Bending of polymer films: a method for obtaining a compressive modulus of thin films

Due to the advent of various foldable electric devices, it is becoming increasingly important to understand the bending properties of film materials. Bending of isotropic materials may be trivial if elastic deformation is small within a range of linear elasticity, which is often the case for bending. However, bending of polymer films, often used in recent foldable devices, may not be the case. Polymer films are frequently fabricated with stretching, which induces anisotropic orientation of molecular chains. In addition, there are many studies on bimodulus materials, which suggest the importance of the difference in tensile and compressive elastic moduli, i.e., the importance of elastic asymmetry, considering that bending involves compression and extension. In this study, we extended the standard linear elastic theory to include elastic anisotropy and elastic asymmetry and developed a method for obtaining compressive moduli of films, which cannot be obtained by a simple compression test because thin films under compression buckle at small strains. Our method is based on a bending test combined with a uniaxial tension test, which allows the measurement of Poisson's ratio in addition to Young's modulus, which are both anisotropic and asymmetric. To test our theory and method, we further performed experiments on biaxially stretched poly(ethylene terephthalate) (PET) films. As a result, we found non-negligible anisotropy in Poisson's ratio and non-negligible asymmetry (bimodulus) in tensile and compressive moduli. We further justify our framework by demonstrating a clear data collapse to show agreement between experiment and theory, clarifying limitations. Our results suggest the importance of elastic anisotropy and elastic asymmetry in bending of industrial films and give fundamental knowledge on this subject, which would be useful for applications. Such applications include the control of the position of the neutral plane and precise measurements of elastic moduli and Poisson's ratio, which are crucial, e.g., for the development of tough flexible electric devices and for the structural designs using compliant mechanisms.