6 Evaluating Path of Stress Triaxiality to Fracture of Thin Steel Sheet Using Stereovision 39 is overlaid by spray painting, creating a speckle-like pattern. The size of the random pattern is selected to oversample the intensity pattern using several sensors for accurate measurement. In this study, each random pattern is oversampled by 10– 40 pixels. The variations in the speckle-like pattern on the specimen are observed by four monochromatic CCD cameras (2048 2048 pixels 8 bits) equipped with a lens with a focal length of 105 mm. A bicubic interpolation method is used for obtaining the continuous speckle pattern. The data processing is implemented using software developed by one author. 6.3 Results Figure 6.3 shows the example set of the specimen surface observed by a stereovision. Using the principle of the stereovision, three-dimensional surface position before and after the load are determined. Then, the three-dimensional displacements are obtained as shown in Fig. 6.4. The strain distributions are computed from the displacement distributions of the both surfaces. Here, it is noted that the logarithmic strains are employed as the strain measure. Figure 6.5 shows the example set of the logarithmic principal strain distributions for the TS980MPa specimen under the load of P D14.4 kN. Note that the third principal strain "3 represents the through-thickness strain. As shown in this figure, it is observed that the strains concentrate at the middle of the specimen and the reduction of the thickness is obvious. From the measured strains, the variations of the stress triaxiality at the center of the specimen are evaluated. The stress triaxialites obtained by various procedures are shown in Fig. 6.6. The symbol ˜e2 represents the stress triaxiality evaluated form the in-plane principal strain increments, ˜e3 gives the value evaluated from the in-plane principal strain increments as well as the through-thickness principal strains. As mentioned in Introduction, the experimentally obtained strain increments are suffered from the greater measurement errors than the strains. Therefore, the stress triaxialities are also evaluated from the stresses that are computed from the strains using the total strain theory [8]. The symbol ˜s2 is the stress triaxiality obtained from the in-plane stresses and the symbol ˜se expresses the value computed from the in-plane and through-thickness stresses. It is observed from this figure that the stress triaxialities change depending on the deformation of the specimens and tend to gradually approach the nominal value ˜ D0.577. The smooth variations are observed for the values obtained from the stresses whereas the values obtained from the strain increments exhibit not smooth variation. Further studies are required for validating these results. Fig. 6.3 Example set of stereo images of front surface for TS980MPa specimen: (a) left image before load; (b) right image before load (c) left image after load (PD14.4KN); (d) right image after load (PD14.4KN)
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