3 Experimental Observations on the Fracture of Metals 37 Fig. 3.22 (a) Visualization of the propagation of the plastic wave instability using a shadowgraph technique [24]; (b) Wave front travelled distance vs. time The specimen represented in Fig. 3.22 is made of aluminum 5052 similar to the material of the specimen shown in Fig. 3.11 and hence has a f.c.c. crystalline structure. The angle of inclination of the wave front is 25◦. The specimen gage length is Lo =102 mm, widthwo =12.7 mm, thickness to =1 mm, ratio width to thickness rwt =wo/to =12.7, and pulling speed of the machine, vpm =127 μm/s. For comparison purposes, we recall those for the specimen of Fig. 3.11: rwt =wo/to =12.5, pulling speed of the machine, vpm =5.83 μm/s, that is both rwt are very close, but the pulling speed of this specimen is almost 22 times greater that the speed applied to the specimen of Fig. 3.11. From Fig. 3.22a, it is possible to correlate the space covered by the plastic wave front with the elapsed times giving a speed of the plastic wave equal to 10 mm/s that agrees with the value indicated in Fig. 3.22. The method applied to measure speed in [24] is based in the visual change of roughness of the specimen surface, and the size of the wave front pulse is not measurable in Fig. 3.22. This speed is measured in a frame attached to the specimen, the specimen is moving with a speed of 0.127 mm/s, that is, the ratio of the velocities is rvl =10/0.127 =78.7. For comparison purposes, the speed of sound in aluminum is 6.3 ×10 6 mm/s, many orders of magnitude larger than the propagation of the plastic wave front. In [24], a model is presented that deals with the propagation of a plastic front at constant stress, that is, at zero stress rate, and the conclusion of the model based on experimental measurements is that vpm =vwB × εp (3.24) In Eq. (3.24), Δεp is the jump on strain across the plastic wave front, and, according to experimental measurements, Δεp is roughly constant and can change in order of magnitude if the stress level changes. To clarify the process of initiation and propagation of the plastic wave front, we can look at the results corresponding to a specimen of the same material than specimens Nos. 1 and 2, [11], but with following dimensions, Lg =65mm, wo =10mm, to =5mm, vpm =0.333 μ/s. Figure 3.23 shows the propagation of the plastic instability from the onset of plasticity frame 1 to frame 9 close to the fracture. The blue points represent the acoustic events related to the dislocation motions captured by the two acoustic emission sensors (A.E.). The fringe patterns are iso-derivatives fringes as previously shown in the paper (Eqs. (3.18) and (3.19)). The specimen is loaded with a special testing machine that pulls both ends symmetrically and keeps the center of the specimen in a fixed position. While frame No. 1 exhibits what in the literature is called a wide band, the rest of the frames show patterns of iso-derivatives that are very complex and are indicative of the heterogeneous structure of the specimen influencing the local patterns of deformation, showing reversal of the inclination of the wave front (frames 5 and 6). Frames 7, 8, and 9 show iso-derivatives similar to iso-derivative patterns of Figs. 3.14 and 3.17. These observed patterns are transient and random.
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