Plane strain indentation of a single crystal by a rigid wedge was analyzed using discrete dislocation plasticity. Two wedge geometries having different sharpness were considered, as specified by the half-angle of the indenter: a = 70° or 85°. The dislocations were all of edge character and modeled as line singularities in a linear elastic material. The crystal has initial sources and obstacles randomly distributed over 3 slip systems. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles, and dislocation annihilation were incorporated through a set of constitutive rules. Several definitions of the contact area (contact length in plane strain) were used to illustrate the sensitivity of the hardness value in the sub-micron indentation regime to the definition of contact area. The size dependence of the indentation hardness was found to be sensitive to the definition of contact area used and to depend on the wedge half-angle. For a relatively sharp indenter, with a half-angle of 70°, an indentation size effect was not obtained when the contact area was small and when the hardness was based upon the actual contact length, while there did appear to be a size effect for some hardness values based upon other measures of contact length.

Contact Area and Size Effects in Discrete Dislocation Modeling of Wedge Indentation. A.Widjaja, E.Van der Giessen, V.S.Deshpande, A.Needleman: Journal of Materials Research, 2007, 22[3], 655-63