Nanoindentation Response analysis of Thin Film Substrates-I: Strain Gradient-Divergence Approach

Abstract

Nanoindentation is a widely-used method for sensitive exploration of the mechanical properties of micromechanical systems. We derive a simple empirical analysis technique to extract stress-strain field (SSF) gradient and divergence representations from nanoindentation data sets. Using this approach, local SSF gradients and structural heterogeneities can be discovered to obtain more detail about the sample's microstructure, thus enhancing the analytic capacity of the nanoindentation technique. We demonstrate the application of the SSF gradient-divergence analysis approach to nanoindentation measurements of bulk silicon.

Nanoindentation Response Analysis of Thin Film Substrates-II: Strain Hardening-Softening Oscillations in Subsurface Layer

“…Results on the bulk solid sample of silicon were reported in the first part of this investigation [7]. For the clarity of the discussion we focus here on reporting a few typical results of the nanoindentation measurements of the CZS sample, which are representative of all the steel samples examined in our investigation.…”

“…The load-displacement curve is contrasted with the corresponding total SSF gradient curve, which was derived using the approach briefly outlined in Methods (see also Ref. 7). Note that we use logarithmic axis for the displacement into surface, h, to highlight nanoindentation responses at the subsurface layers.…”

“…In the first part of this investigation, we derived a simple approach to extract the local stress-strain field (SSF) gradient and divergence representations from the nanoindentation experiment dataset [7]. These representations, in principle, allow discovering weak structural heterogeneities which might point to, for example, interfaces between mechanically distinct local microzones within the subsurface region or work hardening and softening deformation processes induced underneath the indenter.…”

“…These representations, in principle, allow discovering weak structural heterogeneities which might point to, for example, interfaces between mechanically distinct local microzones within the subsurface region or work hardening and softening deformation processes induced underneath the indenter. Here, we applied the strain gradient-divergence approach [7] in the analysis of nanoindentation response of bulk solids commonly used as substrates for thin film deposition: different types of bearing and tooling steels, glass, silicon as well as silica as a reference sample without a pretreated surface. A highly dynamic process occurring in the subsurface layer of the bulk solids was revealed during a nanoindentation experiment: oscillations of the stress-strain field gradient and divergence.…”

Nanostructured TiAlSi-CN:Me/a-CN:Si₃N₄ Composite Coatings Deposited by Advanced PVD Technique

“…The G200 tester was calibrated using a reference sample of fused silica. Elastic modulus, hardness and standard deviations of the load-displacement measurements were calculated from experimentally obtained loading-unloading data sets by the MTS TestWorks-4 software using the well-known Oliver-Pharr method [10] and strain gradient-divergence approach [11].…”