Instrumented indentation experiments, where load and depth of penetration are measured continuously, enable an evaluation of mechanical properties such as Young's modulus, hardening exponent and yield stress. This assessment requires a precise knowledge of the true contact area between the indenter and the indented material, which depends on piling-up and sinking-in at the contact boundary. The aim of this work is to propose a new relationship between the penetration depth of a spherical indenter and the contact radius, which is valid for most metals in elastic-plastic and fully plastic regimes. Numerical simulations results of the indentation of an elastic-plastic half-space by a frictionless rigid paraboloìd of revolution show that the contact radius-indentation depth evolution can be represented by a power law. This law depends on the Young's modulus, the hardening exponent and the yield stress of the indented material. In order to use the proposed formulation for experimental spherical indentations, the model is adapted in the case of a rigid spherical indenter.
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