Small scale yielding around a mode-I crack was analysed using polycrystalline discrete dislocation plasticity. Plane strain analyses were carried out with the dislocations all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, nucleation, interaction with obstacles and annihilation were incorporated through a set of constitutive rules. Grain boundaries were modelled as impenetrable to dislocations. The polycrystalline material was taken to consist of two types of square grains, one of which has a body-centred cubic-like orientation and the other a face-centred cubic-like orientation. For both orientations there were three active slip systems. Alternating rows, alternating columns and a checker-board-like arrangement of the grains was used to construct the polycrystalline materials. Consistent with the increasing yield strength of the polycrystalline material with decreasing grain size, the calculations predict a decrease in both the plastic zone size and the crack-tip opening displacement for a given applied mode I stress intensity factor. Furthermore, slip-band and kink-band formation was inhibited by all grain arrangements and, with decreasing grain size, the stress and strain distributions more closely resemble the HRR fields with the crack-tip opening approximately inversely proportional to the yield strength of the polycrystalline materials. The calculations predict a reduction in fracture toughness with decreasing grain size associated with the grain boundaries acting as effective barriers to dislocation motion.

Discrete Dislocation Plasticity Analysis of Crack-Tip Fields in Polycrystalline Materials. D.S.Balint, V.S.Deshpande, A.Needleman, E.Van der Giessen: Philosophical Magazine, 2005, 85[26-27], 3047-71