The plastic zone size in indentation experiments: The analogy with the expansion of a spherical cavity

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.