A Model to Estimate Forces on Conical Penetrators Into Dry Porous Rock

Abstract

A model to predict the forces on conical-nosed penetrators for normal impact into dry rock targets is developed. The target medium is described by a linear hydrostat, a linear shear failure-pressure relation, and the material density. A cylindrical cavity expansion approximation to the target response permits one-dimensional wave propagation calculations in the radial coordinate. The equations of motion are reduced, via a similarity transformation, to a nonlinear ordinary differential equation. This equation is solved numerically by a shooting technique which employs an asymptotic expansion to the solution near the wave front. Results include stress wave profiles in the target and curves for the stress on the penetrator nose as a function of its velocity for a wide range of realistic target parameters. Finally, results from the theory are compared with the deceleration history of a penetrator in a field test and reasonable correlation is observed.