Elastic contact versus indentation modeling of multi-layered materials

Abstract

The elastic contact problem of a rigid cylindrical punch indenting a multi-layered linear elastic half space is studied and then used to model the unloading phase of a microindentation test of thin fims deposited on a substrate. First, we adopt a moduli-perturbation method to construct a closed-form, first-order-accurate solution for the contact compliance of a nonhomogeneous medium with a piecewise constant (layered) or continuously varying moduli in the depthwise direction. These solutions are used to estimate the unloading compliance associated with the indentation testing of an Aluminum thin film deposited on a Silicon substrate. Comparison with results obtained from numerical computations indicates that the perturbation estimates are approximately valid for a moderate range of material combinations of practical importance. Also, a finite element analysis is performed to investigate the effects of a penny-shaped debonding crack along the film; substrate interface on the unloading compliance, and to analyse the energy release rate which drives the interface crack. Important conclusions include: (i) interface debonding can cause a significant increase in the unloading compliance of an indentation test; (ii) there exists a saturation crack size beyond which the compliance no longer changes significantly with the crack length; (iii) the plastic deformation near the indentcr does not appreciably affect the unloading compliance, but it plays a major role in maintaining the long range energy release rate which drives the crack growth.