Materials Science and Engineering A 494 (2008) 86–91 The influence of a threshold stress for grain boundary sliding on constitutive response of polycrystalline Al during high temperature deformation Ningning Du a , Allan F. Bower a,∗ , Paul E. Krajewski b , Eric M. Taleff c a Division of Engineering, Brown University, Providence, RI 02912, USA b General Motors R&D Center, 30500 Mound Road, Warren, MI 48090, USA c The University of Texas at Austin, Department of Mechanical Engineering, 1 University Station, C2200 Austin, TX 78712-0292, USA Received 25 April 2007; received in revised form 15 July 2007; accepted 15 October 2007 Abstract A continuum polycrystal plasticity model was used to estimate the influence of a threshold stress for grain boundary sliding on the relationship between macroscopic flow stress and strain rate for the aluminum alloy AA5083 when subjected to plane strain uniaxial tension at 450 ◦ C. Under these conditions, AA5083 deforms by dislocation glide at strain rates exceeding 0.001 s −1 , and by grain boundary sliding at lower strain rates. The stress–strain rate response can be approximated by ˙ ε = Aσ n , where A and n depend on grain size and strain rate. We find that a threshold stress less or equal to 4 MPa has only a small influence on flow stress and stress exponent n in the dislocation creep regime (a threshold stress of 2 MPa increases n from 4.2 to 4.5), but substantially increases both flow stress and stress exponent in the grain boundary sliding regime (a threshold stress of 2 MPa increases n from 1.5 to 2.7). In addition, when the threshold stress is included, our model predicts stress versus strain rate behavior that is in good agreement with experimental measurements reported by Kulas et al. [M.A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, T.R. McNelley, Metall. Mater. Trans. A 36 (2005) 1249]. © 2007 Elsevier B.V. All rights reserved. Keywords: Superplasticity; Finite element method; Aluminum alloy; Grain boundary sliding; Threshold stress; Strain rate sensitivity 1. Introduction Complex parts for automobile and aerospace applications are often manufactured using hot blow forming processes such as superplastic forming (SPF) [1] and quick plastic forming (QPF) [2]. SPF involves deformation at low strain rates (<0.001 s −1 ) and high temperatures (>500 ◦ C), while QPF is performed at higher strain rates (>0.001 s −1 ) and lower temperatures (450 ◦ C) [3]. These processes are of particular interest in the automotive industry, where QPF has been found to be a particularly attrac- tive technique for forming complex body parts [3]. The material used for both the SPF and QPF processes is usually aluminum alloy AA5083. The deformation behavior of AA5083 has been extensively studied: under QPF conditions, plastic flow occurs by a combination of grain boundary sliding and solute drag creep [4]. ∗ Corresponding author. Tel.: +1 401 863 1493. E-mail address: Allan Bower@brown.edu (A.F. Bower). There is great interest in developing models that can pre- dict the influence of alloy composition and microstructure on deformation behavior under SPF and QPF conditions, in the hope that such models can be used to develop new materials with improved formability. As part of this effort, Bower and Wininger [5] recently developed a microstructure-level model which accounts in detail for the various processes that contribute to plasticity at elevated temperatures. Their model idealizes a polycrystal as a set of grains (Fig. 1), whose constitutive behav- ior is characterized using a continuum crystal plasticity law. The grains are separated by sharp grain boundaries, which permit sliding and diffusion. Grain boundary sliding is modeled using a linear relation between resolved shear stress and slip rate, while grain boundary diffusion is modeled using a conventional linear diffusion equation. Agarwal et al. [6] compared the predictions of this model with experimental measurements of plastic flow in AA5083 under QPF conditions. The experimental data consisted of (i) the flow stress under uniaxial tension as a function of strain rate, for mate- rials with two different grain size, as illustrated in Fig. 2 (taken 0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.10.089