Steady State Axisymmetric Deformations of a Thermoviscoplastic Rod Penetrating a Thick Thermoviscoplastic Target

The coupled nonlinear partial differential equations governing the thermomechanical and axisymmetric deformations, of a cylindrical rod penetrating into a thick target, also made of a rigid/viscoplastic material, are solved by the finite element method. It is assumed that the deformations of the target and the penetrator as seen by an observer situated at the stagnation point and moving with it are independent of time. Both the rod and the target material are assumed to exhibit strain-rate hardening and thermal softening, and the contact between the penetrator and the target at the common interface is smooth. An effort has been made to assess the effect of the strain-rate hardening and thermal softening on the deformations of the target and the penetrator. It is found that the axial resisting force experienced by the penetrator, the shape and location of the free surface of the deformed penetrator and the target/penetrator interface, and normal tractions on this common interface depend rather strongly upon the speed of the stagnation point and hence on the speed of the striking rod. Results presented graphically include the distribution of the velocity field, the temperature change, the hydrostatic pressure and the second-invariant of the strain-rate tensor. In an attempt to help establish desirable testing regimes for determining constitutive relations appropriate for penetration problems, we also find histories of the effective stress, hydrostatic pressure, temperature and the second invariant of the strain-rate tensor experienced by four penetrator and two target particles.