Rami Masri

Dynamic spherical cavity expansion in an elastoplastic compressible Mises solid

The elastoplastic field induced by a self-similar dynamic expansion of a pressurised spherical cavity is investigated for the compressible Mises solid. The governing system consists of two ordinary differential equations for two stress components where radial velocity and density are known functions of these stresses. Numerical illustrations of radial profiles of field variables are presented for several metals. We introduce a new solution based on expansion in powers of the nondimensionalized cavity expansion velocity, for both elastic/perfectly plastic response and strain-hardening behavior. A Bernoulli-type solution for the dynamic cavitation pressure is obtained from the second-order expansion along with a more accurate third-order solution. These solutions are mathematically closed and do not need any best fit procedure to numerical data, like previous solutions widely used in the literature. The simple solution for elastic/perfectly plastic materials reveals the effects of elastic-compressibility and yield stress on dynamic response. Also, an elegant procedure is suggested to include strain-hardening in the simple elastic/perfectly plastic solution. Numerical examples are presented to demonstrate the validity of the approximate solutions. Applying the present cavitation model to penetration problems reveals good agreement between analytical predictions and penetration depth tests.

Shock Waves in Dynamic Cavity Expansion

High velocity cavitation fields are investigated in the context of large strain J 2 plasticity with strain hardening and elastic compressibility. The problem setting is that of an internally pressurized spherical cavity, embedded in an unbounded medium, which grows spontaneously with constant velocity and pressure. Expansion velocity is expected to be sufficiently high to induce a plastic shock wave, hardly considered in earlier dynamic cavitation studies. Jump conditions across singular spherical surfaces (shock waves) are fully accounted for and numerical illustrations are provided over a wide range of power hardening materials. Simple formulae are derived for shock wave characteristics and for the asymptotic behavior within near cavity wall boundary layer.

Ballistic Limit Predictions with Quasi-Static Cavitation Fields

Recent work on ductile hole enlargement under plane-stress conditions has revealed that while the internal pressure does not reach a saturation level, the energy increment required to create a nominal hole volume increment admits a finite asymptotic value. This specific cavitation energy, which is identified with the cavitation pressure required for plane-strain and spherical cavitation patterns, suggests a possible new view of cavitation states in energetic terms. Based on the specific cavitation energy the ballistic limits of monolithic targets are estimated from a simple energy balance and residual velocities are found from the Recht-Ipson formula. This plate perforation model is independent of projectile head profile and neglects friction. Albeit the simplicity, comparison with experimental and numerical data from various sources, for conical and ogival-nose projectiles, shows good agreement. In fact, over a practical range of h/D ratio, residual velocities are bounded between plane-stress and plane-strain predictions, gradually shifting from plane-stress limit to plane-strain bound as h/D increases. Spherical cavitation fields are also discussed in conjunction with limits of validity of cavity expansion models and connection between plane-stress cavitation and the ultimate tensile stress is demonstrated.

Estimation of Deep Penetration Resistance with Spherical Specific Cavitation Energy

A simple model is suggested for deep penetration resistance of rigid, axially-symmetric, nose-pointed projectiles penetrating ductile metal targets. Model is based on power balance between the power supplied by the projectile during steady-state penetration and elastoplastic power needed for expanding penetration hole. The latter is approximated with the aid of the spherical specific cavitation energy (spherical cavitation pressure). Frictionless model includes an empirical parameter which is found to be practically independent of target material characteristics but reflects the shape of head profile. For ogival nose projectiles (with the spherical nose as a special case) the empirical parameter values are limited to a narrow range, slightly lower than one. Friction resistance is included by the Prandtl friction model leading to a general expression for the deep penetration hardness. Experimental data of spherical and ogival nose projectiles penetrating aluminium targets is compared with analytical predictions for penetration depth and an optimal ogival nose projectile is discussed.