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Finite element simulations are performed to analyze the contact deformation regimes induced by a sharp indenter in elastic – power-law plastic solids. As the yield strength (σys) and strain hardening coefficient (n) decrease or, alternatively, as Young's modulus (E) increases, the contact regime evolves from (i) an elastic–plastic transition, to (ii) a fully plastic contact response, and to (iii) a fully plastic regime where piling-up of material at the contact area prevails. In accordance with preliminary analyses by Johnson, it is found that Tabor's equation, where hardness (H) = 2.7σr, applies within the fully plastic regime of elastic – power-law plastic materials. The results confirm the concept of the uniqueness of the characteristic strain, ∈r = 0.1, that is associated with the uniaxial stress, σr. A contact deformation map is constructed to provide bounds for the elastic–plastic transition and the fully plastic contact regimes for a wide range of values of σ ys, n, and E. Finally, the development of piling-up and sinking-in at the contact area is correlated with uniaxial mechanical properties. The present correlation holds exclusively within the fully plastic contact regime and provides a tool to estimate σ ys and n from indentation experiments.

Following the finite element simulations in our earlier work about the contact deformation regimes, mathematical formulations were derived to correlate hardness and the amount of pileup and sinking-in phenomena around sharp indenters with uniaxial mechanical properties. The formulations are applicable regardless of the deformation regime ruling the contact response of a strain-hardening solid. A methodology was devised where the use of these formulations in mechanical property assessments from indentation experiments was demonstrated. The current results make contact with existing methodologies using the II-theorem in functional analysis to extract uniaxial properties from instrumented indentation load depth of penetration curves. It is argued that since surface deformation is an essential feature of the contact response, it enters directly or indirectly in such existing methodologies. The paper considers how independent knowledge of surface deformation can be used to guide mechanical property assessments from load-depth of penetration curves. A discussion on the uniqueness of mechanical characterizations through indentation experiments is also provided.

This paper provides in-depth examinations of the well-known analogy between indentation experiments and the expansion of a spherical cavity. Closed-form solutions are derived for the extension of the plastic zone in perfectly plastic and strain hardening solids. The theoretical analysis takes into account the role of elastic and plastic deformations in the overall contact response, leading to accurate solutions for cavity inflation. Presently proposed analogy is based on comprehensive finite element simulations of conical, spherical and pyramidal indentation, which allow us to find a correspondence between the parameters describing the contact response and those in expanding cavity formulations. Such parametrical identification has the advantage to hold true both in expanding cavity formulations for perfectly plastic solids and in those derived herein for strain hardening solids. Attention is given to the assessment of the plastic zone along the indented surface, as well as to quantify the influence of further plastic flow induced upon load removal on the plastic zone size.

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