AN APPROXIMATE FORMULATION OF THE EFFECTIVE INDENTATION MODULUS OF ELASTICALLY ANISOTROPIC FILM-ON-SUBSTRATE SYSTEMS

作者：Li T L; Lee J H; Gao Y F^*

来源：International Journal of Applied Mechanics, 2009, 1(3): 515-525.

DOI：10.1142/S1758825109000241

• Indentation modulus
• film-on-substrate system
• anisotropic elasticity

Frictionless contact between an arbitrarily-shaped rigid indenter and an elastically anisotropic film-on-substrate system can be regarded as being superposed incrementally by a flat-ended punch contact, the shape and size of which are determined by the indenter shape, indentation depth (or applied load) and elastic properties of film and substrate. For typical nanoindentation applications, the indentation modulus can thus be approximated from the response of a circular contact with pressure of the form of [1 - (r/a)(2)](-1/2), where r is the radial coordinate and a is the contact radius. The surface-displacement Green's function for elastically anisotropic film-on-substrate system is derived in closed-form by using the Stroh formalism and the two-dimensional Fourier transform. The predicted dependence of the effective modulus on the ratio of film thickness to contact radius agrees well with detailed finite element simulations. Implications in evaluating film modulus by nanoindentation technique are also discussed.

• 出版日期2009-9