Modelling dislocation transmission across tilt grain boundaries in 2D R. Kumar a , F. Székely b , E. Van der Giessen a, * a University of Groningen, Zernike Institute for Advanced Materials, Dept. of Applied Physics, Nyenborgh 4, NL-9747 AG Groningen, The Netherlands b Eötvös University, Dept. of General Physics, Pazmany P. setany 1/b, Pf. 32 H-1518 Budapest, Hungary article info Article history: Received 30 January 2010 Received in revised form 2 April 2010 Accepted 13 April 2010 Available online 14 May 2010 Keywords: Discrete dislocations Slip transfer Thin films abstract A line tension approach is reviewed to model slip transfer across tilt grain boundaries (GBs). It is imple- mented as a constitutive rule in the already existing two-dimensional discrete dislocation plasticity model of polycrystalline thin films. GBs are treated as obstacles to dislocation motion but with a finite strength. Dislocation transmission across a GB is potentially allowed, provided that three known geomet- rical criteria are satisfied. If allowed, the motion of the dislocation across the GB is enabled by dynami- cally creating a GB source near the GB, the stress on which must exceed the boundary strength. To separate transmission effects from other discrete dislocation features of the plastic deformation of thin films, comparisons are carried out by modelling GBs as impenetrable barriers to dislocation motion. It is shown that slip transfer tends to make the film softer if the density of bulk sources is sufficiently low. Since the position of the boundary source lies within the high-stress region of dislocation pile- ups, once activated the transmission process becomes independent of the source strength. In addition, the Bauschinger effect (BE) in thin films has been studied and a decrease of the BE is seen when disloca- tion transmission across GBs is enabled. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Grain boundaries (GBs) can have a significant effect on the plas- tic response of polycrystalline metals. While deformation inside the GBs themselves can directly contribute to plasticity in the case of nanocrystalline materials, GBs primarily play a role in their interaction with dislocations when the grain size is in the (sub- )micrometer range. GBs can absorb or emit dislocations [1,2], and, depending on the misorientation between the adjacent crys- tals, they can act as strong obstacles to dislocation motion and thus inhibit plasticity. In bulk materials, this results in a Hall–Petch [3,4] type relationship for the yield strength as a function of grain size, which is primarily due to the piling-up of dislocations against the GBs [5,6]. In thin films with thicknesses and grain sizes in the micrometer range, the importance of GB–dislocation interac- tion increases due to the increase in area of GBs per unit grain vol- ume (i.e. the GB density) with decreasing size [7]. Thus, the yield properties of such films are strongly governed by the way disloca- tions interact with GBs. Until now, classical crystal plasticity models have treated GBs essentially as planes that separate the slip systems in one grain from those in the adjacent one. There are some modern, nonlocal theories, however, that treat the slip as internal variables for which the GBs can set boundary conditions. Examples are the continuum theories of the type proposed by Gurtin [8] and by Geers and co- workers [9], and discrete dislocation models of crystal plasticity [10]. The typical assumption made in these studies of (sub-)micron grain-sized polycrystals so far has been that GBs block slip; in a continuum model this means that the slip is defined to vanish at the GB, while in discrete dislocation plasticity this translates into treating GBs as impenetrable obstacles. With this assumption, dis- crete dislocation studies have been able, for instance, to predict the Hall–Petch effect [11] of bulk polycrystals and to obtain quantita- tive agreement with the size-dependent yield strength of Cu thin films [12]. Despite this success, the issue remained as to what the possible influence of GB–dislocation interactions could be; yet, approaches to incorporate these into discrete dislocation plas- ticity were lacking. With the advance of computing facilities and atomistic modeling techniques, several efforts have recently been made to understand and quantify these dislocation–GB interac- tions in materials with micron size grains [13–19]. In this work, we address one of the observed types of disloca- tion–GB interactions, namely the transmission of a glide disloca- tion across a GB. A method is developed to handle dislocation transmission across low angle tilt boundaries within a framework of two-dimensional (2D) discrete dislocation plasticity. In this ap- proach, we will borrow the idea from de Koning et al. [13] to treat transmission as the nucleation of a new dislocation from the GB in a way akin to the operation of a Frank-Read source inside the grain. The approach involves the introduction of the strength of a GB source, the value of which can be taken from a line tension model, 0927-0256/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2010.04.018 * Corresponding author. Tel.: +31 50 3638046; fax: +31 50 3634886. E-mail address: E.van.der.Giessen@rug.nl (E. Van der Giessen). Computational Materials Science 49 (2010) 46–54 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci