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 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 the 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 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  different from that in the other group. The conclusion about the dependence of the exponent of the power-law distribution  on the fragmentation mode is made.Dynamic fragmentation of solids caused by impact or explosion has been studied for years . Typical experimental situations in which these phenomena take place correspond to collisions of heavy nuclei in atomic physics [3,4,19,20], collision of macroscopic bodies [1,12,16] (including projectile impact on a massive target [1,17,18,23,25]), shell fragmentation upon explosion [13], and projectile fragmentation upon high-velocity perforation of a thin shield [2, 5, 6, 8-11, 21, 22].A possible critical behavior during fragmentation was originally analyzed in the framework of a problem of nuclear collisions at moderate energies [3,4,19,20] using an approach based on the similarity of the observed distribution of fragments and that predicted by well-known theories of critical phenomena such as liquid-vapor transition and percolation. Later, these methods were applied to studying fragmentation in mechanical systems [8-10, 12-18, 24]. The existence of a critical transition from damage to fragmentation was confirmed for mechanical systems of various types both experimentally [14,15] and numerically [8-10, 11-13, 16-18].The transition from damage to fragmentation (or the degree of fracture) can be characterized in different ways, including the average fragment mass, mass of maximum fragment, fluctuations of the mass of largest fragment, etc. [3,4,12,13,19,20]. In syste...