Contact area and size effects in discrete dislocation modeling of wedge indentation

Plane strain indentation of a single crystal by a rigid wedge is analyzed using discrete dislocation plasticity. We consider two wedge geometries having different sharpness, as specified by the half-angle of the indenter: alpha = 70 degrees and 85 degrees. The dislocations are all of edge character and modeled as line singularities in a linear elastic material. The crystal has initial sources and obstacles randomly distributed over three slip systems. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles, and dislocation annihilation are incorporated through a set of constitutive rules. Several definitions of the contact area (contact length in plane strain) are used to illustrate the sensitivity of the hardness value in the submicron indentation regime to the definition of contact area. The size dependence of the indentation hardness is 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 degrees, an indentation size effect is not obtained when the contact area is small and when the hardness is based on the actual contact length, while there does appear to be a size effect for some hardness values based on other measures of contact length.