Activation volume and deviation from Cottrell–Stokes law at small grain size Cécilie Duhamel a,1 , Yves Brechet b , Yannick Champion a, * a ICMPE-CNRS, Université Paris 12, 6–8 rue Henri Dunant, 94320 Thiais Cedex, France b SIMAP, LTPCM-CNRS, INP Grenoble, BP75, 38402 St Martin d’Hère, France article info Article history: Received 5 June 2009 Received in final revised form 9 October 2009 Available online 17 October 2009 Keywords: Cottrell–Stokes law Fine grained metal Dislocations Grain boundary sliding Activation volume abstract Dependence of activation volume with flow stress is examined for metals with grain size lower than 0.3 lm and larger than few tens of nanometers, where plastic deformation is most likely to be governed by a combination of grain boundary sliding and dislocations activity. The experimentally observed deviation from the classic linear behavior given by Cottrell–Stokes law [Basinski, Z.S., 1974. Forest hardening in face centered cubic metals. Scripta Metallurgica 8, 1301–1308] is analyzed, thanks to a modified Orowan equation tak- ing into account of the grain boundaries sliding coupled to dislocations activity. These results are compared to experimental measurements of the activation volume, between room temperature and 120 °C, for a copper nanostructure with a grain size of 100 nm. A constant activation volume is observed at low stress (or high temperature) followed by an increase of activation volume with stress (inverse Cottrell–Stokes behavior). This anal- ysis follows our initial experiments on this fine grained metal prepared by powder metal- lurgy, which exhibits ductility at near constant stress and strain rate [Champion, Y., Langlois, C., Guérin-Mailly, S., Langlois, P., Bonnentien, J.-L., Hÿtch, M.J., 2003. Near-perfect elastoplasticity in pure nanocrystalline copper. Science 300, 310–311]. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction A physical insight into the elementary mechanisms ruling plastic deformation in ductile crystalline materials is obtained from the change in the macroscopic flow stress (r) with the strain rate ð _ eÞ or temperature. In large grained metals (d >1 lm, with d the grain size), macroscopic tensile or compressive stress experiments usually follow Cottrell–Stokes law: @r=@ ln _ e / r (Basinski, 1974; Bochniak, 1993). This law can be found assuming a power relationship between the strain rate and the flow stress but it has also a direct physical interpretation when plastic flow is governed by thermally activated dis- location glide: the activation area is proportional to the distance between forest dislocations (dislocations pinning points) which is inversely proportional to the flow stress. More precisely, Cottrell–Stokes theory is based on the assumption that the stress is the sum of a thermally activated component r * and an athermal component, r a : r = r a + r * . Only thermally acti- vated component is modified by strain rate jumps. A classical expression for the strain rate is _ e ¼ _ e 0 exp ðDG  0 þ  r  v  =MÞ=kT  where DG 0 is the activation energy, v * the activation volume and M the Taylor factor. From this expression follows a natural interpretation of the strain rate sensitivity in terms of activation volume: @r  =@ ln _ e / 1=v  . The activation volume, v * is the amount of matter involved in the elementary thermally activated events of the deformation process. When 0749-6419/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijplas.2009.10.003 * Corresponding author. Address: Institut de Chimie et des Materiaux Paris-Est – UMR CNRS 7182, Université Paris 12, 6–8 rue Henri Dunant, 94320 Thiais Cedex, France. Tel.: +33 1 56 70 30 41; fax: +33 1 56 70 30 43. E-mail address: champion@glvt-cnrs.fr (Y. Champion). 1 Address: MINES ParisTech, Centre des Matériaux, CNRS UMR 7633, BP 87, 91 003 Evry Cedex, France. International Journal of Plasticity 26 (2010) 747–757 Contents lists available at ScienceDirect International Journal of Plasticity journal homepage: www.elsevier.com/locate/ijplas