Elastic Stress Field beneath an arbitrary axisymmetric punch

Jacques Woirgard (1) , Valerie Audurier (1) , Christophe Tromas (1)

1 LMP - Laboratoire de métallurgie physique

For the analysis of indentation tests it is necessary to estimate the contact area under load, between the sample and the indenter. However this parameter cannot be directly derived from indentation curves and some assumptions are required. A major step in that sense was accomplished by Pharr [1] who proposed to use Solomon's [2] results to take into account the plastic deformation for the analysis of elastic unloading curves. Pharr proposed to replace the indenter by an equivalent one, with a modified shape, producing a loading curve identical to the initial unloading one. Practical equivalent indenters are assumed axisymmetric and obeying power laws, or polynomial ones with integer exponents. The aim of this work is to evaluate the stress and displacement fields beneath such indenters. Most solutions, in the literature, are given for simple indenter shapes, such as flat, conical or spherical indenters. Complete solutions for arbitrary powers of r, integer or not, will be proposed, the stresses being given as the real parts of complex analytical expressions.

Mots clés: Physical Sciences

Jacques Woirgard, Valerie Audurier, Christophe Tromas. Elastic Stress Field beneath an arbitrary axisymmetric punch. Philosophical Magazine, 2008, 88 (10), pp.1511-1523. ⟨10.1080/14786430802206474⟩. ⟨hal-00513906⟩