Contact Analysis Considering Surface Stress and Surface Elasticity: Increase of Indentation Hardness and Yield Stress

Abstract

An increase in indentation hardness with decreasing indentation depth has been observed in nanoindentation studies. It is known as the indentation size effect. The indentation modulus in Molecular Dynamics (MD) contact analysis is larger than that in theoretical analysis (Hertz contact theory). In this paper, elasto-plastic contact analysis for an anisotropic elastic half-space is performed using the surface Green’s function considering surface stress and surface elasticity. A contact analysis is conducted to investigate the effect of surface stress on yield stress and indentation hardness. The discrete convolution, fast Fourier transform method and conjugate gradient method are applied to the contact analysis. The hardening model of the elasto-perfect plastic law is used in this study. The yield stress is determined so that a contact area considering surface stress is agreed with the one ignoring surface stress. Then, the yield stress ignoring surface stress and surface elasticity fixed at a constant. It is found that the yield stress considering surface stress and surface elasticity increases with decreasing the indentation depth. The indentation hardness considering surface stress and surface elasticity is calculated using the determined yield stress. The effects of surface stress and surface elasticity on the indentation hardness and the yield stress is discussed.