Mathematical Modeling of the Shock Action of Fragments of Space Debris On Spacecraft Windows

Abstract

By the methods of continuum mechanics, the authors consider the problems of high-velocity (of the order of 10 km/s) interaction between aluminum and steel spherical particles of diameters no larger than 2·10 –4 cm and a thick fused-quartz (silica) target with account of the destruction and different states of aggregation of a substance, and also of the dependence of the strength characteristics of materials on the internal energy. Mathematical modeling is carried out within the framework of the Prandtl–Reuss elastic perfectly plastic model. The mechanism of destruction is determined by successively developing processes of growth and coalescence of micropores in the volumes under tensile stresses. To describe the behavior of a substance in wide ranges of variation in pressure and temperature, use is made of an interpolation wide-range equation of state which includes a melting curve and a two-phase region. The application-relevant region of interaction of the order of orbital (first) and escape (second) space velocities is difficult to experimentally investigate directly. In this connection, a theoretical analysis and numerical simulation of high-velocity shock phenomena take on particular significance.