An Estimate of Penetration Depth of Rigid Rods Through Materials Susceptible to Microcracking: Part 1 - Theory

Abstract

The present study proposes an approximate model focused on a simplified estimate of depth of penetration of rigid projectiles into quasibrittle solids. Penetration at normal incidence of a slender, rigid rod into massive targets, made of materials predisposed to microcracking due to their inferior tensile strength and heterogeneous structure, is an event characterized by a high level of aleatory variability and epistemic uncertainty. This inherent stochasticity is incorporated into a model developed based on particle dynamics simulations that provide the key modeling ingredient – an estimate of the radial traction necessary to dynamically expand a cylindrical cavity. The penetration depth expressions are derived for the conical and ogive nose projectiles. The related theoretical considerations for spherical nose projectiles are developed to the point where using the cylindrical cavity approximation becomes debatable. The novel use of the power-law radial traction dependence upon the expansion rate yields equations of penetration resistance and penetration depth defined in terms of hypergeometric functions. These expressions are readily evaluated by modern tools for technical computing