Linking Ultra-High Strain Rate Impact Resistance of Polymers from Nano to Macro

Understanding the failure behavior of polymers subjected to an ultra-high strain rate (UHSR) event is crucial for their applications in protective systems. As the size and energy scales associated with these systems can vary over many decades, it has been a challenging endeavor to understand how the various length scales dictate the UHSR behavior of polymers when their molecular architecture and dynamics also need to be considered. In this contribution, we experimentally investigate the UHSR behavior of polymethyl methacrylate (PMMA) by impacting targets with projectiles at the microscale using laser-induced projectile impact testing (LIPIT) and at the macroscale using a ballistic and two-stage light gas gun. We then apply dimensional analysis models based on the Buckingham-П theorem to relate the minimum perforation and residual projectile velocities over these length scales. We show that the ratio of the target thickness to projectile diameter, their density differences, and the velocity of the compressive stress wave within the target govern these scaling relationships. Using this framework, we show that our scaling relationships can be extended to polycarbonates and high-density polyethylene, demonstrating their applicability to multiple material systems to show that our scaling model can successfully predict the impact properties of polymers during UHSR events that are independent of their unique mechanical properties and failure responses.