# Dynamic Response of Copper Plates Subjected to Underwater Impulsive Loading
## 2 Experimental Configuration
### Experimental Details  
A simplified FSI experimental setup was developed in a laboratory setting for resembling underwater explosive loading conditions by [PERSON] and [PERSON] based on [PERSON]'s work [10; 24; 33]. Figure 2 shows the schematic diagram of the FSI experimental setup. In the FSI setup, a steel water chamber is incorporated into a gas gun apparatus. The test copper plate and a steel piston are installed at the rear (left) end and the front end with an O-ring, respectively. A gas gun is used to drive a 5 mm thick flyer plate, to prompt the piston to produce the exponentially decaying pressure history. The impulsive pressure histories at A and B positions (the center and end) are measured by dynamic high-pressure transducers. The material used in this study is ASTM C11000 copper. The mechanical properties of the material are obtained through open literature [34]. The density \(\rho\) is 8930 kg/m\({}^{3}\)and the static tensile yield stress \(\sigma_{y}\) is 205 MPa. The circular specimen plates with a diameter of 200 mm, as shown in Figure 3a, were clamped at the end of the anvil tube by a steel ring and 12 bolts. The plate is only restricted by a steel ring because the bolts do not pass through the plate. The diameter (\(D\)) of the specimen exposed to the water shock loading is 152.4 mm. The strain gauge is used to measure the in-plane components of strain, and is placed at a location 30 mm from the center O, as shown in Figure 3b. The three different thicknesses (\(T\)) of the copper plates are 1 mm, 2 mm, and 3 mm. In order to study the effect of initial damage of the plate on failure modes, except on a copper plate without pre-notch, two kinds of shapes of pre-notches, include cross (+) and ring (\(\Circle\)), are prepared in the center of the specimens, see Figure 3c,d. The width (\(W\)) of the pre-notch is 1 mm, the lengths (\(L\)) of the cross-shaped pre-notches are 30 mm and 50 mm, the depths (\(H\)) are 0.5 mm and 1.5 mm, the depth and diameter (\(D_{\mathrm{c}}\)) of ring-shaped pre-notches are 0.5 mm and 30 mm. In the present study, a 3D DIC technique is used to capture the dynamic response of materials under shock loading. The deformation process of the outside surface of the copper plates was measured by 3D DIC measuring system, see Figure 2. Figure 4a shows the pictures of a 3D DIC measurement system consisting of two halogen lamps and two synchronized high-speed cameras in a stereoscopic setup. Two Photron Fastcam SA5 high-speed digital cameras (Photron Inc., Tokyo, Japan) were positioned behind the water chamber to record the speckles on the outside surface of the copper plate. The safety distance was about 0.8 m and each camera was angled at approximately 10\({}^{\circ}\) with respect to the symmetry plane. The power of the two halogen lamps as the lighting source is 1 kilowatt. The photography system is synchronically triggered by a laser trigger while the flyer impacting the piston. A framing rate of 50,000 frames per second (fps) is chosen in tests with an image resolution of  
Figure 2: Schematic diagram of the experimental setup. \(512\times 272\) pixels. In order to study the fracture process of cross-shaped pre-notches, a higher framing rate of 75,000 fps is used with an image resolution of \(320\times 264\) pixels. Figure 4: Diagrams of the fluid-structure interaction (FSI) experimental setup: (**a**) the 3D digital image correlation (DIC) measuring system with two high-speed digital cameras and two light spots; (**b**) the interest area of the specimen surface with a speckle pattern. Figure 3: Outline of different specimens: (**a**) schematic of insufficient clamping condition; (**b**) schematic of a specimen with strain gauges; (**c**) a copper plate with a cross-shaped pre-notch; (**d**) a copper plate with a ring-shaped pre-notch. Figure 4b shows the specimen coated with a randomized speckle pattern. It is necessary to clean and polish the specimen surface before preparing a randomized speckle pattern.