INDENTATION OF AN ELASTIC HALF SPACE

Jacques Woirgard (1)

1 CNRS - Centre National de la Recherche Scientifique

ABSTRACT Some results on the indentation of an elastic half space are presented. The first part proposes an approximate analytical expression for the stress distribution on a half space under a flat punch, with a cross section in the form of a regular polygon. More accurate values for the beta parameter are also presented for triangular and square cross sections, respectively 1.06142 and 1.02121, corresponding for example to Berkovich and Vickers indenters. In a second part, the influence of radial displacements on the â parameter will be examined, according to a previous idea of Bolshakov and Pharr. An alternative expression for this parameter will be proposed giving lower values. To take into account the fact that in most elastoplastic materials the equivalent indenters used during unloading are rather in the form of paraboloids than cones, as in the well known method of Oliver and Pharr, this case will be examined in details. A simple formula will be also proposed for the calculation of the radial displacements in the case of indenters described by polynoms or obeying power laws with non integer exponents. The conclusions concerning equivalent indenters in the form of paraboloids are then compared with preliminary experimental results obtained with a new indenters made of a cube-corner terminated by a Berkovich part. This indenter and another prismatic one, allows one to directly obtain the contact area, eliminating uncertainties due to the presence of pile-up or sinking-in.

Mots clés: Physical Sciences

Jacques Woirgard. INDENTATION OF AN ELASTIC HALF SPACE. Philosophical Magazine, 2006, 86 (33-35), pp.5199-5217. ⟨10.1080/14786430600651970⟩. ⟨hal-00513680⟩