ART36 sample; (c) ART72 sample; (d) ART108 sample.

Fig. 14. Compressive true stress-strain curves along various directions (a) AR sample; (b) ART36 sample; (c) ART72 sample; (d) ART108 sample.