To investigate the spatial dispersion characteristics of behind-armor debris (BAD) generated by the penetration of tantalum alloy explosively-formed projectile (EFP) into steel targets, a comprehensive study combining experimental testing, numerical simulation, and machine learning prediction was performed. First, X-ray imaging and fragment-distribution experiments were conducted on 45 steel targets penetrated by tantalum alloy EFP to obtain initial experimental data. Subsequently, the finite element-smoothed particle hydrodynamics (FE-SPH) fixed-coupling method, which had been validated by the experimental data, was employed to simulate the perforation process. These numerical simulations were carried out under a wide range of working conditions, specifically varying the projectile velocity and target thickness. Through this process, a comprehensive dataset describing the spatial dispersion of BAD was generated. Finally, to achieve rapid prediction capabilities, a support vector regression (SVR) model was established. The Bayesian optimization algorithm was utilized to train the model using the dense-fragment dispersion angle data extracted from the simulation dataset, thereby creating a robust predictive model for spatial dispersion of BAD. The experimental results indicate that the morphology of the BAD cloud exhibits a typical truncated-ellipsoidal shape. Due to the density difference between tantalum and steel, fragments composed of different materials display distinct radial expansion behaviors, i.e. steel fragments are distributed along the outer surface of the ellipsoid whereas tantalum fragments are concentrated on the inner surface. Spatially, the debris is primarily concentrated within a circular region surrounding the central perforation area 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 analysis reveals that the Bayesian-optimized SVR model enables accurate prediction of dense-fragment dispersion angles under varying target thicknesses and EFP 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.

In order to improve the quantitative characterization of the penetration process of tungsten alloy projectile into the target, the numerical methods such as FEM (finite element method), SPG (smoothed particle Galerkin), SPH (smoothed particle hydrodynamics), and FE-SPH (finite element-smoothed particle hydrodynamics) adaptive simulation methods were employed to simulate the penetration of tungsten alloy projectiles into Q235A steel targets. Based on numerical simulations, a comparison was made of the advantages and disadvantages of the four numerical simulation methods for calculating the residual velocity of the projectile after penetrating the target, the perforation diameter of the target, and the distribution of secondary fragments by the projectile penetration. The results show that, for calculating the residual velocity of the projectile, FEM and FE-SPH adaptive methods strictly rely on the selection of failure criteria and corresponding parameters, as FEM employs an element erosion algorithm to model material failure, while SPG method, as it does not require adjusting the failure parameters in bond failure mode, can obtain relatively accurate calculations; for predicting perforation diameter, FEM and FE-SPH adaptive methods accurately represent material boundaries and perforation morphology, although the perforation diameter varies significantly under different failure criteria, while the SPG method can accurately predict the perforation diameter of target plates due to its insensitive to failure parameters; for analzing secondary fragments generation and distribution, both FE-SPH adaptive and SPH methods effectively characterize these phenomena, while the FE-SPH adaptive method provides detailed information on large fragments, it is less computationally efficient than the SPH method.