# Dynamic Response of Copper Plates Subjected to Underwater Impulsive Loading
## 3 Results and Discussion
### Specimens without Pre-Notches
It can be seen that results from DIC and strain gauges show a good agreement in the initial growth stage until 0.6 ms. From this moment on, strain gauges falling off from the sample cause strain curves to stop rising and start falling. Figure 11 shows photographs of the recovered A5# specimens after the test. It can be seen the main failure mode of the specimen is only a large ductile deformation (mode I), as defined by [PERSON] and [PERSON] [36]. Because the test plate slides out from the clamped location, an annular sliding trace can be clearly observed on the boundary (see Figure 11b). Figure 8: The out-of-plane displacement and velocity profiles: (**a**) profile of displacement along the x-axis; (**b**) profile of velocity along the x-axis. Figure 9: In-plane maximum principal strain fields of the A5# specimen at different time steps. The results of the deformation and failure mode for all seven specimens without pre-notches are summarized in Table 2. The peak pressure \(p_{ms}\) and impulse \(I_{ms}\) are predicted values by Equations (3) and (4), the dimensionless impulse is given by \(\overline{I}=I_{ms}/\overline{M}\sqrt{\sigma_{y}/\rho}\), where \(\overline{M}\) is the dimensionless mass, the final deflection \(\delta_{t1}\) and \(\delta_{t2}\) are obtained by DIC and the altimeter, the dimensionless final deflection \(\delta_{t1}/L\) is also given, where \(L\) = 152.4 mm is the specimen span. The relationship between the dimensionless impulse and normalized final deflection is shown in Figure 12. The result shows that the normalized final deflection of the plate increases linearly with the dimensionless impulse. The failure modes are always large ductile deformations (mode I). The relative out-of-plane measurement errors of DIC for seven tests are from 0.84%-6.83%, which can be estimated by \(|\delta_{t1}-\delta_{t2}|/\delta_{t1}\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**Thickness**} & \multirow{2}{*}{\(V_{0}\) (m/s)} & \multirow{2}{*}{\(p_{ms}\) (MPa)} & \multirow{2}{*}{\(I_{ms}\) (Pa-s)} & \multirow{2}{*}{\(\delta_{t1}\) (mm)} & \multirow{2}{*}{\(\delta_{t2}\) (mm)} & \multirow{2}{*}{\(\delta_{t1}\) (\(\mathbf{L}\))} & \multirow{2}{*}{\(\delta_{t1}\)/\(L\)} & **Measurement** & **Failure** \\  & \multicolumn{2}{c}{**\(T\) (mm)**} & & & & & & & & **Error (\%)** & **Mode** \\ \hline A1\# & 1 & 158.3 & 42.1 & 2769 & 27.9 & 27.3 & 2.05 & 0.183 & 2.15 & Mode I \\ A2\# & 1 & 124.3 & 33.0 & 2174 & 23.9 & 24.1 & 1.61 & 0.157 & 0.84 & Mode I \\ A3\# & 2 & 129.5 & 34.4 & 2264 & 22.2 & 22.8 & 0.84 & 0.146 & 2.7 & Mode I \\ A4\# & 3 & 130.2 & 34.6 & 2277 & 16.1 & 17.2 & 0.56 & 0.106 & 6.83 & Mode I \\ A5\# & 1 & 46.6 & 12.4 & 815 & 18.6 & 17.8 & 0.60 & 0.122 & 4.3 & Mode I \\ A6\# & 1 & 121 & 32.2 & 2116 & 23.6 & 22.2 & 1.57 & 0.155 & 5.93 & Mode I \\ A7\# & 1 & 128.9 & 34.3 & 2254 & 24 & 23.7 & 1.67 & 0.158 & 1.25 & Mode I \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental conditions of specimen plates without pre-notches. Figure 10: Comparison of the normal strain results from DIC and strain gauges; (**a**) strain of x-direction and (**b**) strain of y-direction. Figure 11: Photographs of recovered specimens after shock experiment, (**a**) shows the outside face; (**b**) shows a side view.