22 C.-H. Wang et al. Fig. 4.4 The ratios of 3D DIC determined in-plan displacement uw.r.t averaged in-plane displacement Fig. 4.5 Normalizing in-plan displacement u of different surface w.r.t 3D DIC determined displacement of middle surface. (a) Moving towards Cx- axis to 3, 6 and 9 mm. (b) Moving towards Cx- axis to 9, 12 and 15 mm. (c) Moving towards Cx- axis to 18, 21 and 24 mm Figure 4.4 is the illustration of the determined in-plane displacements of all three surfaces are compared with the averaged values. The results show that the maximum deviation is about 2 pixels which happened to be moving the aluminum block 3 mm away from its origin and then decreased as the displacement increased until the in-plane displacement is 21 mm. It should be emphasize that the deviation-differences can be identified however the difference of the determined in-place displacement in magnitude among three surface are small. Moreover, inspecting Fig. 4.4 carefully, it could be fund that the averaged displacement is closed to the middle surfaces because the middle surface-to-averaged in-plane displacement is 1 with small fluctuation which means the 3D DIC evaluated in-plane displacement can be approximated by the data of middle surface. In addition, Fig. 4.4 also implied that the determined in-plane displacement might be a function of depth. Pleas also be award that the determined in-plane displacement is over 9% higher than the nominal one, therefore, it is important to know that the determined in-plane displacement near the camera-pair is higher/ lower than the determined displacement related far from the camera-pair, by this way the measurement can be improved by increasing/ decreasing the distance between the camera-pair and object or additional in-plane displacement calibration should be performed to ensure the distance between the camera-pair and the testing object is proper. Since the middle surface can be used as a reference of measurement, the measured in-plane displacement of rear and front surfaces are normalized with respect to the middle surface one and the results are shown in Fig. 4.5. By comparing the plotted curves, interesting to know, in this study, that the ratio can be described as a linear function for small in-plane displacement, in this study, from 3 to 15 mm. The slope of the estimated linear functions decreased in magnitude as the in-plane displacement was increased, and then when the determined in-plane displacement is large then 15 mm, then the determined in-plane displacement from front- to rear- surfaces cannot be considered as linear; eventually, the determined in-plane displacement of rear- surface become higher- than the front surface.
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