## 4 Results and Discussions
### Propagation of Elasto-Plastic Wave
The observed solitary wave velocity is a factor of four higher than the pulling rate at pulling rates of 3 and 1 mm/min., a factor of two higher at pulling rate 0.5 mm/min., approximately equal to at pulling rate 0.3 mm/min. and 30% lower at pulling rate 0.1 mm/min. We speculate that the reason why the peak particle velocity (the amplitude of the solitary wave) can be higher than the pulling rate is that the formation of a shear band involves a snapping motion of the material. On the formation of a shear band, the material experiences a recoverable partial fracture and this causes the particles on the opposite sides of the partial fracture to recoil sharply, as if a stretched spring breaks. This speculation is consistent with the instantaneous stress drop accompanied by the formation of a shear band, as a number of authors [54; 55; 56; 57] observed. The reduction in the amplitude of solitary wave relative to the pulling rate indicates that the increase in the mobile dislocation density lowers the amplitude of the solitary wave (because the onset mobile dislocation density is higher for the lower  
Figure 9: Shear band pattern location on specimen and loading curve. Pulling rate is (**a**) 3.0 mm/min, (**b**) 1.0 mm/min, (**c**) 0.3 mm/min and (**d**) 0.1 mm/min. pulling rate). The precise mechanism underlying the relation between the solitary wave amplitude and the mobile dislocation density has not been understood at this time. Solitary wave solution (29) indicates that the width of solitary wave is inversely proportional to parameter \(b\). In refs. [14; 57], the authors observed that the shear band width decreased as the tensile deformation advances toward the final fracture. This reduction is understandable, because it is expected that the stress concentration enhances toward the fracture. Equation (31) indicates two possibilities for \(b\) to increase; hence, the solitary wave becomes narrow. The first is an increase in \(c_{w}\) and the second is a decrease in [PERSON]'s modulus \(E\). These two factors behave oppositely with the development of deformation. As plastic deformation advances, the shear band (solitary wave) velocity \(c_{w}\) decreases as the mobile dislocation density increases (as argued above), and [PERSON]'s modulus \(E\) also decreases as the stress strain curve flattens. The former reduces \(b\) and the latter increases it. Figure 10 plots the change in the shear band width as a function of time. It is seen that the shear band width decreases with time. Moreover, a comparison with Figure 9 indicates that the rate of decrease in the shear band width accelerates when the shear band's propagation velocity (the slope of the time-shear band position plots) decreases for the last time before the shear band becomes stationary, but not yet stationary. It is possible that, at this point, the mobile dislocation density reaches some critical value that makes the effect of \(E\) significantly exceed the effect of \(c_{w}\), resulting in the drastic reduction in the width of the shear band. The loading curves in Figure 9 show the zigzag behavior of the stress known as the serration. The authors of refs. [54; 55; 56; 57] made thorough analyses on the relation between the appearance of shear bands and serration and found clear correlation between them. Basically, a shear band is formed when the stress drops sharply, and it disappears when the stress rises again. This phenomenon is similar to spark discharge in a gas medium and its recovery. When a local region of the gas medium experiences a spark discharge, the voltage drops sharply as the conductivity rises. As the spark discharge disappears for some mechanism that decreases the number density of free charges, the gas medium recovers from  
Figure 10: Temporal change in shear band width. Pulling rate is (**a**) 3.0 mm/min, (**b**) 1.0 mm/min, (**c**) 0.3 mm/min and (**d**) 0.1 mm/min. the temporary partial breakdown.