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Effect of frictional force and nose shape on axisymmetric deformations of a thick thermoviscoplastic target

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Summary

We study thermomechanical deformations of a thermally softening viscoplastic thick target impacted at normal incidence by a cylindrical rod made of a material considerably harder than the target material. Thus we regard the penetrator to be rigid and analyze the effect of the penetrator nose shape and the frictional force at the target/penetrator interface on target's deformations. In the postulated expression for the frictional force, the coefficient of friction, defined as the ratio of the tangential force at a point to the normal force there, is a function of the relative speed of sliding between the two bodies. The computed depth of penetration is found to match very well with that observed in experiments by Forrestal et al. For each nose shape studied, the consideration of frictional forces reduces significantly the computed penetration depth. For the same kinetic energy of the penetrator, the penetrator with a sharp nose gives higher values of the penetration depth as compared to that obtained with a blunt nose.

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References

  1. Longcope, D. B., Forrestal, M. J.: Penetration of targets described by a Mohr-Coulomb failure criterion with a tension cutoff. J. Appl. Mech.50, 327–333 (1983).

    Google Scholar 

  2. Forrestal, M. J.: Penetration into dry porous rock. Int. J. Solids Struct.22, 1485–1500 (1986).

    Google Scholar 

  3. Chen, E. P.: Penetration into dry porous rock: a numerical study on sliding friction simulation. Theoret. and Appl. Fract. Mech.11, 135–141 (1989).

    Google Scholar 

  4. Chen, X., Batra, R. C.: Effect of frictional force on the steady state axisymmetric deformations of a viscoplastic target. Acta Mech.97, 153–168 (1993).

    Google Scholar 

  5. Forrestal, M. J., Brar, N. S., Luk, V. K.: Penetration of strain-hardening targets with rigid sphericalnosed rods. J. Appl. Mech.58, 7–10 (1991).

    Google Scholar 

  6. Backman, M. E., Goldsmith, W.: The mechanics of penetration of projectiles into targets. Int. J. Eng. Sci.16, 1–99 (1978).

    Google Scholar 

  7. Wright, T. W., Frank, K.: Approaches to penetration problems. In: Impact: effects of fast transient loading (Ammann, W. J., Lui, W. K., Studer, J. A., Zimmermann, T., eds.), Rotterdam: Balkema, A. A. 1988.

    Google Scholar 

  8. Anderson, C. E., Bodner, S. R.: The status of ballistic impact modelling. Proc. 3rd TACOM Armor Coordinating Conf., Feb. 17–19, 1987, Monterey, CA.

  9. Zukas, J. A., Nicholas, T., Swift, H. F., Greszczuk, L. B., Curran, D. R.: Impact dynamics. New York: Wiley-Interscience 1982.

    Google Scholar 

  10. Blazynski, T. Z.: In: Materials at high strain rates (Blazynski, T. Z., ed) London New York: Elsevier 1987.

    Google Scholar 

  11. MaCauley, M.: Introduction to impact engineering, London New York: Chapman and Hall 1987.

    Google Scholar 

  12. Zukas, J. A.: High velocity impact dynamics. New York: Wiley 1990.

    Google Scholar 

  13. Awerbuch, J., Bodner, S. R.: Analysis of the mechanics of perforation of projectiles in metallic plates. Int. J. Solids Struct.10, 671–684 (1974).

    Google Scholar 

  14. Ravid, M., Bodner, S. R.: Dynamic perforation of viscoplastic plates by rigid projectiles. Int. J. Eng. Sci.21, 577–591 (1983).

    Google Scholar 

  15. Ravid, M., Bodner, S. R., Holcman, I.: Analysis of very high speed impact. Int. J. Eng. Sci.25, 473–482 (1987).

    Google Scholar 

  16. 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).

    Google Scholar 

  17. Batra, R. C., Chen, X.: An approximate analysis of steady axisymmetric deformations of viscoplastic targets. Int. J. Eng. Sci.28, 1347–1358 (1990).

    Google Scholar 

  18. Batra, R. C.: Steady state penetration of thermoviscoplastic targets. Comp. Mech.3, 1–12 (1988).

    Google Scholar 

  19. Batra, R. C., Jayachandran, R.: Effect of constitutive models on steady state axisymmetric deformations of thermoelastic viscoplastic targets. Int. J. Impact Eng.12, 209–226 (1992).

    Google Scholar 

  20. Batra, R. C., Gobinath, T.: Steady state axisymmetric deformations of a thermoviscoplastic rod penetrating a thick thermoviscoplastic target. Int. J. Impact Eng.11, 1–31 (1991).

    Google Scholar 

  21. Chen, X., Batra, R. C.: Deep penetration of thick thermoviscoplastic target by long rigid rods. (Submitted for publication).

  22. Batra, R. C., Lin, P. R.: Steady state axisymmetric deformations of a thermoviscoplastic rod striking a hemispherical rigid cavity. Int. J. Impact Eng.8, 99–113 (1989).

    Google Scholar 

  23. Batra, R. C., Liu, D. S.: Adiabatic shear banding in plane strain problems. J. Appl. Mech.56, 527–534 (1989).

    Google Scholar 

  24. Lysmer, J., Kuhlemeyer, R. L.: Finite dynamic model for infinite media. ASCE J. Eng. Mech.95, 859–877 (1969).

    Google Scholar 

  25. Hallquist, J. O., Goudreau, G. L., Benson, D. J.: Sliding interfaces with contact-impact in large-scale Lagrangian computations. Comp. Meth. Appl. Mech. Eng.51, 107–137 (1985).

    Google Scholar 

  26. Bathe, K. J.: Finite element procedures in engineering analysis. Englewood Cliffs: Prentice-Hall 1982.

    Google Scholar 

  27. Bai, Y., Dodd, B.: Adiabatic shear localization: occurrence, theories, and applications. New York: Pergamon Press 1992.

    Google Scholar 

  28. Chen, X.: Finite element analysis of axisymmetric deformations of thick thermoviscoplastic targets. Ph. D. dissertation, University of Missouri-Rolla 1993.

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Batra, R.C., Chen, X. Effect of frictional force and nose shape on axisymmetric deformations of a thick thermoviscoplastic target. Acta Mechanica 106, 87–105 (1994). https://doi.org/10.1007/BF01300946

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