M.Sc Student | Rapoport Leonid |
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Subject | Analysis of Spherical Cavity Expansion in Elastic-plastic Media and its Relevance to Penetration Mechanics |

Department | Department of Mechanical Engineering |

Supervisor | Professor Emeritus Miles Rubin |

Full Thesis text |

This work is divided into two independent parts which focus attention on two different aspects of the problem of spherical cavity expansion.

The first part considers the initial small deformation response of an elastic - perfectly - plastic material to an abrupt loading on the cavity’s surface which initially causes plastic response in a region near the cavity. The cavity is bounded by an elastic - plastic boundary, a linear elastic response in a region bounded by the elastic - plastic boundary and by an elastic precursor, and the rest of the material which remains undisturbed. This stage of the expansion process, in which the elastic plastic boundary is propagating at a constant speed, is called “The starting problem” and it can be solved analytically to obtain the displacement fields in both regions. Two termination conditions for the problem will be examined and it will be seen that the starting problem terminates when either the jump in radial stress or the loading function vanishes at the elastic - plastic boundary.

In the second part of the work, a new approach to analyzing penetration mechanics will be compared to a classical one. Specifically, the analytical solution of an ovoid of Rankin shaped projectile penetrating a semi infinite elastic - perfectly plastic target will be used in order to examine the classical cavity expansion approach which uses the steady state solution of a spherical cavity expansion problem in order to find the pressure acting on the projectile’s surface. It is shown that for penetration speeds less than a critical value the target material remains in contact with the projectile, the drag due to inertia vanishes and the drag force due to plastic flow is constant. In contrast, for penetration speeds above this critical value the target material separates from the projectile and the drag force due to inertia depends quadratically on the penetration speed. Moreover, it is shown that in the classical cavity expansion model the drag force acting on the projectile depends on the speed of penetration even at velocities for which the target remains in full contact with the projectile, thus questioning the physical validity of the classical approach.