Reduced ballistic limit velocity of graphene membranes due to cone wave reflection

Recent microscale ballistic experiments have revealed that multilayer graphene membranes exhibit exceptionally high ballistic limit velocity and specific penetration energy. A key feature contributing to the exceptional performance of these systems is the cone wave that develops at impact, which propagates radially at a very high speed for ultra-light and stiff graphene membranes, distributing the kinetic energy of the projectile away from the impact zone. Current theories on ballistic impact consider infinitely wide membranes, and atomistic simulations involve very small projectiles and specimen dimensions, and thus cannot ascertain whether microscale ballistics observations are scalable and size-independent. Here, we discover a particular size effect due to the reflection of cone wave that has not been previously observed or considered. We present molecular dynamics simulations showing that there exists a critical membrane size below which the cone wave reflections from the boundaries induce perforation; a phenomenon that is particularly relevant for microballistic testing of graphene membranes. We present an analytical relationship, verified by simulation data, which predicts the critical membrane size simply as a function of the projectile size, membrane thickness and the ratio of the projectile and membrane densities. Our findings provide timely guidance for future microscale experiments and atomistic simulations for accurate characterization of the impact performance of 2D nanomaterials.