4 On the In-Plane Displacement Measurement by 3D Digital Image Correlation Method 23 Fig. 4.6 Associated out-of-plane displacement by 3D DIC as the object is moved in-plane. (a) Front surface. (b) Middle surface. (c) rare surface Table 4.2 ( w)⁄( u) verus nominal displacement u Averaged Displacement Nominal Displ. u w u w= u Dtan 1 w u 3 – – – – 6 0.7301 3.2770 0.2228 12.5604 9 1.4623 6.5725 0.2225 12.5430 12 2.1975 9.8718 0.2226 12.5499 15 2.9278 13.1732 0.2223 12.5308 18 3.6746 16.4677 0.2231 12.5790 21 4.4183 19.7653 0.2235 12.6006 24 5.1615 23.0602 0.2238 12.6164 Averaged angle 12.5686 4.3.2 Out-of-Plane Displacement Although the testing object was moved along x-axis, out-of-plan displacement was obtained from 3D DIC analyzed results. In this study, the out-of-plane displacement was increased as the in-plane displacement increased. As shown in Fig. 4.6, the out-plane displacement and in-plane displacement can be well fitted by a linear function. The slope of the fit curves are 0.7369, 0.7355 and 0.7312 with respect to front-, middle- and rear- surfaces and the corresponding R2 can be approximated to be 1. In addition, the slope of u-w plots are fitted with respect to the step-height difference by using front-surface as a reference, again, the step-high difference ( h) versus u-w slope (s) can be described as sD 60 10 6 hC0.2457 with corresponding R2 D0.9822. Table 4.2 presents a very interesting result regarding the averaged in-plane displacement . u/ and the averaged out-ofplane displacement . w/ with 3 mm nominal averaged in-plane and out-of-plane displacement as reference. The results show that the calculated ( w) ⁄( u) values are always about 0.2223 which means the increment of wis highly dependent with u. Meanwhile the ( w) ⁄( u) ratio can be converted to an angle defined by u and w. The angle is about 12.5686 ı and this angle is close to the 10.5ı heading angle of camera. In fact, the estimated angle defined by displacement u and w could be the implemented heading angle of the camera used for 3D DIC, however, more evidences based on experimental results before conclusion. 4.3.3 Laser Triangulation Measurement As indicated in 3.2, the out-of-plane displacement can be evaluated by 3D DIC while the object was moved in-planes along x-axis. Although the movement is performed by using a precision stage, however, monitoring the possible out-of-plane displacement caused by geometrical misalignment of camera-pair and testing object is essential. In this study, a laser and cylindrical lens integrated light source was moved together with the aluminum block, the step height of the aluminum block was then evaluated from left- and right- cameras; by this way, if there is unparallel available between the precious stage and base-line of camera-pair, then the unparallel can be detected because of the change of height between steps of the specimen. The measurement results were shown in Fig. 4.7, the height difference between front- and middle- surfaces obtained from left- and right- cameras are almost identical when the displacement is less than 10 mm; but the difference of evaluated
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