The plane strain indentation of single crystal films on a rigid substrate by a rigid wedge indenter was analyzed using discrete dislocation plasticity. The crystals had three slip systems at ±35.3º and 90º with respect to the indentation direction. The analyses were carried out for three values of the film thickness, 2, 10 and 50μm, and with the dislocations all of edge character modeled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation were incorporated through a set of constitutive rules. Over the range of indentation depths considered, the indentation pressure for the 10 and 50μm-thick films decreased with increasing contact size and attains a contact size-independent value for contact lengths, A > 4μm. On the other hand, for the 2μm films, the indentation pressure first decreased with increasing contact size and subsequently increased as the plastic zone reaches the rigid substrate. For the 10 and 50μm-thick films sink-in occurred around the indenter, while pile-up occurred in the 2μm film when the plastic zone reaches the substrate. Comparisons were made with predictions obtained from other formulations: (i) the contact size-independent indentation pressure was compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth was compared with the relation proposed by Nix and Gao; and (iii) the computed contact area was compared with that obtained from the estimation procedure of Oliver and Pharr.

Discrete Dislocation Plasticity Analysis of the Wedge Indentation of Films. D.S.Balint, V.S.Deshpande, A.Needleman, E.Van der Giessen: Journal of the Mechanics and Physics of Solids, 2006, 54[11], 2281-303