Numerical Analysis on Shock of Double-layer Plate with Foamed Aluminum

. The response of structure under shock is very important. For sandwich structures, the foam of other material with good energy absorbing capacity is an effective way to enhance the ability to resist external shock. In this work, numerical shock analysis is conducted for double-layered plate with foamed aluminum. The deformation process is firstly studied in case of initial shock velocity of 8.9m/s, then comparative analysis is conducted on the influence of different shock velocity on structural response.


Introduction
Structures in engineering would be strongly damaged, when it is shocked by explosion other flying pieces. Accurate prediction for deformation process of structure under chock load is very important and it will lay good foundation for shock resistance design of structures. Recently, approaches applied to study the shock characteristics of structures are mainly numerical simulation method and experiment method. Sandwich structures have wild applications in aerospace, ship structures, submarine, and so on. Many researchers have made some work on mechanism and analysis method for sandwich structures [1][2][3]. Besides, Omar et.al [4] studied deformation response of sandwich beam with foamed metal under three-point flexural load, the maximum stress is obtained and the failure mode is also discussed. Colombo et.al [5] analyzed the nonlinear characteristics of beton sandwich beam with three different core materials under four-point flexural load. Kobayashi et.al [6] investigated the response and failure mode for sandwich plate with circular core and honeycomb core under local repeating compressive load. But, research on the deformation process and failure for doubled-layered plate with foam core is few. In this work, in order to get clear the response process of double-layered plate with foamed aluminum, numerical simulation is carried out with software ABAQUS. The deformation process is studied and the influence of shock speed on structural response is also conducted.

Numerical model
The Dynamic/Explicit module is applied. Solid model is constructed for structure and the drop hammer is rigid. Tie link is applied for connect between ring-stiffer and up/down plates.
Structural model. Structural model is shown in figure 1, and so is the mesh and boundary condition. The element is C3D8R, initial speed of drop hammer is calculated with different height. For example, initial speed of drop hammer is 6.5m/s, 8.9m/s, 11.5m/s in cases of height with 2.1m, 4m, 6.7m, respectively. Material. Structure is 304 stainless steel, and the JOHNSON-COOK model is also applied. The mass of drop hammer is 362kg. Compressive foam model is applied for foamed core material, the density is 550 kg/m 3 , Possion's ratio is 0.3, elastic modulus is 300MPa. Test point. In order to output acceleration and displacement for comparative analysis, three different points are selected both for up and down plates, as is shown in figure 2.

shock process analysis
In the case of height 4m for drop hammer, the shock velocity is 8.9m/s, the shock process is plotted in Fig.3, and it's introduced in detail as below. A) Drop hammer contact with the up plate, stress for up plate and ring-stiffer will be born, and the stress for up plate is relative bigger. B) Drop hammer keeps dropping, stress for up plate and ring-stiffer will increase, and deformation is observed, thus the foamed core will be compressed. C) Deformation will be observed for ring-stiffer, but it has no obvious damage, resistance ability for up plate will reach maximum, and its will be torn. At the same time, foamed core will separate from ring-stiffer. D) With the increase of load, crack for the up plate will grow bigger and bigger, deformation of ring-stiffer will also be bigger and bigger. And the foamed core will more and more compressed. E) Crack of up plate increases, and crack is also noted for joint between plate and ring-stiffer, failure is born in left ring-dtiffer, and the foamed core will crush. F) Drop hammer keep dropping, crack of up plate and ring-stiffer will be bigger, while the foamed core will be densification and will be completely damaged. The total deformation will be increase. In the total process, max deformation for up plate is 24.5mm, the stress and strain is shown in figure 4-5. It can be concluded that concentration is very obvious , and the absorbed energy for structure is 4.9×103J.

comparative analysis in case of different shock velocity
Comparative analysis is conducted for deformation and failure of double-layered plate with foamed core under three different shock velocities, the results are shown in figure 6. In the case of relative low shock velocity, 6.5m/s, local plastic deformation is observed for structures. The shock energy is absorbed with light crack and local plastic deformation of up plate, and the foamed core and ringstiffer are lightly compressed. While the shock velocity increase to be 8.9m/s, crack of up plate is more obvous, and crack length and area increases; the foam core near the drop hammer is strongly densification and crushes; failure for the ring-stiffer is born. Shock energy absorption increases a little, due to the crack of up plate and densification of foamed core. While the shock velocity is 11.5m/s, structural failure is more obvious, since the action of drop hammer is more significant. Hammer into the up plate can be noted, and the crack area increases. The densification of foamed core near drop hammer is much more serious, and it crushes and become failure under compressive load. With comparison with the case of 8.9m/s, carrying capacity of ring-stiffer in case of 11.5m/s increases a little, which will result in the obvious increase of plastic deformation of down plate.

Conclusion
In this work, numerical shock analysis is conducted for double-layered plate with foamed aluminum. The deformation process is firstly studied in case of initial shock velocity of 8.9m/s, then comparative analysis is conducted on the influence of different shock velocity on structural response. Conclusions obtained in this work will lay foundation for future work for making good shock test plan for doublelayered plate with foamed aluminum.