# Dynamic Response of Copper Plates Subjected to Underwater Impulsive Loading
## 3 Results and Discussion
### Specimens without Pre-Notches  
As shown in Figure 6, a reduced area surrounded by the red line at the specimen center was selected as the AOI (area of interest) to obtain full-field deformation. The green region corresponding to the strain gauges cannot be correlation calculated, because of the speckle lack. Figure 7 shows the out-of-plane displacement fields of the A5# specimen (\(T\) = 1 mm, \(V_{0}\) = 46.6 m/s) at different time steps. The major component is the out-of-plane displacement (\(\delta\)). The shock wave \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multirow{2}{*}{\(V_{0}\) **(m/s)**} & \multicolumn{2}{c}{\(\boldsymbol{P_{A}}\) **(MPa)**} & \multicolumn{2}{c}{\(\boldsymbol{p_{B}}\) **(MPa)**} \\ \cline{3-6}  & & **Exp.** & **Equation (5)** & **Exp.** & **Equation (6)** \\ \hline A1\# & 158.3 & 84.9 & 86.5 & 50.4 & 47.8 \\ A2\# & 124.3 & 62.8 & 67.9 & 40.3 & 37.6 \\ A3\# & 129.5 & 65.6 & 70.8 & 42.0 & 39.2 \\ A4\# & 130.2 & 66.3 & 71.1 & 42.0 & 39.4 \\ A5\# & 46.6 & 23.4 & 25.5 & 15.5 & 14.1 \\ A6\# & 121 & 64.5 & 66.1 & 39.2 & 36.6 \\ A7\# & 128.9 & 65.7 & 70.4 & 41.8 & 39.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristic parameters of underwater impulsive loads. Figure 5: Typical pressure-time history at positions A and B of the A1# test; (**a**) point A (**b**) point B.  
Figure 6: Diagram of selected area of interest (AOI). acts on the internal surface of the copper plate as a plane shock wave during the early period. More shock waves act on the plate boundary, bringing the clear displacement ring up to 0.08 ms, then the displacement increases from the boundary to the center of the plate until 0.4 ms. Note that the deformable contour exhibits an approximately planar circular shape in the first 0.4 ms, and evolves into a symmetric dome shape after 0.48 ms. The out-of-plane displacement and velocity profiles along the x-axis are shown in Figure 8. Notice that the profiles are plotted from \(-\)60 to 70 mm, while the boundary is located between \(-\)76.2 and 76.2 mm. As indicated in Figure 8a, the plate is forced to move out of the plane underwater shock wave. The displacement is first produced at the boundary region (see lines from 0.02 ms to 0.24 ms), the shape after deforming of the plate is approximately symmetrical and is almost constant until 0.14 ms. The plate continues to deform when the pressure of the shock wave has vanished. At 1.52 ms, the displacement reaches its maximum at the center first, and then rebounds at 2.24 ms, due to elastic recovery. Particles close to the boundary are constrained and have a very limited initial velocity. The plate has the same given velocity at 0.02 ms. From this moment on, the velocity increases from the boundary to the center, because of the centripetal radial flow of water. The outside surface obtains a maximum deformation velocity of 34.1 m/s at 0.42 ms (see Figure 8b), and then presents attenuation of velocity repeatedly. The inertia forces cause the plate to be further deformed. Figure 9 presents the evolution of the in-plane maximum principal strain fields of the A5# specimen at different time steps. It is found that higher principal strain appeared close to the boundaries until 0.30 ms, because the plate's borders are constrained by steel flange. Further, due to the interaction of the inertia forces and refection waves, strain develops towards the center of the plate, and reaches a maximum value at 0.66 ms.  
Figure 7: Out-of-plane displacement fields of the A5# specimen (\(T=1\) mm, \(V_{0}=46.6\) m/s). The comparison of strain histories measured by the DIC and strain gauges (see Figure 3b) are shown in Figure 10. The DIC results are obtained from strain data of the corresponding symmetric points. The evolution trends of the two history curves are similar.