Averaged Displacement, Ui ¼ X n l X m k Ui kl 2 mþn ð Þ " # 1=2 where i ¼1, 2, 3 for coordinates, that is U1; U2; U3 ð Þ¼ U; V; W ð Þ, k and l are index of pixel along row and column, the maximum pixel numbers of row and column are mand n. The averaged displacements determined by 3D DIC show that as the rotation angle is 0 , the difference between the averaged U displacement and the nominal U displacement is minimum where the nominal displacement is +9 mm; as for +23.5 mm, the minimum U-displacement departure occurs at rotation angle is 1 , for both case, the V displacements are also minimum compared with others. However, the W displacements in both cases are relative large. Figure 16.7 shows the difference U displacements between the nominal and the 3D-DIC determined. For U¼+9 mm case, the displacement span increased as the rotation angle increased, different from 2D DIC results, only when rotation angles at 0 and2 , the maximum displacements are almost the same. As for U¼+23.5 mm, as shown in Fig. 16.7b, the U displacement is decreasing from left-upper corner to bottom right corner when the rotation angles are0 and1 , but the displacement is increasing from left-upper corner to bottom right corner at 2 rotation angle. The results indicate that the pointing issues have to consider all three displacement vectors. Again, from Fig. 16.7c, the error-nominal Fig. 16.6 The pseudo strain-nominal displacement relations. (a) Pseudo strain εxx. (b) Pseudo strain εyy. (c) Pseudo strain εxy Table 16.2 The displacement obtained from 3D DIC Nominal displacement +9mm +23.5mm Averaged displacement U V W U V W Rotation angles 0 9.081 0.057 0.233 23.363 0.086 0.280 1 9.147 0.090 0.029 23.421 0.044 0.858 2 9.126 0.094 0.515 23.377 0.087 0.671 140 C.-H. Hwang et al.
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