Geometric scaling laws: From microparticle to macroscale projectile impact testing of materials

Novel nanomaterials tested at the microscale using the laser induced projectile impact testing (LIPIT) technique exhibit record high specific energy absorption (EP*), compared to widely used macroscale protective materials such as aluminum and Kevlar composites. However, harnessing these properties of nanomaterials at the bulk scale requires a clear understanding of the material size effects present at small scales and the geometric scaling laws associated with micro to macro scale ballistic impact tests. To better understand the geometric scaling laws independent of material size effects, we choose polystyrene as the model material and investigate its dynamic behavior at relatively larger lengthscales where the material size effects are not present. We investigate the effects of diameter (D) of the impacting microparticle with respect to the thickness (t) of the target material on the specific energy absorption as well as the deformation and failure modes using LIPIT. While dimensional analyses using Buckingham Pi theorem is typically used to compare experiments performed with dissimilar projectile and material geometric parameters as well as different material properties, we show its deficiency in accounting for the deformation and failure modes leading to potential misinterpretations of scaling behavior. Our experimental results show that the EP* increases with increasing D/t ratio, with different D/t ratios exhibiting different deformation and failure mechanisms. We also observe that the impacts with the same D/t ratio but at smaller projectile diameters exhibit higher EP* compared to the larger projectiles. The geometric scaling analysis we present allows for the comparison of the dynamic behavior of target materials from micro to macroscale impact experiments.