Analytical and numerical description of the PELE fragmentation upon impact with thin target plates

• Analytical model describing fragmentation of PELE ammunition.
• Rankine–Hugoniot relations and wave interactions must be used including the radial rarefaction.
• The model provides fragment mass, size and velocity at any axial position.
• Quantitative and qualitative agreement with experiments is reached.
• Assumptions of the model are verified via numerical simulations.

The PELE ammunition is characterized by a low-density filling material surrounded by a high-density brittle jacket material. An analytical model describing the fragmentation of this ammunition behind a target plate is presented. This model assumes uniaxial strain in the filling and uses the Ranking–Hugoniot relations to calculate the material state. In addition, shock and rarefaction wave interactions at the target free surface and the filling/target interface are accounted for, as well as the radial rarefaction originating from the jacket outer surface. This allows the calculation of the pressure evolution in the filling and the radial acceleration of the jacket at any axial position along the projectile. This model aims at improving previously published analytical models where the acoustic wave approximation was used and the wave interactions were neglected. Experimental results (Paulus and Schirm, 2006) are used to validate the analytical model for different target materials (aluminum and steel), target thicknesses (3 mm and 8 mm), filling materials (polyethylene and aluminum) and impact velocities (900 m/s to 3000 m/s). A qualitative comparison based on X-ray photographs reveals similar features between the model and the experiments, such as smaller and lighter fragments with a greater radial velocity at the front of the projectile compared to the fragment characteristics at the back of the projectile. A quantitative comparison based on the maximum radial velocity of the fragments shows on average a 20% difference between the analytical and experimental results for all impact conditions considered. Despite this difference, the analytical trend follows more closely the experimental one compared to the acoustic approximation especially at high impact velocities. In addition, the acoustic approximation fails to reproduce the jacket fragmentation pattern since the fragmentation length of the jacket is significantly under-predicted. A numerical simulation is also presented using the ANSYS Autodyn 14.0 software. The results show that the numerical and analytical pressure evolution in the filling and the radial velocity of the jacket are in very good agreement, verifying the uniaxial strain assumption. This agreement (together with the experimental agreement) thus suggests that the Rankine–Hugoniot relations, the wave interactions and the radial rarefaction wave must all be included in the model to adequately describe the fragmentation of the PELE ammunition behind a thin target plate.