Evaluation of elastic modulus of materials by adhesive (no–slip) nano–indentation

Abstract

Results of Mossakovskii's analysis for the elastic, adhesive (no–slip) contact between a rigid, axisymmetric punch and an isotropic, elastic half–space are developed in order to show that a simple relation exists between the contact stiffness, the contact area and the elastic modulus. The relation is similar to the Bulychev–Alekhin–Shorshorov equation, which is commonly used for evaluation of elastic modulus of materials by nano–indentation. The final formula differs from the frictionless case by a factor that depends on the Poisson ratio of the material. The bounds for the values of the factor are estimated. Similar to the frictionless analysis performed by Pharr, Oliver and Brotzen, the relation is not dependent on the geometry of the punch.