Indentation load–displacement curve, plastic deformation, and energy

Various methods to access indentation data are considered on the basis of the load P–displacement h curve, its derivative, or its integral. This paper discusses and extends the various analytical models to estimate the indentation P–h curve, the slope, and the dissipated energy to aid the development of a concise methodology to analyze indentation data. Special consideration is given to the effect of pile-up and sink-in. Relationships for sharp and spherical indenters are presented and in addition for sharp indenters with a rounded tip. An overview over analytic expressions for the P–h curve is given and compared to finite element simulations and experimental data. An expression derived for the representative strain at the onset of yield under sharp and spherical indenters compares well with literature results. The effect of a rounded tip on the yielding under a sharp indenter is discussed. The ratio of loading to unloading slope and the ratio of the plastically dissipated energy to the total energy is related to hardness and elastic modulus. In combination these ratios can be used to determine the strain-hardening coefficient.