Spalling-like failure by cylindrical projectiles deteriorates the ballistic performance of multi-layer graphene plates

Ballistic performance of ultra-thin graphene membranes have recently been investigated at the micro and nanoscale. Two open questions that remain unanswered are, how graphitic plates behave when they can no longer be treated as a thin membrane, and how the projectile shape influences the perforation resistance of plates of varying thicknesses. Through coarse-grained molecular dynamics simulations, we show that beyond a critical plate thickness, a cylindrical projectile penetrates the plate at a lower velocity than a spherical one. This counterintuitive phenomenon is explained by spalling-like failure for thicker plates, where the graphene layers at the bottom section undergo a wave-superposition induced failure in the cylindrical case. Finite element simulations are carried out to show that in-plane tensile stress concentrates at the bottom section, resulting from the superposition of incident and reflected stress waves. A mechanics relationship is then proposed to describe the resisting pressure of the graphitic plate during ballistic impact. The analytical relationship indicates that the intensity of stress wave, which affects the spalling-like failure, depends on the projectile initial velocity, plate compressive modulus, and density. Our findings reveal the existence of a new failure mechanism for multi-layer graphene systems, and provide theoretical guidance for future dynamic mechanical property characterization of graphitic barriers.