Equivalent-Volume Model: Estimating Contact Morphology of Spherical Indentation for Metallic Materials

In contrast with elastic deflection in instrumented indentation, the accurate estimation of plastic pile-up height around the indenter in metallic materials has been a challenge due to their diverse plastic deformation behavior arising from their mechanical properties. Previous research has predominantly relied on empirical relations derived from a limited number of indentation parameters from the force–displacement curve to estimate pile-up height. In this study, we suggest an advanced method for predicting contact morphology and estimating tensile properties based on spherical indentation. Indentation contact depth is estimated using an analytical model with stress field from expanding cavity model, geometric shape of the indenter, and plastic migration of indented volume during spherical indentation, without relying on empirical relations. Experimental observations confirm that the model accurately predicts the pileup height for various metallic materials. The model is applied to estimate representative stress–strain curves using the obtained contact morphology. The results indicate a notable improvement in the agreement with tension tests conducted on samples exhibiting power-law and linear-hardening behavior, even at respectively small strains. Graphical Abstract