Issue 42

D. V. Orlova et alii, Frattura ed Integrità Strutturale, 42 (2017) 293-302; DOI: 10.3221/IGF-ESIS.42.31 297 density and, as a consequence, by the decrease in the ultrasound velocity, which is observed when the Luders fronts move in the acoustic measurement area. Figure 3 : Propagation of the Luders band within the yield plateau in steel (G10080) and the change in the velocity of ultrasonic Rayleigh waves. Development of localized plastic deformation at the pre-fracture stage n <0.5 Fig. 4 shows localized deformation versus time for all test alloys. The position of the localized deformation domains is indicated by colored symbols. The time sequence of the localized plasticity domains allows the number of macrostrain zones and their rate to be determined using the slope of curves (displacement coordinate - time ( X-t )). Thus, 4 movable deformation zones and one fixed maximum of deformation localization are formed in steel (G10080) at the pre-fracture stage (Fig. 4a). Such a stationary zone of localized plasticity has the highest amplitude. Fig. 5 shows the distribution of local strain ε xx along the sample at the beginning and at the end of the pre-fracture stage. At the pre-fracture stage, when the index of strain hardening is n < ½, the localized plasticity domains start moving along the tension axis, approaching the high-amplitude zones mentioned above, which were stationary before fracture. During the movement of localized plasticity domains, the values of their velocities become mutually consistent. The farther the localization zone is located from a stationary zone, the higher its velocity is (Tab. 3). This leads to the fact that all zones reach simultaneously the stationary zone of localization, and the graphs for the positions of the movable zones versus time create the bundle of straight lines with the center coordinates of * X and * t . Often, the extrapolation of the dependence   X t is required for large time to determine * X and * t . According to the experimental data of all the materials studied, the location of the sample fracture also coincides with the position of the stationary localization zone. Thus, the question concerning the stationary zone position and, consequently, the pole of the zone movement at the pre- fracture stage acquires a special meaning. For the quantitative description of the kinetics for the zones at the pre-fracture stage, it is reasonable to combine the origin of coordinates with the stationary localization zone. In this case, the coordinate of an arbitrary zone i  is determined by 0 i i X X    , (1) where 0 X and i X are the coordinates of the stationary localization zone and arbitrary zone in the laboratory coordinate system, the origin of which coincides with the fixed testing machine head. In the reference system chosen in this way, the zone movement graphs form a sheaf of straight lines with a single pole, when the velocities of the zones are linearly dependent on their coordinates i  , that is the following relation is met: 0 ( ) i i V      (2) where  and 0  are the empirical constants. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0 10 20 30 40 50 0.998 0.999 1.000 1.001 1.002 1.003 1.004  0.052 mm/s 0.038 mm/s x L (  )  V(  ) x, mm V/V 0