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Formulation of expanding cavity model taking into account the piling-up

Abstract : The Johnson's expanding cavity model estimates the hardness of a perfectly plastic material in a regime called elastic plastic. This relationship is obtained by a differential analysis associated with self-similar nature of the conical indentation. As a first step we obtain a similar result by studying a particular state of the indentation associated with the balance of the hydrostatic core. This new formulation is based on the equivalence between the volume displaced by the indenter and the volume compressed elastically in the solid. In a second step, this principle of equivalence of the displaced volume is used to take into account the presence of a piling-up. The volume displaced by the indenter is equal to the volume compressed elastically in the following zones: the hydrostatic core, elastic zone and plastic zone in which the additional volume of the piling-up must be added. With the knowledge of the contact height obtained by finite element model, which leads to the determination of the volume of the piling-up, the new fundamental relationship is applied to a material with a very low yield stress. The characteristic of this material is similar to that of a rigid perfectly plastic material. By decreasing the cone angle, the indentation regimes are successively the pseudo-elastic regime, elastic-plastic regime and purely plastic regime. The Johnson's model only describes the elastic plastic regime. The new formulation describes the elastic plastic regime and the regime called "purely plastic" where the mean pressure is constant. On the basis of our results, this regime seems not to be a purely plastic regime but rather a plastic elastic regime. This result is in agreement with the results of the study of the influence of Poisson's ratio we have already done.
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Contributor : Olivier Bartier <>
Submitted on : Tuesday, June 10, 2014 - 3:55:52 PM
Last modification on : Friday, July 10, 2020 - 4:09:39 PM


  • HAL Id : hal-01003753, version 1


Xavier Hernot, Olivier Bartier. Formulation of expanding cavity model taking into account the piling-up. international indentation workshop 4, Jul 2011, Séoul, South Korea. ⟨hal-01003753⟩



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