EUROPEAN CONGRESS AND EXHIBITION ON ADVANCED MATERIALS AND PROCESSES - EUROMAT 2021

Hertzian theory is a classical approach to analytically describe an elastic interaction between solids in contact assuming that their mechanical properties are homogenous, the evolved strains are small, and the surfaces in contact are frictionless, continuous and non-conforming. The theory is central to numerous scientific domains and engineering applications, and it is at the foundation of the field of local mechanical characterization of materials using various nanoindentation-based methods. However, when working with composite structures, having multiple interfaces between materials with different mechanical characteristics, Hertz contact assumptions are violated. Therefore, so far, there was no experimental nor analytical approach to measure and quantitatively characterize a contact with two interfacing materials. In this study, employing finite element analysis, we expend the Hertz contact theory and develop an analytical expression that defines the forces between a rigid sphere and an inhomogeneous half-space containing such an interface. We show that the moduli of the two materials, the geometric properties of the tip and the distance from the interface are sufficient to fully describe the elastic forces developed between the two bodies. Furthermore, we validate the obtained relationship by successfully predicting the contact modulus measured across Si/SiO2 and Cu/Steel interfaces using static and dynamic indentation by a conical diamond tip.