The stress–strain response of nanocrystalline metals: A statistical analysis of atomistic simulations E. Bitzek a , P.M. Derlet a , P.M. Anderson b , H. Van Swygenhoven a, * a Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland b Department of Materials Science and Engineering, Ohio State University, 2041 College Road, Columbus, OH 43210, USA Received 27 February 2008; received in revised form 30 May 2008; accepted 30 May 2008 Available online 12 July 2008 Abstract Atomistic simulations of the tensile deformation of three-dimensional nanocrystalline Al samples at constant strain rate and temper- ature are analyzed in terms of grain-averaged shear produced by dislocation slip and the grain-averaged resolved shear stress during deformation. To assess the influence of the grain-boundary character on the deformation behavior, three samples with different micro- structures but the same average grain size were simulated. Detailed analysis of the atomic processes allowed correlation of the stress sig- nature of slip events with typical dislocation processes related to nucleation and propagation. The results of the mesoscopic analysis of the atomistic simulations are discussed in the framework of micromechanic models for nanocrystal plasticity. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nanocrystalline materials; Mechanical properties; Dislocations; Grain boundaries; Molecular dynamics 1. Introduction Nanocrystalline (nc) metals, defined as polycrystals with a mean grain size below 100 nm, have a yield stress that is up to ten times higher compared to coarse-grained counterparts (>1 lm); however, they suffer from limited ductility [1]. Furthermore the deformation mechanisms in nc metals are characterized by higher values of strain-rate sensitivity [2,3] and low activation volumes (10–20 b 3 ) [4,5]. Another peculiarity for nc metals is the large strain that has to be assigned to the microplas- tic regime as has been observed by in situ X-ray experi- ments [6]. Molecular dynamics (MD) simulations have provided considerable insight into the details of deforma- tion mechanisms in face-centered cubic (fcc) nanocrystal- line metals [5,7-9]. Based on these simulations, it is generally believed that grain boundaries (GBs) act as both sources and sinks for dislocations, i.e., dislocations are emitted from stress concentrations at GBs, travel through the grain and are absorbed at the GBs. Atomis- tic simulations have furthermore shown that the emission of dislocations is usually accompanied by atomic shuf- fling and stress-assisted free volume migration [8,10]. More recent simulations have demonstrated that nucle- ated dislocations can become temporarily pinned at GB ledges [5]. This highlights the role of dislocation propa- gation as a possible rate-limiting process. The potential for technological applications of nano- crystalline metals calls for the development of models which are able to predict the deformation behavior of such materials as function of grain size as well as grain-size dis- tribution and texture, strain rate and temperature. The development of such models [11–24] is still in the early stages; for reviews see e.g., Refs. [16,25]. Many of these models describe nanocrystalline materials as two-phase composite materials where the constitutive behavior of the grain-boundary phase is different from the grain inte- rior [11–14]. This approach is, however, questionable, since several high-resolution transmission electron microscopy (HR-TEM) studies show no signs of a disordered grain- 1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.05.043 * Corresponding author. Tel.: +41 56 3102931; fax: +41 56 3103131. E-mail addresses: helena.vs@psi.ch, helena.vanswygenhoven@psi.ch (H. Van Swygenhoven). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 56 (2008) 4846–4857