36 C. A. Sciammarella et al. Fig. 3.20 (a) Force vs. displacement plot of the tensile test. The first square indicate location of the onset of plasticity while the second square corresponds to the onset of fracture; (b) Coordinate system corresponding to the plot of displacements w(y) given in Fig. 3.21 Fig. 3.21 Plot of w(y) for x =0, the values “d” indicate the magnitude of the loading as indicated in Fig. 3.20a: (a) Transition; (b) Maximum tensile force Figure 3.21 shows the values of w(y): (a) is the beginning of the onset of plasticity called in the text diffuse necking, while (b) corresponds to the displacement of the localized necking preceding the fracture of the specimen. The difference between (a) and (b) is that at (a) the plastic instability is propagating along the specimen, while at (b) the propagation of the plastic instability has stopped and the increase of the w(y) values corresponds to the process of transition to fracture of the specimen. In Fig. 3.21a, it is possible to see that, as the load is increased, the magnitude of w(y) is increasing as the plastic instability moves along the specimen. In Fig. 3.21b, the plastic instability is stationary but as the load is increased the values of w(y) increase. The values of w(y) correspond to the observed face of the specimen, assuming that the displacements of the back face are similar to those of the front face. The total maximum change of thickness of the specimen is to = 41.7×2μm 600 μm = 0.14 or 14%. This percentage change of thickness is very close to the change in width of the specimen of Fig. 3.14, 13% in the same region of the force vs. strain displacement plot. From analysis of experimental results in Sects. 3.8 and 3.9, it can be concluded that the presence of signals corresponding to the plastic instability and detected with diverse techniques is correlated to the geometrical changes in the dimensions of the observed specimens called with the generic names of diffuse necking or fully developed necking. It also possible to conclude that the optically observed signals depend on the spatial and temporal resolutions utilized in the observation. 3.11 Propagation Velocity of the Plastic Wave Front In the preceding section, we have analyzed the plastic instability from a geometrical point of view. Now we are going to deal with the fact that we are analyzing a wave propagation phenomenon from the onset of plasticity to the point where the transition to fracture takes place. Following the same approach of the preceding sections, we will start with experimental data contained in [24] and graphically represented in Fig. 3.22.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==