A simplified formula to estimate the load history due to ballistic impacts with bullet splash. Development and validation for finite element simulation of 9x21mm full metal jacket bullets

Abstract

An original simplified formula is proposed to estimate the load history caused by ballistic impacts characterized by the so-called bullet splash phenomenon, consisting in the complete bullet fragmentation with no penetration of the target. The formula is based on the progressive momentum variation of the mass of the bullet impacting on a planar plate normal to the impact direction. The method aims at creating a simplified approach to assess the response of structures by means of explicit finite element simulations without the need of modelling the interaction between impactor and target. The results demonstrate that the proposed method can be used to estimate the forces generated by bullet-splash phenomena of 9x21mm full metal jacket bullets and effectively applied to finite element simulations allowing significant reductions in computational cost.

Ballistic Impacts with Bullet Splash—Load History Estimation for .308 Bullets vs. Hard Steel Targets

“…The approach proved to be effective and extremely efficient for 9 × 21 mm full metal jacket bullets hitting 4 mm AISI 304 plates as well as for monolithic copper .308 rifle bullets hitting high hardness steel plates. The validation confirmed the equivalence between the fluid structure interaction and the load history approach in terms of stress waves propagating from the epicenter of the target, resultant forces at the constraint, and residual deformation fields of the plates [11,12].…”

“…The approach proved to be effective in predicting the local and global effects of bullet splashes due to 9 × 21 mm full metal jacket bullets hitting 4 mm AISI 304 plates [9]. Based on that experience, [10] proposed and validated a further simplified method to make the finite elements simulations more efficient and equally effective by avoiding the hydrodynamic part of the calculation, by introducing an estimated load history approach that consists in decoupling the bullet fragmentation phenomenon and the target reaction to avoid the costs of modelling the bullet, and introducing an equivalent impact force as a load curve F(t) to be directly applied to the impact point on the structure; the intensity vs. time curve is calculated based on the initial impact velocity and the density distribution of the specific bullets. The approach proved to be effective and extremely efficient for 9 × 21 mm full metal jacket bullets hitting 4 mm AISI 304 plates as well as for monolithic copper .308 rifle bullets hitting high hardness steel plates.…”

“…The load histories were calculated according to the progressive fragmentation theory introduced by Andreotti et al in 2022 [10][11][12] for 90 degree bullet splashes. The load history formula allows us to reconstruct the F(t) depending on the density distribution characterizing each section of the bullet and its impact speed.…”