An elementary theory of one-dimensional rod penetration using a new estimate for pressure |
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| Affiliation: | 1. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China;2. Institute for Problems of Metals Superplasticity, Russian Academy of Sciences, Khalturina 39, Ufa 450001, Russia;3. Research Laboratory for Mechanics of New Nanomaterials St. Petersburg State Polytechnical University, Polytechnicheskaya 29 St. Petersburg, 195251, Russia;4. Institute of Physics of Advanced Materials, Ufa State Aviation Technical University, 12K. Marx Street, Ufa 450000, Russia;5. Materials Research Group, Faculty of Engineering and the Environment University of Southampton, Southampton SO17 1BJ, UK;1. National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials, South China University of Technology, Guangzhou 510640, PR China;2. National Engineering Research Center of Powder Metallurgy of Titanium & Rare Metals, Guangdong Institute of Materials and Processing, Guangzhou 510650, PR China;1. Institute of Thermomechanics AS CR, v.v.i., Department of Impact and Waves in Solids, Dolejskova 5, 182 00 Prague 8, Czech Republic;2. NTIS — New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, 306 14 Pilsen, Czech Republic |
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| Abstract: | In this paper, a new pressure law is proposed to replace the modified Bernoulli equation of Tate in 1967 and 1969. It is achieved by decomposing the equation of motion, which was proposed by Jones et al. in 1987, into two parts and incorporating the kinematic equation by Wilson et al. in 1989. The new pressure law takes the effect of mushroom strain into account. From two different considerations, the pressure law is applied to the one-dimensional penetration modeling. First, by assuming that the rod/target interface pressure is approximately constant during the quasi-steady state, the governing equations can be analytically integrated to give a closed form solution for the penetration depth. The prediction is reasonably good in the low velocity regime. Secondly, a velocity-dependent interface pressure is added. A so-called shape factor, which was first introduced without physical interpretation by Alekseevskii in 1966, is substantiated. With this factor, the governing equations can be numerically integrated to give very accurate predictions for the impact velocity range from 1 km/s to 4 km/s. |
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