Computational and experimental study of instrumented indentation

Abstract

The effect of characteristic length scales, through dimensional and microstructural miniaturizations, on mechanical properties is systematically investigated by recourse to instrumented micro- and/or nanoindentation. This technique is capable of extracting mechanical properties accurately down to nanometers, via rigorous interpretation of indentation response. Such interpretation requires fundamental understandings of contact mechanics and underlying deformation mechanisms. Analytical, computational and experimental approaches are utilized to elucidate specifically how empirical constitutive relation can be estimated from the complex multiaxial stress state induced by indentation. Analytical formulations form a framework for parametric finite element analysis. The algorithms are established to predict indentation response from a constitutive relation (hereafter referred to as "forward algorithms") and to extract mechanical properties from indentation curve (hereafter referred to as "reverse algorithms"). Experimental verifications and comprehensive sensitivity analysis are conducted. Similar approaches are undertaken to extend the forward/reverse algorithms to indentations using two ore more tip geometries. Microstructural miniaturization leads to novel class of materials with a grain size smaller than 100 nm, hereafter referred to as "nanocrystalline" material. Its mechanical properties are observed to deviate greatly from the microcrystalline counterparts.

(cont.) In this thesis, experimental, analytical and computational approaches are utilized to elucidate the rate and size dependent mechanical properties observed in nanocrystalline materials. Indentations, as well as micro-tensile tests, are employed to attain various controllable deformation rates. A simple analytical model, hereafter referred to as Grain-Boundary-Affected-Zone (GBAZ) model, is proposed to rationalize possible rate-sensitivity mechanism. Systematic finite element analysis integrating GBAZ model is conducted with calibration against the experiments. The same GBAZ model, further utilized in the parametric finite element study, is capable of predicting the inverse Hall-Petch-type phenomenon (weakening with decreasing grain size) at the range consistent with the literature.