Analytical model for elasto-plastic indentation of a hemispherical surface inclusion

An analytical model is developed to deduce the elastic and plastic properties of a hemispherical inclusion embedded in the surface of a semi-infinite solid from its indentation response. The model differs from the approaches presented in the literature by starting from the analytical expressions for the elastic and elasto-plastic indentation responses of homogeneous solids, and adapting them by replacing the modulus of the homogeneous solid by an effective modulus for the embedded inclusion. The accuracy of the indentation model is established by comparing the analytical results with detailed finite element simulations for various bi-material configurations of inclusion and substrate. The elastic indentation response is substantially influenced by the elastic modulus of the substrate, whereas the plastic response is dictated by the yield strength of the inclusion. The practical applicability of the indentation model is demonstrated by making use of the measured indentation response of an embedded paint sample, as reported in the literature, to deduce the elastic modulus of the paint.