Effects of machine stiffness on the loading-displacement curve during spherical nano-indentation

By taking the machine stiffness into the classic Hertzian solution rather than assuming a constant machine stiffness, we developed an approach to simultaneously derive the spherical indenter tip radius and machine stiffness in arbitrary ranges of loads and indenter radii. In contrast, the direct Hertzian fitting method tends to underestimate the radius, especially for larger indenter tips. The success is based on indention tests on two materials with known material stiffness, and the displacement difference under the same load is not affected by the machine stiffness. A total of eight spherical indenter tips with the radii ranging from a few microns to hundreds of microns have been indented on fused silica and single crystal sapphire. Our method gives correct indenter radii for all indenters. The machine stiffness is found to indeed vary with the indentation load and indenter radius. This method has many potential applications in the area of nano-indentation with spherical indenters, such as indentation size effect, modulus and hardness measurement, and micropillar testing.