Bridging the impact response of polymers from the nanoscale to the macroscale

Impact from a fast-moving object is a common event, but it can vary greatly in terms of scale, speed, and energy depending on the specific case. Recently, it has been suggested that scaling analysis can be used to relate the impact performance of materials at the nano- and microscale to their behavior at the macroscale, which is relevant for most applications. In this study, we explore the broad applicability of this approach by conducting micro- and macroprojectile impact tests on polymethyl methacrylate and polycarbonate films. By applying Buckingham $\Pi$ dimensional analysis to all the impact test results, we demonstrate that the minimum perforation velocity is directly related to the geometric and material properties of each system across a broad range of size and energy scales. Interestingly, we find that the failure stress of the polymer, a critical material property that defines perforation resistance, can be empirically determined based on the deformation of the specific impact test.