We study the effects of wedge bluntness in mechanically exfoliating graphene layers from highly ordered pyrolytic graphite (HOPG), a layered material. Molecular dynamics simulations show that the layer initiation modes strongly depend on the wedge radius. Force and specific energy signatures are also markedly affected by the radius. Cleaving with a larger wedge radius causes buckling ahead of the wedge; larger the radius more the buckling. A critical depth of insertion of 1.6 Ao is seen necessary to cleave a single layer; this is also found to be independent of wedge radius. Hence, with accurate positioning on an atomically flat HOPG surface it is possible to mechanically cleave, using a wedge, a single sheet of graphene even with a blunt wedge. Copyright © 2014 by ASME.