Anisotropy Influence of Cubic Solid on Dynamic Hertzian Contact Stiffness for a Vibrating Rigid Indenter

Problem statement: Resonance-type microscopies have been widely used to evaluate the nanoscaled or microscaled surface elastic properties of materials by the resonance-frequency shifts of an oscillator, which contacts the surface of materials by a spherical tip. Approach: The tip-specimen contact is modeled to be a spring support, whose stiffness is given by the traditional Hertzian contact theory. However, because of the influence of the oscillator vibration and the anisotropy in nanoscaled or microscaled region of materials, the predicted results from the traditional Hertzian contact theory can not coincide with the experimental observations. In order to explain this discrepancy, dynamic contact stiffness at the contact interface between a rigid sphere and a semi-infinite cubic solid is investigated. Results: An oscillating force being superposed on a biasing force excites the oscillation of the sphere contacting with the solid surface, which causes the contact radius to vary with the oscillation. The assumption of sufficiently small oscillating force compared with the biasing force yields an oscillating-contact-pressure distribution of the constant contact radius and then dynamic contact stiffness. Because the oscillating-contact-pressure distribution cannot promise the uniform contact deformation, the influence of contact-displacement conditions is discussed. Conclusion: It is shown that dynamic contact stiffness depends on the oscillating frequency and contact radius of the sphere and the solid anisotropy.