Elastic stress field beneath an arbitrary axisymmetric punch

Abstract

The nanoindentation test is commonly used for the local determination of mechanical properties (hardness, elastic modulus, etc.) and also to study the initial stages of plasticity (dislocation nucleation, dislocation interaction mechanisms) at the nanometre scale. In the latter case, the determination of the elastic stress field beneath the indenter is of primary interest. An analytical expression is derived for the elastic stress and strain fields beneath an axisymmetric punch. Most solutions, in the literature, are given for simple indenter shapes, such as flat, conical or spherical indenters. The complete solution proposed for an arbitrary indenter profile is described by a power law, in which the exponent can be an integer or not. The stress is given as the real part of complex analytical expressions.

Keywords:

• nanoindentation
• elasticity
• elastic contact
• stress field