On establishing elastic–plastic properties of a sphere by indentation testing

Instrumented indentation is a popular technique for determining mechanical properties of materials. Currently, the evaluation techniques of instrumented indentation are mostly limited to a flat substrate being indented by various shaped indenters (e.g., conical or spherical). This work investigates the possibility of extending instrumented indentation to non-flat surfaces. To this end, conical indentation of a sphere is investigated where two methodologies for establishing mechanical properties are explored. In the first approach, a semi-analytical approach is employed to determine the elastic modulus of the sphere utilizing the elastic unloading response (the “unloading slope”). In the second method, reverse analysis based on finite element analysis is used, where non-dimensional characteristic functions derived from the force–displacement response are utilized to determine the elastic modulus and yield strength. To investigate the accuracies of the proposed methodologies, selected numerical experiments have been performed and excellent agreement was obtained.