Nanoindentação de materiais elásticos lineares com espessura finita

Abstract

The mechanical properties of nano and micro systems motivated many studies aiming understanding of how materials are a ected by mechanical interactions in low dimensions. Nanoindentation was developed in the early 1970s and is widely use to extract material mechanical properties, e.g. Young's modulus. It has been observed that classical mathe- matical models of the mechanics of contact based on the Hertz contact solution (which is the derived for the semi-in nite elastic contact), doesn't adequately describe the indenta- tion stress eld due to the e ects of substrate and indenter tip size. The purpose of this work is the modi cation of the model proposed by Hertz to describe the contact between indenters with a surface of nite thickness. The nite element method (FEM) was used to model the spherical and conical geometries of the contact allowing investigation of the mechanical response of these contacts by computational simulations of indentation. By tting the data obtained by FEM for samples with di erent thickness, it was possible to ( i ) to understand the role of the substrate during nanoindentation of thin samples, and ( ii ) to determine the correction factor of the Hertz model to account for sample thickness. These modi cation can be used to analyze nanoindentation experiments performed with atomic force microscopy to study the mechanical properties of small-scale systems