Scaling invariance of spherical projectile fragmentation upon high-velocity impact on a thin continuous shield

Abstract

The problem of aluminum projectile fragmentation upon high-velocity impact on a thin aluminum shield is considered. A distinctive feature of this description is that the fragmentation has been numerically simulated using the complete system of equations of deformed solid mechanics by a method of smoothed particle hydrodynamics in three-dimensional setting. The transition from damage to fragmentation is analyzed and scaling relations are derived in terms of the impact velocity (V), ratio of shield thickness to projectile diameter (h/D), and ultimate strength (σ_p) in the criterion of projectile and shield fracture. Analysis shows that the critical impact velocity V_c (separating the damage and fragmentation regions) is a power function of σ_p and h/D. In the supercritical region (V > V_c), the weight-average fragment mass asymptotically tends to a power function of the impact velocity with exponent independent of h/D and σ_p. Mean cumulative fragment mass distributions at the critical point are scale-invariant with respect to parameters h/D and σ_p. Average masses of the largest fragments are also scale-invariant at V > V_c, but only with respect to variable parameter σ_p.