Summary
Steady state axisymmetric deformations of an elastic perfectly plastic target being penetrated by a fast moving rigid cylindrical rod have been analyzed by the finite element method. The target is assumed to obey the von Mises yield criterion and the associated flow rule. Contact between target and penetrator has been assumed to be smooth. A mixed formulation, in which two components of the velocity and four components of the deviatoric stress tensor at each node point, and the hydrostatic pressure at the centroid of an element are taken as unknowns, is employed. This should give a better estimate of tractions acting on the penetrator nose, and hence of the axial resisting force experienced by the penetrator. The effect of the penetrator speed, its nose shape and the elasticity of the target material on the target deformations, and the axial force experienced by the penetrator, has been studied. The consideration of elastic effects helps delineate the elastic-plastic boundary in the target.
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References
Backman, M. E., Goldsmith, W.: The mechanics of penetration of projectiles into targets. Int. J. Engng. Sci.16, 1–99 (1978).
Wright, T. W., Frank, K.: Approaches to penetration problems. SMIRT Symposium, No. 14, Impact. Lausanne, Switzerland 1987.
Anderson, C. E., Bodner, S. R.: The status of ballistic impact modelling. Int. J. Impact Engng.7, 9–35 (1985).
Zukas, J. A. et al.: Impact dynamics. New York: Wiley-Interscience 1982.
Blazynski, T. Z. In: Materials at high strain rates (Blazynski, T. Z., ed.) London, New York: Elsevier (1987).
MaCauley, M.: Introduction to impact engineering. London, New York: Chapman and Hall 1987.
Awerbuch, J.: Technion-Israel Institute of Technology. MED Report No. 28 (1970).
Awerbuch, J., Bodner, S. R.: Analysis of the mechanics of perforation of projectiles in metallic plates. Int. J. Solids Struct.10, 671–684 (1974).
Ravid, M., Bodner, S. R.: Dynamic perforation of viscoplastic plates by rigid projectiles. Int. J. Engng. Sci.21, 577–591 (1983).
Ravid, M., Bodner, S. R., Holeman, I.: Analysis of very high speed impact. Int. J. Engng. Sci.25, 473–482 (1987).
Forrestal M. J., Okajima, K., Luk, V. K.: Penetration of 6061-T651 Aluminum targets with rigid long rods. J. Appl. Mech.55, 755–760 (1988).
Batra, R. C., Chen, X.: An approximate analysis of steady state axisymmetric deformations of viscoplastic targets. Int. J. Engng. Sci.28, 1347–1358 (1990).
Birkhoff, G., MacDougall, D. P., Pugh, E. M., Taylor, G.: Explosives with lined cavities. J. Appl. Phys.19, 563–582 (1948).
Pack, D. C., Evans, W. M.: Penetration by high-velocity jets. Proc. Phys. Soc. Lond. B64, 298–310 (1951).
Allen, W. A., Rogers, J. W.: Penetration of a rod into a semi-infinite target. J. Franklin Inst.272, 275–284 (1961).
Alekseevskii, V. P.: Penetration of a rod into a target at high velocity. Comb. Expl. and Shock Waves2, 63–66 (1966). (Translation from Russian, Faraday Press, New York)
Tate, A.: A theory for the deceleration of long rods after impact. J. Mech. Phys. Solids15, 387–399 (1967).
Tate, A.: Further results in the theory of long rod penetration. J. Mech. Phys. Solids17, 141–150 (1969).
Tate, A.: Long rod penetration models. Part I. A, flow field model for high speed long rod penetration. Int. J. Mech. Sci.28, 535–548 (1986).
Tate, A.: Long rod penetration models. Part II. Extensions to the hydrodynamic theory of penetration. Int. J. Mech. Sci.28, 599–612 (1986).
Tate, A.: A simple hydrodynamic model for the strain field in a target by the penetration of a high speed long rod projectile. Int. J. Engng. Sci.16, 845–858 (1978).
Pidsley, P. H.: A numerical study of long rod impact onto a large target. J. Mech. Phys. Solids32, 315–333 (1984).
Batra, R. C., Gobinath, T.: Steady state axisymmetric deformations of a thermoviscoplastic rod penetrating a thick thermoviscoplastic target. Int. J. Impact Engng.11, 1–31 (1991).
Gobinath, T., Batra, R. C.: A steady state axisymmetric penetration problem for rigid perfectly plastic materials. Int. J. Engng. Sci.29, 1315–1331 (1991).
Batra, R. C., Wright, T. W.: Steady state penetration of rigid perfectly plastic targets. Int. j. Engng. Sci.24, 41–54 (1986).
Batra, R. C.: Steady state penetration of viscoplastic targets. Int. J. Engng. Sci.25, 1131–1411 (1987).
Batra, R. C.: Steady state penetration of thermoviscoplastic targets. Comp. Mech.3, 1–12 (1988).
Batra, R. C., Lin, P. R.: Steady state deformations of a rigid perfectly plastic rod striking a rigid cavity. Int. J. Engng. Sci.26, 183–192 (1988).
Batra, R. C., Lin, P. R.: Steady state axisymmetric deformations of a thermoviscoplastic rod striking a hemispherical rigid cavity. Int. J. Impact Engng.8, 99–113 (1989).
Batra, R. C., Lin, P. R.: Histories of stress, temperature and spin in steady state deformations of a thermoviscoplastic rod striking a hemispherical rigid cavity. Int. J. Engng. Sci.28, 93–98 (1990).
Lin, P. R., Batra, R. C.: Histories of stress, strain-rate, temperature, and spin in steady state penetration problems. Int. J. Engng. Sci.27, 1155–1165 (1989).
Shimazaki, Y., Thompson, E. G.: Elasto, visco-plastic flow with special attention to boundary conditions. Int. J. Num. Meth. Engng.17, 97–112 (1981).
Hughes, T. J. R.: The finite element method. Linear static and dynamic problems. Englewood Cliffs: Prentice-Hall 1987.
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Jayachandran, R., Batra, R.C. Steady state penetration of elastic perfectly plastic targets. Acta Mechanica 92, 9–27 (1992). https://doi.org/10.1007/BF01174164
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DOI: https://doi.org/10.1007/BF01174164