# Dynamic Response of Copper Plates Subjected to Underwater Impulsive Loading
## 3 Results and Discussion
### Specimens with Pre-Notches  
Table 3 lists the experimental conditions and the corresponding failure mode of the specimens with pre-notches. The specimens with pre-notches have been investigated to understand the effect of pre-notches on the dynamic deformations and failure modes. Figures 13 and 14 show the evolution of the in-plane maximum principal strain of C1# and C2# specimen (\(T\) = 1 mm, \(L\) = 30 mm, and \(H\) = 0.5 mm). The selected frame rate and image resolution are 75,000 fps and 320 \(\times\) 264 pixels for the C1# test. It is very clear from Figure 13 that weak strain concentration has appeared at the center of the outside surface at 559 \(\upmu\)s. From this moment on, because the pre-notch causes the strength of the central region of the plate to decrease, higher principal strain localizes and concentrates around the pre-notch. The shape of strain concentration is close to the cross shape with a 45 degree angle, the position and direction of strain concentration correlate well with the pre-notch. Compared with the test for C1#, the impact velocity has been increased to 118.9 m/s in the C2# test. A framing rate of 50,000 fps is used with an image resolution of \(512\times 272\) pixels. Similarly to the result of the test without a pre-notch, the principal strain increases from the boundary to center regions. Similarly to the test for C1#, a cross-shaped strain concentration appears in the correlated position of the pre-notch at 520 \(\upmu\)s. At 600 \(\upmu\)s, a mismatched region is also found on the displacement profile, demonstrating that a crack rupture occurs in the plate center (labeled \"1\"). After 620 \(\upmu\)s, the water escapes through the crack from the anvil, and the crack continues to expand in the direction of the cross pre-notch. Figure 15 shows the out-of-plane displacement fields on the surface of the R1# specimen with a ring-shaped pre-notch (\(T=1\) mm, \(D_{\mathrm{c}}=30\) mm). The camera framing rate and image resolutions are the same as the test for C2#. The pre-notch is indicated by a white line. At 520 \(\upmu\)s, a crack forms in the center area indicated by white ring A. After this moment, the crack extends along the ring-shaped pre-notch, and then the circular flyer falls off from the plate (see 840 \(\upmu\)s in Figure 15). Figure 16 shows the in-plane maximum principal strain profile along the x-axis. Notice that strain concentration is located at \(\pm 15\) mm from the center, where is the same location as the pre-notch. This explains how strain concentration also occurs around ring pre-notch. Figure 14: In-plane maximum principal strain of the C2# specimen at different time steps. Figure 13: In-plane maximum principle strain of the C1# specimen at different time steps. After underwater loading tests, the specimens with the cross-shaped and ring-shaped pre-notches have been recovered for further analysis. The four typical failure modes observed in these experiments are reported in Figure 17. The 1 mm-thick plate with the depth cross pre-notch of 0.5 mm has been tested using a flyer with a velocity of 101.9 m/s. The larger ductile deformation and a cross-shaped local necking (mode Ic) appear in the center area of the C1# specimen, which is only presented in the pre-notch position marked with a white circle in Figure 17a. Figure 16: The in-plane maximum principal strain profile along the x-axis of the R1# specimen. Figure 15: Out-of-plane displacement fields of the R1# specimen at different time steps. For the same case, while the velocity of the flyer is increased to 118.9 m/s and 140.8 m/s, the failure modes of the C2# and C4# specimens evolve to splitting of pre-notch and tearing (mode IIc), see Figure 17c, the new cracks grow from the pre-notch tips. Scanning electron microscopy (SEM) was used to measure the microstructure of the fracture surfaces of the C2# specimen. Figure 18 shows the microstructures of different fracture surfaces of the C2# specimen, including the pre-notched part labeled by the white lines and the new crack part labeled by the red line.