Spherical indentation model for evaluating the elastic properties of the shell of microsphere with core-shell structure

Abstract

The indentation of a microcapsule with a spherical indenter is an effective technique to evaluate the elastic properties of microcapsule shells. The spherical indentation of a microcapsule could be modelled as a microsphere with core–shell structure indented by a rigid sphere. Based on the assumption that the deformed pattern of microcapsule is axisymmetric at small indentation displacement, the deformed profile of shell was divided into five regions according to curvature change. The strain energy of shell was then obtained by adding the bending and membrane strain energy of each region together. The strain energy of core is mainly caused by the volume change of core. The microcapsule was treated as a system and its total potential energy is the sum of the strain energy of shell and core minus the work done by external load. Applying the minimum total potential principle, a spherical indentation model that establishes the relationship among the indentation load, the indentation displacement, and the elastic properties and geometric parameters of microcapsules was proposed. Experiments were carried out on PMMA microcapsules with different dimensions to validate the newly proposed spherical indentation model. The average value of elastic moduli obtained by conventional nanoindentation tests on bulk PMMA and the cross-section of PMMA shell was regarded as the nominal value. The average elastic modulus of PMMA shells determined by the proposed model shows a good agreement with the nominal value. Finally, finite element simulations combined with the proposed model were used to predict the indentation behaviors of microcapsules with different dimensions.