Dimensionless Analysis to Determine Elastoplastic Properties of Thin Films by Indentation

Abstract

By assuming the elastoplastic properties of thin-film materials, a reverse analysis method is proposed by deriving a dimensionless function for the indentation process. The substrate effect is taken into account by assuming a perfect interface between thin-film and substrate materials. In order to obtain the applied load–penetration depth (P-h) curves, the indentation process is numerically modeled as an axisymmetric problem with a rigid-body Berkovich indenter on the semi-infinite substrate when performing finite element (FE) simulations. As a typical soft film/hard substrate problem, the elastic substrate is assumed and the power–law model is used to describe the constitutive properties of thin-film materials. Varying elastic modulus (10–50 GPa), yield strength (60–300 MPa), and hardening exponent (0.1–0.5) characterize different elastoplastic mechanical properties of thin-film materials with film thickness of 10–30 μm. Owing to the good trending P-h curves with the maximum indentation depth up to the 2/3 film thickness for different elastoplastic thin-film materials, a dimensionless function is derived and validated based on the predictions by reliable FE simulations. The proposed dimensionless function elegantly elucidates the essential relationship between the elastoplastic mechanical properties of the thin-film material and indentation responses (e.g., loading and unloading variables). The elastoplastic constitutive curves predicted by the proposed reverse method are confirmed to be in good agreement with the stress-strain curves of materials by FE simulations with the randomly selected elastoplastic mechanical properties and film thicknesses. This study provides a theoretical guidance to understand the explicit relationship between elastoplastic mechanical properties of the thin-film material and indentation responses.