Discrete dislocation modeling of fracture in plastically anisotropic metals S. Olarnrithinun a,d , S.S. Chakravarthy b , W.A. Curtin c,n a Brown University, School of Engineering, Providence, RI 02912, USA b Northeastern University, Mechanical and Industrial Engineering, Boston, MA 02115, USA c Ecole Polytechnique Federale de Lausanne, Institute of Mechanical Engineering, 1015 Lausanne, Switzerland d National Metal and Materials Technology Center, 114 Thailand Science Park, Paholyothin Road, Klong Nung, Klong Luang, Pathumthani 12120, Thailand article info Article history: Received 19 March 2012 Received in revised form 30 January 2013 Accepted 2 February 2013 Available online 13 February 2013 Keywords: Discrete dislocations Crack growth Plastic anisotropy Stress gradient plasticity Micro-crack abstract The intrinsic lattice resistance to dislocation motion, or Peierls stress, depends on the core structure of the dislocation and is one essential feature controlling plastic anisotropy in materials such as HCP Zn, Mg, and Ti. Here, we implement an anisotropic Peierls model as a friction stress within a 2d discrete dislocation (DD) plasticity model and investigate the role of plastic anisotropy on the crack tip stress fields, crack growth, toughening, and micro- cracking. First, tension tests for a pure single crystal with no obstacles to dislocation motion are carried out to capture the general flow behavior in pure HCP-like materials having slip on basal and pyramidal planes. Then Mode-I crack growth in such a single crystal of the HCP material is analyzed using the 2d-DD model. Results show that the fracture toughness scales inversely with the tensile yield stress, largely independent of the plastic anisotropy, so that increasing Peierls stress on the pyramidal planes gives decreasing resistance to crack growth, consistent with recent experiments on Zn. Analyzing the results within the framework of Stress Gradient Plasticity concepts shows that the equilibrium dislocation dipole spacing serves as an internal material length scale for controlling fracture toughness. Furthermore, the fracture toughness of materials with flow stress controlled by a Peierls stress (this work) and of materials with flow stress controlled by dislocation obstacles (prior literature) is unified through the Stress Gradient Plasticity concept. Finally, the DD simulations show that local stress concentrations exist sporadically along the pyramidal plane(s) that emanate from the current crack tip, suggesting an origin for experimentally observed basal-plane microcracking near the tip of large cracks. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction The dislocation core structure in an atomic lattice dictates that a finite stress, the Peierl stress, is required to move a dislocation through the perfect lattice (Nabarro, 1947). Experiments (Caillard, 2010; Castany et al., 2007; Kruml et al., 2002; Spence and Koch, 2001) and many computer simulations (Aubry et al., 2011; Khater and Bacon, 2010; Nogaret et al., 2010; Leyson et al., 2010; Xiang et al., 2008; Tapasa et al., 2007) demonstrate these atomic effects in a variety of materials. In FCC materials, the Peierls stress is generally low and, given the many identical slip systems, the initial plastic flow stress is fairly isotropic. In HCP systems, the Peierls stress varies widely among slip systems, with basal and/or prism slip being Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jmps Journal of the Mechanics and Physics of Solids 0022-5096/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jmps.2013.02.001 n Corresponding author at: EPFL STI IGM LAMMM, ME C1 365 (Bˆ atiment ME), Station 9, CH-1015 Lausanne. Tel.: þ41 21 69 37366/37313. E-mail address: william.curtin@epfl.ch (W.A. Curtin). Journal of the Mechanics and Physics of Solids 61 (2013) 1391–1406