EVALUATING CONTACT STRESSES IN AN IMPACTOR PENETRATING A HARD SOIL

Finite formulas have been derived for evaluating contact stresses in a rigid impactor penetrating a soil, taking into account the friction in the framework of the local interaction model. In analyzing dynamic deformation of the soil, its volumetric compressibility, shear resistance and initial strength are accounted for. The obtained evaluations of resistance to penetration of an impactor into the soil are based on a quadratic relation between the stress normal to the impactor surface and impact velocity. The authors have pioneered in deriving finite expressions for coefficients of a trinomial approximation as a function of experimentally determined physical-mechanical parameters of the soil - a dynamic compressibility diagram (a shock adiabat) and a yield strength - pressure diagram. Impact compressibility of soils is described based on Hugoniot's adiabat - a linear relation between shock wave velocity and mass velocity of the medium particles behind the shockwave front. Plastic deformation obeys the Mohr - Coulomb yield criterion with a constraint on the limiting value of maximal tangential stresses according to Tresca's criterion - the Mohr - Coulomb - Tresca plasticity condition. An earlier obtained analytical solution of a one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a half-space occupied by a plastic soil medium is used. A formula for determining critical pressure (a minimal pressure required for the formation of a cavity, accounting for internal pressure in the framework of Mohr - Coulomb's yield criterion) is also used, which generalizes a known solution for an elastic ideally plastic medium with Tresca's criterion. The derived formulas have been verified by comparing their results with the available data from experiments on the penetration of a steel conical impactor into a frozen sandy soil. It is shown that the disagreement between the numerical and experimental results is within 10%.

Melting behind the front of the shock wave

A simple caloric model of the equation of state is proposed to describe thermodynamic properties of solid materials with phase transitions with the minimum number of parameters as initial data. Thermodynamic characteristics are calculated in the wide range of densities and pressures. The equation of state of the solid phase was modified by introducing configurational entropy, which made it possible to describe a liquid medium by the same functional dependence, but with its initial parameters. This allowed us not only to construct the equation of state for the liquid, but also to determine the dependence of the melting point on pressure as the boundary between the phases with the corresponding state. It is shown that the melting process is practically not noticeable on the shock adiabat in the pressure - volume plane; however, sharp adiabatic breaks are observed in the temperature - pressure plane. The calculated position of the melting curve agrees with the experimental data found; although this does not fully justify the conclusion about the accuracy of the calculation of the liquid phase adiabat, but fully confirms the qualitative picture.

Numerical Research on Implosion of Condensed Liners Used in Study of Shock Adiabat of Materials

Research on material properties under extreme conditions plays a great role in material science and high energy physics. Condensed liner accelerated by powerful pulse facilities has been used to compress the target liner. The motion of liner implosion driven by a pulse of current of several microseconds rise time and 70~90 MA has been numerically studied in this paper. Liners state and velocities are discussed. Results of 2D magnetohydrodynamics liner implosion computations are presented in order to study the development of interface instability.