4.7 Article

Effective elastic modulus of film-on-substrate systems under normal and tangential contact

Journal

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 56, Issue 2, Pages 402-416

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2007.05.015

Keywords

effective elastic modulus; thin film substrate system; Dundurs parameters

Ask authors/readers for more resources

Load and depth sensing indentation methods have 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 Fourier space, we have derived an 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 fiat-ended punch contact. Therefore, assuming a 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. The analytical representations of the correction factors in the relationship between the contact stiffness and effective modulus are derived at infinite friction conditions. (C) 2007 Elsevier Ltd. All rights reserved.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.7
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available