Spatial dispersion characteristics of behind-armor debris generated during the penetration of tantalum alloy Explosively Formed Projectile

To investigate the spatial dispersion of behind-armor debris (BAD) generated by tantalum alloy explosively formed projectile (EFP) during target perforation, X-ray imaging and fragment-distribution experiments were first conducted for tantalum EFP penetration of 45# steel targets. Next, an experimentally validated FE–SPH (finite element–smoothed particle hydrodynamics) fixed-coupling method was employed to simulate normal EFP perforation under various projectile and target configurations, thereby generating a dataset of BAD spatial dispersion. Finally, a Bayesian-optimized support vector regression (SVR) model was trained using dense-fragment dispersion angle data to establish a predictive model. Experimental observations indicate that the BAD cloud exhibits a typical truncated-ellipsoidal morphology. Due to the density difference between tantalum and steel, fragments composed of different materials display distinct radial expansion behaviors: steel fragments are distributed along the outer surface of the ellipsoid, whereas tantalum fragments are concentrated on the inner surface. The BAD is primarily concentrated within a circular region surrounding the central perforation of the witness plate. The FE–SPH fixed-coupling method successfully reproduced the BAD formation process, yielding debris-cloud morphologies that closely match the experimental results. The relative error between the simulated and measured mean maximum fragment dispersion angles is less than 10%, thereby confirming the accuracy of the numerical simulations. Furthermore, the Bayesian-optimized SVR model enables accurate prediction of dense-fragment dispersion angles under varying target thicknesses and impact velocities, with maximum relative errors below 10%. Based on these predictions, the damage area on witness plates within a certain distance behind the target can be rapidly estimated.