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

Abstract

In the present 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 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. The 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 falling within the projectile diameter. It is found that the dependence of the critical velocity Vc 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 Vc on the projectile diameter and the mesh parameters for the both modes of the fragmentation. It is shown that the average cumulative mass distributions constructed at Vc exhibit the property of scale invariance, splitting into two groups of distributions exactly corresponding 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 the each group of distributions has a power-law distribution with an exponent tau different from that in the other group. The conclusion about the dependence of the exponent of the power-law distribution tau on the fragmentation mode is made.