Finite Element and Gradient-Based Optimization Tools for Multi-Parameter Nanoindentation Characterization of Materials With Non-Linear Stress/Strain Behavior

The nanoindentation method is becoming increasingly popular for materials characterization, particularly for thin-films, coatings, and other materials that do not easily lend themselves to standard mechanical test methods. However, nanoindentation methods are limited when it comes to their description of a material behavior that deviates from simple elastic or visco-elastic responses. In this paper, we describe a four-parameter constitutive model that has been implemented in a PC-based analysis tool that combines non-linear finite element modeling with data mining gradient-based optimization methods to solve for the unknown parameters from an experimental nanoindentation creep curve. This “VNDM” (virtual nanoindentation and data mining) method, then, is used to complement experimental nanoindentation creep tests for more thorough material characterization. The results verify that the parametric model is capable of describing a wide-range of material behavior, including elastic, visco-elastic, and visco-plastic responses.