Analytical correlation of indentation experiments

We improve the analysis of indentation by employing a model of the expansion of a spherical cavity in which a generalization of the velocity field proposed by Avitzur for metal extrusion is considered; its components vary with the distance to the indenter apex r as 1/rs , with s a free parameter. By neglecting the material displacement we apply this model to conical indentation (apical angle 2θ) of an elastic solid (Young's modulus E), a rigid–perfectly plastic (RPP) solid (yield stress σ0) and elastic–perfectly plastic (EPP) solids with indentation index X = (E*/σ0) cot θ and estimate the hardness H and the shape ratio cp = h c/h, where h and h c are the penetration depth and the contact depth respectively. s is determined by minimizing the total work (elastic case) and the plastic power (RPP and EPP cases). The results of the model are in agreement with the available exact results (elastic case) and numerical results (RPP and EPP cases).