### Abstract

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.

Original language | English |
---|---|

Pages (from-to) | 801-831 |

Number of pages | 31 |

Journal | International Journal of Impact Engineering |

Volume | 16 |

Issue number | 5-6 |

Publication status | Published - 1995 Oct 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality
- Ocean Engineering
- Mechanics of Materials
- Mechanical Engineering
- Civil and Structural Engineering
- Automotive Engineering
- Aerospace Engineering

### Cite this

*International Journal of Impact Engineering*,

*16*(5-6), 801-831.

**Penetration of a rigid projectile into an elastic-plastic target of finite thickness.** / Yarin, Alexander; Rubin, M. B.; Roisman, I. V.

Research output: Contribution to journal › Article

*International Journal of Impact Engineering*, vol. 16, no. 5-6, pp. 801-831.

}

TY - JOUR

T1 - Penetration of a rigid projectile into an elastic-plastic target of finite thickness

AU - Yarin, Alexander

AU - Rubin, M. B.

AU - Roisman, I. V.

PY - 1995/10/1

Y1 - 1995/10/1

N2 - This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.

AB - This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.

UR - http://www.scopus.com/inward/record.url?scp=0001698337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001698337&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 801

EP - 831

JO - International Journal of Impact Engineering

JF - International Journal of Impact Engineering

SN - 0734-743X

IS - 5-6

ER -