4 A Digital Laser Speckle Technique for Generating Slope, Curvature, and Deflection Contours of Bent Plates 47 4.4 Results In this experiment, we tested the deformation of a circular disk under a central transverse load using the proposed laser speckle method. The plate was made of polycarbonate (diameter =10.16 cm, thickness =6.35 mm) and loaded by a central deflection of 12.7 μm. A 15 mW expanded He-Ne laser beam (λ =0.6328 μm) was used to illuminate the object from 2.2 m away. The digital camera was situated 2.1 m away from the plate and focused on a parallel plane 17.5 cm in front of the specimen surface. Figure 4.3 shows a set of slope fringes obtained by processing a before and after loading image with CASI. There are situations in which deflection of a plate is needed, such as the warpage of an electronic package chip caused by different thermal expansion of different materials. These deflections can be simply calculated using a numeric integration of the slope data; such deflection contours are plotted in Fig. 4.4. In the case of determining the stresses, bending, and twisting moments, the curvature contours are needed, they are produced through a numeric differentiation of the slope data, and a set of curvatures are shown in Fig. 4.5. As the contours are numerically determined and all of the data is stored in an array manipulation to determine the stresses, bending and twisting moments becomes rather easy. The central deflection of the plate shown in Fig. 4.4 has a value of 12.75μm which compares favorably with the actual deflection of 12.7μm. The curvatures numerically derived have a good agreement with both theory and pervious experiments. Fig. 4.3 Fringe patterns of partial slope contours of a clamped circular polycarbonate plate under concentrated central load (a) ∂w/∂x–field (b) ∂w/∂y–field Fig. 4.4 Fringe patterns of deflection contours of a clamped circular polycarbonate plate under concentrated central load
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