Indentation has been the simplest and the fastest experiment method to measure the mechanical properties of materials such as the elastic modulus, hardness, strain–hardening, plastic or viscous parameters of materials from the experimental readings of indenter load ( P ) and the depth of indentation ( h ). The rapid and drastic development of the nanomaterials leads this experimental method to nanoscale. However, size-dependent behaviors in nanoindentation are extensively reported in measuring nanomaterials’ mechanical properties. Physically, surface effects play a prominent role in the mechanical behaviors of nanomaterials and nanostructures at nanoscales. In this work, thereby, surface effects on nanoindentation are studied in a continuum framework to explain the indentation s...[ Read more ]

Indentation has been the simplest and the fastest experiment method to measure the mechanical properties of materials such as the elastic modulus, hardness, strain–hardening, plastic or viscous parameters of materials from the experimental readings of indenter load ( P ) and the depth of indentation ( h ). The rapid and drastic development of the nanomaterials leads this experimental method to nanoscale. However, size-dependent behaviors in nanoindentation are extensively reported in measuring nanomaterials’ mechanical properties. Physically, surface effects play a prominent role in the mechanical behaviors of nanomaterials and nanostructures at nanoscales. In this work, thereby, surface effects on nanoindentation are studied in a continuum framework to explain the indentation size-dependent behavior. By adopting Gurtin’s surface elasticity, a continuum model of nanoindentation including both surface and bulk elasticity is proposed. An approximate solution of nanoindentation is given as a result which is simplified but reliable enough to reflect the surface effect on nanoindentation behaviors. Moreover, it can contribute to measuring the surface elastic parameters of nanomaterials. By conducting FEM simulations of nanoindentation, we find that the extracted values of surface parameters are comparable with the nanomaterials’ properties.