In this paper, the influence of mesh sensitivity on the fracture predictions during penetration and perforation of hardened blunt-nose cylindrical steel projectiles in plates of Weldox 460E, Weldox 700E, and Weldox 900E steel has been studied. The main objective is to try to describe the experimentally obtained trend of a decrease in ballistic limit velocity with increased target strength when the plates are impacted by blunt projectiles. This behavior is due to the occurrence of highly localized shear bands as the target strength increases. The impact tests are analyzed using the explicit solver of a nonlinear finite element code. A thermoelastic-thermoviscoplastic constitutive model with coupled or uncoupled ductile damage was used in the simulations. It was found that the residual velocity continuously increases when the element size is decreased from to in the shear zone, and that this increase is significantly stronger for impact velocities close to the ballistic limit. The ballistic limit decreases by up to 25% when the size of the element is decreased from to ; the decrease being somewhat greater for the two steels with the highest strength. Even with the finest mesh, the experimental trend of a decreasing ballistic limit with increasing target strength was not predicted in the simulations, neither with coupled nor uncoupled damage. Nonlocal simulations based on smoothing of the damage and temperature fields, which are the two variables causing the softening, were carried out for the Weldox steels and a mesh size of . These simulations indicate a reduction in the mesh sensitivity for both the coupled and uncoupled damage approaches when nonlocal averaging is employed.