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Based on the linear hardening plastic constitutive model, the theoretical solution of the elastic-plastic spherical stress wave field under impact load is established. Firstly, the influence of the impact load unloading rate on the propagation of the spherical stress wave is analyzed, and three different types of propagation images are obtained. On this basis, the method of theoretically calculating the spherical wave equation in elastic stage, plastic loading stage and unloading stage is established separately, and the calculation scheme of particle displacement, particle velocity, stress and strain is given. Compared with the existing theoretical methods, this method takes into account the different propagation patterns of the stress waves under different unloading rates, and shows how to calculate the stress wave parameters in unloading stage, which is more applicable. This method is used to calculate the elastic-plastic spherical stress wave field under constant shock load and exponential attenuation shock load. The calculated results are in good agreement with those from the existing theoretical method and numerical simulation results in the elastic stage and also in the plastic loading stage. In the unloading stage, the existing theoretical method is no longer applicable, while the results obtained in this paper are in good agreement with the numerical simulation results, which verifies the correctness of the theoretical method.
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Keywords:
- elastic-plastic /
- spherical stress wave /
- linear hardening model /
- unloading rate
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Li X L 2000 Explo. Shock Waves 20 186
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Deng D Q, Li Z Q 1992 Proceedings of the 3rd National Conference on Rock Dynamics Guilin, 1992 p152 (in Chinese)
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Xiao J H, Sun W T 1997 Oil Geophys. Prospect. 32 809
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Google Scholar
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Wang L L 2005 Foundation of Stress Waves (2nd Ed.) (Beijing: National Defense Industry Press) p236 (in Chinese)
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图 1 畸变律曲线
Figure 1. Curve of the distortion law.
图 2 应力波传播示意图 (a) 载荷卸载较快; (b) 载荷卸载较慢; (c) 载荷卸载速率介于上述二者之间
Figure 2. Schematic diagrams of the stress wave propagation (a) Rapid unloading; (b) slow unloading; (c) middle unloading.
图 3 网格无关性 (a) 空腔壁面位移时间历程; (b) 径向应力空间分布
Figure 3. Gird independence: (a) Time history of the cavity surface displacement; (b) radial stress distribution.
图 4 径向应力时间历程 (a) r = 0.5 m; (b) r = 0.8 m; (c) r = 1.4 m和径向应力空间分布 (d) t = 0.1 ms; (e) t = 0.2 ms; (f) t = 0.3 ms (恒定冲击载荷)
Figure 4. Time history of the radial stress: (a) r = 0.5 m; (b) r = 0.8 m; (c) r = 1.4 m and the radial stress distribution: (d) t = 0.1 ms; (e) t = 0.2 ms; (f) t = 0.3 ms (constant impact loading).
图 5 径向应力时间历程 (a) r = 0.3 m; (b) r = 0.5 m; (c) r = 0.6 m和径向应力空间分布 (d) t = 0.05 ms; (e) t = 0.2 ms; (f) t = 0.6 ms (T0 = 0.01 ms)
Figure 5. Time history of the radial stress: (a) r = 0.3 m; (b) r = 0.5 m; (c) r = 0.6 m and the radial stress distribution: (d) t = 0.05 ms; (e) t = 0.2 ms; (f) t = 0.6 ms (T0 = 0.01 ms).
图 7 径向应力时间历程 (a) r = 0.4 m; (b) r = 0.6 m; (c) r = 0.7 m和径向应力空间分布 (d) t = 0.1 ms; (e) t = 0.2 ms; (f) t = 0.6 ms (T0 = 0.03 ms)
Figure 7. Time history of the radial stress: (a) r = 0.4 m; (b) r = 0.6 m; (c) r = 0.7 m; and the radial stress distribution: (d) t = 0.1 ms; (e) t = 0.2 ms; (f) t = 0.6 ms (T0 = 0.03 ms).
图 6 径向应力时间历程 (a) r = 0.5 m; (b) r = 0.75 m; (c) r = 1.25 m和径向应力空间分布 (d) t = 0.1 ms; (e) t = 0.2 ms; (f) t = 0.6 ms (T0 = 0.2 ms)
Figure 6. Time history of the radial stress: (a) r = 0.5 m; (b) r = 0.75 m; (c) r = 1.25 m and the radial stress distribution: (d) t = 0.1 ms; (e) t = 0.2 ms; (f) t = 0.6 ms (T0 = 0.2 ms).
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[1] Wlodarczyk E, Zielenkiewicz M 2009 J. Theor. App. Mech. 47 127
[2] Wlodarczyk E, Zielenkiewicz M 2009 J. Theor. App. Mech. 47 761
[3] Wlodarczyk E, Zielenkiewicz M 2009 Shock Waves 18 465
Google Scholar
[4] Wlodarczyk E, Zielenkiewicz M 2011 J. Theor. App. Mech. 49 457
[5] Biswas S 2021 Indian J. Phys. 95 705
Google Scholar
[6] 李孝兰 2000 爆炸与冲击 20 186
Google Scholar
Li X L 2000 Explo. Shock Waves 20 186
Google Scholar
[7] 李孝兰 2000 爆炸与冲击 20 283
Google Scholar
Li X L 2000 Explo. Shock Waves 20 283
Google Scholar
[8] 肖建华 2001 石油地球物理勘探 36 160
Google Scholar
Xiao J H 2001 Oil Geophys. Prospect. 36 160
Google Scholar
[9] 肖建华 2004 石油地球物理勘探 39 249
Google Scholar
Xiao J H 2004 Oil Geophys. Prospect. 39 249
Google Scholar
[10] Xu C J, Chen Q Z, Zhou J, Cai Y Q 2015 J. Civ. Eng. 19 2035
Google Scholar
[11] 卢强, 王占江, 王礼立, 赖华伟, 杨黎明 2013 爆炸与冲击 33 463
Google Scholar
Lu Q, Wang Z J, Wang L L, Lai H W, Yang L M 2013 Explo. Shock Waves 33 463
Google Scholar
[12] 卢强, 王占江 2015 物理学报 64 108301
Google Scholar
Lu Q, Wang Z J 2015 Acta Phys. Sin. 64 108301
Google Scholar
[13] Lu Q, Wang Z J 2016 J. Sound Vib. 371 183
Google Scholar
[14] 邓德全, 李兆权 1992 第三届全国岩石动力学学术会议论文集, 桂林, 1992, 第152页
Deng D Q, Li Z Q 1992 Proceedings of the 3rd National Conference on Rock Dynamics Guilin, 1992 p152 (in Chinese)
[15] 赖华伟, 王占江, 杨黎明, 王礼立 2013 爆炸与冲击 33 1
Google Scholar
Lai H W, Wang Z J, Yang L M, Wang L L 2013 Explo. Shock Waves 33 1
Google Scholar
[16] Yang C Y 1970 Int. J. Solids Struct. 6 757
Google Scholar
[17] Morland L W 1971 J. Mech. Phys. Solids 19 295
Google Scholar
[18] Milne P C, Morland L W, Yeung W 1988 J. Mech. Phys. Solids 36 15
Google Scholar
[19] Milne P C, Morland L W 1988 J. Mech. Phys. Solids 36 215
Google Scholar
[20] Rapoport L, Katzir Z, Rubin M B 2011 Wave Motion 48 441
Google Scholar
[21] Santos T, Brezolin A, Rossi R, Rodriguez-Martinez J A 2020 Acta Mech. 231 2381
Google Scholar
[22] 肖建华, 孙文涛 1997 石油地球物理勘探 32 809
Xiao J H, Sun W T 1997 Oil Geophys. Prospect. 32 809
[23] Chen S, Wu J, Zhang Z 2017 J. Eng. Mech. 143 04017034
Google Scholar
[24] 王礼立 2005 应力波基础 (第二版) (北京: 国防工业出版社) 第236页
Wang L L 2005 Foundation of Stress Waves (2nd Ed.) (Beijing: National Defense Industry Press) p236 (in Chinese)
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