Fundamental limitations at the determination of initial yield stress using nano-indentation with spherical tips

Abstract

Abstract Nano-indentation with spherical indenters can be used to determine the local initial yield stress with an approach consisting of i) detection of the onset of plastic deformation applying a loading-partial-unloading (LPU) procedure and ii) calculation of the spatial distribution of the von Mises stress in the sample for the state of the system where plastic deformation just starts. The spatial maximum of the von Mises stress is taken as a measure of the initial yield stress. This approach, however, is subject to a fundamental restriction due to the fact that the plastic deformation starts within the volume of the sample and only limited information about this is available at the specimen surface. Since the displacement resolution of the indentation device is always limited, this leads to a fundamental overestimation of the initial yield stress. In this paper, the limitation of the approach is investigated by using finite element simulations of spherical LPU experiments for various sample parameters and sphere radii. With reference to the displacement resolution of the used nano-indentation device, the overestimation of the initial yield has been quantified and used to correct experimental results. The comparison of these corrected yield stresses to reference values clearly shows that the initially obtained dependence on the sphere radius was due to the fundamental overestimation of the yield stresses determined via spherical nano-indentation (Fig. 5).