3 Experimental Observations on the Fracture of Metals 25 Fig. 3.5 Optical setup to obtain patterns of the iso-derivative fringes The experimental determination of the iso-derivative fringes can be achieved by using different optical setups. The most general setup requires high-speed cameras for recording images as load or displacements are applied to the observed specimen. Also, it is necessary to introduce software that provides the derivatives of the displacements with respect to the coordinates x–y, (x), for increasing loads or applied displacements, for example, tagging on the specimen an orthogonal system of carrier lines. Then, one can resolve the carrier gratings utilizing, for example, the optical set up shown in Fig. 3.5 and non-coherent illumination. With this system, it is possible to resolve the printed grating at different scales by changing the magnification of the system, and by filtering it is possible to get the components εu (x, P) and εv (x, P). The necessary computations can be done by utilizing digital moiré [21]. The setup shown in Fig. 3.5 can be used to determine iso-derivatives fringes in the microscopic range. An alternative way to determine the iso-derivative fringes is to use coherent illumination and two or four beams speckle interferometry setups. First, it is necessary to remember that, as shown in [21], speckle patterns provide isothetic lines as the moiré method does but with limitations arising from decorrelation and noise content. Examples of the determination of the iso-derivative fringes utilizing speckle interferometry are given in [2–5] and [8–11]; in these references, tensile specimens were studied. In [4], two interferometers were utilized, one with the sensitivity S1 in the longitudinal direction of the specimen to make measurements in one face of the specimen. The other interferometer with the sensitivity vector S2 transversal to the specimen to make measurements in the other face of the specimen. Both interferometers record images by means of a high-speed camera. The data processing is done so that the obtained patterns represent finite differences of the iso-derivative fringes. In [10, 11], only longitudinal displacements are recorded by a CCD camera, only one of the two families is determined at certain points the stress-strain curve. Figure 3.6 illustrates the schematic process utilized in [4] to obtain the finite differences of u(x,P), and a similar process can be applied to obtain v(x,P), u(x, P) x ≈εu (x, P) (3.17) v(x, P) y ≈εv (x, P) (3.18) In [4], the utilized specimen is a thin foil plate 100 mm long and 0.4 mm thick, a thin specimen. To define a critical area where the transitions to plasticity and fracture are localized, one side of the specimen is made curved. The upper width of the specimen is wo =20 mm and the middle section wm =15 mm. This design causes the tensile specimen to be subjected to tension and also to bending (see Fig. 3.7). This fact is important because the obtained results depend on the geometrical configuration and boundary conditions. Specklegrams are acquired by a movie camera at the speed of 30 frames/s, and the specimen is pulled at the speed of 4μm/s. The acquisition software is designed in such a way that according to the scheme of
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