A dynamic expansion of a cylindrical cavity in a compressible elastic-plastic medium. The analysis of medium resistance to dynamic penetration of a sharp-nosed impactor

This paper presents the solution of the problem related to the dynamic cylindrical cavity expansion in a compressible elastic-plastic medium. Finite strains, nonlinear compressibility and dependence of the yield stress versus pressure are taken into account in the problem formulation. The study targets at developing a new engineering model on the penetration of a sharp-nosed impactor in the range of middle impact velocities based on the problem analysis results of the cylindrical cavity expansion in a half-space (cylindrical cavity expansion approximation). Based on the analytical approach a model is obtained that determines the resistance of the medium to dynamic cavity expansion. The main parameters of the model depend on the mechanical properties of the medium. For these dependences we proposed approximating relations based on manipulation of the mechanical properties of a number of materials (some alloys and soils). To derive the dynamic penetration model the A.Ya. Sagomonyan assumption of the radial expansion of the hole is used. It is assumed that particles of the medium material move in a radial direction from the surface of the impactor penetrating into the shield. Such assumption can be applied for the class of impactors in the form of slender sharp-nosed bodies of revolution. Based on the assumptions we obtained a model of the medium resistance to the dynamic penetration of a slender sharp-nosed body of revolution. The new model, in addition to the "standard" strength and inertial components, contains the "attached mass", which changes during the penetration process. The experimental validation of the new penetration model using a series of experimental studies on the penetration of various forms of impactors into aluminum alloys is considered. The influence of the “attached mass” and inertial forces of the medium resistance to the penetration is estimated. The conditions of applicability of the new model are obtained: the penetration model is applicable for estimation of the resistance of a compressible medium to penetration of a thin sharp-nosed body of revolution at impact velocities of 200-800 m/s.