Size effects on the dynamic indentation modulus of films

The dynamic mechanical characteristics of viscoelastic films play a significant role in the load-bearing functions of various engineering and natural composite materials systems. Identifying these film characteristics is a prime objective in both fundamental and applicative materials science fields. However, as the film thickness decreases, its analysis by dynamic nanoindentation methods becomes convoluted due to the emergence of mechanical coupling between the film and its underlying substrate. These yet unexplored size effects pose major limitations in approaching the elemental mechanical characteristics of thin films. Here, we analyze the film size effects on its dynamic indentation modulus by theoretical modeling and Finite-Element simulations. We develop compact analytical formulae that link the indentation modulus magnitude, loss coefficient, storage modulus, and loss modulus to those of the pristine film, draw functional insights into the energy-storage and energy-dissipation capabilities of the integrated film–substrate laminate, and outline an approach to back-calculate the elemental film characteristics via simple linear scaling of its dynamic indentation modulus measurements. Our analysis generally holds for synthetic and biological film materials—paving the way to identify the dynamic mechanical characteristics of various thin-film configurations, such as polymeric assemblies, functional surfaces, and biomechanical coatings.