A study was made of the indentation of a model polycrystal using 2-dimensional discrete dislocation plasticity. The polycrystal consisted of square grains having the same orientation. Grain boundaries were modelled as being impenetrable to dislocations. Every grain had three slip systems, with a random distribution of initial sources and obstacles, and edge dislocations that glide in a drag-controlled manner. The indenter was wedge shaped, so that the indentation depth was the only geometrical length scale. The microstructural length scale upon which attention was focussed was the grain size, which varied from 0.625 to 5μm. While the predicted uniaxial yield strength of the polycrystals followed the Hall–Petch relation, this grain size dependence couples to the dependence upon indentation depth. Polycrystals with a sufficiently large grain size exhibited the same “smaller was harder” dependence upon indentation depth as single crystals, but an inverse indentation depth dependence occurred for fine-grained materials. For sufficiently deep indentation, the predicted nominal hardness was found to scale with grain size d according to H = Hs(1+d*/d)½, where H was the single-crystal nominal hardness and d* was a material length-scale.

Discrete Dislocation Analysis of the Wedge Indentation of Polycrystals. A.Widjaja, E.Van der Giessen, A.Needleman: Acta Materialia, 2007, 55[19], 6408-15