Analysis of sharp-tip-indentation load–depth curve for contact area determination taking into account pile-up and sink-in effects

Hardness and elastic modulus of micromaterials can be evaluated by analyzing instrumented sharp-tip-indentation load–depth curves. The present study quantified the effects of tip-blunting and pile-up or sink-in on the contact area by analyzing indentation curves. Finite-element simulation and theoretical modeling were used to describe the detailed contact morphologies. The ratio f of contact depth, i.e., the depth including elastic deflection and pile-up and sink-in, to maximum indentation depth, i.e., the depth measured only by depth sensing, ignoring elastic deflection and pile-up and sink-in, was proposed as a key indentation parameter in evaluating real contact depth during indentation. This ratio can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and the ratio of elastic indentation energy to total indentation energy. In addition, the value of f was found to be independent of indentation depth, and furthermore the real contact area can be determined and hardness and elastic modulus can be evaluated from f. This curve-analysis method was verified in finite-element simulations and nanoindentation experiments.