Contact deformation regimes around sharp indentations and the concept of the characteristic strain

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 (sigma(ys)) 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) = 2.7sigma(r), applies within the fully plastic regime of elastic - power-law plastic materials. The results confirm the concept of the uniqueness of the characteristic strain, epsilon(r) = 0.1, that is associated with the uniaxial stress, sigma(r). 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 sigma(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 sigma(ys) and n from indentation experiments.