40 C. A. Sciammarella et al. Figure 3.24c corresponds to the specimen of Fig. 3.11 and the measured B=13 mm. For this specimen, wo =25mm, the ratio B/wo =0.52 ±0.2 and since for the specimen of Fig. 3.14, it holds Ln ≈2wo, the relation is valid also for the current specimen leading to B≈0.25 Ln. From Fig. 3.24b, one obtains B/wo =0.50 ±0.3. This result means that this ratio is geometrically determined and independent of the speed of propagation. 3.13 Discussion and Conclusions The subject matter of this paper has a sizeable amount of papers that deal with it [26] and a variety of interpretations of different aspects of experimental and theoretical approaches. The methodology in this paper has been to utilize an Experimental Mechanics tool and the iso-derivative fringes (moiré method) via speckle interferometry to obtain information about the processes that arise from the onset of plastic instability in tensile specimens with rectangular cross sections. This process has an initiation of the instability, followed by a transition to fracture. The first step in the analysis of the problem is the characterization of the displacement field in a tensile specimen in the elastic range and then determining the effect of the onset of plasticity in the displacement field. After briefly reviewing the scale effect on recordings of processes, it introduced a family of fringes and the iso-derivatives fringes, and the properties of these fringes are outlined. The transition from the elastic behavior to the onset of plasticity is illustrated with an example showing that this transition can be pinpointed without ambiguity in a sequence of frames of a movie recording of the process. The next step is the analysis of what happens after the onset of plastic instability, the transition between plasticity and final fracture. This is a more difficult problem that in the current state of the literature and in spite of the very many papers published is not fully explained. The concept of instability of the plastic flow is reviewed, and an illustrative simplified example of a particular case is shown connecting dislocation motion with a feature that is observed in optical recordings, a wide band, either directly with isothetic fringes or through computation for example using digital image correlation (DIC). In the analysis of the plastic instability, an important aspect is the geometrical changes that take place in the specimen that are contained in the concept of necking with two variants diffuse necking and necking. Both concepts are experimentally illustrated with the utilization of iso-derivatives applied to examples from the literature. The diffuse necking that corresponds to the propagation or formation of the instability, necking leading to the fracture. The next stage is to consider the dynamic effect associated with the transition from onset of plasticity to final fracture. The plastic instability is associated with a wave front that moves with a speed depending on the speed of the application of displacements by the testing machine. Examples from the literature are utilized to evaluate the relationship between the rate of application of the displacement of the machine and the velocity of the wave front. Since the propagation of a plastic wave front is associated with the presence in the image of wide bands, the first step is to establish the optical format of the signal, the effect of the time and space resolutions in the recorded of the images to analyze different cases. In the high spatial and time resolution examples, characteristics of necking process, whether diffuse or non-propagating, are provided by the iso-derivatives, and it shows the influence of the molecular structure of the metal, which according to the available slip lines and the presence of other factors determines the position of the axial resultant in the fracture mode that in the simplified 2D plane stress case results in a mode-1 fracture or when the position resultant force produces bending stresses that result in a mixed mode fracture mode-1 and mode-2. All the analyzed examples correspond to f.c.c metals, and this explains the approximately equal characteristic angle of the fracture processes. In the case of low spatial and time resolution, the wide bands are characterized by two parameters, the parameter B characterizing the width of the signal, and the angle α that, as indicated before, is connected to the presence of bending in the plane of the specimen. In the paper, it is concluded that B mainly depends of geometric factors and is independent of the speed of propagation. One of the most discussed factors in the literature is the propagation part of the wave front and the source of many different arguments and proposed “classifications” and nomenclatures. Let us first address the propagation problem. There are two main types of plastic instabilities: (1) non-propagating and (2) propagating. An example of non-propagating instability is illustrated by the specimen of Figs. 3.7 and 3.11, the geometry of the specimen determines where the onset of fracture will take place. After the local necking starts, the process of fracture will be similar to that of the plastic analysis of structures [27]. The other case is the presence of defects of different types in the metal that determine where the plastic instability manifests and leads to fracture. The most complex case to discuss is the propagating case, where the variety of possible outcomes is practically innumerable. Also, the use of the nomenclature is confusing, the name of Luders’ bands or shear bands applies to all cases of propagation in the sense that the passage of the plastic wave implies an increment of the roughness of the surface of a specimens as shown in Fig. 3.22. We have analyzed this process and documented the roughness change in the plastic
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