1 Diagnosis of Deformation Stages with Optical Interferometric Technique and Comprehensive Theory of Deformation and Fracture 5 Fig. 1.5 Shear band propagation speed as a function of time for different pulling rates slant and linear. The numerical vx pattern indicates the more concentrated feature, and the numerical vy pattern shows slanted feature. These features are consistent with the experimental patterns (see the areas enclosed by a circle). In a later stage (c), when the normal strain is approximately 18% and the stress reaches the peak value on the stress-strain curve from where it decreases gradually, the experimental patterns of vx andvy are more concentrated and become similar to each other. A recent study [14] indicates that the similarity between the differential displacement component reveals that the pre-fracture condition is about to establish. The solitary wave representing the pre-fracture stage appears in a fringe image as a shear band. A theoretical consideration [15] indicates that in the case of tensile loading, the solitary wave velocity is proportional to the pulling rate. It has also been found that when the solitary wave velocity becomes zero, the volume expansion rate of the unit volume becomes infinite and that causes material discontinuity. These indicate that the speed of shear band is fundamentally related to the fracture mechanism, and it is worthwhile considering more deeply. Figure 1.5 [16] plots the propagation speed of the shear band as a function of time for four different pulling rates. The horizontal axis represents the time elapsed from the beginning of the tensile loading. Two features are seen. First, the higher the pulling rate, the earlier the shear band starts to appear. It should be noted that the appearance of the first shear band (the onset time) is not necessarily determined by the total elongation. When the pulling rate is 3 mm/min, the first shear band appears approximately in 6.6 s. Inversely proportional to the pulling rate, the same total elongation occurs around 19.8 s (6.6 ×3 =19.8), 39.6 s, 66 s, and 198 s for the pulling rates of 1, 0.5, 0.3, and 0.1 mm/min, respectively. However, Fig. 1.5 indicates that the onset times for these pulling rates are 30 s, 150 s, 400 s, and 2400 s. Apparently, the actual onset times are greater than the onset times estimated based on the highest pulling rate (3 mm/min). This indicates that the faster the pulling rate the easier the generation of the shear band becomes. The second feature seen in Fig. 1.5 is that the propagation speed of the shear band falls on a single curve as a function of the elapsed time regardless of the pulling rate. Numerical fitting indicates that this function has the form of a/(t +b) where a and b are constants. It is interesting to note that the average speed of mobile dislocations τ is in the form of τ =L/(t +ts) where L is the average distance between neighboring barrier and ts is the interaction time of mobile dislocations with each barrier [17]. The mechanism that determines the propagation speed of shear band is not understood at this time. However, this observation strongly indicates that the shear band is formed by a physical process dependent on time and independent of pulling rate.
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