Scaling Invariance and Characteristics of the Cloud of Spherical Projectile Fragmentation Products upon High-Velocity Impact on a Thin Mesh Shield

摘要

In this paper, we consider the problem of the fragmentation of an aluminum projectile on a thin steel mesh shield at high-velocity impact in a three-dimensional (3D) setting. The numerical simulations are carried out by the smoothed particle hydrodynamics method applied to the equations of mechanics of deformable solids. Quantitative characteristics of the projectile fragmentation are obtained by studying statistics of the cloud of fragments. Considerable attention is given to scaling laws accompanying the fragmentation of the projectile. Scaling is carried out using the parameter K, which defines the number of the mesh cells in the projectile diameter. It is found that the dependence of the critical velocity V (c) of fragmentation on the parameter K consists of two branches that correspond to two modes of the projectile fragmentation associated with the "small" and "large" aperture of the mesh cell. We obtain the dependences of the critical velocity V (c) on the projectile diameter and the mesh parameters for both modes of the fragmentation. It is shown that the average cumulative mass distributions constructed at V (c) exhibit the property of scale invariance, splitting into two groups of distributions corresponding exactly to the modes of the projectile fragmentation. In each group, the average cumulative distributions show good coincidence in the entire mass region; moreover, in the intermediate mass region, each group of distributions has a power-law distribution with an exponent tau different from that in the other group. Conclusions about the dependence of the exponent of the power-law distribution tau on the fragmentation mode are made.