Effective Elastic Modulus of Film-on-Substrate Systems under Normal and Tangential Contact
- ORNL
- MTS Nanoinstruments Innovation Center, Oak Ridge
The load and depth sensing indentation method has been widely used to characterize the mechanical properties of the thin film-substrate systems. The measurement accuracy critically depends on our knowledge of the effective elastic modulus of this heterogeneous system. In this work, based on the exact solution of the Green's function in the Fourier space, we have derived the analytical relationship between the surface tractions and displacements, which depends on the ratio of the film thickness to contact size and the generalized Dundurs parameters that describe the modulus mismatch between the film and substrate materials. The use of the cumulative superposition method shows that the contact stiffness of any axisymmetric contact is the same as that of a flat-ended punch contact. Therefore, assuming the surface traction of the form of [1-(r/a)2]-1/2 with radial coordinate r and contact size a, we can obtain an approximate representation of the effective elastic moduli, which agree extremely well with the finite element simulations for both normal and tangential contacts. Motivated by a recently developed multidimensional nanocontact system, we also explore the dependence of the ratio of tangential to normal contact stiffness on the ratio of film thickness to contact radius and the Dundurs parameters.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Shared Research Equipment Collaborative Research Center; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences (NCCS)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 930885
- Journal Information:
- Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 2; ISSN 0022-5096
- Country of Publication:
- United States
- Language:
- English
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