Acceleration Characteristics of Discrete Fragments Generated from Explosively-Driven Cylindrical Metal Shells
Abstract
:1. Introduction
2. Theoretical Analysis
2.1. Equation of Motion
- The explosive detonates instantaneously, after which the detonation gas inside the shell has a uniform density of ρ. The velocity of the detonation gas increases linearly from the charge center to the inner surface of the shell, as shown in Figure 1b. Then, for any radial position r inside the shell, we have
- The shell fractures radially. After the shell ruptures, fragments scatter at the same radial velocity with a fixed orientation. The mass loss of the fragments during the explosion is neglected.
- The cylindrical shell is assumed to be infinite. We investigate the motion of the detonation gas and the shell cut out from the central part of the shell, where the end effect induced by the rarefaction wave can be neglected. Thus, the problem can be treated as a two-dimensional (2D) problem.
2.2. Pre-Disintegration Acceleration
2.3. Post-Disintegration Acceleration
2.3.1. Equation for Locally Isentropic Expansion
2.3.2. Model of Gas Leakage
3. Verification of Theoretical Model
3.1. Natural Fragment Acceleration
3.2. Preformed Fragment Acceleration
3.2.1. Numerical Simulation Model
3.2.2. Verification of Fragment Acceleration
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Numbers | Fragment Type | The Critical Parameter Values for Calculation | ||||||
R0 (m) | Rf (m) | β | γ | D (m/s) | Vf (m/s) 1 | Step | ||
1-1 | Natural fragment | 0.025 | 0.04575 | 0.4 | 3 | 6700 | 1167 | 1% R/R0 |
1-2 | Preformed fragment | 0.06302 | 0.0818 | 0.926 | 3 | 8200 | 1610 | 1% R/R0 |
Numbers | Fragment Type | Final Fragment Velocity (m/s) | ||||||
Gurney Formula [1] | Theoretical Prediction | Experimental Data [4,14] | Charron Formula [24] | Kim Formula [25] | Numerical Simulation | Error | ||
1-1 | Natural fragment | 1330 | 1209 | 1231 [4] | — | — | — | 1.79% |
1-2 | Preformed fragment | 2243 | 1915 | 1970 [14] | 2073 | 1810 | 1990 2, 2000 3 | 2.79% |
Density (g/cm3) | Detonation Velocity (D, m/s) | C-J Pressure (GPa) | E0 (kJ/m3) | C1 (GPa) | C2 (GPa) | r1 | r2 | ω |
---|---|---|---|---|---|---|---|---|
1.776 | 8210 | 31.1 | 8.9 × 106 | 700 | 12.12 | 4.5 | 1.1 | 0.3 |
Material | Density (g/cm3) | A (MPa) | B (MPa) | n | C | m | Tmelt (K) |
---|---|---|---|---|---|---|---|
1018 steel | 7.9 | 735 | 309 | 0.44 | 0.0064 | 1.05 | 1793 |
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Zhou, M.; Wu, C.; An, F.; Liao, S.; Yuan, X.; Xue, D.; Liu, J. Acceleration Characteristics of Discrete Fragments Generated from Explosively-Driven Cylindrical Metal Shells. Materials 2020, 13, 2066. https://doi.org/10.3390/ma13092066
Zhou M, Wu C, An F, Liao S, Yuan X, Xue D, Liu J. Acceleration Characteristics of Discrete Fragments Generated from Explosively-Driven Cylindrical Metal Shells. Materials. 2020; 13(9):2066. https://doi.org/10.3390/ma13092066
Chicago/Turabian StyleZhou, Mingxue, Cheng Wu, Fengjiang An, Shasha Liao, Xiaoxia Yuan, Dongyu Xue, and Jian Liu. 2020. "Acceleration Characteristics of Discrete Fragments Generated from Explosively-Driven Cylindrical Metal Shells" Materials 13, no. 9: 2066. https://doi.org/10.3390/ma13092066