The effect of indenter shape on sub-micron indentation according to discrete dislocation plasticity

Two-dimensional discrete dislocation simulations of indentation in the submicron range are presented for wedge indenters with a sharp tip and for indenters with a circular tip. Plane strain calculations are carried out for single crystals that are initially free of mobile dislocations and with all dislocations nucleating from a specified distribution of internal sources. The hardness is expressed in terms of the indentation force divided by the actual contact area accounting for roughness of the surface in contact with the indenter. For wedge indenters the hardness is found to decrease with increasing indentation depth, while for indenters with a circular tip the hardness increases somewhat with increasing indentation depth. However, at a given indentation depth, the indentation hardness of circular indenters increases with decreasing tip radius. The difference in hardness evolution for the two tip shapes is mainly due to the manner in which the evolution of the contact area depends on indenter tip shape. The nominal hardness, i.e. that based on the geometric contact area neglecting material sink-in or pile-up and surface roughness, is found to follow the inverse square root size dependence predicted by Nix and Gao [1] and by Swadener et al [2], even though the plastic zone found in the simulations differs significantly in shape and size from that assumed in deriving the scaling laws.