Plate tearing by a cone

The present paper is concerned with steady-state plate tearing by a cone. This is a scenario where a cone is forced through a ductile metal plate with a constant lateral tip penetration in a motion in the plane of the plate. The considered process could be an idealisation of the damage, which develops in a ship bottom raking accident or a collision with a floating object. The deformation involves a complex mixture of large plastic deformations, fracture and friction. The observed mode of deformation is idealised by a simplified, kinematically admissible deformation mode, and the rate of internal energy dissipation in plasticity, fracture and friction is quantified accordingly by analytical expressions. The idealised mode has two free parameters which are determined from the postulate that they adjust to give the least rate of energy dissipation. The theory is compared to a series of measurements. The coefficient of friction was not measured, so the calculations are presented for different realistic values and it is shown that, for a coefficient of friction of about 0.2, there is a reasonably good agreement between theory and measurements for the in-plane resistance force as well as for the out-of-plane reaction force.