Fig. 1 Schematic diagram showing the PTRA processing. The black dashed arrows represent the processing sequence. The second rolling direction (RD2) is parallel to the ND of the AR sheets

Fig. 2 Representative microstructures and texture characteristics of the AR AZ31 plate in the RD-TD plane: a EBSD inverse pole figure (IPF) map along RD; b (0002) pole figure (PF)

Fig. 3 Microstructural evolution under PTRA processing. IPF maps of the a AR sample, b PT sample, c PTR sample, d PTRA sample; corresponding (0002) PF of the e AR sample, f PT sample, g PTR sample, h PTRA sample. Grains in dashed boxes of b and c are marked as Grains A and B for subsequent analysis of microstructure evolution, respectively

Fig. 4 Tensile engineering stress-strain curves of the AR (along the ND) and PTRA (along the RD2) AZ31 Mg alloy sheets

Fig. 5 Representative microstructures of the AR and PTRA samples after tensile deformation. The first column: EBSD IPF maps of a the AR-2% sample, d the AR-10% sample, g the PTRA-2% sample, and j the PTRA-10% sample; the second column: grain boundary (black lines) and twin boundary (red lines) maps of b the AR-2% sample, e the AR-10% sample, h the PTRA-2% sample, and k the PTRA-10% sample; the third column: density distribution of geometrically necessary dislocation (GND) of c the AR-2% sample, f the AR-10% sample, i the PTRA-2% sample, and l the PTRA-10% sample. Note that grains in the black boxes of a,d, g, and j are marked as Grains C, D, E, and F, respectively

Fig. 6 Analysis of the activation of dislocation slip in the tensile AR and PTRA samples by IGMA: a IGMA distribution of Grain C in the AR-2% sample, b distribution of misorientation axes for all the points-pair between points C1 and C2; c IGMA distribution of Grain (twin) D in the AR-10% sample, d distribution of misorientation axes for all the points-pair between points D1 and D2; e IGMA distribution of Grain E in the PTRA-2% sample, f distribution of misorientation axes for all the points-pair between points E1 and E2; g IGMA distribution of Grain F in the PTRA-10% sample, h distribution of misorientation axes for all the points-pair between point F1 and F2. In the IGMA distribution map, the numbers before and after the slash represent the minimum and maximum intensity values of the IGMA concentration, respectively

Fig. 7 Statistical histogram of the activated slip systems in terms of global SF distribution in the a AR; b PTRA samples with 2% and 10% tensile strain. The first two numbers in parentheses represent the total number of grains showing a particular slip system at 2% and 10% tensile strain in sequence. Percentages in the parentheses represent the proportion of grains showing a particular slip system in the total grains showing dislocation slip

Fig. 8 Representative Grain A showing the morphology and crystallographic characteristics of twins in the PT sample: a IPF map of Grain A; MA and AT1-AT6 represent the matrix and six {10-12} tension twin variants, respectively; b scattered (0002) PF of MA and AT1-AT6 showing crystallographic relationship; c Scattered (10-12) PF of MA, AT1, and AT5 demonstrating their orientation relationship of twinning

Fig. 9 Representative Grain B showing the morphology and crystallographic characteristics of twins in the PTR sample: a IPF map of Grain B; MB and BT1-BT6 represent matrix and six {10-12} tension twin variants, respectively. BT34 and BT36 denote the {10-12}-{10-12} secondary tension twins in the primary BT3 twin; b scattered (0002) PF of MB, BT1-BT6, BT34, and BT36 showing crystallographic relationship; c scattered (10-12) PF of MB, BT3, and BT34 demonstrating their orientation relationship of twinning

Fig. 10 KAM maps of (a) the PT sample; b the PTR sample; c corresponding statistical curve

Fig. 11 a Representative Grain G with no twins, Grain H with single twin variant, and Grain I with multiple twin variants selected from the PT sample showing the inhomogeneous distribution of KAM; Grain J with composite reticular twins selected from PTR sample showing the more homogeneous distribution of KAM; b statistical diagram of KAM value of Grains G-J; c the distribution of KAM of line AB (area away from twins) and line CD (area close to twins) in Grain I showing the heterogeneous distribution of KAM inside grains

Fig. 12 Distribution of SF of different deformation modes (slip/twinning) for the AR and PTRA samples in tension along the ND. The value in the upper left corner of each figure represents the corresponding mean value of the SF

Fig. 13 Deformation mode analysis based on the criterion of the minimum activation stress (CRSS/SF) in the AR and PTRA samples: a SF as a function of θ and α; b distribution of the minimum activation stress as a function of θ. c Schematic diagram illustrating the distribution of θ in the AR and PTRA samples based on the texture characteristics, as shown in Figs. 2b and 3h