Philosophical Magazine, Vol. 85, Nos. 26–27, 11–21 September 2005, 3047–3071 Discrete dislocation plasticity analysis of crack-tip fields in polycrystalline materials D. S. BALINTy, V. S. DESHPANDEy, A. NEEDLEMAN*z and E. VAN DER GIESSEN} yCambridge University, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, UK zBrown University, Division of Engineering, Providence, RI 02912, USA }University of Groningen, Department of Applied Physics, Nyenborgh 4, 9747 AG Groningen, The Netherlands (Received 12 November 2004; in final form 17 January 2005) Small scale yielding around a mode I crack is analysed using polycrystalline discrete dislocation plasticity. Plane strain analyses are 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 are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. The polycrystalline material is taken to consist of two types of square grains, one of which has a bcc-like orientation and the other an fcc-like orientation. For both orientations there are three active slip systems. Alternating rows, alternating columns and a checker-board-like arrangement of the grains is 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 is 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. 1. Introduction The plastic dissipation around a crack tip in crystalline metals results in the work of fracture being much larger than the work required to separate the crack surfaces (e.g. Irwin [1] and Tvergaard and Hutchinson [2]). Hence, plastic flow in the vicinity of a crack tip is key for determining the fracture resistance of ductile metals. Indeed, the analyses of asymptotic crack-tip fields in isotropic strain hardening solids by Hutchinson [3] and Rice and Rosengren [4] (the HRR fields), and in ideally plastic *Corresponding author. Email: alan_needleman@brown.edu Philosophical Magazine ISSN 1478–6435 print/ISSN 1478–6443 online # 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/14786430500073887