Issue 24

E.I. Kraus et alii, Frattura ed Integrità Strutturale, 24 (2013) 138-150; DOI: 10.3221/IGF-ESIS.24.15 138 Special Issue: Russian Fracture Mechanics School Impact loading of a space nuclear powerplant Evgeny I. Kraus, Ivan I. Shabalin Khristianovich Institute of Theoretical and Applied Mechanics of Siberian Branch of RAS Institutskaya str. 4/1, Novosibirsk 630090, Russia kraus@itam.nsc.ru A BSTRACT . Preferred formulation of the problem in two space dimensions are described for solving the three fundamental equations of mechanics (conservation of mass, conservation of momentum, and conservation of energy). Models of the behavior of materials provide the closure to the three fundamentals equations for applications to problems in compressible fluid flow and solid mechanics. Models of fracture and damage are described. A caloric model of the equation of state is proposed to describe thermodynamic properties of solid materials with the phase transitions. Two-dimensional problems of a high-velocity impact of a space nuclear propulsion system reactor are solved. High-velocity impact problems of destruction of reactor are solved for the two cases: 1) at its crash landing on the Earth surface (the impact velocity being up to 400 m/s); 2) at its impact (with velocity up to 16 km/s) with the space debris fragments. K EYWORDS . Equation of state; Shock waves; High-velocity impact. I NTRODUCTION he problem of quantitative description of the impact is a rather complex task, therefore it is connected with a whole scientific and technical research area rapidly developing lately. The bodies collision is accompanied by various processes, which emergence and relative role depend on the shape and physical characteristics of the objects and, more importantly, on the relative velocity of their collision. Moreover, the collision is often accompanied by penetration of one body into the other. In the process of high-speed collision, one or both of the bodies collided can collapse, scatter, or disperse, followed by dissipation of a significant amount of energy. In emergency situations, modern space vehicles with thermionic reactors “shoot off” (jettison) the nuclear powerplants (a simplified sketch of such a powerplant is shown in Fig. 1). There is a certain probability, however, that the reactor fragment containing the nuclear fuel reaches the Earth’s surface despite considerable thermal and mechanical loads in dense atmospheric layers. The velocity of the impact of the remaining part of the reactor system can reach 400 m/s. It is next to impossible to solve impact problems of real engineering objects though the computational engineering development level is rather high and fairly realistic mathematical models of material behavior are available. The reasons are the complicated spatial locations of the reactor fragments and the multiscale character of the problem. In such situations, the object considered is simplified, which makes it possible to construct a number of models aimed at studying the influence of the impact parameters on particular basic fragment of the object. The simplification used implies that the materials of small-scale parts were averaged inside the reactor zone in the additive approximation. The mass of the non-principal materials was assumed to be too small (beryllium, uranium dioxide and zirconium hydride compose 95—97 % of the reactor mass) to exert any significant effect on the shock-wave amplitude. As such a medium (mixture) does not have the volume defects, its specific volume on the wave front can be calculated as T