Analytical correlation of indentation experiments

International audienceWe improve the analysis of indentation by the model of the expansion of a spherical cavity by considering a generalisation of the velocity field proposed by Avitzur for metal extrusion: 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 c=hc/h where h and hc are the penetration depth and the contact depth. s is determined by minimising 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 ones(RPP and EPP cases)