Singular Plastic Fields in Steady Penetration of a Rigid Cone

Abstract

The essential features of the active plastic zone at the tip of a penetrating rigid cone are investigated for a rigid/perfectly plastic solid. An exact solution is suggested for the plastic zone. A rigid zone exists ahead of the cone and is separated from the plastic zone by a conical surface of discontinuity. It is assumed that the material yields instantaneously by going through a “shear shock” across the rigid/plastic interface. The orientation of the interface is determined by an ad hoc requirement for minimum shear strain jump at the shear shock. Results are presented for different cone angles and friction factors. The stresses within the plastic zone admit a logarithmic singularity whose level increases with cone angle and wall friction.