Abstract
Problem statement: Resonance-type microscopies have been widely used to evaluate the nanoscaled or microscaled surface elastic propertie s of materials by the resonance-frequency shifts of an oscillator, which contacts the surface of materi als by a spherical tip. Approach: The tip-specimen contact is modeled to be a spring support, whose st iffness is given by the traditional Hertzian contac t theory. However, because of the influence of the os cillator vibration and the anisotropy in nanoscaled or microscaled region of materials, the predicted r esults 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, wh ich causes the contact radius to vary with the oscillation. The assumption of sufficiently small o scillating 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-displ acement 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.
Highlights
The quantitative evaluation of the surface elastic properties of materials in nanoscaled or microscaled is of great importance in material engineering (Kester et al, 1999), which can be determined by Atomic Force Microscopy (AFM) (Yamanaka and Nakano, 1998; Yamanaka et al, 1999; Rabe et al, 1998) and Resonance Ultrasound Microscopy (RUS) (Ogi et al, 2003; Tian et al, 2004; Tian et al, 2008)
These evidences show that the static contact model may fails in deducing the elastic constants of materials from the resonance-frequency shifts of the oscillator in resonance-type microscopies, which has been verified by the experiments (Tian et al, 2004)
Neglecting higher-order terms, Eq 5 can be simplified into: Response of the semi-infinite cubic solid subjected to the oscillating contact pressure distribution: we consider surface displacements in the semiinfinite cubic solid caused by the oscillating pressure distribution δf(x,y)eiωt, where the term eiωt will be neglected in the following analysis
Summary
The quantitative evaluation of the surface elastic properties of materials in nanoscaled or microscaled is of great importance in material engineering (Kester et al, 1999), which can be determined by Atomic Force Microscopy (AFM) (Yamanaka and Nakano, 1998; Yamanaka et al, 1999; Rabe et al, 1998) and Resonance Ultrasound Microscopy (RUS) (Ogi et al, 2003; Tian et al, 2004; Tian et al, 2008). The vibration of the oscillator has great influence on the contact stiffness at the contact interface because the contact effect is sensitive to the contact deformation at the contact interface These evidences show that the static contact model may fails in deducing the elastic constants of materials from the resonance-frequency shifts of the oscillator in resonance-type microscopies, which has been verified by the experiments (Tian et al, 2004). The evaluation of dynamic Hertzian contact for anisotropic solids is a key issue in resonance-type microscopies
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: American Journal of Engineering and Applied Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
