Critical Penetration Depth for Nano/Micro Indentation Test to Determine Elastic-Plastic Film Properties Deposited on Hard Substrates

The critical indentation depth to obtain proper elastic-plastic properties of thin film when the indentation tests are done on film/substrate system with sharp indenters is investigated. We focus on the characterization problem of soft film material, whose material properties are unknown, deposited on hard substrates. The critical depth is analyzed based on the finite element analysis (FEA) results. In order to extract the mechanical properties of the film from those of the film/substrate compound, we have to restrict the maximum penetration depth within a certain value. In this paper the relation between the load, P, and the depth, h, is analyzed in a power law relation, P = Ch^m, where the exponent m is a function of h. From extensive FEA results, we found that this exponent m starts to depart from 2 faster with increasing indenter apex angle and increasing hardening exponent of the film material. This means that the critical indentation depth decreases with increasing indenter apex angle and increasing hardening exponent. Based on this analysis, we propose a simple formula to evaluate the critical penetration depth h₀, as a function of apex angle, θ, of the indenter: h₀/d = 0.243cot θ, where d is the film thickness.