Discrete dislocation analysis of the wedge indentation of polycrystals

Abstract

This paper reports a study of the indentation of a model polycrystal using two-dimensional discrete dislocation plasticity. The polycrystal consists of square grains having the same orientation. Grain boundaries are modelled as being impenetrable to dislocations. Every grain has three slip systems, with a random distribution of initial sources and obstacles, and edge dislocations that glide in a drag-controlled manner. The indenter is wedge shaped, so that the indentation depth is the only geometrical length scale. The microstructural length scale on which we focus attention is the grain size, which is varied from 0.625 to 5 μm. While the predicted uniaxial yield strength of the polycrystals follows the Hall–Petch relation, this grain size dependence couples to the dependence on indentation depth. Polycrystals with a sufficiently large grain size exhibit the same “smaller is harder” dependence on indentation depth as single crystals, but an inverse indentation depth dependence occurs for fine-grained materials. For sufficiently deep indentation, the predicted nominal hardness is found to scale with grain size d according to H N = H N ∞ ( 1 + d * / d ) 1 / 2 , where H N ∞ is the single-crystal nominal hardness and d * is a material length scale.