Indentation of freestanding pre-stressed films: Extracting elastic modulus and pre-tension, elucidating finite-sized indenter effect

Abstract

The indentation test is an important method for characterizing the mechanical properties of solid films. However, how to extract the elastic modulus of pre-stressed circular films through the indentation test is still debatable due to the transition between linear membrane, nonlinear membrane, and plate behavior. This study proposes a method for extracting elastic modulus and pre-tension of freestanding film simultaneously by integrating an indentation test and theoretical modeling. Firstly, we introduce the experimental setting and results of polydimethylsiloxane (PDMS) films. The theoretical model for the cylindrical indentation of freestanding circular film is then presented, considering the combined contribution of pre-tension, additional stretching, and bending stiffness to mechanical response. After that, the elastic modulus and pre-tension are extracted by iteratively solving the full governing equations until the difference between numerical and experimental load-deflection curves is minimized. The asymptotic results derived from the full governing equations are compared with classical asymptotic solutions in the linear membrane, nonlinear membrane, and plate regimes to verify the theoretical modeling. Finally, the explicit indentation force-depth formula for the finite-sized indenter is proposed. The underlying mechanism of the synergistic effect of pre-tension, additional stretching and bending stiffness on indentation behavior in the transition region is elucidated.