## 3 Experimental Results
### Strain Nephograms of the Deformation Waves  
Four snapshots at the compaction and elastic stages were chosen during the loading process (see Figure 6). The strain nephograms of the three strain components, \(\varepsilon_{xx}\), \(\varepsilon_{yy}\) and \(\varepsilon_{xy}\), are presented at these four time moments, as shown in Figure 7. For data processing, negative strain values under compression were represented by blue and light blue in the nephograms, while positive strain values under tension were represented by red and yellow. As indicated by the strain component \(\varepsilon_{xx}\), the micro-grains on the sample surface prior to loading were in a disordered and dispersed state. During the compression process, there was a region of tensile deformation between the regions of compressive deformation. As the loading continued, these micro-grains near flow channels moved closer to the flow channels (at an angle of about 60\({}^{\circ}\) relative to the \(x\)-axis, i.e., the sample axial direction. Points 1 and 2, represented by dotted lines in Figure 7) and gradually became connected along the flow channels. These flow channels cross symmetrically with each other and are distributed in a grid pattern. Figure 6: Stress-strain and stress-time curves at a loading rate of 0.1 mm/min. Throughout the loading process, the values of the strain components \(\varepsilon_{yy}\) and \(\varepsilon_{xy}\) were very small. Among them, the distribution of the \(\varepsilon_{yy}\) cloud image shows obvious vertical distribution characteristics, and gradually shifts to the middle with the loading time. The areas on both sides of the \(\varepsilon_{xy}\) strain cloud map show periodic strong tensile deformation zones from the beginning. For example, in the nephograms (Figure 7), corresponding to points 2 and 3 in Figure 6, the strong tensile deformation, as indicated by the strain component \(\varepsilon_{xy}\), periodically appeared at 20-60 mm, with a magnitude of about 0.1% (as indicated by the arrowhead at the point 3 in Figure 7). These regions of strong tensile (deformation corresponded to the flow channels observed in the nephogram of \(\varepsilon_{xx}\). This phenomenon was observed throughout the compaction and elastic stages of loading. As observed in the nephogram of \(\varepsilon_{xx}\), the nucleation of Luders bands (LB), i.e., shear bands formed in regions of stress concentration, occurred during the loading process (point 2 in Figure 7). At first, the nuclei had small oval cross-sections and appeared in pairs. One of them was a region of compressive strain with the maximum strain value being \(-0.5\%\); the other was a region of tensile strain with the maximum strain value being \(0.2\%\). The grain deformation and LB nucleations were more conspicuous in the nephogram of \(\varepsilon_{xy}\) and observed roughly at the same positions as those in the nephogram of \(\varepsilon_{xx}\). The maximum strain value was \(0.15\%\). The observed nucleation pattern can be explained as follows. The displacements originated from the sample surface, whose deformation exceeded the bulk one, i.e., the average deformation of the sample. During the sample's  
Figure 7: Strain nephograms corresponding to points 1 to 4 of the stress-strain curve in Figure 6.  
loading-induced deformation, the displacement was rapidly released, thereby resulting in the LB nucleation. After grain deformation and LB nucleation, the Luders bands were gradually formed. In the beginning, the Luders bands were obscure. As the loading continued, the Luders bands became clearer and began to show more conspicuous banding features. This trend started from both sides of the sample simultaneously, with slow interconnection and penetration in the transverse direction. This phenomenon indicated that the Luders bands were already formed (points 3 and 4 in the nephogram of \(\varepsilon_{xx}\) in Figure 7) before the plastic deformation stage.