Calculation of Air Shock Wave Pressure on the Back of an Explosive Flying Plate Colliding with a Thick Steel Plate

When the explosive flying plate collided with the thick steel plate, Zhou Tingqing, Wang Fengying, and Liu Tiansheng from the Department of Modern Mechanics at the University of Science and Technology of China in Hefei (230026) and the Department of Environmental and Safety Engineering at North China Institute of Technology in Taiyuan (030051) conducted a numerical analysis of the free surface movement of the steel plate. The interface between the steel plate and the air was also used to simulate the spherical symmetry of the shock wave propagation in the air behind the steel plate. The results showed a good agreement with the actual measurements. The study focused on the stress wave generated in the thick steel plate due to the explosion-driven flying plate. While the calculation and propagation of the stress wave and its destructive effects were well handled, the behavior of the shock wave in the air on the back side of the steel plate remained challenging. To address this, the paper employed a two-dimensional axisymmetric dynamic finite element method to simulate the free surface motion of the thick steel plate under the impact of the explosive plate. By applying the condition of equal velocity between the steel plate and the air interface, a spherical symmetric numerical analysis of the shock wave propagation in the air was carried out. The overpressure distribution behind the thick steel plate as a function of distance was obtained, and the results matched well with experimental data. In the model, the explosive charge was assumed to be flat and thin, acting as the flying plate, while the thick steel plate served as the target. The air medium was considered as the surrounding environment. Due to the high velocity of the thin explosive plate upon impact, the collision was modeled as an inelastic process. The significant density difference between the steel plate and the air medium led to the assumption that the interaction between them was a short-lived surface contact, with minimal plastic deformation on the steel plate. Thus, the steel plate was treated as an elastic material during the stress wave transmission. The speed of the thin plate after the explosion was determined based on the principle of adiabatic expansion. The impulse generated by the explosion was used to calculate the velocity of the plate, taking into account the uneven distribution of the explosion energy. The mass of the thin plate and the conservation of momentum were also considered in the calculations. The impact pressure and duration on the thick steel plate were estimated using average values, and the resulting free surface velocity was calculated accordingly. A numerical analysis method was applied to simulate the collision process, and the thickness of the free surface was calculated based on the air shock wave pressure. The speed-time curve of the free surface of the steel plate was analyzed to understand the dynamic response. Using this data, the shock wave overpressure in the air behind the thick steel plate was calculated. At 0.005 seconds, the initial pressure time history curve of the shock wave in the air was obtained. At 45 degrees, the pressure distribution on the air interface of the thick steel plate was studied. The attenuation law of the shock wave with distance was compared to the case of an infinite medium. The results showed that the overpressure decreased significantly with distance. For example, when the shock wave moved 0.1 meters away from the steel plate, the peak overpressure dropped by nearly 20 times. Even at 5 meters, the overpressure was still relatively high, decreasing only slightly. A comparison between the calculated and experimental results showed that the measured overpressure was only slightly higher than the calculated value, with an error margin of about 0.013 atmospheres. This small discrepancy can be attributed to the assumptions made in the numerical model. Overall, the results from the proposed numerical model were in excellent agreement with the experimental data. References include works by Zhou Gongong, Liu Xiaomin, and others, focusing on numerical analysis of stress waves and their propagation in various media. The study contributes to a better understanding of shock wave dynamics and provides a reliable method for simulating such complex physical phenomena.

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