Microplasticity characteristics obtained through nano-indentation measurements: application to surface hardened steels

A method for obtaining the local plastic properties of materials from nano-indentation measurements is described. The nano-indentation technique is used to measure the residual displacement dr of a spherical indenter, following loading-unloading cycles at increasing maximal force Fmax. First, the direct problem, i.e. simulating by the finite element method the nano-indentation response, dr (Fmax), from the knowledge of the strain-hardening law, σ (εp), is studied. It is validated on steel specimens, which are carburised homogeneously with different carbon concentrations. Second, the inverse problem, i.e. obtaining the strain-hardening law from the nano-indentation response, is studied on carburised and nitrided layers. To solve this problem, it is shown that both dr (Fmax) and σ (εp) responses can be fitted with simple analytical laws with a single characteristic parameter depending on the carbon or nitrogen concentration. Hence, the plastic behaviour for small strains is obtained through the identification of this characteristic nano-indentation parameter. Finally, the validity of the method is discussed in terms of the volume of material investigated, the strain range and the influence of residual stresses.