Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

doi:10.1007/s10483-014-1842-7

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (8): 1039-1050.doi: https://doi.org/10.1007/s10483-014-1842-7

Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

甄明, 蒋志刚, 宋殿义, 刘飞

College of Basic Education, National University of Defense Technology, Changsha 410073, P. R. China

收稿日期:2013-07-10 修回日期:2013-11-14 出版日期:2014-08-01 发布日期:2014-08-01
通讯作者: Zhi-gang JIANG, Professor, Ph.D., E-mail: 13508489165@163.com E-mail:13508489165@163.com
基金资助:
Project supported by the Research Project of National University of Defense Technology (No. S130901)

Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

Ming ZHEN, Zhi-gang JIANG, Dian-yi SONG, Fei LIU

College of Basic Education, National University of Defense Technology, Changsha 410073, P. R. China

Received:2013-07-10 Revised:2013-11-14 Online:2014-08-01 Published:2014-08-01
Supported by:
Project supported by the Research Project of National University of Defense Technology (No. S130901)

摘要/Abstract

摘要： Analytical solutions for the dynamic cylindrical cavity expansion in a compressible elastic-plastic cylinder with a finite radius are developed by taking into account of the effect of lateral free boundary, which are different from the traditional cavity expansion models for targets with infinite dimensions. The finite cylindrical cavity expansion process begins with an elastic-plastic stage followed by a plastic stage. The elastic-plastic stage ends and the plastic stage starts when the plastic wave front reaches the lateral free boundary. Approximate solutions of radial stress on cavity wall are derived by using the Von-Mise yield criterion and Forrestal's similarity transformation method. The effects of the lateral free boundary and finite radius on the radial stress on the cavity wall are discussed, and comparisons are also conducted with the finite cylindrical cavity expansion in incompressible elastic-plastic materials. Numerical results show that the lateral free boundary has significant influence on the cavity expansion process and the radial stress on the cavity wall of metal cylinder with a finite radius.

关键词: penetration, cavity expansion, metal target, free boundary, radial stress

Abstract: Analytical solutions for the dynamic cylindrical cavity expansion in a compressible elastic-plastic cylinder with a finite radius are developed by taking into account of the effect of lateral free boundary, which are different from the traditional cavity expansion models for targets with infinite dimensions. The finite cylindrical cavity expansion process begins with an elastic-plastic stage followed by a plastic stage. The elastic-plastic stage ends and the plastic stage starts when the plastic wave front reaches the lateral free boundary. Approximate solutions of radial stress on cavity wall are derived by using the Von-Mise yield criterion and Forrestal's similarity transformation method. The effects of the lateral free boundary and finite radius on the radial stress on the cavity wall are discussed, and comparisons are also conducted with the finite cylindrical cavity expansion in incompressible elastic-plastic materials. Numerical results show that the lateral free boundary has significant influence on the cavity expansion process and the radial stress on the cavity wall of metal cylinder with a finite radius.

Key words: penetration, cavity expansion, metal target, free boundary, radial stress

中图分类号:

TU511

甄明;蒋志刚;宋殿义;刘飞. Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(8): 1039-1050.

Ming ZHEN;Zhi-gang JIANG;Dian-yi SONG;Fei LIU. Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(8): 1039-1050.

参考文献

[1] Forrestal, M. J., Longcope, D. B., and Norwood, F. R. A model to estimate forces on conical penetrators into dry porous rock. Journal of Applied Mechanics, 48, 25-29 (1981)
[2] Longcope, D. B. and Forrestal, M. J. Penetration of targets described by a Mohr-Coulomb failure criterion with a tension cutoff. Journal of Applied Mechanics, 50, 327-333 (1983)
[3] Forrestal, M. J. and Luk, V. K. Dynamic spherical cavity-expansion in a compressible elastic-plastic solid. Journal of Applied Mechanics, 55, 275-279 (1988)
[4] Forrestal, M. J., Luk, V. K., and Bar, N. S. Perforation of aluminum armor plates with conical-nose projectiles. Mechanics of Materials, 10, 97-105 (1990)
[5] Luk, V. K., Forrestal, M. J., and Amos, D. E. Dynamic spherical cavity expansion of strain-hardening materials. Journal of Applied Mechanics, 58, 1-6 (1991)
[6] Luk, V. K. and Amos, D. E. Dynamic cylindrical cavity expansion of compressible strain-hardening materials. Journal of Applied Mechanics, 58, 334-340 (1991)
[7] Warren, T. W. and Forrestal, M. J. Effects of harding and strain-rate sensitivity on penetration of aluminum targets with spherical-nosed rods. International Journal of Solids and Structures, 35, 3737-3753 (1998)
[8] Forrestal, M. J. and Warren, T. W. Penetration equations for ogive-nose rods into aluminum targets. International Journal of Impact Engineering, 35, 727-730 (2008)
[9] Forrestal, M. J. and Warren, T. W. Perforation equations for conical and ogival nose rigid pro-jectiles into aluminum target plates. International Journal of Impact Engineering, 36, 210-215 (2009)
[10] Rosenberg, Z. and Dekel, E. A numerical study of the cavity expansion process and its application to long-rod penetration mechanics. International Journal of Impact Engineering, 35, 147-154 (2008)
[11] Rosenberg, Z. and Dekel, E. Analytical solution of the spherical cavity expansion process. International Journal of Impact Engineering, 36, 193-198 (2009)
[12] Rosenberg, Z. and Dekel, E. The penetration of rigid rods-revisited. International Journal of Impact Engineering, 36, 551-564 (2009)
[13] Durban, D. and Masri, R. Dynamic spherical cavity expansion in an elastoplastic compressible Mises solid. International Journal of Solids and Structures, 41, 5697-5716 (2004)
[14] Masri, R. and Durban, D. Dynamic spherical cavity expansion in a pressure sensitive solid. Journal of Applied Mechanics, 72, 887-898 (2005)
[15] Masri, R. and Durban, D. Deep penetration analysis with dynamic cylindrical cavitation fields. International Journal of Impact Engineering, 36, 830-841 (2009)
[16] Littlefield, D. L., Anderson, C. E., Partom, Y., and Bless, S. J. The penetration of steel targets finite in radial extent. International Journal of Impact Engineering, 19, 49-62 (1997)
[17] Macek, R. W. and Duffey, T. A. Finite cavity expansion method for near-surface effects and layering during Earth penetration. International Journal of Impact Engineering, 24, 239-258 (2000)
[18] Jiang, Z. G., Zeng, S. Y., and Zhou, J. P. An analytical model for penetration into finite thickness metallic target struck by rigid sharp-nosed projectiles (in Chinese). Acta Armamentarii, 28(8), 923-929 (2007)
[19] Jiang, Z. G., Zeng, S. Y., and Zhou, J. P. A Three-stage model for the perforation of moderately thick metallic plates (in Chinese). Acta Armamentarii, 28(9), 1046-1052 (2007)
[20] Jiang, Z. G., Song, D. Y., and Zeng, S. Y. A finite cylindrical cavity expansion theory and its application (in Chinese). Journal of Vibration and Shock, 30(4), 139-143 (2011)
[21] Song, D. Y., Liu, F., and Jiang, Z. G. An analytical model for penetration into cylindrical metallic thick target by rigid sharp-nosed projectiles (in Chinese). Engineering Mechanics, 31(1), 31-36 (2013)
[22] Jiang, Z. G., Song, D. Y., and Liu, F. A finite cylindrical cavity expansion and penetration model of exponential strain-hardening materials. Advanced Materials Research, 634-638, 2781-2786 (2013)

Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

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