Calculation of Air Shock Wave Pressure on the Back of an Explosive Flying Plate Colliding with a Thick Steel Plate
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When the explosive flying plate collided with the thick steel plate, researchers Zhou Tingqing, Wang Fengying, and Liu Tiansheng from the Department of Modern Mechanics at the University of Science and Technology of China (Hefei 230026) and the Department of Environmental and Safety Engineering at North China Institute of Technology (Taiyuan 030051) conducted a numerical simulation to study the rapid deformation of the plate. The interaction between the steel plate and the surrounding air was also analyzed using spherical symmetry to model the propagation of the shock wave in the air behind the plate. The results were found to be in good agreement with experimental measurements.
The paper discusses the stress wave generated within the thick steel plate due to the impact of the explosive-driven flying plate. While the calculation and propagation of the stress wave and subsequent damage to the steel plate were well handled, the formation and evolution of the shock wave in the air on the backside of the steel plate remained a challenge. To address this, the authors employed a two-dimensional axisymmetric dynamic finite element method to simulate the free surface movement of the thick steel plate under the impact of the explosive-driven plate. They also performed a spherical symmetric analysis of the shock wave propagation in the air, taking into account the velocity matching condition at the interface between the steel plate and the air. This approach allowed them to determine the distribution of overpressure behind the steel plate as a function of distance, which matched well with actual measurements.
In their model, the explosive charge is assumed to be flat with a thin layer, acting as the flying plate. The thick steel plate has a defined thickness, and the explosive is modeled as an instantaneous adiabatic detonation due to its short duration. The collision between the thin explosive plate and the thick steel plate is considered inelastic, given the high impact velocity. Since the density difference between the steel and air is significant, the contact between the thin plate and the thick steel plate is treated as a surface interaction with minimal plastic deformation, allowing the steel plate to be modeled as an elastic medium during stress wave transmission.
To determine the velocity of the thin plate after the explosion, the principle of adiabatic expansion and impulse conservation was applied. The velocity was calculated based on the mass of the plate and the energy released by the explosion. The pressure and duration of the impact on the thick steel plate were also estimated, leading to the calculation of the free surface velocity of the steel plate. A finite element analysis was used to simulate the collision process and track the shock wave propagation through the air.
The speed-time curve of the free surface of the steel plate was analyzed, showing continuous changes in velocity. Using this data, the propagation of the shock wave was simulated based on local acoustic wave speeds. The incident wave at the air-steel interface was calculated, and the pressure in the air behind the plate was determined. At 0.005 seconds, the initial pressure time history of the shock wave in the air was recorded.
The pressure distribution on the air interface of the steel plate was studied, and the attenuation of the shock wave with distance was analyzed. It was observed that the shock wave followed an infinite medium model, and the results showed a significant reduction in overpressure as the distance increased. At 0.1 meters away from the steel plate, the peak overpressure was reduced by nearly 20 times, and even at 5 meters, the reduction was only about 0.01.
Comparing the calculated results with experimental data, the peak overpressure measured was slightly higher than the calculated value by 0.013 atmospheres. This discrepancy is attributed to the assumptions made in the numerical model. However, the overall agreement between the simulation and the experiment indicates that the proposed numerical approach is valid and reliable.
References include works by Zhou Gongong, Liu Xiaomin, and others, focusing on numerical analysis of stress waves and their propagation in various media.
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