3 Experimental Observations on the Fracture of Metals 31 Fig. 3.12 Shape of a rectangular specimen when the plastic instability sets on, the rectangular cross-sectional dimensions wo and to are reduced Fig. 3.13 Cross section in the axis of symmetry of specimen [11] notation in preceding sections, the longitudinal axis of the specimen coincides with the y-axis of the Cartesian coordinatesaxes and the corresponding displacements belong to the V(x,P) family of the iso-derivatives. The sensitivity S1 along the specimen axis has a modulus |S1|=0.447 μm. Figure 3.14 shows the iso-derivatives fringe patterns in the segments of the plot force F vs. the strain around the maximum load and also includes a picture of the broken specimen. The snapshot of Fig. 3.15a corresponds to an area where the wave front has already passed through and shows isoderivatives corresponding to the pattern “V” of Fig. 3.1. Since the rate of change is decreasing, spatial derivatives correspond to the condition dσ dε →0. The length of the neck region at maximum load from Fig. 3.13b is Ln =7.18 mm, and the ratio between Ln and wo is rlw =7.18/3.6 =1.9. This result indicates that within the dispersion of the experimental results, this ratio is approximately equal to 2. This value is consistent with the Saint-Venant’s principle of decay of solutions of four order differential equations [22]. This approximation is confirmed by the results plotted in Fig. 3.16 of the final shape of the neck after the fracture of the specimen, Ln =7.7 and rlw =7.7/3.6 =2.14. From the above-presented data analysis, the following overall view of the propagation of the plastic instability emerges in a material that is homogeneous and is loaded under very stable conditions. At the onset of plasticity, Fig. 3.14, the shape of the specimen changes to a configuration similar to the configuration that is outlined in Fig. 3.12 and that in the literature is referred as diffuse necking. As the load is increased, the geometrical configuration is basically preserved but the magnitude of w(P) and t(P) change until the maximum load is reached. At this point, the wave propagation stops and the process of fracture begins.
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