Numerical simulation of spallation in thick-walled shells under explosive loads of various types

Abstract

Problems of explosive expansion and failure of thick-walled shells are of interest from the viewpoint of technical applications and attract the attention of specialists [1][2][3][4]. The motion of cylindrical shells under the action of detonation products (DP) was discussed by Odintsov et al. [1] in Eulerian formulation and by Levitan et al. [2,3] in Lagrangian formulation. Relatively uniform strains are typical for expanding shells, while the outflowing detonation products are characterized by very high levels of displacements and strains. Therefore, the Lagrangian approach, which is convenient for study of expansion of closed shells, becomes inapplicable in the case of free DP flow into the surrounding space.Eulerian description of motion of a continuous medium leads to some difficulties in location and accurate determination of contact and boundary surfaces and in keeping track of fracture zones. These contradictory requirements on the numerical method of calculation of expanding shells can be satisfied by using Euler coordinates to describe DP motion and Lagrange coordinates to describe shell motion. One possible variant of the combined Euler-Lagrange method for solution of problems of expansion of thick elastoplastic shells accompanied by DP effusion into vacuum was proposed by Gerasimov and Lyukshin [4]. This variant is based on a combination of the methods of [5,6]; it combines the advantages of both methods and avoids their drawbacks. Problems of determination of parameters of the stress-strained state of expanding shells have been extensively investigated, whereas the numerical simulation of shell failure in a three-dimensional axisimmetric formulation has been studied much less [2,3]. Failure of an elastic shell was studied by Levitan and Moiseenko [2], and failure of an elastoplastic shell caused by a glancing detonation wave was studied by Kostin et al. [3].Below, using the approach proposed in [4], we study damage growth and the possibility of spallation in the walls of thick-walled elastoplastic shells both under the action of glancing detonation and in throwing of a liner shell onto the internal surface of the main shell. The model of a porous ideal elastoplastic body of [7,8] is applied to describe the behavior of damaged material. Failure is treated as a process of accumulation and growth of microcracks (micropores) by means of the kinetic equation proposed in [7]. A nonviscous nonthermoconducting gas model was used in description of DP.1. Statement of the Problem. We study a thick-walled cylindrical elastoplastic shell with the bottom filled with a high-explosive (HE) charge (see Fig. la). In the second variant (Fig. lb) the HE is in contact with a thin liner shell. There is clearance h between the liner and the main shell. On the left end OE the shell is not closed. Initially, a plane detonation wave (DW) is formed at this end. This wave propagates through the HE in the bottom direction. An oblique shock wave proragates along the liner shell, accelerating the particles of the material, while D...