Failure initiation during impact of metal spheres onto ceramic targets

A combined analytical/numerical framework is developed for ascertaining the critical impact velocities required to initiate failure in flat, back-supported ceramic targets when impacted by spherical metal projectiles. Four inelastic modes are considered: yielding, microcracking followed by comminution, cone cracking, and radial cracking. The time histories of contact pressure and contact force for a wide range of projectile yield strength and impact velocity are obtained through finite element analyses (FEA). The results are used to assess and calibrate analytic models for peak values of contact stress and force. Additionally, temporal and spatial evolutions of subsurface stresses computed by FEA are analyzed. Within the velocity range of present interest (<1000 m/s), the maximum dynamic subsurface stresses due to impact can be well approximated by the quasi-static solutions for a uniform pressure load of appropriate magnitude. The maximum back face stress is also well approximated by the corresponding quasi-static solution. The computed stresses and forces are combined with established criteria for each of the four failure modes to ascertain the minimum projectile velocity necessary to activate each. In turn, the results are used to identify the sequence of failure modes that occur, specifically, upon impact of metal spheres onto a confined alumina target. Reasonably good quantitative correlations are obtained between predictions and corresponding experimental observations.