The depth dependent hardness of bicrystals with dislocation transmission through grain boundaries: A theoretical model

Abstract

In this paper, a dislocation density based theoretical model is proposed to explain the depth dependent hardness of bicrystals. The density of geometrically necessary dislocations (GNDs) is affected by the grain boundary (GB) through the consideration of the truncation and limited expansion of the plasticity affected region (PAR) when the indenter is in the vicinity of the GB. The latter is found to be the dominant reason for the increase of hardness when the GB impedes the movement of GNDs and prevents the slip transfer behavior. Once the accumulated stress originating from the piled up dislocations triggers the transmission of dislocations through the GB interface, the density of GNDs under the indenter decreases leading to the reduction of hardness. Based on this model, the dislocation transmission through a dedicated GB interface can be quantitatively analyzed, which involves the evolution of the density of GNDs and PAR in adjacent grains during the slip transfer process. The rationality and accuracy of the proposed model are validated by comparing the fitted theoretical results with experimental data through nano-indentation (NI). Moreover, the prediction of the model can match well with experimental results.